Finite Group Databasebeta

← #31740218

Subgroups — #31740218

Order 17152.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574314C211yesmaximal, characteristic, complemented
2#22573217C211yesmaximal, characteristic, complemented
3#22573084C211yesmaximal, characteristic, complemented
4#22572971C211yesmaximal, characteristic, complemented
5#22572962C211yesmaximal, characteristic, complemented
6#22572809C211yesmaximal, characteristic, complemented
7#22572804C211yesmaximal, characteristic, complemented
8#22572778C211yesmaximal, characteristic, complemented
9#22572365C211yesmaximal, characteristic, complemented
10#22572329C211yesmaximal, characteristic, complemented
11#22572230C211yesmaximal, characteristic, complemented
12#22572194C211yesmaximal, characteristic, complemented
13#22572105C211yesmaximal, characteristic, complemented
14#22572059C211yesmaximal, characteristic, complemented
15#22571836C211yesmaximal, characteristic, complemented
16#22571836C211yesmaximal, characteristic, complemented
17#22571825C211yesmaximal, characteristic, complemented
18#22570932C211yesmaximal, characteristic, complemented
19#22570853C211yesmaximal, characteristic, complemented
20#22570820C211yesmaximal, characteristic, complemented
21#22570495C211yesmaximal, characteristic, complemented
22#22570465C211yesmaximal, characteristic, complemented
23#22570408C211yesmaximal, characteristic, complemented
24#22570393C211yesmaximal, characteristic, complemented
25#22570256C211yesmaximal, characteristic, complemented
26#22570221C211yesmaximal, characteristic, complemented
27#22569214C211yesmaximal, characteristic, complemented
28#22569048C211yesmaximal, characteristic, complemented
29#22569041C211yesmaximal, characteristic, complemented
30C4×#14524069C211yesmaximal, characteristic, complemented
31C67×#3513C211yesmaximal, characteristic, complemented
32C2×#14524073C2211yescharacteristic
33C2×#14524069C2211yescharacteristic
34C2×#14524069C2211yescharacteristic
35#16864131C2211yescharacteristic, complemented
36#16864130—21no—
37#16864124C2211yescharacteristic, complemented
38#16864111C2211yescharacteristic, complemented
39#16864108—21no—
40#16864092C2211yescharacteristic, complemented
41#16864091—21no—
42#16864086C2211yescharacteristic
43#16864078—21no—
44#16864067C2211yescharacteristic
45#16864055C2211yescharacteristic, complemented
46#16864055C2211yescharacteristic, complemented
47#16864017C2211yescharacteristic, complemented
48#16864016—21no—
49#16864001C2211yescharacteristic, complemented
50#16863996—21no—
51#16863930C2211yescharacteristic, complemented
52#16863929—21no—
53#16863929—21no—
54#16863876C2211yescharacteristic, complemented
55#16863873C2211yescharacteristic, complemented
56C4×#11761628C2211yescharacteristic, complemented
57#16863795C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863792C2211yescharacteristic, complemented
60#16863778C2211yescharacteristic, complemented
61#16863778C2211yescharacteristic, complemented
62#16863772C2211yescharacteristic
63#16863762C2211yescharacteristic, complemented
64#16863760C2211yescharacteristic
65#16863758C2211yescharacteristic, complemented
66#16863755C2211yescharacteristic, complemented
67#16863753C2211yescharacteristic, complemented
68#16863750C2211yescharacteristic, complemented
69#16863737C2211yescharacteristic, complemented
70#16863734C2211yescharacteristic, complemented
71#16863731C2211yescharacteristic, complemented
72#16863729C2211yescharacteristic, complemented
73#16863720C2211yescharacteristic, complemented
74#16863717C2211yescharacteristic
75#16863717C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic, complemented
77#16863714C2211yescharacteristic, complemented
78#16863714C2211yescharacteristic, complemented
79#16863709C2211yescharacteristic, complemented
80#16863707C2211yescharacteristic
81#16863703C2211yescharacteristic, complemented
82#16863700C2211yescharacteristic, complemented
83#16863700C2211yescharacteristic, complemented
84#16863700C2211yescharacteristic, complemented
85#16863696C2211yescharacteristic
86#16863696C2211yescharacteristic
87#16863696C2211yescharacteristic, complemented
88#16863693C2211yescharacteristic, complemented
89#16863688C2211yescharacteristic, complemented
90#16863686C2211yescharacteristic, complemented
91#16863676C2211yescharacteristic
92#16863673C2211yescharacteristic, complemented
93#16863652C2211yescharacteristic, complemented
94#16863652C2211yescharacteristic, complemented
95#16863647C2211yescharacteristic
96#16863647C2211yescharacteristic
97#16863647C2211yescharacteristic, complemented
98#16863647C2211yescharacteristic, complemented
99#16863644C2211yescharacteristic, complemented
100#16863640C2211yescharacteristic
101#16863630C2211yescharacteristic, complemented
102#16863630C2211yescharacteristic, complemented
103#16863627C2211yescharacteristic, complemented
104#16863623C2211yescharacteristic
105#16863615C2211yescharacteristic, complemented
106#16863615C2211yescharacteristic, complemented
107#16863611C2211yescharacteristic
108#16863611C2211yescharacteristic
109#16863611C2211yescharacteristic, complemented
110#16863611C2211yescharacteristic, complemented
111#16863608C2211yescharacteristic, complemented
112#16863608C2211yescharacteristic, complemented
113#16863596C2211yescharacteristic, complemented
114#16863593C2211yescharacteristic
115#16863593C2211yescharacteristic
116#16863591C2211yescharacteristic
117#16863556C2211yescharacteristic, complemented
118#16863556C2211yescharacteristic, complemented
119#16863547C2211yescharacteristic
120#16863547C2211yescharacteristic
121#16863541C2211yescharacteristic
122#16863541C2211yescharacteristic
123#16863539C2211yescharacteristic
124#16863539C2211yescharacteristic
125#16863534C2211yescharacteristic, complemented
126#16863534C2211yescharacteristic, complemented
127#16863530C2211yescharacteristic
128#16863530C2211yescharacteristic
129#16863527C2211yescharacteristic, complemented
130Q8×C67⋊C8C2211yescharacteristic, complemented
131#16863506C2211yescharacteristic
132#16863506C2211yescharacteristic
133#16863506C2211yescharacteristic, complemented
134#16863506C2211yescharacteristic, complemented
135#16863501C2211yescharacteristic, complemented
136#16863501C2211yescharacteristic, complemented
137#16863496C2211yescharacteristic
138#16863496C2211yescharacteristic
139#16863496C2211yescharacteristic, complemented
140#16863496C2211yescharacteristic, complemented
141#16863496C2211yescharacteristic, complemented
142#16863494C2211yescharacteristic, complemented
143C4×#11761618C2211yescharacteristic, complemented
144C4×#11761618C2211yescharacteristic, complemented
145C4×#11761615C2211yescharacteristic, complemented
146C4×#11761616C2211yescharacteristic
147C4×#11761616C2211yescharacteristic
148C4×#11761616C2211yescharacteristic
149C4×#11761616C2211yescharacteristic
150C4×#11761616C2211yescharacteristic, complemented
151C4×#11761616C2211yescharacteristic, complemented
152C4×#11761616C2211yescharacteristic, complemented
153C4×#11761613C2211yescharacteristic
154C4×#11761613C2211yescharacteristic
155C4×#11761613C2211yescharacteristic, complemented
156C4×#11761613C2211yescharacteristic, complemented
157C4×#11761613C2211yescharacteristic, complemented
158C4×#11761613C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic
160#16863474C2211yescharacteristic, complemented
161#16863474C2211yescharacteristic, complemented
162#16863468C2211yescharacteristic
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
172#16863395C2211yescharacteristic, complemented
173#16863392C2211yescharacteristic
174#16863390C2211yescharacteristic, complemented
175C2×#14523966C2211yescharacteristic, complemented
176C2×#14523964C2211yescharacteristic
177#16863352C2211yescharacteristic, complemented
178#16863352C2211yescharacteristic, complemented
179C4×#11761612C2211yescharacteristic, complemented
180#559×C67C2211yescharacteristic
181#554×C67C2211yescharacteristic
182#553×C67—21no—
183#553×C67C2211yescharacteristic
184#552×C67C2211yescharacteristic
185#551×C67—21no—
186#551×C67—21no—
187#547×C67C2211yescharacteristic
188#546×C67—21no—
189#546×C67C2211yescharacteristic
190#546×C67C2211yescharacteristic
191D42×C67C2211yescharacteristic
192#542×C67C2211yescharacteristic
193#540×C67C2211yescharacteristic
194#539×C67—21no—
195#538×C67—21no—
196#529×C67C2211yescharacteristic
197#529×C67C2211yescharacteristic
198#525×C67—21no—
199C2×#123×C67—21no—
200#520×C67C2211yescharacteristic
201#518×C67C2211yescharacteristic
202C2×C4×D4×C67C2211yescharacteristic
203C2×#11761628C2311yescharacteristic
204C2×#11761628C2311yescharacteristic
205C22×Dic134C2311yescharacteristic
206#14524073—24no—
207#14524069—24no—
208#14524069—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#14524041—21no—
233#14524040C2311yescharacteristic
234#14524039—21no—
235#14524038—21no—
236#14524038—21no—
237#14524037—21no—
238#14524036—21no—
239#14524035C2311yescharacteristic
240#14524035C2311yescharacteristic
241#14524033—21no—
242#14524033—21no—
243#14524033—21no—
244#14524032—21no—
245#14524031C2311yescharacteristic
246#14524031C2311yescharacteristic
247#14524029—21no—
248#14524029—21no—
249#14524029—21no—
250#14524029—21no—
251#14524029—21no—
252#14524028—21no—
253#14524028—21no—
254#14524028—21no—
255#14524028—21no—
256#14524026—21no—
257#14524025—21no—
258#14524025—21no—
259#14524024—21no—
260#14524022C2311yescharacteristic
261#14524022C2311yescharacteristic
262#14524021—21no—
263#14524021—21no—
264#14524021—21no—
265#14524017C2311yescharacteristic
266#14524017C2311yescharacteristic
267#14524017C2311yescharacteristic
268#14524017C2311yescharacteristic
269#14524016—21no—
270#14524016—21no—
271#14524016—21no—
272#14524016—21no—
273#14524015—21no—
274#14524015—21no—
275#14524015—21no—
276#14524014—21no—
277C4×Dic134C2311yescharacteristic
278C4×Dic134C2311yescharacteristic
279C4×Dic134C2311yescharacteristic
280C4×Dic134C2311yescharacteristic
281C4×Dic134C2311yescharacteristic
282C4×Dic134C2311yescharacteristic
283#14524008—21no—
284#14524008—21no—
285#14524008—21no—
286C4×D268C2311yescharacteristic
287C4×D268C2311yescharacteristic
288C4×D268C2311yescharacteristic
289C4×D268C2311yescharacteristic
290#14524005—21no—
291#14524005—21no—
292C4×C22⋊D67—21no—
293C4×C22⋊D67—21no—
294C4×C22⋊D67—21no—
295(C22⋊D67)⋊C4—21no—
296(C22⋊D67)⋊C4—21no—
297(C22⋊D67)⋊C4—21no—
298(C22⋊D67)⋊C4—21no—
299(C22⋊D67)⋊C4—21no—
300#14524002C2311yescharacteristic
301#14524002C2311yescharacteristic
302#14524001—21no—
303#14524001—21no—
304#14524000—21no—
305#14524000—21no—
306#14523999—21no—
307#14523999—21no—
308#14523999—21no—
309C2×C4⋊Dic67C2311yescharacteristic
310C4⋊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
481#11761628—22no—
482#11761628—22no—
483#11761628—41no—
484#11761628—41no—
485C2×Dic134—22no—
486C2×Dic134—21no—
487C2×Dic134—21no—
488C2×Dic134—41no—
489C2×Dic134C2411yescharacteristic
490C2×Dic134C2411yescharacteristic
491C2×D268—21no—
492C2×D268—21no—
493C2×D268C2411yescharacteristic
494C2×D268C2411yescharacteristic
495C2×C22⋊D67—21no—
496C2×C22⋊D67—21no—
497C2×C22⋊D67—21no—
498C2×C22⋊D67—21no—
499C2×C22⋊D67—21no—
500C2×C22⋊D67—21no—
501C22×Dic67—21no—
502C22×Dic67—21no—
503C2×C4×D67—21no—
504C2×C4×D67—21no—
505C2×C4×D67—21no—
506C2×C4×D67—21no—
507C2×C4×D67—21no—
508C2×C4×D67—21no—
509#11761618—22no—
510#11761618—22no—
511#11761616—22no—
512#11761616—22no—
513#11761616—22no—
514#11761616—41no—
515#11761616—41no—
516#11761616#4114yescomplemented
517#11761615—41no—
518#11761615—41no—
519#11761613—22no—
520#11761613—22no—
521#11761613—22no—
522#11761613—22no—
523#11761613—41no—
524#11761613—41no—
525#11761612—22no—
526#11761612—22no—
527#11761612—22no—
528#11761612—41no—
529C2×C67⋊C8—41no—
530C2×C67⋊C8—41no—
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C2×C67⋊C8C2411yescharacteristic
534C2×C67⋊C8C2411yescharacteristic
535C2×C67⋊C8C2411yescharacteristic
536C2×C67⋊C8C2411yescharacteristic
537C2×C67⋊C8C2411yescharacteristic
538C2×C67⋊C8C2411yescharacteristic
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—
561(C2×D67)⋊C4—21no—
562(C2×D67)⋊C4—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—
573C4×Dic67—21no—
574C4×Dic67—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—
703Q8×C67—21no—
704Q8×C67—21no—
705Q8×C67—41no—
706Q8×C67—81no—
707D4×C67—21no—
708D4×C67—21no—
709D4×C67—21no—
710D4×C67—21no—
711D4×C67—21no—
712D4×C67—41no—
713D4×C67—41no—
714D4×C67—41no—
715D4×C67—42no—
716D4×C67—42no—
717D4×C67—42no—
718D4×C67—42no—
719D4×C67—81no—
720D4×C67—81no—
721D4×C67—81no—
722D4×C67—81no—
723D4×C67—81no—
724D4×C67C2×#4112yes—
725C2×C4×C67—21no—
726C2×C4×C67—21no—
727C2×C4×C67—21no—
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—41no—
737C2×C4×C67—41no—
738C2×C4×C67—42no—
739C2×C4×C67—42no—
740C2×C4×C67—81no—
741C2×C4×C67—81no—
742C2×C4×C67—81no—
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×C67C22×D411yescharacteristic
750C2×C4×C67C22×D411yescharacteristic
751C2×C4×C67C22×D411yescharacteristic
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×C67C2511yescharacteristic
761C22⋊D67—42no—
762C22⋊D67—42no—
763C22⋊D67—81no—
764C22⋊D67—81no—
765C22⋊D67—81no—
766C22⋊D67—81no—
767C2×Dic67—21no—
768C2×Dic67—21no—
769C2×Dic67—21no—
770C2×Dic67—21no—
771C2×Dic67—21no—
772C2×Dic67—21no—
773C2×Dic67—42no—
774C2×Dic67—81no—
775D268—21no—
776D268—21no—
777D268—21no—
778D268—21no—
779D268—81no—
780D268—81no—
781C4×D67—42no—
782C4×D67—42no—
783C4×D67—81no—
784C4×D67—81no—
785C4×D67—81no—
786C4×D67—81no—
787Dic134—21no—
788Dic134—21no—
789Dic134—21no—
790Dic134—42no—
791Dic134—81no—
792Dic134C2×#4112yes—
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—41no—
823C2×D67—41no—
824C2×D67—41no—
825C2×D67—41no—
826C2×D67—41no—
827C2×D67—41no—
828C4×C67—21no—
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—41no—
840C4×C67—41no—
841C4×C67—41no—
842C4×C67—41no—
843C4×C67—41no—
844C4×C67C22×#4111yescharacteristic
845C4×C67#58511yescharacteristic
846Dic67—22no—
847Dic67—41no—
848Dic67—41no—
849Dic67—41no—
850Dic67—41no—
851Dic67—41no—
852#61547—671nomaximal, Sylow
853C2×C67—41no—
854C2×C67—41no—
855C2×C67—41no—
856C2×C67—42no—
857C2×C67—81no—
858C2×C67—81no—
859C2×C67D4×#4111yescharacteristic
860C2×C67#358411yescharacteristic
861C2×C67#358511yescharacteristic
862D67—81no—
863D67—81no—
864#3524—671no—
865#3513D6711yescharacteristic, complemented
866#3396—671no—
867#3381—671no—
868#3371—671no—
869#3370—671no—
870#3355—671no—
871#3354—671no—
872#3352—671no—
873#3319—671no—
874#3317—671no—
875#3310—671no—
876#3308—671no—
877#3301—671no—
878#3297—671no—
879#3275—671no—
880#3275—671no—
881#3274—671no—
882#3183—671no—
883#3176—671no—
884#3173—671no—
885#3126—671no—
886#3124—671no—
887#3119—671no—
888#3118—671no—
889#3105—671no—
890#3102—671no—
891#2969—671no—
892#2947—671no—
893#2946—671no—
894C4×AGL(1,ℤ/8)—671no—
895C67#6154711yescharacteristic, complemented, Sylow
896C2×#137—671no—
897C2×AGL(1,ℤ/8)—671no—
898C2×AGL(1,ℤ/8)—671no—
899#559—671no—
900#559—1341no—
901#559C2×D6711yescharacteristic
902#557—671no—
903#555—671no—
904#555—1341no—
905#554C2×D6711yescharacteristic
906#553—21no—
907#553—671no—
908#553—1341no—
909#553C2×D6711yescharacteristic
910#552—671no—
911#552—1341no—
912#552C2×D6711yescharacteristic
913#551—21no—
914#551—21no—
915#550—671no—
916#548—671no—
917#548—671no—
918#547C2×D6711yescharacteristic
919#546—21no—
920#546C2×D6711yescharacteristic
921#546C2×D6711yescharacteristic
922D42C2×D6711yescharacteristic
923#542—671no—
924#542—1341no—
925#542C2×D6711yescharacteristic
926#540—671no—
927#540—1341no—
928#540C2×D6711yescharacteristic
929#539—21no—
930#538—21no—
931#529—671no—
932#529—1341no—
933#529—1341no—
934#529C2×D6711yescharacteristic
935#529C2×D6711yescharacteristic
936#525—21no—
937C2×#123—21no—
938#520—671no—
939#520C2×D6711yescharacteristic
940#519—671no—
941#518C2×D6711yescharacteristic
942C4×#41—671no—
943C2×C4×D4C2×D6711yescharacteristic
944#499—671no—
945#499—671no—
946#498—671no—
947#495—671no—
948#495—671no—
949#493—671no—
950#490—671no—
951#490—671no—
952#489—671no—
953#489—671no—
954#488—671no—
955#488—671no—
956#485—671no—
957#485—671no—
958#484—671no—
959#484—671no—
960#482—671no—
961#482—671no—
962#482—671no—
963#482—671no—
964#481—671no—
965#481—671no—
966#480—671no—
967#480—671no—
968#479—671no—
969#479—671no—
970#479—671no—
971#479—671no—
972#478—671no—
973#478—671no—
974#478—671no—
975#478—671no—
976#477—671no—
977#476—671no—
978#474—671no—
979#474—671no—
980#470—671no—
981#470—671no—
982#469—671no—
983#469—671no—
984#469—671no—
985#469—671no—
986#468—671no—
987#468—671no—
988#466—671no—
989#466—671no—
990#465—671no—
991#465—671no—
992#464—671no—
993#464—671no—
994#463—671no—
995#463—671no—
996#463—671no—
997#463—671no—
998#463—671no—
999#463—671no—
1000#460—671no—
1001#460—671no—
1002#460—671no—
1003#459—671no—
1004#452—671no—
1005#452—671no—
1006#450—671no—
1007#450—671no—
1008#449—671no—
1009#449—671no—
1010#449—671no—
1011#449—671no—
1012#448—671no—
1013#448—671no—
1014#447—671no—
1015#447—671no—
1016#446—671no—
1017C8×Q8—671no—
1018#442—671no—
1019#442—671no—
1020#442—671no—
1021#442—671no—
1022#441—671no—
1023#441—671no—
1024#440—671no—
1025#440—671no—
1026#440—671no—
1027#440—671no—
1028#440—671no—
1029#440—671no—
1030C4×Q16—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—
1046#436—671no—
1047#436—671no—
1048#436—671no—
1049#435—671no—
1050#435—671no—
1051C8×D4—671no—
1052#433—671no—
1053#433—671no—
1054#431—671no—
1055#428—671no—
1056#428—671no—
1057#428—671no—
1058#418—671no—
1059#417—671no—
1060#416—671no—
1061#416—671no—
1062C2×#103—671no—
1063C2×#102—671no—
1064#405—671no—
1065#405—671no—
1066C4×M16—671no—
1067C2×#41—21no—
1068C2×#41—671no—
1069C2×#41—671no—
1070C2×#41C22×D6711yescharacteristic
1071C22×Q8—671no—
1072C22×D4—21no—
1073C22×D4C22×D6711yescharacteristic
1074C22×D4C22×D6711yescharacteristic
1075C23×C4—21no—
1076#137—1344no—
1077AGL(1,ℤ/8)—1344no—
1078AGL(1,ℤ/8)—1344no—
1079C2×Q16—671no—
1080C2×Q16—671no—
1081C2×SD16—671no—
1082C2×SD16—671no—
1083C2×SD16—671no—
1084C2×SD16—671no—
1085C2×SD16—671no—
1086C2×SD16—671no—
1087C2×SD16—671no—
1088C2×SD16—671no—
1089C2×D8—671no—
1090C2×D8—671no—
1091C2×D8—671no—
1092C2×D8—671no—
1093C2×D8—671no—
1094C2×D8—671no—
1095C2×M16—671no—
1096C2×M16—671no—
1097C2×M16—671no—
1098C2×M16—671no—
1099C22×C8—671no—
1100C22×C8—671no—
1101C4⋊Q8—671no—
1102C4⋊Q8—1341no—
1103C4⋊Q8C22×D6711yescharacteristic
1104#127—671no—
1105#127—1341no—
1106#127C22×D6711yescharacteristic
1107#126—21no—
1108#126—21no—
1109#126—21no—
1110#126—21no—
1111#126—1341no—
1112#126—1341no—
1113#126—1341no—
1114#126—1341no—
1115#126C22⋊D6711yescharacteristic
1116#126C22⋊D6711yescharacteristic
1117#125—21no—
1118#125—671no—
1119#125—671no—
1120#125—1341no—
1121#125—1341no—
1122#125—1341no—
1123#125C22⋊D6711yescharacteristic
1124#125C22×D6711yescharacteristic
1125#125C22×D6711yescharacteristic
1126#124—21no—
1127#124—21no—
1128#124—671no—
1129#124—671no—
1130#124—1341no—
1131#124—1341no—
1132#124—1341no—
1133#124—1341no—
1134#124—1341no—
1135#124—1341no—
1136#124C22⋊D6711yescharacteristic
1137#124C22×D6711yescharacteristic
1138#124C22×D6711yescharacteristic
1139#123—21no—
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—1341no—
1152#123—1341no—
1153#123—1341no—
1154#123—1341no—
1155#123—1341no—
1156#123—1341no—
1157#123—1341no—
1158#123—1341no—
1159#123C22⋊D6711yescharacteristic
1160#123C22⋊D6711yescharacteristic
1161C22⋊Q8—21no—
1162C22⋊Q8—21no—
1163C22⋊Q8—21no—
1164C22⋊Q8—21no—
1165C22⋊Q8—21no—
1166C22⋊Q8—671no—
1167C22⋊Q8—671no—
1168C22⋊Q8—1341no—
1169C22⋊Q8—1341no—
1170C22⋊Q8—1341no—
1171C22⋊Q8C22⋊D6711yescharacteristic
1172C22⋊Q8C22×D6711yescharacteristic
1173C22⋊Q8C22×D6711yescharacteristic
1174#121—21no—
1175#121—21no—
1176#121—21no—
1177#121—21no—
1178#121—21no—
1179#121—21no—
1180#121—671no—
1181#121—671no—
1182#121—671no—
1183#121—671no—
1184#121—1341no—
1185#121—1341no—
1186#121—1341no—
1187#121—1341no—
1188#121—1341no—
1189#121—1341no—
1190#121—1341no—
1191#121—1341no—
1192#121C22⋊D6711yescharacteristic
1193#121C22×D6711yescharacteristic
1194#121C22×D6711yescharacteristic
1195#121C22×D6711yescharacteristic
1196#121C22×D6711yescharacteristic
1197#120—21no—
1198#120—21no—
1199#120—21no—
1200#120—21no—
1201C4×Q8—671no—
1202C4×Q8—671no—
1203C4×Q8—671no—
1204C4×Q8—671no—
1205C4×Q8—671no—
1206C4×Q8—671no—
1207C4×Q8—1341no—
1208C4×Q8—1341no—
1209C4×Q8—1341no—
1210C4×Q8C22×D6711yescharacteristic
1211C4×Q8C22×D6711yescharacteristic
1212C4×Q8C22×D6711yescharacteristic
1213C4×D4—21no—
1214C4×D4—21no—
1215C4×D4—21no—
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—21no—
1219C4×D4—21no—
1220C4×D4—21no—
1221C4×D4—21no—
1222C4×D4—671no—
1223C4×D4—671no—
1224C4×D4—671no—
1225C4×D4—671no—
1226C4×D4—1341no—
1227C4×D4—1341no—
1228C4×D4—1341no—
1229C4×D4—1341no—
1230C4×D4—1341no—
1231C4×D4—1341no—
1232C4×D4—1341no—
1233C4×D4—1341no—
1234C4×D4—1341no—
1235C4×D4—1341no—
1236C4×D4C22×D6711yescharacteristic
1237C4×D4C22×D6711yescharacteristic
1238C4×D4C22×D6711yescharacteristic
1239C4×D4C22×D6711yescharacteristic
1240C4×D4C22×D6711yescharacteristic
1241C4×D4C22×D6711yescharacteristic
1242C4×D4C22×D6711yescharacteristic
1243C4×D4C22×D6711yescharacteristic
1244C4×D4C22×D6711yescharacteristic
1245C4×D4C22×D6711yescharacteristic
1246C4×D4C22×D6711yescharacteristic
1247#117—21no—
1248#117—21no—
1249#117—21no—
1250#117—671no—
1251#117—671no—
1252#117—1341no—
1253#117—1341no—
1254#117—1341no—
1255#117—1341no—
1256#117—1341no—
1257#117—1341no—
1258#117—1341no—
1259#117C22×D6711yescharacteristic
1260#117C22×D6711yescharacteristic
1261#117C22×D6711yescharacteristic
1262C2×C4⋊C4—21no—
1263C2×C4⋊C4—21no—
1264C2×C4⋊C4—671no—
1265C2×C4⋊C4—1341no—
1266C2×C4⋊C4C22×D6711yescharacteristic
1267C2×C4⋊C4C22×D6711yescharacteristic
1268C2×C22⋊C4—21no—
1269C2×C22⋊C4—21no—
1270C2×C22⋊C4—21no—
1271C2×C22⋊C4—21no—
1272C2×C22⋊C4—21no—
1273C2×C42—1341no—
1274C2×C42C22×D6711yescharacteristic
1275#107—671no—
1276#107—671no—
1277#107—671no—
1278#107—671no—
1279#107—671no—
1280#107—671no—
1281#107—671no—
1282#107—671no—
1283#106—671no—
1284#106—671no—
1285#106—671no—
1286#106—671no—
1287#106—671no—
1288#106—671no—
1289#106—671no—
1290#106—671no—
1291C4⋊C8—671no—
1292C4⋊C8—671no—
1293C4⋊C8—671no—
1294C4⋊C8—671no—
1295C4⋊C8—671no—
1296C4⋊C8—671no—
1297#103—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#102—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—
1329C22⋊C8—671no—
1330C22⋊C8—671no—
1331C22⋊C8—671no—
1332C22⋊C8—671no—
1333C22⋊C8—671no—
1334C22⋊C8—671no—
1335#97—671no—
1336#97—671no—
1337#97—671no—
1338#97—671no—
1339C4×C8—671no—
1340C4×C8—671no—
1341C4×C8—671no—
1342C4×C8—671no—
1343C4×C8—671no—
1344C4×C8—671no—
1345C24—21no—
1346C24—21no—
1347#41—22no—
1348#41—41no—
1349#41—82no—
1350#41—2681no—
1351#41—2681no—
1352#41—1342no—
1353#41—1342no—
1354C2×Q8—21no—
1355C2×Q8—2681no—
1356C2×Q8—671no—
1357C2×Q8—671no—
1358C2×Q8—1342no—
1359C2×Q8—1341no—
1360C2×Q8—1341no—
1361C2×Q8C2×C22⋊D6711yescharacteristic
1362C2×Q8C23×D6711yescharacteristic
1363C2×D4—22no—
1364C2×D4—22no—
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—21no—
1374C2×D4—41no—
1375C2×D4—41no—
1376C2×D4—82no—
1377C2×D4—671no—
1378C2×D4—671no—
1379C2×D4—1341no—
1380C2×D4—1341no—
1381C2×D4—1341no—
1382C2×D4—1341no—
1383C2×D4—1341no—
1384C2×D4—1341no—
1385C2×D4—1341no—
1386C2×D4—1341no—
1387C2×D4C2×C22⋊D6711yescharacteristic
1388C2×D4C2×C22⋊D6711yescharacteristic
1389C2×D4C2×C22⋊D6711yescharacteristic
1390C2×D4C23×D6711yescharacteristic
1391C2×D4C23×D6711yescharacteristic
1392C2×D4C23×D6711yescharacteristic
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—21no—
1403C22×C4—21no—
1404C22×C4—82no—
1405C22×C4—1341no—
1406C22×C4—1341no—
1407C22×C4—1341no—
1408C22×C4—1341no—
1409C22×C4—1341no—
1410C22×C4—1341no—
1411C22×C4—1341no—
1412C22×C4—1341no—
1413C22×C4C2×C22⋊D6711yescharacteristic
1414C22×C4C2×C22⋊D6711yescharacteristic
1415C22×C4C23×D6711yescharacteristic
1416C22×C4C23×D6711yescharacteristic
1417C22×C4C23×D6711yescharacteristic
1418Q16—1342no—
1419Q16—1342no—
1420SD16—2681no—
1421SD16—2681no—
1422SD16—2681no—
1423SD16—2681no—
1424SD16—674no—
1425SD16—1342no—
1426SD16—1342no—
1427SD16—1342no—
1428D8—2681no—
1429D8—2681no—
1430D8—1342no—
1431D8—1342no—
1432D8—1342no—
1433D8—1342no—
1434M16—2681no—
1435M16—1342no—
1436M16—1342no—
1437M16—1342no—
1438C2×C8—2681no—
1439C2×C8—2681no—
1440C2×C8—671no—
1441C2×C8—671no—
1442C2×C8—671no—
1443C2×C8—671no—
1444C2×C8—671no—
1445C2×C8—671no—
1446C2×C8—671no—
1447C2×C8—671no—
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—21no—
1459C4⋊C4—671no—
1460C4⋊C4—671no—
1461C4⋊C4—671no—
1462C4⋊C4—671no—
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⋊C4C2×C22⋊D6711yescharacteristic
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⋊C4C23×D6711yescharacteristic
1488C4⋊C4C23×D6711yescharacteristic
1489C4⋊C4C23×D6711yescharacteristic
1490C4⋊C4C23×D6711yescharacteristic
1491C22⋊C4—21no—
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—1341no—
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⋊C4C2×C22⋊D6711yescharacteristic
1527C22⋊C4C2×C22⋊D6711yescharacteristic
1528C22⋊C4C2×C22⋊D6711yescharacteristic
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
1536C42—21no—
1537C42—21no—
1538C42—21no—
1539C42—1341no—
1540C42—1341no—
1541C42—1341no—
1542C42—1341no—
1543C42—1341no—
1544C42—1341no—
1545C42—1341no—
1546C42—1341no—
1547C42C2×C22⋊D6711yescharacteristic
1548C42C2×C22⋊D6711yescharacteristic
1549C42C23×D6711yescharacteristic
1550C42C23×D6711yescharacteristic
1551C42C23×D6711yescharacteristic
1552C42C23×D6711yescharacteristic
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—42no—
1557C23—42no—
1558C23—42no—
1559C23—81no—
1560C23—81no—
1561C23—81no—
1562C23—1341no—
1563C23—1341no—
1564C23C22×C22⋊D6711yescharacteristic
1565C23C22×C22⋊D6711yescharacteristic
1566C23C22×C22⋊D6711yescharacteristic
1567Q8—21no—
1568Q8—21no—
1569Q8—41no—
1570Q8—81no—
1571Q8—2682no—
1572Q8—5361no—
1573Q8—672no—
1574Q8—1341no—
1575Q8—1341no—
1576Q8—1341no—
1577D4—21no—
1578D4—21no—
1579D4—21no—
1580D4—21no—
1581D4—21no—
1582D4—41no—
1583D4—41no—
1584D4—41no—
1585D4—42no—
1586D4—42no—
1587D4—42no—
1588D4—42no—
1589D4—81no—
1590D4—81no—
1591D4—81no—
1592D4—81no—
1593D4—81no—
1594D4—2682no—
1595D4—2682no—
1596D4—5361no—
1597D4—5361no—
1598D4—5361no—
1599D4—5361no—
1600D4—5361no—
1601D4—5361no—
1602D4—1341no—
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—2682no—
1634C2×C4—5361no—
1635C2×C4—5361no—
1636C2×C4—5361no—
1637C2×C4—5361no—
1638C2×C4—5361no—
1639C2×C4—1341no—
1640C2×C4—1341no—
1641C2×C4—1341no—
1642C2×C4—1341no—
1643C2×C4—1341no—
1644C2×C4—1341no—
1645C2×C4C22×C22⋊D6711yescharacteristic
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×C4C24×D6711yescharacteristic
1657C8—672no—
1658C8—1341no—
1659C8—1341no—
1660C8—1341no—
1661C8—1341no—
1662C8—1341no—
1663C8—1341no—
1664C8—1341no—
1665C22—21no—
1666C22—21no—
1667C22—21no—
1668C22—22no—
1669C22—21no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—21no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—84no—
1684C22—2681no—
1685C22—2681no—
1686C22—2681no—
1687C22—2681no—
1688C22—2681no—
1689C22—2681no—
1690C22—162no—
1691C22C23×C22⋊D6711yescharacteristic
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—21no—
1696C4—21no—
1697C4—21no—
1698C4—21no—
1699C4—21no—
1700C4—21no—
1701C4—21no—
1702C4—21no—
1703C4—41no—
1704C4—41no—
1705C4—41no—
1706C4—41no—
1707C4—41no—
1708C4—2681no—
1709C4—2681no—
1710C4—2681no—
1711C4—2681no—
1712C4—2681no—
1713C4—1342no—
1714C4C2×#41×D6711yescharacteristic
1715C4#1686423211yescharacteristic
1716C2—41no—
1717C2—41no—
1718C2—41no—
1719C2—42no—
1720C2—81no—
1721C2—81no—
1722C2—5361no—
1723C2—5361no—
1724C2#41×C22⋊D6711yescharacteristic
1725C2#2257498011yescharacteristic
1726C2#2257498911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3513C2
socleC22×C67C23×D4
hypercenter#3513D67
hypocenterC67#61547
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. #22574314C2semidirect
2. #22573217C2semidirect
3. #22573084C2semidirect
4. #22572971C2semidirect
5. #22572962C2semidirect
6. #22572809C2semidirect
7. #22572804C2semidirect
8. #22572778C2semidirect
9. #22572365C2semidirect
10. #22572329C2semidirect
11. #22572230C2semidirect
12. #22572194C2semidirect
13. #22572105C2semidirect
14. #22572059C2semidirect
15. #22571836C2semidirect
16. #22571836C2semidirect
17. #22571825C2semidirect
18. #22570932C2semidirect
19. #22570853C2semidirect
20. #22570820C2semidirect
21. #22570495C2semidirect
22. #22570465C2semidirect
23. #22570408C2semidirect
24. #22570393C2semidirect
25. #22570256C2semidirect
26. #22570221C2semidirect
27. #22569214C2semidirect
28. #22569048C2semidirect
29. #22569041C2semidirect
30. C4×#14524069C2semidirect
31. C67×#3513C2semidirect
35. #16864131C22semidirect
37. #16864124C22semidirect
38. #16864111C22semidirect
40. #16864092C22semidirect
45. #16864055C22semidirect
46. #16864055C22semidirect
47. #16864017C22semidirect
49. #16864001C22semidirect
51. #16863930C22semidirect
54. #16863876C22semidirect
55. #16863873C22semidirect
56. C4×#11761628C22semidirect
57. #16863795C22semidirect
58. #16863795C22semidirect
59. #16863792C22semidirect
60. #16863778C22semidirect
61. #16863778C22semidirect
63. #16863762C22semidirect
65. #16863758C22semidirect
66. #16863755C22semidirect
67. #16863753C22semidirect
68. #16863750C22semidirect
69. #16863737C22semidirect
70. #16863734C22semidirect
71. #16863731C22semidirect
72. #16863729C22semidirect
73. #16863720C22semidirect
75. #16863717C22semidirect
76. #16863717C22semidirect
77. #16863714C22semidirect
78. #16863714C22semidirect
79. #16863709C22semidirect
81. #16863703C22semidirect
82. #16863700C22semidirect
83. #16863700C22semidirect
84. #16863700C22semidirect
87. #16863696C22semidirect
88. #16863693C22semidirect
89. #16863688C22semidirect
90. #16863686C22semidirect
92. #16863673C22semidirect
93. #16863652C22semidirect
94. #16863652C22semidirect
97. #16863647C22semidirect
98. #16863647C22semidirect
99. #16863644C22semidirect
101. #16863630C22semidirect
102. #16863630C22semidirect
103. #16863627C22semidirect
105. #16863615C22semidirect
106. #16863615C22semidirect
109. #16863611C22semidirect
110. #16863611C22semidirect
111. #16863608C22semidirect
112. #16863608C22semidirect
113. #16863596C22semidirect
117. #16863556C22semidirect
118. #16863556C22semidirect
125. #16863534C22semidirect
126. #16863534C22semidirect
129. #16863527C22semidirect
130. Q8×C67⋊C8C22semidirect
133. #16863506C22semidirect
134. #16863506C22semidirect
135. #16863501C22semidirect
136. #16863501C22semidirect
139. #16863496C22semidirect
140. #16863496C22semidirect
141. #16863496C22semidirect
142. #16863494C22semidirect
143. C4×#11761618C22semidirect
144. C4×#11761618C22semidirect
145. C4×#11761615C22semidirect
150. C4×#11761616C22semidirect
151. C4×#11761616C22semidirect
152. C4×#11761616C22semidirect
155. C4×#11761613C22semidirect
156. C4×#11761613C22semidirect
157. C4×#11761613C22semidirect
158. C4×#11761613C22semidirect
160. #16863474C22semidirect
161. #16863474C22semidirect
163. #16863468C22semidirect
164. D4×C67⋊C8C22semidirect
165. #16863457C22semidirect
166. #16863457C22semidirect
167. #16863449C22semidirect
168. #16863439C22semidirect
169. #16863436C22semidirect
170. #16863436C22semidirect
172. #16863395C22semidirect
174. #16863390C22semidirect
175. C2×#14523966C22semidirect
177. #16863352C22semidirect
178. #16863352C22semidirect
179. C4×#11761612C22semidirect
516. #11761616#41semidirect
865. #3513D67semidirect
895. C67#61547semidirect

Maximal subgroups

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

subgroupindex
#225743142
#225732172
#225730842
#225729712
#225729622
#225728092
#225728042
#225727782
#225723652
#225723292
#225722302
#225721942
#225721052
#225720592
#225718362
#225718252
#225709322
#225708532
#225708202
#225704952
#225704652
#225704082
#225703932
#225702562
#225702212
#225692142
#225690482
#225690412
C4×#145240692
C67×#35132
#6154767