Finite Group Databasebeta

← #31740249

Subgroups — #31740249

Order 17152.

1850 conjugacy classes of subgroups.

The subgroup lattice has 1730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574281C211yesmaximal, characteristic, complemented
2#22573201C211yesmaximal, characteristic, complemented
3#22573072C211yesmaximal, characteristic, complemented
4#22573036C211yesmaximal, characteristic, complemented
5#22572956C211yesmaximal, characteristic, complemented
6#22572793C211yesmaximal, characteristic, complemented
7#22572769C211yesmaximal, characteristic, complemented
8#22572763C211yesmaximal, characteristic, complemented
9#22572350C211yesmaximal, characteristic, complemented
10#22572299C211yesmaximal, characteristic, complemented
11#22572245C211yesmaximal, characteristic, complemented
12#22572164C211yesmaximal, characteristic, complemented
13#22572053C211yesmaximal, characteristic, complemented
14#22572044C211yesmaximal, characteristic, complemented
15#22571816C211yesmaximal, characteristic, complemented
16#22571816C211yesmaximal, characteristic, complemented
17#22571805C211yesmaximal, characteristic, complemented
18#22570932C211yesmaximal, characteristic, complemented
19#22570842C211yesmaximal, characteristic, complemented
20#22570831C211yesmaximal, characteristic, complemented
21#22570480C211yesmaximal, characteristic, complemented
22#22570447C211yesmaximal, characteristic, complemented
23#22570423C211yesmaximal, characteristic, complemented
24#22570393C211yesmaximal, characteristic, complemented
25#22570256C211yesmaximal, characteristic, complemented
26#22570221C211yesmaximal, characteristic, complemented
27#22569214C211yesmaximal, characteristic, complemented
28#22569041C211yesmaximal, characteristic, complemented
29#22569037C211yesmaximal, characteristic, complemented
30C4×#14524069C211yesmaximal, characteristic, complemented
31C67×#3513C211yesmaximal, characteristic, complemented
32C2×#14524069C2211yescharacteristic
33C2×#14524069C2211yescharacteristic
34C2×#14524068C2211yescharacteristic
35#16864119C2211yescharacteristic, complemented
36#16864116C2211yescharacteristic, complemented
37#16864106C2211yescharacteristic, complemented
38#16864092C2211yescharacteristic
39#16864091—21no—
40#16864086C2211yescharacteristic, complemented
41#16864078—21no—
42#16864076—21no—
43#16864074—21no—
44#16864051C2211yescharacteristic
45#16864042C2211yescharacteristic, complemented
46#16864042C2211yescharacteristic, complemented
47#16864017C2211yescharacteristic, complemented
48#16864008C2211yescharacteristic, complemented
49#16863992—21no—
50#16863978—21no—
51#16863930C2211yescharacteristic, complemented
52#16863929—21no—
53#126×D67—21no—
54#16863876C2211yescharacteristic, complemented
55#16863870C2211yescharacteristic, complemented
56C4×#11761628C2211yescharacteristic, complemented
57#16863799C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863795C2211yescharacteristic, complemented
60#16863778C2211yescharacteristic, complemented
61#16863778C2211yescharacteristic, complemented
62#16863768C2211yescharacteristic, complemented
63#16863766C2211yescharacteristic, complemented
64#16863760C2211yescharacteristic, complemented
65#16863758C2211yescharacteristic, complemented
66#16863755C2211yescharacteristic, complemented
67#16863753C2211yescharacteristic, complemented
68#16863750C2211yescharacteristic, complemented
69#16863737C2211yescharacteristic, complemented
70#16863734C2211yescharacteristic, complemented
71#16863731C2211yescharacteristic, complemented
72#16863731C2211yescharacteristic, complemented
73#16863726C2211yescharacteristic, complemented
74#16863724C2211yescharacteristic, complemented
75#16863720C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic, complemented
77#16863717C2211yescharacteristic, complemented
78#16863717C2211yescharacteristic, complemented
79#16863714C2211yescharacteristic, complemented
80#16863712C2211yescharacteristic, 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#16863678C2211yescharacteristic, complemented
92#16863676C2211yescharacteristic, complemented
93#16863652C2211yescharacteristic, complemented
94#16863647C2211yescharacteristic
95#16863644C2211yescharacteristic, complemented
96#16863644C2211yescharacteristic, complemented
97#16863640C2211yescharacteristic, complemented
98#16863640C2211yescharacteristic, complemented
99#16863640C2211yescharacteristic, complemented
100#16863640C2211yescharacteristic, complemented
101#16863635C2211yescharacteristic, complemented
102#16863630C2211yescharacteristic
103#16863623C2211yescharacteristic, complemented
104#16863623C2211yescharacteristic, complemented
105#16863615C2211yescharacteristic, complemented
106#16863615C2211yescharacteristic, complemented
107#16863611C2211yescharacteristic
108#16863611C2211yescharacteristic
109#16863611C2211yescharacteristic, complemented
110#16863611C2211yescharacteristic, complemented
111#16863608C2211yescharacteristic, complemented
112#16863608C2211yescharacteristic, complemented
113#16863606C2211yescharacteristic, complemented
114#16863601C2211yescharacteristic, complemented
115#16863588C2211yescharacteristic
116#16863588C2211yescharacteristic
117#16863558C2211yescharacteristic
118#16863558C2211yescharacteristic
119#16863556C2211yescharacteristic, complemented
120#16863556C2211yescharacteristic, complemented
121#16863547C2211yescharacteristic, complemented
122#16863547C2211yescharacteristic, complemented
123#16863539C2211yescharacteristic
124#16863539C2211yescharacteristic
125#16863530C2211yescharacteristic
126#16863530C2211yescharacteristic
127#16863529C2211yescharacteristic, complemented
128#16863529C2211yescharacteristic, complemented
129#16863527C2211yescharacteristic, complemented
130Q8×C67⋊C8C2211yescharacteristic, complemented
131#16863506C2211yescharacteristic
132#16863506C2211yescharacteristic
133#16863506C2211yescharacteristic, complemented
134#16863506C2211yescharacteristic, complemented
135#16863506C2211yescharacteristic, complemented
136#16863501C2211yescharacteristic, complemented
137#16863496C2211yescharacteristic, complemented
138#16863496C2211yescharacteristic, complemented
139#16863496C2211yescharacteristic, complemented
140#16863496C2211yescharacteristic, complemented
141#16863494C2211yescharacteristic, complemented
142#16863494C2211yescharacteristic, complemented
143C4×#11761618C2211yescharacteristic, complemented
144C4×#11761615C2211yescharacteristic, complemented
145C4×#11761615C2211yescharacteristic, complemented
146C4×#11761616C2211yescharacteristic, complemented
147C4×#11761616C2211yescharacteristic, complemented
148C4×#11761616C2211yescharacteristic, complemented
149C4×#11761616C2211yescharacteristic, complemented
150C4×#11761616C2211yescharacteristic, complemented
151C4×#11761616C2211yescharacteristic, complemented
152C4×#11761613C2211yescharacteristic
153C4×#11761613C2211yescharacteristic
154C4×#11761613C2211yescharacteristic
155C4×#11761613C2211yescharacteristic
156C4×#11761613C2211yescharacteristic, complemented
157C4×#11761613C2211yescharacteristic, complemented
158C4×#11761613C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic, complemented
160#16863474C2211yescharacteristic, complemented
161#16863474C2211yescharacteristic, complemented
162#16863468C2211yescharacteristic, complemented
163#16863468C2211yescharacteristic, complemented
164D4×C67⋊C8C2211yescharacteristic, complemented
165#16863457C2211yescharacteristic, complemented
166#16863457C2211yescharacteristic, complemented
167#16863449C2211yescharacteristic, complemented
168#16863439C2211yescharacteristic, complemented
169#16863436C2211yescharacteristic, complemented
170#16863436C2211yescharacteristic, complemented
171#16863401C2211yescharacteristic, complemented
172#16863395C2211yescharacteristic, complemented
173#16863392C2211yescharacteristic
174#16863390C2211yescharacteristic, complemented
175C2×#14523964C2211yescharacteristic, complemented
176C2×#14523963C2211yescharacteristic, complemented
177#16863352C2211yescharacteristic, complemented
178#16863352C2211yescharacteristic, complemented
179C4×#11761612C2211yescharacteristic, complemented
180#559×C67C2211yescharacteristic, complemented
181#554×C67C2211yescharacteristic, complemented
182#553×C67—21no—
183#553×C67C2211yescharacteristic
184#552×C67C2211yescharacteristic, complemented
185#551×C67—21no—
186#551×C67—21no—
187#547×C67C2211yescharacteristic
188#546×C67—21no—
189#546×C67C2211yescharacteristic
190#546×C67C2211yescharacteristic
191D42×C67C2211yescharacteristic, complemented
192#542×C67C2211yescharacteristic, complemented
193#540×C67C2211yescharacteristic
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
201#518×C67C2211yescharacteristic, complemented
202C2×C4×D4×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761628C2311yescharacteristic
205C22×D268C2311yescharacteristic
206#14524069—24no—
207#14524069—24no—
208#14524068—24no—
209C2×#11761618C2311yescharacteristic
210C2×#11761618C2311yescharacteristic
211C2×#11761616C2311yescharacteristic
212C2×#11761616C2311yescharacteristic
213C2×#11761616C2311yescharacteristic
214C2×#11761616C2311yescharacteristic
215C2×#11761616C2311yescharacteristic
216C2×#11761616C2311yescharacteristic
217C2×#11761615C2311yescharacteristic
218C2×#11761615C2311yescharacteristic
219C2×#11761613C2311yescharacteristic
220C2×#11761613C2311yescharacteristic
221C2×#11761613C2311yescharacteristic
222C2×#11761613C2311yescharacteristic
223C2×#11761613C2311yescharacteristic
224C2×#11761613C2311yescharacteristic
225C2×#11761612C2311yescharacteristic
226C2×#11761612C2311yescharacteristic
227C2×#11761612C2311yescharacteristic
228C2×#11761612C2311yescharacteristic
229C22×C67⋊C8C2311yescharacteristic
230C22×C67⋊C8C2311yescharacteristic
231#14524043C2311yescharacteristic
232#14524043C2311yescharacteristic
233#14524038—21no—
234#14524038—21no—
235#14524038—21no—
236#14524038—21no—
237#14524037—21no—
238#14524036—21no—
239#14524036—21no—
240#14524036—21no—
241#14524036—21no—
242#14524036—21no—
243#14524035C2311yescharacteristic
244#14524035C2311yescharacteristic
245#14524033—21no—
246#14524033—21no—
247#14524033—21no—
248#14524031C2311yescharacteristic
249#14524031C2311yescharacteristic
250#14524030—21no—
251#14524029—21no—
252#14524028—21no—
253#14524028—21no—
254#14524026—21no—
255#14524025—21no—
256#14524025—21no—
257#14524025—21no—
258#14524025—21no—
259#14524024—21no—
260#14524022C2311yescharacteristic
261#14524022C2311yescharacteristic
262#14524022C2311yescharacteristic
263#14524022C2311yescharacteristic
264#14524021—21no—
265#14524021—21no—
266#14524021—21no—
267#14524019—21no—
268#14524019—21no—
269#14524017C2311yescharacteristic
270#14524017C2311yescharacteristic
271#14524016—21no—
272#14524016—21no—
273#14524015—21no—
274#14524014—21no—
275#14524011—21no—
276#14524011—21no—
277C4×Dic134C2311yescharacteristic
278C4×Dic134C2311yescharacteristic
279C4×Dic134C2311yescharacteristic
280C4×Dic134C2311yescharacteristic
281#14524008—21no—
282C4×D268C2311yescharacteristic
283C4×D268C2311yescharacteristic
284C4×D268C2311yescharacteristic
285C4×D268C2311yescharacteristic
286C4×D268C2311yescharacteristic
287C4×D268C2311yescharacteristic
288#14524005—21no—
289#14524005—21no—
290C4×C22⋊D67—21no—
291C4×C22⋊D67—21no—
292C4×C22⋊D67—21no—
293(C22⋊D67)⋊C4—21no—
294(C22⋊D67)⋊C4—21no—
295(C22⋊D67)⋊C4—21no—
296#14524002C2311yescharacteristic
297#14524002C2311yescharacteristic
298#14524001—21no—
299#14524001—21no—
300#14524000—21no—
301#14524000—21no—
302#14523999—21no—
303C2×C4⋊Dic67C2311yescharacteristic
304C4⋊C4×D67—21no—
305C4⋊C4×D67—21no—
306C4⋊C4×D67—21no—
307C22⋊C4×D67—21no—
308C22⋊C4×D67—21no—
309C22⋊C4×D67—21no—
310C22⋊C4×D67—21no—
311C42×D67—21no—
312#14523976C2311yescharacteristic
313#14523976C2311yescharacteristic
314#14523976C2311yescharacteristic
315#14523976C2311yescharacteristic
316#14523976C2311yescharacteristic
317#14523976C2311yescharacteristic
318#14523976C2311yescharacteristic
319#14523976C2311yescharacteristic
320#14523974C2311yescharacteristic
321#14523974C2311yescharacteristic
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#14523966C2311yescharacteristic
343#14523966C2311yescharacteristic
344#14523966C2311yescharacteristic
345#14523966C2311yescharacteristic
346#14523964C2311yescharacteristic
347#14523964C2311yescharacteristic
348#14523964C2311yescharacteristic
349#14523964C2311yescharacteristic
350#14523964C2311yescharacteristic
351#14523964C2311yescharacteristic
352#14523964C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523964C2311yescharacteristic
355#14523964C2311yescharacteristic
356#14523964C2311yescharacteristic
357#14523964C2311yescharacteristic
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—
482#11761628—22no—
483#11761628—22no—
484#11761628—41no—
485#11761628—41no—
486C2×Dic134—21no—
487C2×Dic134C2411yescharacteristic
488C2×Dic134C2411yescharacteristic
489C2×D268—22no—
490C2×D268—21no—
491C2×D268—41no—
492C2×D268C2411yescharacteristic
493C2×D268C2411yescharacteristic
494C2×C22⋊D67—21no—
495C2×C22⋊D67—21no—
496C2×C22⋊D67—21no—
497C2×C22⋊D67—21no—
498C22×Dic67—21no—
499C2×C4×D67—21no—
500C2×C4×D67—21no—
501C2×C4×D67—21no—
502C2×C4×D67—21no—
503C2×C4×D67—21no—
504C2×C4×D67—21no—
505C2×C4×D67—21no—
506C2×C4×D67—21no—
507#11761618—41no—
508#11761618—41no—
509#11761616—22no—
510#11761616—22no—
511#11761616—22no—
512#11761616—22no—
513#11761616—41no—
514#11761616—41no—
515#11761615—22no—
516#11761615—22no—
517#11761613—22no—
518#11761613—22no—
519#11761613—22no—
520#11761613—41no—
521#11761613—41no—
522#11761613#4114yescomplemented
523#11761612—22no—
524#11761612—22no—
525#11761612—22no—
526#11761612—41no—
527C2×C67⋊C8—41no—
528C2×C67⋊C8—41no—
529C2×C67⋊C8C2411yescharacteristic
530C2×C67⋊C8C2411yescharacteristic
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C2×C67⋊C8C2411yescharacteristic
534C2×C67⋊C8C2411yescharacteristic
535C2×C67⋊C8C2411yescharacteristic
536C2×C67⋊C8C2411yescharacteristic
537C4⋊Dic67—21no—
538C4⋊Dic67—21no—
539C4⋊Dic67—21no—
540C4⋊Dic67—21no—
541C4⋊Dic67C2411yescharacteristic
542C4⋊Dic67C2411yescharacteristic
543C4⋊Dic67C2411yescharacteristic
544C4⋊Dic67C2411yescharacteristic
545Dic67⋊C4—21no—
546Dic67⋊C4—21no—
547Dic67⋊C4—21no—
548Dic67⋊C4—21no—
549Dic67⋊C4—21no—
550Dic67⋊C4—21no—
551Dic67⋊C4—21no—
552Dic67⋊C4—21no—
553Dic67⋊C4—21no—
554Dic67⋊C4—21no—
555Dic67⋊C4—21no—
556Dic67⋊C4—21no—
557C22⋊Dic67—21no—
558C22⋊Dic67—21no—
559C22⋊Dic67—21no—
560C22⋊Dic67—21no—
561C22⋊Dic67—21no—
562C22⋊Dic67—21no—
563(C2×D67)⋊C4—21no—
564(C2×D67)⋊C4—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—
575C4×Dic67—21no—
576C4×Dic67—21no—
577C4×Dic67—21no—
578C4×Dic67—21no—
579C4×Dic67—21no—
580C4×Dic67—21no—
581C24×C67—21no—
582C24×C67—21no—
583#41×C67—22no—
584#41×C67—41no—
585#41×C67—82no—
586C2×Q8×C67—21no—
587C2×Q8×C67C2×D411yescharacteristic
588C2×Q8×C67C2411yescharacteristic
589C2×D4×C67—22no—
590C2×D4×C67—22no—
591C2×D4×C67—21no—
592C2×D4×C67—21no—
593C2×D4×C67—21no—
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—41no—
601C2×D4×C67—41no—
602C2×D4×C67—82no—
603C2×D4×C67C2×D411yescharacteristic
604C2×D4×C67C2×D411yescharacteristic
605C2×D4×C67C2×D411yescharacteristic
606C2×D4×C67C2411yescharacteristic
607C2×D4×C67C2411yescharacteristic
608C2×D4×C67C2411yescharacteristic
609C22×C4×C67—21no—
610C22×C4×C67—21no—
611C22×C4×C67—21no—
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—82no—
621C22×C4×C67C2×D411yescharacteristic
622C22×C4×C67C2×D411yescharacteristic
623C22×C4×C67C2411yescharacteristic
624C22×C4×C67C2411yescharacteristic
625C22×C4×C67C2411yescharacteristic
626C4⋊C4×C67—21no—
627C4⋊C4×C67—21no—
628C4⋊C4×C67—21no—
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×C67C2×D411yescharacteristic
638C4⋊C4×C67C2×D411yescharacteristic
639C4⋊C4×C67C2×D411yescharacteristic
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×C67C2411yescharacteristic
648C4⋊C4×C67C2411yescharacteristic
649C4⋊C4×C67C2411yescharacteristic
650C4⋊C4×C67C2411yescharacteristic
651C22⋊C4×C67—21no—
652C22⋊C4×C67—21no—
653C22⋊C4×C67—21no—
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×C67C2×D411yescharacteristic
671C22⋊C4×C67C2×D411yescharacteristic
672C22⋊C4×C67C2×D411yescharacteristic
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
680C42×C67—21no—
681C42×C67—21no—
682C42×C67—21no—
683C42×C67C2×D411yescharacteristic
684C42×C67C2×D411yescharacteristic
685C42×C67C2411yescharacteristic
686C42×C67C2411yescharacteristic
687C42×C67C2411yescharacteristic
688C42×C67C2411yescharacteristic
689C23×C67—21no—
690C23×C67—21no—
691C23×C67—21no—
692C23×C67—42no—
693C23×C67—42no—
694C23×C67—42no—
695C23×C67—81no—
696C23×C67—81no—
697C23×C67—81no—
698C23×C67C22×D411yescharacteristic
699C23×C67C22×D411yescharacteristic
700C23×C67C22×D411yescharacteristic
701C22×D67—21no—
702C22×D67—21no—
703C22×D67—42no—
704C22×D67—81no—
705C22×D67—81no—
706Q8×C67—21no—
707Q8×C67—21no—
708Q8×C67—41no—
709Q8×C67—81no—
710D4×C67—21no—
711D4×C67—21no—
712D4×C67—21no—
713D4×C67—21no—
714D4×C67—21no—
715D4×C67—41no—
716D4×C67—41no—
717D4×C67—41no—
718D4×C67—42no—
719D4×C67—42no—
720D4×C67—42no—
721D4×C67—42no—
722D4×C67—81no—
723D4×C67—81no—
724D4×C67—81no—
725D4×C67—81no—
726D4×C67—81no—
727D4×C67C2×#4112yes—
728C2×C4×C67—21no—
729C2×C4×C67—21no—
730C2×C4×C67—21no—
731C2×C4×C67—21no—
732C2×C4×C67—21no—
733C2×C4×C67—21no—
734C2×C4×C67—21no—
735C2×C4×C67—21no—
736C2×C4×C67—21no—
737C2×C4×C67—21no—
738C2×C4×C67—21no—
739C2×C4×C67—41no—
740C2×C4×C67—41no—
741C2×C4×C67—42no—
742C2×C4×C67—42no—
743C2×C4×C67—81no—
744C2×C4×C67—81no—
745C2×C4×C67—81no—
746C2×C4×C67—81no—
747C2×C4×C67—81no—
748C2×C4×C67—81no—
749C2×C4×C67—81no—
750C2×C4×C67—81no—
751C2×C4×C67—81no—
752C2×C4×C67C22×D411yescharacteristic
753C2×C4×C67C22×D411yescharacteristic
754C2×C4×C67C22×D411yescharacteristic
755C2×C4×C67C22×D411yescharacteristic
756C2×C4×C67C22×D411yescharacteristic
757C2×C4×C67C22×D411yescharacteristic
758C2×C4×C67C22×D411yescharacteristic
759C2×C4×C67C22×D411yescharacteristic
760C2×C4×C67C22×D411yescharacteristic
761C2×C4×C67C22×D411yescharacteristic
762C2×C4×C67C22×D411yescharacteristic
763C2×C4×C67C2511yescharacteristic
764C22⋊D67—42no—
765C22⋊D67—42no—
766C22⋊D67—81no—
767C22⋊D67—81no—
768C2×Dic67—21no—
769C2×Dic67—21no—
770C2×Dic67—21no—
771C2×Dic67—21no—
772C2×Dic67—21no—
773C2×Dic67—21no—
774C2×Dic67—81no—
775D268—21no—
776D268—21no—
777D268—21no—
778D268—42no—
779D268C2×#4112yes—
780C4×D67—42no—
781C4×D67—42no—
782C4×D67—81no—
783C4×D67—81no—
784C4×D67—81no—
785C4×D67—81no—
786C4×D67—81no—
787C4×D67—81no—
788Dic134—21no—
789Dic134—21no—
790Dic134—21no—
791Dic134—21no—
792Dic134—81no—
793C67⋊C8—21no—
794C67⋊C8—21no—
795C67⋊C8—21no—
796C67⋊C8—21no—
797C67⋊C8—21no—
798C67⋊C8—21no—
799C67⋊C8—21no—
800C67⋊C8C2×#4112yes—
801C22×C67—21no—
802C22×C67—21no—
803C22×C67—21no—
804C22×C67—21no—
805C22×C67—21no—
806C22×C67—21no—
807C22×C67—21no—
808C22×C67—21no—
809C22×C67—21no—
810C22×C67—22no—
811C22×C67—41no—
812C22×C67—41no—
813C22×C67—41no—
814C22×C67—41no—
815C22×C67—41no—
816C22×C67—41no—
817C22×C67—41no—
818C22×C67—41no—
819C22×C67—84no—
820C22×C67—162no—
821C22×C67C23×D411yescharacteristic
822C2×D67—22no—
823C2×D67—41no—
824C2×D67—41no—
825C2×D67—41no—
826C2×D67—41no—
827C2×D67—41no—
828C2×D67—162no—
829C4×C67—21no—
830C4×C67—21no—
831C4×C67—21no—
832C4×C67—21no—
833C4×C67—21no—
834C4×C67—21no—
835C4×C67—21no—
836C4×C67—21no—
837C4×C67—21no—
838C4×C67—21no—
839C4×C67—21no—
840C4×C67—41no—
841C4×C67—41no—
842C4×C67—41no—
843C4×C67—41no—
844C4×C67—41no—
845C4×C67C22×#4111yescharacteristic
846C4×C67#58511yescharacteristic
847Dic67—41no—
848Dic67—41no—
849Dic67—41no—
850Dic67—41no—
851Dic67—41no—
852Dic67—41no—
853#61548—671nomaximal, Sylow
854C2×C67—41no—
855C2×C67—41no—
856C2×C67—41no—
857C2×C67—42no—
858C2×C67—81no—
859C2×C67—81no—
860C2×C67D4×#4111yescharacteristic
861C2×C67#358411yescharacteristic
862C2×C67#358511yescharacteristic
863D67—42no—
864D67—81no—
865#3521—671no—
866#3513D6711yescharacteristic, complemented
867#3394—671no—
868#3380—671no—
869#3376—671no—
870#3370—671no—
871#3353—671no—
872#3351—671no—
873#3351—671no—
874#3318—671no—
875#3315—671no—
876#3311—671no—
877#3306—671no—
878#3297—671no—
879#3296—671no—
880#3273—671no—
881#3273—671no—
882#3272—671no—
883#3183—671no—
884#3175—671no—
885#3174—671no—
886#3125—671no—
887#3122—671no—
888#3120—671no—
889#3118—671no—
890#3105—671no—
891#3102—671no—
892#2969—671no—
893#2946—671no—
894#2946—671no—
895C4×AGL(1,ℤ/8)—671no—
896C67#6154811yescharacteristic, complemented, Sylow
897C2×AGL(1,ℤ/8)—671no—
898C2×AGL(1,ℤ/8)—671no—
899C2×AGL(1,ℤ/8)—671no—
900#559C2×D6711yescharacteristic, complemented
901#556—671no—
902#556—671no—
903#554—671no—
904#554C2×D6711yescharacteristic, complemented
905#553—21no—
906#553—671no—
907#553—1341no—
908#553C2×D6711yescharacteristic
909#552—671no—
910#552—1341no—
911#552C2×D6711yescharacteristic, complemented
912#551—21no—
913#551—21no—
914#551—1341no—
915#551—1341no—
916#547—671no—
917#547C2×D6711yescharacteristic
918#546—21no—
919#546—671no—
920#546—671no—
921#546C2×D6711yescharacteristic
922#546C2×D6711yescharacteristic
923D42C2×D6711yescharacteristic, complemented
924#542—671no—
925#542C2×D6711yescharacteristic, complemented
926#541—671no—
927#540C2×D6711yescharacteristic
928#539—21no—
929#539—1341no—
930#538—21no—
931#538—1341no—
932#529—671no—
933#529—1341no—
934#529C2×D6711yescharacteristic
935#529C2×D6711yescharacteristic, complemented
936C2×#126—1341no—
937#525—21no—
938C2×#123—21no—
939#520—671no—
940#520C2×D6711yescharacteristic
941#518—671no—
942#518C2×D6711yescharacteristic, complemented
943C4×#41—671no—
944C2×C4×D4C2×D6711yescharacteristic, complemented
945#500—671no—
946#499—671no—
947#499—671no—
948#495—671no—
949#495—671no—
950#492—671no—
951#491—671no—
952#490—671no—
953#489—671no—
954#489—671no—
955#488—671no—
956#488—671no—
957#485—671no—
958#485—671no—
959#484—671no—
960#484—671no—
961#483—671no—
962#483—671no—
963#482—671no—
964#482—671no—
965#482—671no—
966#482—671no—
967#481—671no—
968#481—671no—
969#479—671no—
970#479—671no—
971#478—671no—
972#478—671no—
973#478—671no—
974#478—671no—
975#478—671no—
976#478—671no—
977#476—671no—
978#476—671no—
979#475—671no—
980#474—671no—
981#470—671no—
982#469—671no—
983#468—671no—
984#468—671no—
985#468—671no—
986#468—671no—
987#468—671no—
988#468—671no—
989#467—671no—
990#466—671no—
991#465—671no—
992#465—671no—
993#464—671no—
994#464—671no—
995#463—671no—
996#463—671no—
997#463—671no—
998#463—671no—
999#463—671no—
1000#463—671no—
1001#462—671no—
1002#461—671no—
1003#459—671no—
1004#459—671no—
1005#452—671no—
1006#452—671no—
1007#452—671no—
1008#452—671no—
1009#450—671no—
1010#450—671no—
1011#449—671no—
1012#449—671no—
1013#447—671no—
1014#447—671no—
1015#447—671no—
1016#447—671no—
1017#446—671no—
1018C8×Q8—671no—
1019#442—671no—
1020#442—671no—
1021#442—671no—
1022#442—671no—
1023#442—671no—
1024#441—671no—
1025#440—671no—
1026#440—671no—
1027#440—671no—
1028#440—671no—
1029#440—671no—
1030#440—671no—
1031C4×Q16—671no—
1032C4×SD16—671no—
1033C4×SD16—671no—
1034C4×SD16—671no—
1035C4×SD16—671no—
1036C4×SD16—671no—
1037C4×SD16—671no—
1038C4×SD16—671no—
1039C4×SD16—671no—
1040C4×D8—671no—
1041C4×D8—671no—
1042C4×D8—671no—
1043C4×D8—671no—
1044C4×D8—671no—
1045C4×D8—671no—
1046C4×D8—671no—
1047#436—671no—
1048#436—671no—
1049#436—671no—
1050#435—671no—
1051#435—671no—
1052C8×D4—671no—
1053#433—671no—
1054#433—671no—
1055#431—671no—
1056#428—671no—
1057#428—671no—
1058#428—671no—
1059#418—671no—
1060#417—671no—
1061#416—671no—
1062#416—671no—
1063C2×#102—671no—
1064C2×#102—671no—
1065#405—671no—
1066#405—671no—
1067C4×M16—671no—
1068C2×#41—21no—
1069C2×#41—671no—
1070C2×#41—671no—
1071C2×#41C22×D6711yescharacteristic
1072C22×D4—21no—
1073C22×D4—671no—
1074C22×D4C22×D6711yescharacteristic
1075C22×D4C22×D6711yescharacteristic
1076C23×C4—21no—
1077AGL(1,ℤ/8)—1344no—
1078AGL(1,ℤ/8)—1344no—
1079AGL(1,ℤ/8)—1344no—
1080C2×Q16—671no—
1081C2×Q16—671no—
1082C2×SD16—671no—
1083C2×SD16—671no—
1084C2×SD16—671no—
1085C2×SD16—671no—
1086C2×SD16—671no—
1087C2×SD16—671no—
1088C2×SD16—671no—
1089C2×SD16—671no—
1090C2×D8—671no—
1091C2×D8—671no—
1092C2×D8—671no—
1093C2×D8—671no—
1094C2×D8—671no—
1095C2×D8—671no—
1096C2×M16—671no—
1097C2×M16—671no—
1098C2×M16—671no—
1099C2×M16—671no—
1100C22×C8—671no—
1101C22×C8—671no—
1102C4⋊Q8—671no—
1103C4⋊Q8—671no—
1104C4⋊Q8C22×D6711yescharacteristic
1105#127C22×D6711yescharacteristic
1106#126—21no—
1107#126—21no—
1108#126—21no—
1109#126—21no—
1110#126—1341no—
1111#126—1341no—
1112#126—1341no—
1113#126—1341no—
1114#126—1341no—
1115#126—1341no—
1116#126—1341no—
1117#126—1341no—
1118#126—1341no—
1119#126—1341no—
1120#126C22⋊D6711yescharacteristic
1121#126C22⋊D6711yescharacteristic
1122#125—21no—
1123#125—671no—
1124#125—671no—
1125#125—1341no—
1126#125—1341no—
1127#125—1341no—
1128#125C22⋊D6711yescharacteristic
1129#125C22×D6711yescharacteristic
1130#125C22×D6711yescharacteristic
1131#124—21no—
1132#124—21no—
1133#124—671no—
1134#124—671no—
1135#124—1341no—
1136#124—1341no—
1137#124C22⋊D6711yescharacteristic
1138#124C22×D6711yescharacteristic
1139#124C22×D6711yescharacteristic
1140#123—21no—
1141#123—21no—
1142#123—21no—
1143#123—21no—
1144#123—21no—
1145#123—21no—
1146#123—21no—
1147#123—21no—
1148#123—21no—
1149#123—21no—
1150#123—21no—
1151#123—21no—
1152#123—1341no—
1153#123—1341no—
1154#123—1341no—
1155#123—1341no—
1156#123—1341no—
1157#123—1341no—
1158#123—1341no—
1159#123—1341no—
1160#123C22⋊D6711yescharacteristic
1161#123C22⋊D6711yescharacteristic
1162C22⋊Q8—21no—
1163C22⋊Q8—21no—
1164C22⋊Q8—21no—
1165C22⋊Q8—21no—
1166C22⋊Q8—21no—
1167C22⋊Q8—671no—
1168C22⋊Q8—671no—
1169C22⋊Q8—671no—
1170C22⋊Q8—671no—
1171C22⋊Q8—1341no—
1172C22⋊Q8—1341no—
1173C22⋊Q8—1341no—
1174C22⋊Q8—1341no—
1175C22⋊Q8—1341no—
1176C22⋊Q8C22⋊D6711yescharacteristic
1177C22⋊Q8C22×D6711yescharacteristic
1178C22⋊Q8C22×D6711yescharacteristic
1179#121—21no—
1180#121—21no—
1181#121—21no—
1182#121—21no—
1183#121—21no—
1184#121—21no—
1185#121—671no—
1186#121—671no—
1187#121—1341no—
1188#121—1341no—
1189#121—1341no—
1190#121—1341no—
1191#121C22⋊D6711yescharacteristic
1192#121C22×D6711yescharacteristic
1193#121C22×D6711yescharacteristic
1194#121C22×D6711yescharacteristic
1195#121C22×D6711yescharacteristic
1196#120—21no—
1197#120—21no—
1198#120—21no—
1199#120—21no—
1200#120—1341no—
1201#120—1341no—
1202C4×Q8—671no—
1203C4×Q8—671no—
1204C4×Q8—671no—
1205C4×Q8—671no—
1206C4×Q8—1341no—
1207C4×Q8C22×D6711yescharacteristic
1208C4×Q8C22×D6711yescharacteristic
1209C4×Q8C22×D6711yescharacteristic
1210C4×D4—21no—
1211C4×D4—21no—
1212C4×D4—21no—
1213C4×D4—21no—
1214C4×D4—21no—
1215C4×D4—21no—
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—21no—
1219C4×D4—671no—
1220C4×D4—671no—
1221C4×D4—671no—
1222C4×D4—671no—
1223C4×D4—671no—
1224C4×D4—671no—
1225C4×D4—1341no—
1226C4×D4—1341no—
1227C4×D4—1341no—
1228C4×D4—1341no—
1229C4×D4—1341no—
1230C4×D4—1341no—
1231C4×D4—1341no—
1232C4×D4—1341no—
1233C4×D4C22×D6711yescharacteristic
1234C4×D4C22×D6711yescharacteristic
1235C4×D4C22×D6711yescharacteristic
1236C4×D4C22×D6711yescharacteristic
1237C4×D4C22×D6711yescharacteristic
1238C4×D4C22×D6711yescharacteristic
1239C4×D4C22×D6711yescharacteristic
1240C4×D4C22×D6711yescharacteristic
1241C4×D4C22×D6711yescharacteristic
1242C4×D4C22×D6711yescharacteristic
1243C4×D4C22×D6711yescharacteristic
1244#117—21no—
1245#117—21no—
1246#117—21no—
1247#117—671no—
1248#117—671no—
1249#117—1341no—
1250#117—1341no—
1251#117—1341no—
1252#117—1341no—
1253#117—1341no—
1254#117C22×D6711yescharacteristic
1255#117C22×D6711yescharacteristic
1256#117C22×D6711yescharacteristic
1257C2×C4⋊C4—21no—
1258C2×C4⋊C4—21no—
1259C2×C4⋊C4—671no—
1260C2×C4⋊C4—1341no—
1261C2×C4⋊C4—1341no—
1262C2×C4⋊C4—1341no—
1263C2×C4⋊C4C22×D6711yescharacteristic
1264C2×C4⋊C4C22×D6711yescharacteristic
1265C2×C22⋊C4—21no—
1266C2×C22⋊C4—21no—
1267C2×C22⋊C4—21no—
1268C2×C22⋊C4—21no—
1269C2×C22⋊C4—21no—
1270C2×C22⋊C4—1341no—
1271C2×C22⋊C4—1341no—
1272C2×C22⋊C4—1341no—
1273C2×C22⋊C4—1341no—
1274C2×C42—1341no—
1275C2×C42C22×D6711yescharacteristic
1276#107—671no—
1277#107—671no—
1278#107—671no—
1279#107—671no—
1280#107—671no—
1281#107—671no—
1282#107—671no—
1283#107—671no—
1284#106—671no—
1285#106—671no—
1286#106—671no—
1287#106—671no—
1288#106—671no—
1289#106—671no—
1290#106—671no—
1291#106—671no—
1292C4⋊C8—671no—
1293C4⋊C8—671no—
1294C4⋊C8—671no—
1295C4⋊C8—671no—
1296C4⋊C8—671no—
1297C4⋊C8—671no—
1298#103—671no—
1299#103—671no—
1300#103—671no—
1301#103—671no—
1302#103—671no—
1303#103—671no—
1304#103—671no—
1305#103—671no—
1306#103—671no—
1307#103—671no—
1308#103—671no—
1309#103—671no—
1310#102—671no—
1311#102—671no—
1312#102—671no—
1313#102—671no—
1314#102—671no—
1315#102—671no—
1316#102—671no—
1317#102—671no—
1318#102—671no—
1319#102—671no—
1320#102—671no—
1321#102—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—
1330C22⋊C8—671no—
1331C22⋊C8—671no—
1332C22⋊C8—671no—
1333C22⋊C8—671no—
1334C22⋊C8—671no—
1335C22⋊C8—671no—
1336#97—671no—
1337#97—671no—
1338#97—671no—
1339#97—671no—
1340C4×C8—671no—
1341C4×C8—671no—
1342C4×C8—671no—
1343C4×C8—671no—
1344C4×C8—671no—
1345C4×C8—671no—
1346C24—21no—
1347C24—21no—
1348C24—1341no—
1349#41—22no—
1350#41—41no—
1351#41—82no—
1352#41—2681no—
1353#41—2681no—
1354#41—1342no—
1355#41—1342no—
1356C2×Q8—21no—
1357C2×Q8—671no—
1358C2×Q8—671no—
1359C2×Q8—1341no—
1360C2×Q8C2×C22⋊D6711yescharacteristic
1361C2×Q8C23×D6711yescharacteristic
1362C2×D4—22no—
1363C2×D4—22no—
1364C2×D4—21no—
1365C2×D4—21no—
1366C2×D4—21no—
1367C2×D4—21no—
1368C2×D4—21no—
1369C2×D4—21no—
1370C2×D4—21no—
1371C2×D4—21no—
1372C2×D4—21no—
1373C2×D4—41no—
1374C2×D4—41no—
1375C2×D4—82no—
1376C2×D4—2681no—
1377C2×D4—671no—
1378C2×D4—671no—
1379C2×D4—1342no—
1380C2×D4—1341no—
1381C2×D4—1341no—
1382C2×D4—1341no—
1383C2×D4—1341no—
1384C2×D4—1341no—
1385C2×D4C2×C22⋊D6711yescharacteristic
1386C2×D4C2×C22⋊D6711yescharacteristic
1387C2×D4C2×C22⋊D6711yescharacteristic
1388C2×D4C23×D6711yescharacteristic
1389C2×D4C23×D6711yescharacteristic
1390C2×D4C23×D6711yescharacteristic
1391C22×C4—21no—
1392C22×C4—21no—
1393C22×C4—21no—
1394C22×C4—21no—
1395C22×C4—21no—
1396C22×C4—21no—
1397C22×C4—21no—
1398C22×C4—21no—
1399C22×C4—21no—
1400C22×C4—21no—
1401C22×C4—21no—
1402C22×C4—82no—
1403C22×C4—1341no—
1404C22×C4—1341no—
1405C22×C4—1341no—
1406C22×C4—1341no—
1407C22×C4—1341no—
1408C22×C4—1341no—
1409C22×C4—1341no—
1410C22×C4—1341no—
1411C22×C4—1341no—
1412C22×C4C2×C22⋊D6711yescharacteristic
1413C22×C4C2×C22⋊D6711yescharacteristic
1414C22×C4C23×D6711yescharacteristic
1415C22×C4C23×D6711yescharacteristic
1416C22×C4C23×D6711yescharacteristic
1417Q16—2681no—
1418Q16—2681no—
1419SD16—2681no—
1420SD16—2681no—
1421SD16—1342no—
1422SD16—1342no—
1423SD16—1342no—
1424SD16—1342no—
1425SD16—1342no—
1426SD16—1342no—
1427D8—2681no—
1428D8—2681no—
1429D8—674no—
1430D8—1342no—
1431D8—1342no—
1432D8—1342no—
1433M16—2681no—
1434M16—1342no—
1435M16—1342no—
1436M16—1342no—
1437C2×C8—2681no—
1438C2×C8—2681no—
1439C2×C8—671no—
1440C2×C8—671no—
1441C2×C8—671no—
1442C2×C8—671no—
1443C2×C8—671no—
1444C2×C8—671no—
1445C2×C8—671no—
1446C2×C8—671no—
1447C4⋊C4—21no—
1448C4⋊C4—21no—
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—21no—
1455C4⋊C4—21no—
1456C4⋊C4—21no—
1457C4⋊C4—21no—
1458C4⋊C4—671no—
1459C4⋊C4—671no—
1460C4⋊C4—671no—
1461C4⋊C4—671no—
1462C4⋊C4—1341no—
1463C4⋊C4—1341no—
1464C4⋊C4—1341no—
1465C4⋊C4—1341no—
1466C4⋊C4—1341no—
1467C4⋊C4—1341no—
1468C4⋊C4—1341no—
1469C4⋊C4—1341no—
1470C4⋊C4—1341no—
1471C4⋊C4—1341no—
1472C4⋊C4—1341no—
1473C4⋊C4—1341no—
1474C4⋊C4—1341no—
1475C4⋊C4—1341no—
1476C4⋊C4—1341no—
1477C4⋊C4—1341no—
1478C4⋊C4C2×C22⋊D6711yescharacteristic
1479C4⋊C4C2×C22⋊D6711yescharacteristic
1480C4⋊C4C2×C22⋊D6711yescharacteristic
1481C4⋊C4C2×C22⋊D6711yescharacteristic
1482C4⋊C4C2×C22⋊D6711yescharacteristic
1483C4⋊C4C2×C22⋊D6711yescharacteristic
1484C4⋊C4C2×C22⋊D6711yescharacteristic
1485C4⋊C4C2×C22⋊D6711yescharacteristic
1486C4⋊C4C2×C22⋊D6711yescharacteristic
1487C4⋊C4C2×C22⋊D6711yescharacteristic
1488C4⋊C4C23×D6711yescharacteristic
1489C4⋊C4C23×D6711yescharacteristic
1490C4⋊C4C23×D6711yescharacteristic
1491C4⋊C4C23×D6711yescharacteristic
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4—21no—
1507C22⋊C4—21no—
1508C22⋊C4—21no—
1509C22⋊C4—21no—
1510C22⋊C4—21no—
1511C22⋊C4—1341no—
1512C22⋊C4—1341no—
1513C22⋊C4—1341no—
1514C22⋊C4—1341no—
1515C22⋊C4—1341no—
1516C22⋊C4—1341no—
1517C22⋊C4—1341no—
1518C22⋊C4—1341no—
1519C22⋊C4—1341no—
1520C22⋊C4—1341no—
1521C22⋊C4—1341no—
1522C22⋊C4—1341no—
1523C22⋊C4—1341no—
1524C22⋊C4—1341no—
1525C22⋊C4—1341no—
1526C22⋊C4—1341no—
1527C22⋊C4—1341no—
1528C22⋊C4—1341no—
1529C22⋊C4C2×C22⋊D6711yescharacteristic
1530C22⋊C4C2×C22⋊D6711yescharacteristic
1531C22⋊C4C2×C22⋊D6711yescharacteristic
1532C22⋊C4C2×C22⋊D6711yescharacteristic
1533C22⋊C4C2×C22⋊D6711yescharacteristic
1534C22⋊C4C2×C22⋊D6711yescharacteristic
1535C22⋊C4C2×C22⋊D6711yescharacteristic
1536C22⋊C4C2×C22⋊D6711yescharacteristic
1537C22⋊C4C2×C22⋊D6711yescharacteristic
1538C22⋊C4C2×C22⋊D6711yescharacteristic
1539C42—21no—
1540C42—21no—
1541C42—21no—
1542C42—1341no—
1543C42—1341no—
1544C42—1341no—
1545C42—1341no—
1546C42—1341no—
1547C42—1341no—
1548C42C2×C22⋊D6711yescharacteristic
1549C42C2×C22⋊D6711yescharacteristic
1550C42C23×D6711yescharacteristic
1551C42C23×D6711yescharacteristic
1552C42C23×D6711yescharacteristic
1553C42C23×D6711yescharacteristic
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—42no—
1558C23—42no—
1559C23—42no—
1560C23—81no—
1561C23—81no—
1562C23—81no—
1563C23—2682no—
1564C23—5361no—
1565C23—5361no—
1566C23—1341no—
1567C23—1341no—
1568C23C22×C22⋊D6711yescharacteristic
1569C23C22×C22⋊D6711yescharacteristic
1570C23C22×C22⋊D6711yescharacteristic
1571Q8—21no—
1572Q8—21no—
1573Q8—41no—
1574Q8—81no—
1575Q8—5361no—
1576Q8—1341no—
1577Q8—1341no—
1578Q8—1341no—
1579Q8—1341no—
1580D4—21no—
1581D4—21no—
1582D4—21no—
1583D4—21no—
1584D4—21no—
1585D4—41no—
1586D4—41no—
1587D4—41no—
1588D4—42no—
1589D4—42no—
1590D4—42no—
1591D4—42no—
1592D4—81no—
1593D4—81no—
1594D4—81no—
1595D4—81no—
1596D4—81no—
1597D4—2682no—
1598D4—2682no—
1599D4—2682no—
1600D4—5361no—
1601D4—5361no—
1602D4—672no—
1603D4—1341no—
1604D4—1341no—
1605D4—1341no—
1606D4#41×D6712yes—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—41no—
1619C2×C4—41no—
1620C2×C4—42no—
1621C2×C4—42no—
1622C2×C4—81no—
1623C2×C4—81no—
1624C2×C4—81no—
1625C2×C4—81no—
1626C2×C4—81no—
1627C2×C4—81no—
1628C2×C4—81no—
1629C2×C4—81no—
1630C2×C4—81no—
1631C2×C4—2682no—
1632C2×C4—2682no—
1633C2×C4—5361no—
1634C2×C4—5361no—
1635C2×C4—5361no—
1636C2×C4—5361no—
1637C2×C4—5361no—
1638C2×C4—5361no—
1639C2×C4—5361no—
1640C2×C4—1341no—
1641C2×C4—1341no—
1642C2×C4—1341no—
1643C2×C4—1341no—
1644C2×C4—1341no—
1645C2×C4—1341no—
1646C2×C4C22×C22⋊D6711yescharacteristic
1647C2×C4C22×C22⋊D6711yescharacteristic
1648C2×C4C22×C22⋊D6711yescharacteristic
1649C2×C4C22×C22⋊D6711yescharacteristic
1650C2×C4C22×C22⋊D6711yescharacteristic
1651C2×C4C22×C22⋊D6711yescharacteristic
1652C2×C4C22×C22⋊D6711yescharacteristic
1653C2×C4C22×C22⋊D6711yescharacteristic
1654C2×C4C22×C22⋊D6711yescharacteristic
1655C2×C4C22×C22⋊D6711yescharacteristic
1656C2×C4C22×C22⋊D6711yescharacteristic
1657C2×C4C24×D6711yescharacteristic
1658C8—672no—
1659C8—1341no—
1660C8—1341no—
1661C8—1341no—
1662C8—1341no—
1663C8—1341no—
1664C8—1341no—
1665C8—1341no—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—22no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—21no—
1675C22—21no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—84no—
1685C22—2681no—
1686C22—2681no—
1687C22—2681no—
1688C22—2681no—
1689C22—2681no—
1690C22—162no—
1691C22—10722no—
1692C22—1342no—
1693C22C23×C22⋊D6711yescharacteristic
1694C4—21no—
1695C4—21no—
1696C4—21no—
1697C4—21no—
1698C4—21no—
1699C4—21no—
1700C4—21no—
1701C4—21no—
1702C4—21no—
1703C4—21no—
1704C4—21no—
1705C4—41no—
1706C4—41no—
1707C4—41no—
1708C4—41no—
1709C4—41no—
1710C4—2681no—
1711C4—2681no—
1712C4—2681no—
1713C4—2681no—
1714C4—2681no—
1715C4—2681no—
1716C4C2×#41×D6711yescharacteristic
1717C4#1686423211yescharacteristic
1718C2—41no—
1719C2—41no—
1720C2—41no—
1721C2—42no—
1722C2—81no—
1723C2—81no—
1724C2—2682no—
1725C2—5361no—
1726C2#41×C22⋊D6711yescharacteristic
1727C2#2257498011yescharacteristic
1728C2#2257498911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3513C2
socleC22×C67C23×D4
hypercenter#3513D67
hypocenterC67#61548
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. #22574281C2semidirect
2. #22573201C2semidirect
3. #22573072C2semidirect
4. #22573036C2semidirect
5. #22572956C2semidirect
6. #22572793C2semidirect
7. #22572769C2semidirect
8. #22572763C2semidirect
9. #22572350C2semidirect
10. #22572299C2semidirect
11. #22572245C2semidirect
12. #22572164C2semidirect
13. #22572053C2semidirect
14. #22572044C2semidirect
15. #22571816C2semidirect
16. #22571816C2semidirect
17. #22571805C2semidirect
18. #22570932C2semidirect
19. #22570842C2semidirect
20. #22570831C2semidirect
21. #22570480C2semidirect
22. #22570447C2semidirect
23. #22570423C2semidirect
24. #22570393C2semidirect
25. #22570256C2semidirect
26. #22570221C2semidirect
27. #22569214C2semidirect
28. #22569041C2semidirect
29. #22569037C2semidirect
30. C4×#14524069C2semidirect
31. C67×#3513C2semidirect
35. #16864119C22semidirect
36. #16864116C22semidirect
37. #16864106C22semidirect
40. #16864086C22semidirect
45. #16864042C22semidirect
46. #16864042C22semidirect
47. #16864017C22semidirect
48. #16864008C22semidirect
51. #16863930C22semidirect
54. #16863876C22semidirect
55. #16863870C22semidirect
56. C4×#11761628C22semidirect
57. #16863799C22semidirect
58. #16863795C22semidirect
59. #16863795C22semidirect
60. #16863778C22semidirect
61. #16863778C22semidirect
62. #16863768C22semidirect
63. #16863766C22semidirect
64. #16863760C22semidirect
65. #16863758C22semidirect
66. #16863755C22semidirect
67. #16863753C22semidirect
68. #16863750C22semidirect
69. #16863737C22semidirect
70. #16863734C22semidirect
71. #16863731C22semidirect
72. #16863731C22semidirect
73. #16863726C22semidirect
74. #16863724C22semidirect
75. #16863720C22semidirect
76. #16863717C22semidirect
77. #16863717C22semidirect
78. #16863717C22semidirect
79. #16863714C22semidirect
80. #16863712C22semidirect
81. #16863703C22semidirect
82. #16863700C22semidirect
83. #16863696C22semidirect
84. #16863696C22semidirect
85. #16863696C22semidirect
86. #16863693C22semidirect
87. #16863693C22semidirect
88. #16863693C22semidirect
89. #16863686C22semidirect
90. #16863683C22semidirect
91. #16863678C22semidirect
92. #16863676C22semidirect
93. #16863652C22semidirect
95. #16863644C22semidirect
96. #16863644C22semidirect
97. #16863640C22semidirect
98. #16863640C22semidirect
99. #16863640C22semidirect
100. #16863640C22semidirect
101. #16863635C22semidirect
103. #16863623C22semidirect
104. #16863623C22semidirect
105. #16863615C22semidirect
106. #16863615C22semidirect
109. #16863611C22semidirect
110. #16863611C22semidirect
111. #16863608C22semidirect
112. #16863608C22semidirect
113. #16863606C22semidirect
114. #16863601C22semidirect
119. #16863556C22semidirect
120. #16863556C22semidirect
121. #16863547C22semidirect
122. #16863547C22semidirect
127. #16863529C22semidirect
128. #16863529C22semidirect
129. #16863527C22semidirect
130. Q8×C67⋊C8C22semidirect
133. #16863506C22semidirect
134. #16863506C22semidirect
135. #16863506C22semidirect
136. #16863501C22semidirect
137. #16863496C22semidirect
138. #16863496C22semidirect
139. #16863496C22semidirect
140. #16863496C22semidirect
141. #16863494C22semidirect
142. #16863494C22semidirect
143. C4×#11761618C22semidirect
144. C4×#11761615C22semidirect
145. C4×#11761615C22semidirect
146. C4×#11761616C22semidirect
147. C4×#11761616C22semidirect
148. C4×#11761616C22semidirect
149. C4×#11761616C22semidirect
150. C4×#11761616C22semidirect
151. C4×#11761616C22semidirect
156. C4×#11761613C22semidirect
157. C4×#11761613C22semidirect
158. C4×#11761613C22semidirect
159. #16863474C22semidirect
160. #16863474C22semidirect
161. #16863474C22semidirect
162. #16863468C22semidirect
163. #16863468C22semidirect
164. D4×C67⋊C8C22semidirect
165. #16863457C22semidirect
166. #16863457C22semidirect
167. #16863449C22semidirect
168. #16863439C22semidirect
169. #16863436C22semidirect
170. #16863436C22semidirect
171. #16863401C22semidirect
172. #16863395C22semidirect
174. #16863390C22semidirect
175. C2×#14523964C22semidirect
176. C2×#14523963C22semidirect
177. #16863352C22semidirect
178. #16863352C22semidirect
179. C4×#11761612C22semidirect
180. #559×C67C22semidirect
181. #554×C67C22semidirect
184. #552×C67C22semidirect
191. D42×C67C22semidirect
192. #542×C67C22semidirect
197. #529×C67C22semidirect
201. #518×C67C22semidirect
202. C2×C4×D4×C67C22semidirect
522. #11761613#41semidirect
866. #3513D67semidirect
896. C67#61548semidirect
900. #559C2×D67semidirect
904. #554C2×D67semidirect
911. #552C2×D67semidirect
923. D42C2×D67semidirect
925. #542C2×D67semidirect
935. #529C2×D67semidirect
942. #518C2×D67semidirect
944. C2×C4×D4C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225742812
#225732012
#225730722
#225730362
#225729562
#225727932
#225727692
#225727632
#225723502
#225722992
#225722452
#225721642
#225720532
#225720442
#225718162
#225718052
#225709322
#225708422
#225708312
#225704802
#225704472
#225704232
#225703932
#225702562
#225702212
#225692142
#225690412
#225690372
C4×#145240692
C67×#35132
#6154867