Finite Group Databasebeta

← #31738202

Subgroups — #31738202

Order 17152.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574153C211yesmaximal, characteristic, complemented
2#22573217C211yesmaximal, characteristic, complemented
3#22573072C211yesmaximal, characteristic, complemented
4#22572962C211yesmaximal, characteristic, complemented
5#22572956C211yesmaximal, characteristic, complemented
6#22572605C211yesmaximal, characteristic, complemented
7#22572571C211yesmaximal, characteristic, complemented
8#22572552C211yesmaximal, characteristic, complemented
9#22572410C211yesmaximal, characteristic, complemented
10#22572404C211yesmaximal, characteristic, complemented
11#22572230C211yesmaximal, characteristic, complemented
12#22572224C211yesmaximal, characteristic, complemented
13#22572170C211yesmaximal, characteristic, complemented
14#22572164C211yesmaximal, characteristic, complemented
15#22571890C211yesmaximal, characteristic, complemented
16#22571890C211yesmaximal, characteristic, complemented
17D4×#11761613C211yesmaximal, characteristic, complemented
18#22570853C211yesmaximal, characteristic, complemented
19#22570842C211yesmaximal, characteristic, complemented
20#22570773C211yesmaximal, characteristic, complemented
21#22570408C211yesmaximal, characteristic, complemented
22#22570402C211yesmaximal, characteristic, complemented
23#22570393C211yesmaximal, characteristic, complemented
24#22570387C211yesmaximal, characteristic, complemented
25#22570347C211yesmaximal, characteristic, complemented
26#22570343C211yesmaximal, characteristic, complemented
27#22569185C211yesmaximal, characteristic, complemented
28#22569082C211yesmaximal, characteristic, complemented
29#22569059C211yesmaximal, characteristic, complemented
30C2×C4×#11761613C211yesmaximal, characteristic, complemented
31C67×#3513C211yesmaximal, characteristic, complemented
32C2×#14524063C2211yescharacteristic
33C22×#11761613C2211yescharacteristic
34C22×#11761613C2211yescharacteristic
35#16864131C2211yescharacteristic, complemented
36#16864106C2211yescharacteristic, complemented
37#16864097—21no—
38#16864092C2211yescharacteristic, complemented
39#16864086C2211yescharacteristic
40#16864073—21no—
41#16864071—21no—
42#16864050C2211yescharacteristic, complemented
43#16864042C2211yescharacteristic, complemented
44#16864042C2211yescharacteristic, complemented
45#16864035—21no—
46D4×D268C2211yescharacteristic
47#16864017C2211yescharacteristic, complemented
48#16864001C2211yescharacteristic, complemented
49#16863994—21no—
50#16863980—21no—
51#16863930C2211yescharacteristic, complemented
52#16863904—21no—
53#123×D67—21no—
54#16863876C2211yescharacteristic, complemented
55#16863870C2211yescharacteristic, complemented
56C2×C4×D268C2211yescharacteristic, complemented
57#16863799C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863795C2211yescharacteristic, complemented
60#16863778C2211yescharacteristic, complemented
61#16863778C2211yescharacteristic, complemented
62#16863772C2211yescharacteristic
63#16863762C2211yescharacteristic, complemented
64#16863760C2211yescharacteristic, complemented
65#16863758C2211yescharacteristic, complemented
66#16863755C2211yescharacteristic, complemented
67#16863753C2211yescharacteristic, complemented
68#16863750C2211yescharacteristic, complemented
69#16863737C2211yescharacteristic, complemented
70#16863734C2211yescharacteristic, complemented
71#16863726C2211yescharacteristic, complemented
72#16863724C2211yescharacteristic, complemented
73#16863720C2211yescharacteristic, complemented
74#16863717C2211yescharacteristic, complemented
75#16863714C2211yescharacteristic, complemented
76#16863712C2211yescharacteristic, complemented
77#16863709C2211yescharacteristic, complemented
78#16863709C2211yescharacteristic, complemented
79#16863707C2211yescharacteristic, complemented
80#16863707C2211yescharacteristic, complemented
81#16863703C2211yescharacteristic, complemented
82#16863700C2211yescharacteristic, complemented
83#16863696C2211yescharacteristic, complemented
84#16863696C2211yescharacteristic, complemented
85#16863696C2211yescharacteristic, complemented
86#16863693C2211yescharacteristic, complemented
87#16863693C2211yescharacteristic, complemented
88#16863693C2211yescharacteristic, complemented
89#16863686C2211yescharacteristic, complemented
90#16863683C2211yescharacteristic, complemented
91#16863676C2211yescharacteristic, complemented
92#16863673C2211yescharacteristic, complemented
93#16863647C2211yescharacteristic, complemented
94#16863647C2211yescharacteristic, complemented
95#16863644C2211yescharacteristic, complemented
96#16863640C2211yescharacteristic, complemented
97#16863635C2211yescharacteristic, complemented
98#16863635C2211yescharacteristic, complemented
99#16863630C2211yescharacteristic
100#16863630C2211yescharacteristic
101#16863630C2211yescharacteristic, complemented
102#16863630C2211yescharacteristic, complemented
103#16863627C2211yescharacteristic, complemented
104#16863623C2211yescharacteristic, complemented
105#16863611C2211yescharacteristic, complemented
106#16863611C2211yescharacteristic, complemented
107#16863611C2211yescharacteristic, complemented
108#16863611C2211yescharacteristic, complemented
109#16863608C2211yescharacteristic, complemented
110#16863608C2211yescharacteristic, complemented
111#16863608C2211yescharacteristic, complemented
112#16863608C2211yescharacteristic, complemented
113#16863596C2211yescharacteristic, complemented
114#16863593C2211yescharacteristic, complemented
115#16863591C2211yescharacteristic
116#16863588C2211yescharacteristic
117#16863547C2211yescharacteristic, complemented
118#16863547C2211yescharacteristic, complemented
119#16863546C2211yescharacteristic, complemented
120#16863546C2211yescharacteristic, complemented
121#16863541C2211yescharacteristic, complemented
122#16863541C2211yescharacteristic, complemented
123#16863539C2211yescharacteristic, complemented
124#16863539C2211yescharacteristic, complemented
125#16863530C2211yescharacteristic
126#16863530C2211yescharacteristic
127#16863529C2211yescharacteristic
128#16863529C2211yescharacteristic
129#16863527C2211yescharacteristic, complemented
130Q8×C67⋊C8C2211yescharacteristic, complemented
131#16863506C2211yescharacteristic, complemented
132#16863506C2211yescharacteristic, complemented
133#16863506C2211yescharacteristic, complemented
134#16863506C2211yescharacteristic, complemented
135#16863506C2211yescharacteristic, complemented
136#16863506C2211yescharacteristic, complemented
137#16863496C2211yescharacteristic, complemented
138#16863496C2211yescharacteristic, complemented
139#16863496C2211yescharacteristic, complemented
140#16863494C2211yescharacteristic, complemented
141#16863494C2211yescharacteristic, complemented
142#16863494C2211yescharacteristic, complemented
143C4×#11761618C2211yescharacteristic, complemented
144C4×#11761618C2211yescharacteristic, complemented
145C4×#11761615C2211yescharacteristic, complemented
146C4×#11761616C2211yescharacteristic, complemented
147C4×#11761613C2211yescharacteristic
148C4×#11761613C2211yescharacteristic
149C4×#11761613C2211yescharacteristic
150C4×#11761613C2211yescharacteristic
151C4×#11761613C2211yescharacteristic, complemented
152C4×#11761613C2211yescharacteristic, complemented
153C4×#11761613C2211yescharacteristic, complemented
154C4×#11761613C2211yescharacteristic, complemented
155C4×#11761613C2211yescharacteristic, complemented
156C4×#11761613C2211yescharacteristic, complemented
157C4×#11761613C2211yescharacteristic, complemented
158C4×#11761613C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic, complemented
160#16863468C2211yescharacteristic
161#16863468C2211yescharacteristic, complemented
162D4×C67⋊C8C2211yescharacteristic
163D4×C67⋊C8C2211yescharacteristic, complemented
164D4×C67⋊C8C2211yescharacteristic, complemented
165#16863457C2211yescharacteristic, complemented
166#16863457C2211yescharacteristic, complemented
167#16863453C2211yescharacteristic, complemented
168#16863432C2211yescharacteristic, complemented
169C2×#14523976C2211yescharacteristic, complemented
170C2×#14523976C2211yescharacteristic, complemented
171#16863401C2211yescharacteristic, complemented
172#16863400C2211yescharacteristic, complemented
173#16863397C2211yescharacteristic, complemented
174#16863395C2211yescharacteristic, complemented
175C2×#14523964C2211yescharacteristic, complemented
176C2×#14523963C2211yescharacteristic, complemented
177#16863352C2211yescharacteristic, complemented
178#16863352C2211yescharacteristic, complemented
179C2×C4×C67⋊C8C2211yescharacteristic, complemented
180#559×C67C2211yescharacteristic, complemented
181#554×C67C2211yescharacteristic, complemented
182#553×C67—21no—
183#553×C67C2211yescharacteristic, complemented
184#552×C67C2211yescharacteristic
185#551×C67—21no—
186#551×C67—21no—
187#547×C67C2211yescharacteristic, complemented
188#546×C67—21no—
189#546×C67C2211yescharacteristic, complemented
190#546×C67C2211yescharacteristic, complemented
191D42×C67C2211yescharacteristic
192#542×C67C2211yescharacteristic, complemented
193#540×C67C2211yescharacteristic, complemented
194#539×C67—21no—
195#538×C67—21no—
196#529×C67C2211yescharacteristic
197#529×C67C2211yescharacteristic, complemented
198#525×C67—21no—
199C2×#123×C67—21no—
200#520×C67C2211yescharacteristic, complemented
201#518×C67C2211yescharacteristic, complemented
202C2×C4×D4×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761627—21no—
205C22×D268C2311yescharacteristic
206C22×D268C2311yescharacteristic
207C2×D4×D67—21no—
208C22×C4×D67—21no—
209#14524063—24no—
210C2×#11761618C2311yescharacteristic
211C2×#11761616C2311yescharacteristic
212C2×#11761616C2311yescharacteristic
213C2×#11761616C2311yescharacteristic
214C2×#11761615C2311yescharacteristic
215C2×#11761615C2311yescharacteristic
216C2×#11761615C2311yescharacteristic
217C2×#11761613—24no—
218C2×#11761613—24no—
219C2×#11761613C2311yescharacteristic
220C2×#11761613C2311yescharacteristic
221C2×#11761613C2311yescharacteristic
222C2×#11761613C2311yescharacteristic
223C2×#11761613C2311yescharacteristic
224C2×#11761613C2311yescharacteristic
225C2×#11761613C2311yescharacteristic
226C2×#11761613C2311yescharacteristic
227C2×#11761613C2311yescharacteristic
228C2×#11761612C2311yescharacteristic
229C2×#11761612C2311yescharacteristic
230C22×C67⋊C8C2311yescharacteristic
231C22×C67⋊C8C2311yescharacteristic
232C22×C67⋊C8C2311yescharacteristic
233C22×C67⋊C8C2311yescharacteristic
234#14524043C2311yescharacteristic
235#14524040C2311yescharacteristic
236#14524038—21no—
237#14524038—21no—
238#14524037—21no—
239#14524036—21no—
240#14524035C2311yescharacteristic
241#14524035C2311yescharacteristic
242#14524033—21no—
243#14524032—21no—
244#14524031C2311yescharacteristic
245#14524031C2311yescharacteristic
246#14524029—21no—
247#14524028—21no—
248#14524028—21no—
249#14524028—21no—
250#14524028—21no—
251#14524028—21no—
252#14524028—21no—
253#14524027—21no—
254#14524027—21no—
255#14524026—21no—
256#14524025—21no—
257#14524025—21no—
258#14524024—21no—
259#14524023—21no—
260#14524022C2311yescharacteristic
261#14524022C2311yescharacteristic
262#14524021—21no—
263#14524021—21no—
264#14524021—21no—
265#14524019—21no—
266#14524018—21no—
267#14524017C2311yescharacteristic
268#14524017C2311yescharacteristic
269#14524017C2311yescharacteristic
270#14524017C2311yescharacteristic
271#14524016—21no—
272#14524016—21no—
273#14524016—21no—
274#14524016—21no—
275#14524015—21no—
276#14524013—21no—
277#14524013—21no—
278#14524011—21no—
279#14524011—21no—
280C4×Dic134C2311yescharacteristic
281C4×Dic134C2311yescharacteristic
282C4×D268—21no—
283C4×D268—21no—
284C4×D268C2311yescharacteristic
285C4×D268C2311yescharacteristic
286C4×D268C2311yescharacteristic
287C4×D268C2311yescharacteristic
288C4×D268C2311yescharacteristic
289C4×D268C2311yescharacteristic
290C4×D268C2311yescharacteristic
291C4×D268C2311yescharacteristic
292#14524005—21no—
293#14524005—21no—
294#14524005—21no—
295C4×C22⋊D67—21no—
296(C22⋊D67)⋊C4—21no—
297(C22⋊D67)⋊C4—21no—
298(C22⋊D67)⋊C4—21no—
299#14524002C2311yescharacteristic
300#14524001—21no—
301#14524000—21no—
302#14523999—21no—
303C2×C4⋊Dic67C2311yescharacteristic
304C2×C4⋊Dic67C2311yescharacteristic
305C4⋊C4×D67—21no—
306C4⋊C4×D67—21no—
307C2×(C2×D67)⋊C4—21no—
308C22⋊C4×D67—21no—
309C22⋊C4×D67—21no—
310C22⋊C4×D67—21no—
311C22⋊C4×D67—21no—
312#14523976C2311yescharacteristic
313#14523976C2311yescharacteristic
314#14523976C2311yescharacteristic
315#14523976C2311yescharacteristic
316#14523976C2311yescharacteristic
317#14523976C2311yescharacteristic
318#14523976C2311yescharacteristic
319#14523976C2311yescharacteristic
320#14523976C2311yescharacteristic
321#14523976C2311yescharacteristic
322#14523974C2311yescharacteristic
323#14523974C2311yescharacteristic
324#14523974C2311yescharacteristic
325#14523974C2311yescharacteristic
326#14523974C2311yescharacteristic
327#14523974C2311yescharacteristic
328C4⋊(C67⋊C8)C2311yescharacteristic
329C4⋊(C67⋊C8)C2311yescharacteristic
330C4⋊(C67⋊C8)C2311yescharacteristic
331C4⋊(C67⋊C8)C2311yescharacteristic
332C4⋊(C67⋊C8)C2311yescharacteristic
333C4⋊(C67⋊C8)C2311yescharacteristic
334#14523967C2311yescharacteristic
335#14523967C2311yescharacteristic
336#14523967C2311yescharacteristic
337#14523967C2311yescharacteristic
338#14523966C2311yescharacteristic
339#14523966C2311yescharacteristic
340#14523966C2311yescharacteristic
341#14523966C2311yescharacteristic
342#14523964C2311yescharacteristic
343#14523964C2311yescharacteristic
344#14523964C2311yescharacteristic
345#14523964C2311yescharacteristic
346#14523964C2311yescharacteristic
347#14523964C2311yescharacteristic
348#14523964C2311yescharacteristic
349#14523964C2311yescharacteristic
350#14523964C2311yescharacteristic
351#14523964C2311yescharacteristic
352#14523964C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523963C2311yescharacteristic
355#14523963C2311yescharacteristic
356#14523963C2311yescharacteristic
357#14523963C2311yescharacteristic
358#14523963C2311yescharacteristic
359#14523963C2311yescharacteristic
360#14523963C2311yescharacteristic
361#14523963C2311yescharacteristic
362#14523963C2311yescharacteristic
363#14523963C2311yescharacteristic
364#14523963C2311yescharacteristic
365#14523963C2311yescharacteristic
366C22⋊(C67⋊C8)C2311yescharacteristic
367C22⋊(C67⋊C8)C2311yescharacteristic
368C22⋊(C67⋊C8)C2311yescharacteristic
369C22⋊(C67⋊C8)C2311yescharacteristic
370C22⋊(C67⋊C8)C2311yescharacteristic
371C22⋊(C67⋊C8)C2311yescharacteristic
372#14523954C2311yescharacteristic
373#14523954C2311yescharacteristic
374#14523954C2311yescharacteristic
375#14523954C2311yescharacteristic
376C4×C67⋊C8C2311yescharacteristic
377C4×C67⋊C8C2311yescharacteristic
378C4×C67⋊C8C2311yescharacteristic
379C4×C67⋊C8C2311yescharacteristic
380C4×C67⋊C8C2311yescharacteristic
381C4×C67⋊C8C2311yescharacteristic
382C2×#41×C67—21no—
383C2×#41×C67C2311yescharacteristic
384C22×D4×C67—21no—
385C22×D4×C67C2311yescharacteristic
386C22×D4×C67C2311yescharacteristic
387C23×C4×C67—21no—
388C4⋊Q8×C67C2311yescharacteristic
389#127×C67C2311yescharacteristic
390#126×C67—21no—
391#126×C67—21no—
392#126×C67—21no—
393#126×C67—21no—
394#126×C67D411yescharacteristic
395#126×C67D411yescharacteristic
396#125×C67—21no—
397#125×C67D411yescharacteristic
398#125×C67C2311yescharacteristic
399#125×C67C2311yescharacteristic
400#124×C67—21no—
401#124×C67—21no—
402#124×C67D411yescharacteristic
403#124×C67C2311yescharacteristic
404#124×C67C2311yescharacteristic
405#123×C67—21no—
406#123×C67—21no—
407#123×C67—21no—
408#123×C67—21no—
409#123×C67—21no—
410#123×C67—21no—
411#123×C67—21no—
412#123×C67—21no—
413#123×C67—21no—
414#123×C67—21no—
415#123×C67—21no—
416#123×C67—21no—
417#123×C67D411yescharacteristic
418#123×C67D411yescharacteristic
419C22⋊Q8×C67—21no—
420C22⋊Q8×C67—21no—
421C22⋊Q8×C67—21no—
422C22⋊Q8×C67—21no—
423C22⋊Q8×C67—21no—
424C22⋊Q8×C67D411yescharacteristic
425C22⋊Q8×C67C2311yescharacteristic
426C22⋊Q8×C67C2311yescharacteristic
427#121×C67—21no—
428#121×C67—21no—
429#121×C67—21no—
430#121×C67—21no—
431#121×C67—21no—
432#121×C67—21no—
433#121×C67D411yescharacteristic
434#121×C67C2311yescharacteristic
435#121×C67C2311yescharacteristic
436#121×C67C2311yescharacteristic
437#121×C67C2311yescharacteristic
438#120×C67—21no—
439#120×C67—21no—
440#120×C67—21no—
441#120×C67—21no—
442C4×Q8×C67C2311yescharacteristic
443C4×Q8×C67C2311yescharacteristic
444C4×Q8×C67C2311yescharacteristic
445C4×D4×C67—21no—
446C4×D4×C67—21no—
447C4×D4×C67—21no—
448C4×D4×C67—21no—
449C4×D4×C67—21no—
450C4×D4×C67—21no—
451C4×D4×C67—21no—
452C4×D4×C67—21no—
453C4×D4×C67—21no—
454C4×D4×C67C2311yescharacteristic
455C4×D4×C67C2311yescharacteristic
456C4×D4×C67C2311yescharacteristic
457C4×D4×C67C2311yescharacteristic
458C4×D4×C67C2311yescharacteristic
459C4×D4×C67C2311yescharacteristic
460C4×D4×C67C2311yescharacteristic
461C4×D4×C67C2311yescharacteristic
462C4×D4×C67C2311yescharacteristic
463C4×D4×C67C2311yescharacteristic
464C4×D4×C67C2311yescharacteristic
465#117×C67—21no—
466#117×C67—21no—
467#117×C67—21no—
468#117×C67C2311yescharacteristic
469#117×C67C2311yescharacteristic
470#117×C67C2311yescharacteristic
471C2×C4⋊C4×C67—21no—
472C2×C4⋊C4×C67—21no—
473C2×C4⋊C4×C67C2311yescharacteristic
474C2×C4⋊C4×C67C2311yescharacteristic
475C2×C22⋊C4×C67—21no—
476C2×C22⋊C4×C67—21no—
477C2×C22⋊C4×C67—21no—
478C2×C22⋊C4×C67—21no—
479C2×C22⋊C4×C67—21no—
480C2×C42×C67C2311yescharacteristic
481C23×D67—21no—
482C23×D67—21no—
483#11761628—22no—
484#11761628—41no—
485#11761627—82no—
486C2×Dic134—21no—
487C2×Dic134C2411yescharacteristic
488C2×D268—22no—
489C2×D268—22no—
490C2×D268—21no—
491C2×D268—21no—
492C2×D268—21no—
493C2×D268—21no—
494C2×D268—41no—
495C2×D268—41no—
496C2×D268C2411yescharacteristic
497C2×D268C2411yescharacteristic
498C2×D268C2411yescharacteristic
499C2×C22⋊D67—21no—
500C2×C22⋊D67—21no—
501C2×C22⋊D67—21no—
502C2×C22⋊D67—21no—
503C2×C22⋊D67—21no—
504D4×D67—82no—
505C22×Dic67—21no—
506C22×Dic67—21no—
507C2×C4×D67—21no—
508C2×C4×D67—21no—
509C2×C4×D67—21no—
510C2×C4×D67—21no—
511C2×C4×D67—21no—
512C2×C4×D67—21no—
513C2×C4×D67—21no—
514C2×C4×D67—21no—
515C2×C4×D67—21no—
516C2×C4×D67—82no—
517#11761618—22no—
518#11761616—22no—
519#11761616—41no—
520#11761616—41no—
521#11761615—22no—
522#11761615—41no—
523#11761615—41no—
524#11761613—22no—
525#11761613—22no—
526#11761613—22no—
527#11761613—22no—
528#11761613—22no—
529#11761613—22no—
530#11761613—41no—
531#11761613—41no—
532#11761613#4114yescomplemented
533#11761612—41no—
534#11761612—41no—
535C2×C67⋊C8—22no—
536C2×C67⋊C8—22no—
537C2×C67⋊C8—22no—
538C2×C67⋊C8—41no—
539C2×C67⋊C8C2411yescharacteristic
540C2×C67⋊C8C2411yescharacteristic
541C2×C67⋊C8C2411yescharacteristic
542C2×C67⋊C8C2411yescharacteristic
543C2×C67⋊C8C2411yescharacteristic
544C2×C67⋊C8C2411yescharacteristic
545C2×C67⋊C8C2411yescharacteristic
546C2×C67⋊C8C2411yescharacteristic
547C4⋊Dic67—21no—
548C4⋊Dic67—21no—
549C4⋊Dic67—21no—
550C4⋊Dic67C2411yescharacteristic
551C4⋊Dic67C2411yescharacteristic
552C4⋊Dic67C2411yescharacteristic
553C4⋊Dic67C2411yescharacteristic
554Dic67⋊C4—21no—
555Dic67⋊C4—21no—
556Dic67⋊C4—21no—
557Dic67⋊C4—21no—
558Dic67⋊C4—21no—
559Dic67⋊C4—21no—
560Dic67⋊C4—21no—
561Dic67⋊C4—21no—
562C22⋊Dic67—21no—
563C22⋊Dic67—21no—
564C22⋊Dic67—21no—
565(C2×D67)⋊C4—21no—
566(C2×D67)⋊C4—21no—
567(C2×D67)⋊C4—21no—
568(C2×D67)⋊C4—21no—
569(C2×D67)⋊C4—21no—
570(C2×D67)⋊C4—21no—
571(C2×D67)⋊C4—21no—
572(C2×D67)⋊C4—21no—
573(C2×D67)⋊C4—21no—
574(C2×D67)⋊C4—21no—
575(C2×D67)⋊C4—21no—
576(C2×D67)⋊C4—21no—
577(C2×D67)⋊C4—21no—
578(C2×D67)⋊C4—21no—
579(C2×D67)⋊C4—21no—
580(C2×D67)⋊C4—21no—
581C4×Dic67—21no—
582C4×Dic67—21no—
583C4×Dic67—21no—
584C24×C67—21no—
585C24×C67—21no—
586#41×C67—22no—
587#41×C67—41no—
588#41×C67—82no—
589C2×Q8×C67—21no—
590C2×Q8×C67C2×D411yescharacteristic
591C2×Q8×C67C2411yescharacteristic
592C2×D4×C67—22no—
593C2×D4×C67—22no—
594C2×D4×C67—21no—
595C2×D4×C67—21no—
596C2×D4×C67—21no—
597C2×D4×C67—21no—
598C2×D4×C67—21no—
599C2×D4×C67—21no—
600C2×D4×C67—21no—
601C2×D4×C67—21no—
602C2×D4×C67—21no—
603C2×D4×C67—41no—
604C2×D4×C67—41no—
605C2×D4×C67—82no—
606C2×D4×C67C2×D411yescharacteristic
607C2×D4×C67C2×D411yescharacteristic
608C2×D4×C67C2×D411yescharacteristic
609C2×D4×C67C2411yescharacteristic
610C2×D4×C67C2411yescharacteristic
611C2×D4×C67C2411yescharacteristic
612C22×C4×C67—21no—
613C22×C4×C67—21no—
614C22×C4×C67—21no—
615C22×C4×C67—21no—
616C22×C4×C67—21no—
617C22×C4×C67—21no—
618C22×C4×C67—21no—
619C22×C4×C67—21no—
620C22×C4×C67—21no—
621C22×C4×C67—21no—
622C22×C4×C67—21no—
623C22×C4×C67—82no—
624C22×C4×C67C2×D411yescharacteristic
625C22×C4×C67C2×D411yescharacteristic
626C22×C4×C67C2411yescharacteristic
627C22×C4×C67C2411yescharacteristic
628C22×C4×C67C2411yescharacteristic
629C4⋊C4×C67—21no—
630C4⋊C4×C67—21no—
631C4⋊C4×C67—21no—
632C4⋊C4×C67—21no—
633C4⋊C4×C67—21no—
634C4⋊C4×C67—21no—
635C4⋊C4×C67—21no—
636C4⋊C4×C67—21no—
637C4⋊C4×C67—21no—
638C4⋊C4×C67—21no—
639C4⋊C4×C67—21no—
640C4⋊C4×C67C2×D411yescharacteristic
641C4⋊C4×C67C2×D411yescharacteristic
642C4⋊C4×C67C2×D411yescharacteristic
643C4⋊C4×C67C2×D411yescharacteristic
644C4⋊C4×C67C2×D411yescharacteristic
645C4⋊C4×C67C2×D411yescharacteristic
646C4⋊C4×C67C2×D411yescharacteristic
647C4⋊C4×C67C2×D411yescharacteristic
648C4⋊C4×C67C2×D411yescharacteristic
649C4⋊C4×C67C2×D411yescharacteristic
650C4⋊C4×C67C2411yescharacteristic
651C4⋊C4×C67C2411yescharacteristic
652C4⋊C4×C67C2411yescharacteristic
653C4⋊C4×C67C2411yescharacteristic
654C22⋊C4×C67—21no—
655C22⋊C4×C67—21no—
656C22⋊C4×C67—21no—
657C22⋊C4×C67—21no—
658C22⋊C4×C67—21no—
659C22⋊C4×C67—21no—
660C22⋊C4×C67—21no—
661C22⋊C4×C67—21no—
662C22⋊C4×C67—21no—
663C22⋊C4×C67—21no—
664C22⋊C4×C67—21no—
665C22⋊C4×C67—21no—
666C22⋊C4×C67—21no—
667C22⋊C4×C67—21no—
668C22⋊C4×C67—21no—
669C22⋊C4×C67—21no—
670C22⋊C4×C67—21no—
671C22⋊C4×C67—21no—
672C22⋊C4×C67—21no—
673C22⋊C4×C67C2×D411yescharacteristic
674C22⋊C4×C67C2×D411yescharacteristic
675C22⋊C4×C67C2×D411yescharacteristic
676C22⋊C4×C67C2×D411yescharacteristic
677C22⋊C4×C67C2×D411yescharacteristic
678C22⋊C4×C67C2×D411yescharacteristic
679C22⋊C4×C67C2×D411yescharacteristic
680C22⋊C4×C67C2×D411yescharacteristic
681C22⋊C4×C67C2×D411yescharacteristic
682C22⋊C4×C67C2×D411yescharacteristic
683C42×C67—21no—
684C42×C67—21no—
685C42×C67—21no—
686C42×C67C2×D411yescharacteristic
687C42×C67C2×D411yescharacteristic
688C42×C67C2411yescharacteristic
689C42×C67C2411yescharacteristic
690C42×C67C2411yescharacteristic
691C42×C67C2411yescharacteristic
692C23×C67—21no—
693C23×C67—21no—
694C23×C67—21no—
695C23×C67—42no—
696C23×C67—42no—
697C23×C67—42no—
698C23×C67—81no—
699C23×C67—81no—
700C23×C67—81no—
701C23×C67C22×D411yescharacteristic
702C23×C67C22×D411yescharacteristic
703C23×C67C22×D411yescharacteristic
704C22×D67—21no—
705C22×D67—21no—
706C22×D67—21no—
707C22×D67—42no—
708C22×D67—42no—
709C22×D67—42no—
710C22×D67—81no—
711C22×D67—81no—
712C22×D67—81no—
713Q8×C67—21no—
714Q8×C67—21no—
715Q8×C67—41no—
716Q8×C67—81no—
717D4×C67—22no—
718D4×C67—22no—
719D4×C67—21no—
720D4×C67—21no—
721D4×C67—21no—
722D4×C67—21no—
723D4×C67—21no—
724D4×C67—41no—
725D4×C67—42no—
726D4×C67—42no—
727D4×C67—42no—
728D4×C67—42no—
729D4×C67—81no—
730D4×C67—81no—
731D4×C67—81no—
732D4×C67—81no—
733D4×C67—81no—
734D4×C67C2×#4112yes—
735C2×C4×C67—22no—
736C2×C4×C67—21no—
737C2×C4×C67—21no—
738C2×C4×C67—21no—
739C2×C4×C67—21no—
740C2×C4×C67—21no—
741C2×C4×C67—21no—
742C2×C4×C67—21no—
743C2×C4×C67—21no—
744C2×C4×C67—21no—
745C2×C4×C67—21no—
746C2×C4×C67—21no—
747C2×C4×C67—41no—
748C2×C4×C67—42no—
749C2×C4×C67—42no—
750C2×C4×C67—81no—
751C2×C4×C67—81no—
752C2×C4×C67—81no—
753C2×C4×C67—81no—
754C2×C4×C67—81no—
755C2×C4×C67—81no—
756C2×C4×C67—81no—
757C2×C4×C67—81no—
758C2×C4×C67—81no—
759C2×C4×C67C22×D411yescharacteristic
760C2×C4×C67C22×D411yescharacteristic
761C2×C4×C67C22×D411yescharacteristic
762C2×C4×C67C22×D411yescharacteristic
763C2×C4×C67C22×D411yescharacteristic
764C2×C4×C67C22×D411yescharacteristic
765C2×C4×C67C22×D411yescharacteristic
766C2×C4×C67C22×D411yescharacteristic
767C2×C4×C67C22×D411yescharacteristic
768C2×C4×C67C22×D411yescharacteristic
769C2×C4×C67C22×D411yescharacteristic
770C2×C4×C67C2511yescharacteristic
771C22⋊D67—42no—
772C22⋊D67—42no—
773C22⋊D67—81no—
774C22⋊D67—81no—
775C22⋊D67—81no—
776C2×Dic67—21no—
777C2×Dic67—21no—
778C2×Dic67—21no—
779C2×Dic67—21no—
780C2×Dic67—21no—
781C2×Dic67—42no—
782C2×Dic67—81no—
783D268—21no—
784D268—21no—
785D268—21no—
786D268—21no—
787D268—21no—
788D268—42no—
789D268—42no—
790D268—81no—
791D268—81no—
792D268C2×#4112yes—
793C4×D67—42no—
794C4×D67—81no—
795C4×D67—81no—
796C4×D67—81no—
797C4×D67—81no—
798C4×D67—81no—
799C4×D67—81no—
800C4×D67—81no—
801C4×D67—81no—
802Dic134—21no—
803Dic134—21no—
804Dic134—81no—
805C67⋊C8—21no—
806C67⋊C8—21no—
807C67⋊C8—21no—
808C67⋊C8—21no—
809C67⋊C8—21no—
810C67⋊C8—21no—
811C67⋊C8—21no—
812C67⋊C8C2×#4112yes—
813C22×C67—21no—
814C22×C67—21no—
815C22×C67—21no—
816C22×C67—21no—
817C22×C67—21no—
818C22×C67—21no—
819C22×C67—22no—
820C22×C67—21no—
821C22×C67—21no—
822C22×C67—41no—
823C22×C67—41no—
824C22×C67—41no—
825C22×C67—41no—
826C22×C67—41no—
827C22×C67—41no—
828C22×C67—41no—
829C22×C67—41no—
830C22×C67—84no—
831C22×C67—162no—
832C22×C67#57612yes—
833C22×C67C23×D411yescharacteristic
834C2×D67—22no—
835C2×D67—41no—
836C2×D67—41no—
837C2×D67—41no—
838C2×D67—41no—
839C2×D67—41no—
840C2×D67—41no—
841C2×D67—41no—
842C2×D67—41no—
843C2×D67—84no—
844C2×D67—162no—
845C4×C67—21no—
846C4×C67—21no—
847C4×C67—21no—
848C4×C67—21no—
849C4×C67—21no—
850C4×C67—21no—
851C4×C67—21no—
852C4×C67—21no—
853C4×C67—21no—
854C4×C67—21no—
855C4×C67—21no—
856C4×C67—41no—
857C4×C67—41no—
858C4×C67—41no—
859C4×C67—41no—
860C4×C67—41no—
861C4×C67C22×#4111yescharacteristic
862C4×C67#58511yescharacteristic
863Dic67—41no—
864Dic67—41no—
865Dic67—41no—
866Dic67—41no—
867Dic67—41no—
868#61471—671nomaximal, Sylow
869C2×C67—22no—
870C2×C67—41no—
871C2×C67—41no—
872C2×C67—42no—
873C2×C67—81no—
874C2×C67—81no—
875C2×C67D4×#4111yescharacteristic
876C2×C67C2×#57611yescharacteristic
877C2×C67#358411yescharacteristic
878D67—42no—
879D67—81no—
880D67—81no—
881#3513—671no—
882#3513D6711yescharacteristic, complemented
883#3396—671no—
884#3380—671no—
885#3370—671no—
886#3370—671no—
887#3339—671no—
888#3336—671no—
889#3334—671no—
890#3322—671no—
891#3322—671no—
892#3310—671no—
893#3310—671no—
894#3306—671no—
895#3306—671no—
896#3280—671no—
897#3280—671no—
898D4×D8—671no—
899#3176—671no—
900#3175—671no—
901#3168—671no—
902#3119—671no—
903#3119—671no—
904#3118—671no—
905#3118—671no—
906#3114—671no—
907#3114—671no—
908#2966—671no—
909#2951—671no—
910#2948—671no—
911C2×C4×D8—671no—
912C67#6147111yescharacteristic, complemented, Sylow
913C2×#135—671no—
914C22×D8—671no—
915C22×D8—671no—
916#559—671no—
917#559C2×D6711yescharacteristic, complemented
918#554—671no—
919#554C2×D6711yescharacteristic, complemented
920#553—21no—
921#553—671no—
922#553—1341no—
923#553C2×D6711yescharacteristic, complemented
924#552—671no—
925#552C2×D6711yescharacteristic
926#551—21no—
927#551—21no—
928#551—1341no—
929#551—1341no—
930#547—671no—
931#547C2×D6711yescharacteristic, complemented
932#546—21no—
933#546—671no—
934#546—671no—
935#546—1341no—
936#546C2×D6711yescharacteristic, complemented
937#546C2×D6711yescharacteristic, complemented
938D42—671no—
939D42C2×D6711yescharacteristic
940#542—671no—
941#542C2×D6711yescharacteristic, complemented
942#540—671no—
943#540C2×D6711yescharacteristic, complemented
944#539—21no—
945#539—1341no—
946#538—21no—
947#538—1341no—
948#529—671no—
949#529C2×D6711yescharacteristic
950#529C2×D6711yescharacteristic, complemented
951#525—21no—
952#525—1341no—
953C2×#123—21no—
954C2×#123—1341no—
955#520—671no—
956#520C2×D6711yescharacteristic, complemented
957#518—671no—
958#518C2×D6711yescharacteristic, complemented
959C2×C4×D4—671no—
960C2×C4×D4C2×D6711yescharacteristic, complemented
961#500—671no—
962#499—671no—
963#499—671no—
964#495—671no—
965#495—671no—
966#493—671no—
967#490—671no—
968#490—671no—
969#489—671no—
970#489—671no—
971#488—671no—
972#488—671no—
973#485—671no—
974#485—671no—
975#483—671no—
976#483—671no—
977#482—671no—
978#482—671no—
979#481—671no—
980#481—671no—
981#480—671no—
982#480—671no—
983#480—671no—
984#480—671no—
985#479—671no—
986#479—671no—
987#478—671no—
988#478—671no—
989#478—671no—
990#478—671no—
991#478—671no—
992#478—671no—
993#476—671no—
994#476—671no—
995#474—671no—
996#474—671no—
997#469—671no—
998#469—671no—
999#468—671no—
1000#468—671no—
1001#467—671no—
1002#467—671no—
1003#466—671no—
1004#466—671no—
1005#466—671no—
1006#466—671no—
1007#465—671no—
1008#465—671no—
1009#463—671no—
1010#463—671no—
1011#463—671no—
1012#463—671no—
1013#463—671no—
1014#463—671no—
1015#463—671no—
1016#463—671no—
1017#460—671no—
1018#460—671no—
1019#459—671no—
1020#459—671no—
1021#450—671no—
1022#450—671no—
1023#450—671no—
1024#450—671no—
1025#449—671no—
1026#449—671no—
1027#449—671no—
1028#449—671no—
1029#447—671no—
1030#447—671no—
1031#447—671no—
1032#447—671no—
1033#446—671no—
1034C8×Q8—671no—
1035#442—671no—
1036#442—671no—
1037#442—671no—
1038#442—671no—
1039#442—671no—
1040#442—671no—
1041#440—671no—
1042#440—671no—
1043#440—671no—
1044#440—671no—
1045#440—671no—
1046#440—671no—
1047C4×Q16—671no—
1048C4×Q16—671no—
1049C4×SD16—671no—
1050C4×SD16—671no—
1051C4×D8—671no—
1052C4×D8—671no—
1053C4×D8—671no—
1054C4×D8—671no—
1055C4×D8—671no—
1056C4×D8—671no—
1057C4×D8—671no—
1058C4×D8—671no—
1059C4×D8—671no—
1060C4×D8—671no—
1061C4×D8—671no—
1062C4×D8—671no—
1063#436—671no—
1064#435—671no—
1065#435—671no—
1066C8×D4—671no—
1067C8×D4—671no—
1068C8×D4—671no—
1069#433—671no—
1070#433—671no—
1071#432—671no—
1072#427—671no—
1073C2×#107—671no—
1074C2×#107—671no—
1075#418—671no—
1076#418—671no—
1077#417—671no—
1078#417—671no—
1079C2×#102—671no—
1080C2×#102—671no—
1081#405—671no—
1082#405—671no—
1083C2×C4×C8—671no—
1084C2×#41—21no—
1085C2×#41—671no—
1086C2×#41—1341no—
1087C2×#41C22×D6711yescharacteristic
1088C22×D4—21no—
1089C22×D4—671no—
1090C22×D4—671no—
1091C22×D4—1341no—
1092C22×D4C22×D6711yescharacteristic
1093C22×D4C22×D6711yescharacteristic
1094C23×C4—21no—
1095C23×C4—1341no—
1096#135—1344no—
1097C2×Q16—671no—
1098C2×SD16—671no—
1099C2×SD16—671no—
1100C2×SD16—671no—
1101C2×SD16—671no—
1102C2×SD16—671no—
1103C2×SD16—671no—
1104C2×D8—671no—
1105C2×D8—671no—
1106C2×D8—671no—
1107C2×D8—671no—
1108C2×D8—671no—
1109C2×D8—671no—
1110C2×D8—671no—
1111C2×D8—671no—
1112C2×D8—671no—
1113C2×D8—1344no—
1114C2×D8—1344no—
1115C2×M16—671no—
1116C2×M16—671no—
1117C22×C8—671no—
1118C22×C8—671no—
1119C22×C8—671no—
1120C22×C8—671no—
1121C4⋊Q8—671no—
1122C4⋊Q8C22×D6711yescharacteristic
1123#127—671no—
1124#127C22×D6711yescharacteristic
1125#126—21no—
1126#126—21no—
1127#126—21no—
1128#126—21no—
1129#126—1341no—
1130#126—1341no—
1131#126—1341no—
1132#126—1341no—
1133#126C22⋊D6711yescharacteristic
1134#126C22⋊D6711yescharacteristic
1135#125—21no—
1136#125—671no—
1137#125—671no—
1138#125—1341no—
1139#125C22⋊D6711yescharacteristic
1140#125C22×D6711yescharacteristic
1141#125C22×D6711yescharacteristic
1142#124—21no—
1143#124—21no—
1144#124—671no—
1145#124—671no—
1146#124—1341no—
1147#124—1341no—
1148#124C22⋊D6711yescharacteristic
1149#124C22×D6711yescharacteristic
1150#124C22×D6711yescharacteristic
1151#123—21no—
1152#123—21no—
1153#123—21no—
1154#123—21no—
1155#123—21no—
1156#123—21no—
1157#123—21no—
1158#123—21no—
1159#123—21no—
1160#123—21no—
1161#123—21no—
1162#123—21no—
1163#123—1341no—
1164#123—1341no—
1165#123—1341no—
1166#123—1341no—
1167#123—1341no—
1168#123—1341no—
1169#123—1341no—
1170#123—1341no—
1171#123—1341no—
1172#123—1341no—
1173#123—1341no—
1174#123—1341no—
1175#123C22⋊D6711yescharacteristic
1176#123C22⋊D6711yescharacteristic
1177C22⋊Q8—21no—
1178C22⋊Q8—21no—
1179C22⋊Q8—21no—
1180C22⋊Q8—21no—
1181C22⋊Q8—21no—
1182C22⋊Q8—671no—
1183C22⋊Q8—671no—
1184C22⋊Q8—1341no—
1185C22⋊Q8—1341no—
1186C22⋊Q8—1341no—
1187C22⋊Q8—1341no—
1188C22⋊Q8—1341no—
1189C22⋊Q8C22⋊D6711yescharacteristic
1190C22⋊Q8C22×D6711yescharacteristic
1191C22⋊Q8C22×D6711yescharacteristic
1192#121—21no—
1193#121—21no—
1194#121—21no—
1195#121—21no—
1196#121—21no—
1197#121—21no—
1198#121—671no—
1199#121—671no—
1200#121—671no—
1201#121—671no—
1202#121—1341no—
1203#121—1341no—
1204#121—1341no—
1205#121—1341no—
1206#121—1341no—
1207#121—1341no—
1208#121C22⋊D6711yescharacteristic
1209#121C22×D6711yescharacteristic
1210#121C22×D6711yescharacteristic
1211#121C22×D6711yescharacteristic
1212#121C22×D6711yescharacteristic
1213#120—21no—
1214#120—21no—
1215#120—21no—
1216#120—21no—
1217#120—1341no—
1218#120—1341no—
1219#120—1341no—
1220#120—1341no—
1221C4×Q8—671no—
1222C4×Q8—671no—
1223C4×Q8C22×D6711yescharacteristic
1224C4×Q8C22×D6711yescharacteristic
1225C4×Q8C22×D6711yescharacteristic
1226C4×D4—21no—
1227C4×D4—21no—
1228C4×D4—21no—
1229C4×D4—21no—
1230C4×D4—21no—
1231C4×D4—21no—
1232C4×D4—21no—
1233C4×D4—21no—
1234C4×D4—21no—
1235C4×D4—671no—
1236C4×D4—671no—
1237C4×D4—671no—
1238C4×D4—671no—
1239C4×D4—671no—
1240C4×D4—671no—
1241C4×D4—671no—
1242C4×D4—671no—
1243C4×D4—1341no—
1244C4×D4—1341no—
1245C4×D4—1341no—
1246C4×D4—1341no—
1247C4×D4—1341no—
1248C4×D4—1341no—
1249C4×D4—1341no—
1250C4×D4—1341no—
1251C4×D4—1341no—
1252C4×D4C22×D6711yescharacteristic
1253C4×D4C22×D6711yescharacteristic
1254C4×D4C22×D6711yescharacteristic
1255C4×D4C22×D6711yescharacteristic
1256C4×D4C22×D6711yescharacteristic
1257C4×D4C22×D6711yescharacteristic
1258C4×D4C22×D6711yescharacteristic
1259C4×D4C22×D6711yescharacteristic
1260C4×D4C22×D6711yescharacteristic
1261C4×D4C22×D6711yescharacteristic
1262C4×D4C22×D6711yescharacteristic
1263#117—21no—
1264#117—21no—
1265#117—21no—
1266#117—671no—
1267#117—1341no—
1268#117—1341no—
1269#117—1341no—
1270#117C22×D6711yescharacteristic
1271#117C22×D6711yescharacteristic
1272#117C22×D6711yescharacteristic
1273C2×C4⋊C4—21no—
1274C2×C4⋊C4—21no—
1275C2×C4⋊C4—671no—
1276C2×C4⋊C4—671no—
1277C2×C4⋊C4—1341no—
1278C2×C4⋊C4—1341no—
1279C2×C4⋊C4C22×D6711yescharacteristic
1280C2×C4⋊C4C22×D6711yescharacteristic
1281C2×C22⋊C4—21no—
1282C2×C22⋊C4—21no—
1283C2×C22⋊C4—21no—
1284C2×C22⋊C4—21no—
1285C2×C22⋊C4—21no—
1286C2×C22⋊C4—1341no—
1287C2×C22⋊C4—1341no—
1288C2×C22⋊C4—1341no—
1289C2×C22⋊C4—1341no—
1290C2×C22⋊C4—1341no—
1291C2×C42C22×D6711yescharacteristic
1292#107—671no—
1293#107—671no—
1294#107—671no—
1295#107—671no—
1296#107—671no—
1297#107—671no—
1298#107—671no—
1299#107—671no—
1300#107—671no—
1301#107—671no—
1302#106—671no—
1303#106—671no—
1304#106—671no—
1305#106—671no—
1306#106—671no—
1307#106—671no—
1308C4⋊C8—671no—
1309C4⋊C8—671no—
1310C4⋊C8—671no—
1311C4⋊C8—671no—
1312C4⋊C8—671no—
1313C4⋊C8—671no—
1314#103—671no—
1315#103—671no—
1316#103—671no—
1317#103—671no—
1318#103—671no—
1319#103—671no—
1320#103—671no—
1321#103—671no—
1322#102—671no—
1323#102—671no—
1324#102—671no—
1325#102—671no—
1326#102—671no—
1327#102—671no—
1328#102—671no—
1329#102—671no—
1330#102—671no—
1331#102—671no—
1332#102—671no—
1333#102—671no—
1334#102—671no—
1335#102—671no—
1336#102—671no—
1337#102—671no—
1338#102—671no—
1339#102—671no—
1340#102—671no—
1341#102—671no—
1342#102—671no—
1343#102—671no—
1344#102—671no—
1345#102—671no—
1346C22⋊C8—671no—
1347C22⋊C8—671no—
1348C22⋊C8—671no—
1349C22⋊C8—671no—
1350C22⋊C8—671no—
1351C22⋊C8—671no—
1352#97—671no—
1353#97—671no—
1354#97—671no—
1355#97—671no—
1356C4×C8—671no—
1357C4×C8—671no—
1358C4×C8—671no—
1359C4×C8—671no—
1360C4×C8—671no—
1361C4×C8—671no—
1362C24—21no—
1363C24—21no—
1364C24—1341no—
1365C24—1341no—
1366#41—22no—
1367#41—41no—
1368#41—82no—
1369#41—2681no—
1370#41—5362no—
1371#41—1342no—
1372C2×Q8—21no—
1373C2×Q8—671no—
1374C2×Q8—1341no—
1375C2×Q8C2×C22⋊D6711yescharacteristic
1376C2×Q8C23×D6711yescharacteristic
1377C2×D4—22no—
1378C2×D4—22no—
1379C2×D4—21no—
1380C2×D4—21no—
1381C2×D4—21no—
1382C2×D4—21no—
1383C2×D4—21no—
1384C2×D4—21no—
1385C2×D4—21no—
1386C2×D4—21no—
1387C2×D4—21no—
1388C2×D4—41no—
1389C2×D4—41no—
1390C2×D4—82no—
1391C2×D4—2681no—
1392C2×D4—2681no—
1393C2×D4—5362no—
1394C2×D4—671no—
1395C2×D4—671no—
1396C2×D4—671no—
1397C2×D4—1342no—
1398C2×D4—1342no—
1399C2×D4—1341no—
1400C2×D4—1341no—
1401C2×D4—1341no—
1402C2×D4—1341no—
1403C2×D4—1341no—
1404C2×D4—1341no—
1405C2×D4—1341no—
1406C2×D4—1341no—
1407C2×D4—1341no—
1408C2×D4C2×C22⋊D6711yescharacteristic
1409C2×D4C2×C22⋊D6711yescharacteristic
1410C2×D4C2×C22⋊D6711yescharacteristic
1411C2×D4C23×D6711yescharacteristic
1412C2×D4C23×D6711yescharacteristic
1413C2×D4C23×D6711yescharacteristic
1414C22×C4—21no—
1415C22×C4—21no—
1416C22×C4—21no—
1417C22×C4—21no—
1418C22×C4—21no—
1419C22×C4—21no—
1420C22×C4—21no—
1421C22×C4—21no—
1422C22×C4—21no—
1423C22×C4—21no—
1424C22×C4—21no—
1425C22×C4—82no—
1426C22×C4—5362no—
1427C22×C4—1341no—
1428C22×C4—1341no—
1429C22×C4—1341no—
1430C22×C4—1341no—
1431C22×C4—1341no—
1432C22×C4—1341no—
1433C22×C4—1341no—
1434C22×C4—1341no—
1435C22×C4—1341no—
1436C22×C4—1341no—
1437C22×C4—1341no—
1438C22×C4C2×C22⋊D6711yescharacteristic
1439C22×C4C2×C22⋊D6711yescharacteristic
1440C22×C4C23×D6711yescharacteristic
1441C22×C4C23×D6711yescharacteristic
1442C22×C4C23×D6711yescharacteristic
1443Q16—1342no—
1444SD16—2681no—
1445SD16—2681no—
1446SD16—2681no—
1447SD16—2681no—
1448SD16—1342no—
1449SD16—1342no—
1450D8—2681no—
1451D8—2681no—
1452D8—674no—
1453D8—1342no—
1454D8—1342no—
1455D8—1342no—
1456D8—1342no—
1457D8—1342no—
1458D8—1342no—
1459M16—2681no—
1460M16—2681no—
1461C2×C8—2681no—
1462C2×C8—671no—
1463C2×C8—671no—
1464C2×C8—671no—
1465C2×C8—671no—
1466C2×C8—671no—
1467C2×C8—671no—
1468C2×C8—671no—
1469C2×C8—671no—
1470C2×C8—1342no—
1471C2×C8—1342no—
1472C2×C8—1342no—
1473C4⋊C4—21no—
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—21no—
1481C4⋊C4—21no—
1482C4⋊C4—21no—
1483C4⋊C4—21no—
1484C4⋊C4—671no—
1485C4⋊C4—671no—
1486C4⋊C4—671no—
1487C4⋊C4—671no—
1488C4⋊C4—1341no—
1489C4⋊C4—1341no—
1490C4⋊C4—1341no—
1491C4⋊C4—1341no—
1492C4⋊C4—1341no—
1493C4⋊C4—1341no—
1494C4⋊C4—1341no—
1495C4⋊C4—1341no—
1496C4⋊C4—1341no—
1497C4⋊C4—1341no—
1498C4⋊C4—1341no—
1499C4⋊C4C2×C22⋊D6711yescharacteristic
1500C4⋊C4C2×C22⋊D6711yescharacteristic
1501C4⋊C4C2×C22⋊D6711yescharacteristic
1502C4⋊C4C2×C22⋊D6711yescharacteristic
1503C4⋊C4C2×C22⋊D6711yescharacteristic
1504C4⋊C4C2×C22⋊D6711yescharacteristic
1505C4⋊C4C2×C22⋊D6711yescharacteristic
1506C4⋊C4C2×C22⋊D6711yescharacteristic
1507C4⋊C4C2×C22⋊D6711yescharacteristic
1508C4⋊C4C2×C22⋊D6711yescharacteristic
1509C4⋊C4C23×D6711yescharacteristic
1510C4⋊C4C23×D6711yescharacteristic
1511C4⋊C4C23×D6711yescharacteristic
1512C4⋊C4C23×D6711yescharacteristic
1513C22⋊C4—21no—
1514C22⋊C4—21no—
1515C22⋊C4—21no—
1516C22⋊C4—21no—
1517C22⋊C4—21no—
1518C22⋊C4—21no—
1519C22⋊C4—21no—
1520C22⋊C4—21no—
1521C22⋊C4—21no—
1522C22⋊C4—21no—
1523C22⋊C4—21no—
1524C22⋊C4—21no—
1525C22⋊C4—21no—
1526C22⋊C4—21no—
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—1341no—
1533C22⋊C4—1341no—
1534C22⋊C4—1341no—
1535C22⋊C4—1341no—
1536C22⋊C4—1341no—
1537C22⋊C4—1341no—
1538C22⋊C4—1341no—
1539C22⋊C4—1341no—
1540C22⋊C4—1341no—
1541C22⋊C4—1341no—
1542C22⋊C4—1341no—
1543C22⋊C4—1341no—
1544C22⋊C4—1341no—
1545C22⋊C4—1341no—
1546C22⋊C4—1341no—
1547C22⋊C4—1341no—
1548C22⋊C4—1341no—
1549C22⋊C4—1341no—
1550C22⋊C4—1341no—
1551C22⋊C4C2×C22⋊D6711yescharacteristic
1552C22⋊C4C2×C22⋊D6711yescharacteristic
1553C22⋊C4C2×C22⋊D6711yescharacteristic
1554C22⋊C4C2×C22⋊D6711yescharacteristic
1555C22⋊C4C2×C22⋊D6711yescharacteristic
1556C22⋊C4C2×C22⋊D6711yescharacteristic
1557C22⋊C4C2×C22⋊D6711yescharacteristic
1558C22⋊C4C2×C22⋊D6711yescharacteristic
1559C22⋊C4C2×C22⋊D6711yescharacteristic
1560C22⋊C4C2×C22⋊D6711yescharacteristic
1561C42—21no—
1562C42—21no—
1563C42—21no—
1564C42—1341no—
1565C42—1341no—
1566C42—1341no—
1567C42C2×C22⋊D6711yescharacteristic
1568C42C2×C22⋊D6711yescharacteristic
1569C42C23×D6711yescharacteristic
1570C42C23×D6711yescharacteristic
1571C42C23×D6711yescharacteristic
1572C42C23×D6711yescharacteristic
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23—42no—
1577C23—42no—
1578C23—42no—
1579C23—81no—
1580C23—81no—
1581C23—81no—
1582C23—2682no—
1583C23—2682no—
1584C23—2682no—
1585C23—5361no—
1586C23—5361no—
1587C23—5361no—
1588C23—1341no—
1589C23—1341no—
1590C23—1341no—
1591C23C22×C22⋊D6711yescharacteristic
1592C23C22×C22⋊D6711yescharacteristic
1593C23C22×C22⋊D6711yescharacteristic
1594Q8—21no—
1595Q8—21no—
1596Q8—41no—
1597Q8—81no—
1598Q8—5361no—
1599Q8—1341no—
1600Q8—1341no—
1601D4—22no—
1602D4—22no—
1603D4—21no—
1604D4—21no—
1605D4—21no—
1606D4—21no—
1607D4—21no—
1608D4—41no—
1609D4—42no—
1610D4—42no—
1611D4—42no—
1612D4—42no—
1613D4—81no—
1614D4—81no—
1615D4—81no—
1616D4—81no—
1617D4—81no—
1618D4—2682no—
1619D4—2682no—
1620D4—2682no—
1621D4—2682no—
1622D4—5361no—
1623D4—5361no—
1624D4—5361no—
1625D4—5361no—
1626D4—5361no—
1627D4—672no—
1628D4—1341no—
1629D4—1341no—
1630D4—1341no—
1631D4—1341no—
1632D4—1341no—
1633D4#41×D6712yes—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—41no—
1647C2×C4—42no—
1648C2×C4—42no—
1649C2×C4—81no—
1650C2×C4—81no—
1651C2×C4—81no—
1652C2×C4—81no—
1653C2×C4—81no—
1654C2×C4—81no—
1655C2×C4—81no—
1656C2×C4—81no—
1657C2×C4—81no—
1658C2×C4—2682no—
1659C2×C4—2682no—
1660C2×C4—5361no—
1661C2×C4—5361no—
1662C2×C4—5361no—
1663C2×C4—5361no—
1664C2×C4—5361no—
1665C2×C4—5361no—
1666C2×C4—5361no—
1667C2×C4—5361no—
1668C2×C4—5361no—
1669C2×C4—1341no—
1670C2×C4—1341no—
1671C2×C4—1341no—
1672C2×C4—1341no—
1673C2×C4—1341no—
1674C2×C4C22×C22⋊D6711yescharacteristic
1675C2×C4C22×C22⋊D6711yescharacteristic
1676C2×C4C22×C22⋊D6711yescharacteristic
1677C2×C4C22×C22⋊D6711yescharacteristic
1678C2×C4C22×C22⋊D6711yescharacteristic
1679C2×C4C22×C22⋊D6711yescharacteristic
1680C2×C4C22×C22⋊D6711yescharacteristic
1681C2×C4C22×C22⋊D6711yescharacteristic
1682C2×C4C22×C22⋊D6711yescharacteristic
1683C2×C4C22×C22⋊D6711yescharacteristic
1684C2×C4C22×C22⋊D6711yescharacteristic
1685C2×C4C24×D6711yescharacteristic
1686C8—672no—
1687C8—1341no—
1688C8—1341no—
1689C8—1341no—
1690C8—1341no—
1691C8—1341no—
1692C8—1341no—
1693C8—1341no—
1694C22—21no—
1695C22—21no—
1696C22—21no—
1697C22—21no—
1698C22—21no—
1699C22—21no—
1700C22—22no—
1701C22—21no—
1702C22—21no—
1703C22—41no—
1704C22—41no—
1705C22—41no—
1706C22—41no—
1707C22—41no—
1708C22—41no—
1709C22—41no—
1710C22—41no—
1711C22—84no—
1712C22—2681no—
1713C22—2681no—
1714C22—2681no—
1715C22—2681no—
1716C22—2681no—
1717C22—2681no—
1718C22—2681no—
1719C22—2681no—
1720C22—162no—
1721C22—5364no—
1722C22—10722no—
1723C22—1342no—
1724C22#1686419912yes—
1725C22C23×C22⋊D6711yescharacteristic
1726C4—21no—
1727C4—21no—
1728C4—21no—
1729C4—21no—
1730C4—21no—
1731C4—21no—
1732C4—21no—
1733C4—21no—
1734C4—21no—
1735C4—21no—
1736C4—21no—
1737C4—41no—
1738C4—41no—
1739C4—41no—
1740C4—41no—
1741C4—41no—
1742C4—2681no—
1743C4—2681no—
1744C4—2681no—
1745C4—2681no—
1746C4—2681no—
1747C4C2×#41×D6711yescharacteristic
1748C4#1686423211yescharacteristic
1749C2—22no—
1750C2—41no—
1751C2—41no—
1752C2—42no—
1753C2—81no—
1754C2—81no—
1755C2—2682no—
1756C2—5361no—
1757C2—5361no—
1758C2#41×C22⋊D6711yescharacteristic
1759C2C2×#1686419911yescharacteristic
1760C2#2257498011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3513C2
socleC22×C67C23×D4
hypercenter#3513D67
hypocenterC67#61471
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #529 ◁ #3513

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22574153C2semidirect
2. #22573217C2semidirect
3. #22573072C2semidirect
4. #22572962C2semidirect
5. #22572956C2semidirect
6. #22572605C2semidirect
7. #22572571C2semidirect
8. #22572552C2semidirect
9. #22572410C2semidirect
10. #22572404C2semidirect
11. #22572230C2semidirect
12. #22572224C2semidirect
13. #22572170C2semidirect
14. #22572164C2semidirect
15. #22571890C2semidirect
16. #22571890C2semidirect
17. D4×#11761613C2semidirect
18. #22570853C2semidirect
19. #22570842C2semidirect
20. #22570773C2semidirect
21. #22570408C2semidirect
22. #22570402C2semidirect
23. #22570393C2semidirect
24. #22570387C2semidirect
25. #22570347C2semidirect
26. #22570343C2semidirect
27. #22569185C2semidirect
28. #22569082C2semidirect
29. #22569059C2semidirect
30. C2×C4×#11761613C2semidirect
31. C67×#3513C2semidirect
35. #16864131C22semidirect
36. #16864106C22semidirect
38. #16864092C22semidirect
42. #16864050C22semidirect
43. #16864042C22semidirect
44. #16864042C22semidirect
47. #16864017C22semidirect
48. #16864001C22semidirect
51. #16863930C22semidirect
54. #16863876C22semidirect
55. #16863870C22semidirect
56. C2×C4×D268C22semidirect
57. #16863799C22semidirect
58. #16863795C22semidirect
59. #16863795C22semidirect
60. #16863778C22semidirect
61. #16863778C22semidirect
63. #16863762C22semidirect
64. #16863760C22semidirect
65. #16863758C22semidirect
66. #16863755C22semidirect
67. #16863753C22semidirect
68. #16863750C22semidirect
69. #16863737C22semidirect
70. #16863734C22semidirect
71. #16863726C22semidirect
72. #16863724C22semidirect
73. #16863720C22semidirect
74. #16863717C22semidirect
75. #16863714C22semidirect
76. #16863712C22semidirect
77. #16863709C22semidirect
78. #16863709C22semidirect
79. #16863707C22semidirect
80. #16863707C22semidirect
81. #16863703C22semidirect
82. #16863700C22semidirect
83. #16863696C22semidirect
84. #16863696C22semidirect
85. #16863696C22semidirect
86. #16863693C22semidirect
87. #16863693C22semidirect
88. #16863693C22semidirect
89. #16863686C22semidirect
90. #16863683C22semidirect
91. #16863676C22semidirect
92. #16863673C22semidirect
93. #16863647C22semidirect
94. #16863647C22semidirect
95. #16863644C22semidirect
96. #16863640C22semidirect
97. #16863635C22semidirect
98. #16863635C22semidirect
101. #16863630C22semidirect
102. #16863630C22semidirect
103. #16863627C22semidirect
104. #16863623C22semidirect
105. #16863611C22semidirect
106. #16863611C22semidirect
107. #16863611C22semidirect
108. #16863611C22semidirect
109. #16863608C22semidirect
110. #16863608C22semidirect
111. #16863608C22semidirect
112. #16863608C22semidirect
113. #16863596C22semidirect
114. #16863593C22semidirect
117. #16863547C22semidirect
118. #16863547C22semidirect
119. #16863546C22semidirect
120. #16863546C22semidirect
121. #16863541C22semidirect
122. #16863541C22semidirect
123. #16863539C22semidirect
124. #16863539C22semidirect
129. #16863527C22semidirect
130. Q8×C67⋊C8C22semidirect
131. #16863506C22semidirect
132. #16863506C22semidirect
133. #16863506C22semidirect
134. #16863506C22semidirect
135. #16863506C22semidirect
136. #16863506C22semidirect
137. #16863496C22semidirect
138. #16863496C22semidirect
139. #16863496C22semidirect
140. #16863494C22semidirect
141. #16863494C22semidirect
142. #16863494C22semidirect
143. C4×#11761618C22semidirect
144. C4×#11761618C22semidirect
145. C4×#11761615C22semidirect
146. C4×#11761616C22semidirect
151. C4×#11761613C22semidirect
152. C4×#11761613C22semidirect
153. C4×#11761613C22semidirect
154. C4×#11761613C22semidirect
155. C4×#11761613C22semidirect
156. C4×#11761613C22semidirect
157. C4×#11761613C22semidirect
158. C4×#11761613C22semidirect
159. #16863474C22semidirect
161. #16863468C22semidirect
163. D4×C67⋊C8C22semidirect
164. D4×C67⋊C8C22semidirect
165. #16863457C22semidirect
166. #16863457C22semidirect
167. #16863453C22semidirect
168. #16863432C22semidirect
169. C2×#14523976C22semidirect
170. C2×#14523976C22semidirect
171. #16863401C22semidirect
172. #16863400C22semidirect
173. #16863397C22semidirect
174. #16863395C22semidirect
175. C2×#14523964C22semidirect
176. C2×#14523963C22semidirect
177. #16863352C22semidirect
178. #16863352C22semidirect
179. C2×C4×C67⋊C8C22semidirect
180. #559×C67C22semidirect
181. #554×C67C22semidirect
183. #553×C67C22semidirect
187. #547×C67C22semidirect
189. #546×C67C22semidirect
190. #546×C67C22semidirect
192. #542×C67C22semidirect
193. #540×C67C22semidirect
197. #529×C67C22semidirect
200. #520×C67C22semidirect
201. #518×C67C22semidirect
202. C2×C4×D4×C67C22semidirect
532. #11761613#41semidirect
882. #3513D67semidirect
912. C67#61471semidirect
917. #559C2×D67semidirect
919. #554C2×D67semidirect
923. #553C2×D67semidirect
931. #547C2×D67semidirect
936. #546C2×D67semidirect
937. #546C2×D67semidirect
941. #542C2×D67semidirect
943. #540C2×D67semidirect
950. #529C2×D67semidirect
956. #520C2×D67semidirect
958. #518C2×D67semidirect
960. C2×C4×D4C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225741532
#225732172
#225730722
#225729622
#225729562
#225726052
#225725712
#225725522
#225724102
#225724042
#225722302
#225722242
#225721702
#225721642
#225718902
D4×#117616132
#225708532
#225708422
#225707732
#225704082
#225704022
#225703932
#225703872
#225703472
#225703432
#225691852
#225690822
#225690592
C2×C4×#117616132
C67×#35132
#6147167