Finite Group Databasebeta

← #31752910

Subgroups — #31752910

Order 17152.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574281C211yesmaximal, characteristic, complemented
2#22573163C211yesmaximal, characteristic, complemented
3#22573104C211yesmaximal, characteristic, complemented
4#22573036C211yesmaximal, characteristic, complemented
5#22572927C211yesmaximal, characteristic, complemented
6#22572748C211yesmaximal, characteristic, complemented
7#22572724C211yesmaximal, characteristic, complemented
8#22572709C211yesmaximal, characteristic, complemented
9#22572643C211yesmaximal, characteristic, complemented
10#22572622C211yesmaximal, characteristic, complemented
11#22572605C211yesmaximal, characteristic, complemented
12#22572359C211yesmaximal, characteristic, complemented
13#22572359C211yesmaximal, characteristic, complemented
14#22572179C211yesmaximal, characteristic, complemented
15#22572164C211yesmaximal, characteristic, complemented
16#22572131C211yesmaximal, characteristic, complemented
17#22572053C211yesmaximal, characteristic, complemented
18#22571655C211yesmaximal, characteristic, complemented
19#22571614C211yesmaximal, characteristic, complemented
20#22571529C211yesmaximal, characteristic, complemented
21#22571507C211yesmaximal, characteristic, complemented
22#22571477C211yesmaximal, characteristic, complemented
23#22571449C211yesmaximal, characteristic, complemented
24#22570447C211yesmaximal, characteristic, complemented
25#22570402C211yesmaximal, characteristic, complemented
26#22570354C211yesmaximal, characteristic, complemented
27#22570056C211yesmaximal, characteristic, complemented
28#22570034C211yesmaximal, characteristic, complemented
29#22569991C211yesmaximal, characteristic, complemented
30#22569348C211yesmaximal, characteristic, complemented
31C67×#3547C211yesmaximal, characteristic, complemented
32#16864119C2211yescharacteristic
33#16864116C2211yescharacteristic
34#16864106C2211yescharacteristic
35#16864092C2211yescharacteristic
36#16864091—21no—
37#16864086C2211yescharacteristic
38#16864078—21no—
39#16864076—21no—
40#16864074—21no—
41#16864051C2211yescharacteristic
42#16864042C2211yescharacteristic
43#16864042C2211yescharacteristic
44#16864017C2211yescharacteristic
45#16864008C2211yescharacteristic
46#16863992—21no—
47#16863978—21no—
48#16863930C2211yescharacteristic
49#16863929—21no—
50#126×D67—21no—
51#16863876C2211yescharacteristic
52#16863870C2211yescharacteristic
53C4×#11761628C2211yescharacteristic
54#16863806C2211yescharacteristic, complemented
55#16863802C2211yescharacteristic, complemented
56#16863802C2211yescharacteristic, complemented
57#16863802C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863792C2211yescharacteristic, complemented
60#16863766C2211yescharacteristic, complemented
61#16863758C2211yescharacteristic
62#16863758C2211yescharacteristic
63#16863758C2211yescharacteristic
64#16863753C2211yescharacteristic
65#16863748C2211yescharacteristic, complemented
66#16863737C2211yescharacteristic
67#16863737C2211yescharacteristic
68#16863737C2211yescharacteristic, complemented
69#16863737C2211yescharacteristic, complemented
70#16863737C2211yescharacteristic, complemented
71#16863731C2211yescharacteristic
72#16863726C2211yescharacteristic
73#16863726C2211yescharacteristic, complemented
74#16863720C2211yescharacteristic
75#16863720C2211yescharacteristic
76#16863720C2211yescharacteristic
77#16863717C2211yescharacteristic
78#16863717C2211yescharacteristic
79#16863717C2211yescharacteristic, complemented
80#16863717C2211yescharacteristic, complemented
81#16863714C2211yescharacteristic
82#16863712C2211yescharacteristic, complemented
83#16863707C2211yescharacteristic, complemented
84#16863700C2211yescharacteristic, complemented
85#16863700C2211yescharacteristic, complemented
86#16863700C2211yescharacteristic, complemented
87#16863700C2211yescharacteristic, complemented
88#16863700C2211yescharacteristic, complemented
89#16863696C2211yescharacteristic, complemented
90#16863696C2211yescharacteristic, complemented
91#16863696C2211yescharacteristic, complemented
92#16863696C2211yescharacteristic, complemented
93#16863693C2211yescharacteristic
94#16863693C2211yescharacteristic
95#16863693C2211yescharacteristic
96#16863693C2211yescharacteristic
97#16863693C2211yescharacteristic
98#16863693C2211yescharacteristic
99#16863693C2211yescharacteristic
100#16863688C2211yescharacteristic, complemented
101#16863688C2211yescharacteristic, complemented
102#16863688C2211yescharacteristic, complemented
103#16863686C2211yescharacteristic, complemented
104#16863683C2211yescharacteristic
105#16863683C2211yescharacteristic
106#16863683C2211yescharacteristic
107#16863678C2211yescharacteristic, complemented
108#16863678C2211yescharacteristic, complemented
109#16863676C2211yescharacteristic, complemented
110#16863673C2211yescharacteristic
111#16863673C2211yescharacteristic
112#16863673C2211yescharacteristic
113#16863673C2211yescharacteristic
114#16863647C2211yescharacteristic
115#16863640C2211yescharacteristic
116#16863640C2211yescharacteristic
117#16863640C2211yescharacteristic, complemented
118#16863630C2211yescharacteristic
119#16863630C2211yescharacteristic
120#16863630C2211yescharacteristic
121#16863623C2211yescharacteristic
122#16863623C2211yescharacteristic
123#16863623C2211yescharacteristic, complemented
124#16863623C2211yescharacteristic, complemented
125#16863623C2211yescharacteristic, complemented
126#16863611C2211yescharacteristic
127#16863611C2211yescharacteristic
128#16863611C2211yescharacteristic
129#16863611C2211yescharacteristic
130#16863601C2211yescharacteristic, complemented
131#16863601C2211yescharacteristic, complemented
132#16863593C2211yescharacteristic, complemented
133#16863593C2211yescharacteristic, complemented
134#16863588C2211yescharacteristic
135#16863588C2211yescharacteristic
136#16863539C2211yescharacteristic
137#16863539C2211yescharacteristic
138#16863539C2211yescharacteristic
139#16863539C2211yescharacteristic
140#16863529C2211yescharacteristic
141#16863529C2211yescharacteristic
142#16863527C2211yescharacteristic, complemented
143#16863527C2211yescharacteristic, complemented
144#16863506C2211yescharacteristic
145#16863506C2211yescharacteristic
146#16863506C2211yescharacteristic
147#16863506C2211yescharacteristic
148#16863506C2211yescharacteristic
149#16863496C2211yescharacteristic, complemented
150#16863496C2211yescharacteristic, complemented
151#16863496C2211yescharacteristic, complemented
152C4×#11761616C2211yescharacteristic, complemented
153C4×#11761613C2211yescharacteristic
154C4×#11761613C2211yescharacteristic
155C4×#11761613C2211yescharacteristic
156#16863468C2211yescharacteristic
157#16863468C2211yescharacteristic
158#16863468C2211yescharacteristic
159#16863468C2211yescharacteristic, complemented
160D4×C67⋊C8C2211yescharacteristic
161D4×C67⋊C8C2211yescharacteristic, complemented
162#16863457C2211yescharacteristic
163#16863457C2211yescharacteristic, complemented
164#16863453C2211yescharacteristic, complemented
165#16863439C2211yescharacteristic, complemented
166#16863436C2211yescharacteristic
167#16863432C2211yescharacteristic
168#16863432C2211yescharacteristic, complemented
169#16863432C2211yescharacteristic, complemented
170C2×#14523976C2211yescharacteristic, complemented
171#16863423C2211yescharacteristic
172#16863423C2211yescharacteristic, complemented
173C2×C4⋊(C67⋊C8)C2211yescharacteristic, complemented
174#16863400C2211yescharacteristic
175#16863395C2211yescharacteristic
176#16863390C2211yescharacteristic
177#16863390C2211yescharacteristic
178#16863390C2211yescharacteristic
179C2×#14523963C2211yescharacteristic
180#562×C67—21no—
181#562×C67—21no—
182#555×C67C2211yescharacteristic
183#555×C67C2211yescharacteristic
184#555×C67C2211yescharacteristic, complemented
185#554×C67C2211yescharacteristic, complemented
186#553×C67C2211yescharacteristic
187#553×C67C2211yescharacteristic, complemented
188#552×C67—21no—
189D4×Q8×C67C2211yescharacteristic, complemented
190#548×C67—21no—
191#547×C67C2211yescharacteristic
192#544×C67C2211yescharacteristic
193#544×C67C2211yescharacteristic, complemented
194#542×C67—21no—
195#542×C67—21no—
196#540×C67C2211yescharacteristic
197#540×C67C2211yescharacteristic, complemented
198#537×C67—21no—
199#536×C67—21no—
200#533×C67C2211yescharacteristic, complemented
201#532×C67C2211yescharacteristic, complemented
202#529×C67C2211yescharacteristic
203C2×#11761628C2311yescharacteristic
204C2×#11761628C2311yescharacteristic
205C22×D268C2311yescharacteristic
206C2×#11761616C2311yescharacteristic
207C2×#11761616C2311yescharacteristic
208C2×#11761616C2311yescharacteristic
209C2×#11761616C2311yescharacteristic
210C2×#11761613C2311yescharacteristic
211C2×#11761613C2311yescharacteristic
212C2×#11761613C2311yescharacteristic
213C2×#11761613C2311yescharacteristic
214C2×#11761612C2311yescharacteristic
215C2×#11761612C2311yescharacteristic
216C22×C67⋊C8C2311yescharacteristic
217C22×C67⋊C8C2311yescharacteristic
218C22×C67⋊C8C2311yescharacteristic
219C22×C67⋊C8C2311yescharacteristic
220#14524043C2311yescharacteristic
221#14524043C2311yescharacteristic
222#14524038—21no—
223#14524038—21no—
224#14524038—21no—
225#14524038—21no—
226#14524037—21no—
227#14524036—21no—
228#14524036—21no—
229#14524036—21no—
230#14524036—21no—
231#14524036—21no—
232#14524035C2311yescharacteristic
233#14524035C2311yescharacteristic
234#14524033—21no—
235#14524033—21no—
236#14524033—21no—
237#14524031C2311yescharacteristic
238#14524031C2311yescharacteristic
239#14524030—21no—
240#14524029—21no—
241#14524028—21no—
242#14524028—21no—
243#14524026—21no—
244#14524025—21no—
245#14524025—21no—
246#14524025—21no—
247#14524025—21no—
248#14524024—21no—
249#14524022C2311yescharacteristic
250#14524022C2311yescharacteristic
251#14524022C2311yescharacteristic
252#14524022C2311yescharacteristic
253#14524021—21no—
254#14524021—21no—
255#14524021—21no—
256#14524019—21no—
257#14524019—21no—
258#14524017C2311yescharacteristic
259#14524017C2311yescharacteristic
260#14524016—21no—
261#14524016—21no—
262#14524015—21no—
263#14524014—21no—
264#14524011—21no—
265#14524011—21no—
266C4×Dic134C2311yescharacteristic
267C4×Dic134C2311yescharacteristic
268C4×Dic134C2311yescharacteristic
269C4×Dic134C2311yescharacteristic
270#14524008—21no—
271C4×D268C2311yescharacteristic
272C4×D268C2311yescharacteristic
273C4×D268C2311yescharacteristic
274C4×D268C2311yescharacteristic
275C4×D268C2311yescharacteristic
276C4×D268C2311yescharacteristic
277#14524005—21no—
278#14524005—21no—
279C4×C22⋊D67—21no—
280C4×C22⋊D67—21no—
281C4×C22⋊D67—21no—
282(C22⋊D67)⋊C4—21no—
283(C22⋊D67)⋊C4—21no—
284(C22⋊D67)⋊C4—21no—
285#14524002C2311yescharacteristic
286#14524002C2311yescharacteristic
287#14524001—21no—
288#14524001—21no—
289#14524000—21no—
290#14524000—21no—
291#14523999—21no—
292C2×C4⋊Dic67C2311yescharacteristic
293C4⋊C4×D67—21no—
294C4⋊C4×D67—21no—
295C4⋊C4×D67—21no—
296C22⋊C4×D67—21no—
297C22⋊C4×D67—21no—
298C22⋊C4×D67—21no—
299C22⋊C4×D67—21no—
300C42×D67—21no—
301#14523976C2311yescharacteristic
302#14523976C2311yescharacteristic
303#14523976C2311yescharacteristic
304#14523976C2311yescharacteristic
305#14523976C2311yescharacteristic
306#14523976C2311yescharacteristic
307#14523976C2311yescharacteristic
308#14523976C2311yescharacteristic
309#14523976C2311yescharacteristic
310#14523976C2311yescharacteristic
311#14523976C2311yescharacteristic
312#14523976C2311yescharacteristic
313#14523974C2311yescharacteristic
314#14523974C2311yescharacteristic
315#14523974C2311yescharacteristic
316#14523974C2311yescharacteristic
317#14523974C2311yescharacteristic
318#14523974C2311yescharacteristic
319#14523974C2311yescharacteristic
320#14523974C2311yescharacteristic
321#14523974C2311yescharacteristic
322#14523974C2311yescharacteristic
323#14523974C2311yescharacteristic
324#14523974C2311yescharacteristic
325C4⋊(C67⋊C8)C2311yescharacteristic
326C4⋊(C67⋊C8)C2311yescharacteristic
327C4⋊(C67⋊C8)C2311yescharacteristic
328C4⋊(C67⋊C8)C2311yescharacteristic
329C4⋊(C67⋊C8)C2311yescharacteristic
330C4⋊(C67⋊C8)C2311yescharacteristic
331C4⋊(C67⋊C8)C2311yescharacteristic
332C4⋊(C67⋊C8)C2311yescharacteristic
333C4⋊(C67⋊C8)C2311yescharacteristic
334C4⋊(C67⋊C8)C2311yescharacteristic
335#14523966C2311yescharacteristic
336#14523966C2311yescharacteristic
337#14523966C2311yescharacteristic
338#14523966C2311yescharacteristic
339#14523966C2311yescharacteristic
340#14523966C2311yescharacteristic
341#14523966C2311yescharacteristic
342#14523966C2311yescharacteristic
343#14523966C2311yescharacteristic
344#14523966C2311yescharacteristic
345#14523966C2311yescharacteristic
346#14523966C2311yescharacteristic
347#14523964C2311yescharacteristic
348#14523964C2311yescharacteristic
349#14523964C2311yescharacteristic
350#14523964C2311yescharacteristic
351#14523964C2311yescharacteristic
352#14523964C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523964C2311yescharacteristic
355#14523963C2311yescharacteristic
356#14523963C2311yescharacteristic
357#14523963C2311yescharacteristic
358#14523963C2311yescharacteristic
359#14523963C2311yescharacteristic
360#14523963C2311yescharacteristic
361#14523963C2311yescharacteristic
362#14523963C2311yescharacteristic
363#14523963C2311yescharacteristic
364#14523963C2311yescharacteristic
365#14523963C2311yescharacteristic
366#14523963C2311yescharacteristic
367C22⋊(C67⋊C8)C2311yescharacteristic
368C22⋊(C67⋊C8)C2311yescharacteristic
369C22⋊(C67⋊C8)C2311yescharacteristic
370C22⋊(C67⋊C8)C2311yescharacteristic
371C22⋊(C67⋊C8)C2311yescharacteristic
372C22⋊(C67⋊C8)C2311yescharacteristic
373#14523954C2311yescharacteristic
374#14523954C2311yescharacteristic
375#14523954C2311yescharacteristic
376#14523954C2311yescharacteristic
377C4×C67⋊C8C2311yescharacteristic
378C4×C67⋊C8C2311yescharacteristic
379C2×#41×C67—21no—
380C2×#41×C67—21no—
381C22×Q8×C67—21no—
382C4⋊Q8×C67—21no—
383C4⋊Q8×C67—21no—
384C4⋊Q8×C67C2311yescharacteristic
385C4⋊Q8×C67C2311yescharacteristic
386C4⋊Q8×C67C2311yescharacteristic
387C4⋊Q8×C67C2311yescharacteristic
388C4⋊Q8×C67C2311yescharacteristic
389#127×C67C2311yescharacteristic
390#126×C67—21no—
391#126×C67—21no—
392#126×C67D411yescharacteristic
393#126×C67D411yescharacteristic
394#125×C67—21no—
395#125×C67—21no—
396#125×C67D411yescharacteristic
397#125×C67C2311yescharacteristic
398#125×C67C2311yescharacteristic
399#125×C67C2311yescharacteristic
400#125×C67C2311yescharacteristic
401#124×C67—21no—
402#124×C67—21no—
403#124×C67—21no—
404#124×C67—21no—
405#124×C67—21no—
406#124×C67—21no—
407#124×C67—21no—
408#124×C67D411yescharacteristic
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×C67—21no—
425C22⋊Q8×C67—21no—
426C22⋊Q8×C67—21no—
427C22⋊Q8×C67—21no—
428C22⋊Q8×C67—21no—
429C22⋊Q8×C67—21no—
430C22⋊Q8×C67—21no—
431C22⋊Q8×C67—21no—
432C22⋊Q8×C67D411yescharacteristic
433#121×C67—21no—
434#121×C67—21no—
435#121×C67—21no—
436#121×C67—21no—
437#121×C67—21no—
438#121×C67—21no—
439#121×C67—21no—
440#121×C67—21no—
441#121×C67—21no—
442#121×C67—21no—
443#121×C67D411yescharacteristic
444#121×C67C2311yescharacteristic
445#121×C67C2311yescharacteristic
446#121×C67C2311yescharacteristic
447#121×C67C2311yescharacteristic
448#121×C67C2311yescharacteristic
449#121×C67C2311yescharacteristic
450C4×Q8×C67—21no—
451C4×Q8×C67—21no—
452C4×Q8×C67C2311yescharacteristic
453C4×D4×C67—21no—
454C4×D4×C67—21no—
455C4×D4×C67—21no—
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
471#117×C67C2311yescharacteristic
472#117×C67C2311yescharacteristic
473#117×C67C2311yescharacteristic
474C2×C4⋊C4×C67—21no—
475C2×C4⋊C4×C67C2311yescharacteristic
476C2×C4⋊C4×C67C2311yescharacteristic
477C2×C42×C67C2311yescharacteristic
478C23×D67—21no—
479#11761628—22no—
480#11761628—22no—
481#11761628—41no—
482#11761628—41no—
483C2×Dic134—21no—
484C2×Dic134C2411yescharacteristic
485C2×Dic134C2411yescharacteristic
486C2×D268—22no—
487C2×D268—21no—
488C2×D268—41no—
489C2×D268C2411yescharacteristic
490C2×D268C2411yescharacteristic
491C2×C22⋊D67—21no—
492C2×C22⋊D67—21no—
493C2×C22⋊D67—21no—
494C2×C22⋊D67—21no—
495C22×Dic67—21no—
496C2×C4×D67—21no—
497C2×C4×D67—21no—
498C2×C4×D67—21no—
499C2×C4×D67—21no—
500C2×C4×D67—21no—
501C2×C4×D67—21no—
502C2×C4×D67—21no—
503C2×C4×D67—21no—
504#11761616—41no—
505#11761616—41no—
506#11761616—41no—
507#11761616—41no—
508#11761613—22no—
509#11761613—22no—
510#11761613—41no—
511#11761613—41no—
512#11761612—41no—
513#11761612—41no—
514C2×C67⋊C8—41no—
515C2×C67⋊C8—41no—
516C2×C67⋊C8—41no—
517C2×C67⋊C8—41no—
518C2×C67⋊C8C2411yescharacteristic
519C2×C67⋊C8C2411yescharacteristic
520C2×C67⋊C8C2411yescharacteristic
521C2×C67⋊C8C2411yescharacteristic
522C2×C67⋊C8C2411yescharacteristic
523C2×C67⋊C8C2411yescharacteristic
524C2×C67⋊C8C2411yescharacteristic
525C2×C67⋊C8C2411yescharacteristic
526C4⋊Dic67—21no—
527C4⋊Dic67—21no—
528C4⋊Dic67—21no—
529C4⋊Dic67—21no—
530C4⋊Dic67C2411yescharacteristic
531C4⋊Dic67C2411yescharacteristic
532C4⋊Dic67C2411yescharacteristic
533C4⋊Dic67C2411yescharacteristic
534Dic67⋊C4—21no—
535Dic67⋊C4—21no—
536Dic67⋊C4—21no—
537Dic67⋊C4—21no—
538Dic67⋊C4—21no—
539Dic67⋊C4—21no—
540Dic67⋊C4—21no—
541Dic67⋊C4—21no—
542Dic67⋊C4—21no—
543Dic67⋊C4—21no—
544Dic67⋊C4—21no—
545Dic67⋊C4—21no—
546C22⋊Dic67—21no—
547C22⋊Dic67—21no—
548C22⋊Dic67—21no—
549C22⋊Dic67—21no—
550C22⋊Dic67—21no—
551C22⋊Dic67—21no—
552(C2×D67)⋊C4—21no—
553(C2×D67)⋊C4—21no—
554(C2×D67)⋊C4—21no—
555(C2×D67)⋊C4—21no—
556(C2×D67)⋊C4—21no—
557(C2×D67)⋊C4—21no—
558(C2×D67)⋊C4—21no—
559(C2×D67)⋊C4—21no—
560(C2×D67)⋊C4—21no—
561(C2×D67)⋊C4—21no—
562(C2×D67)⋊C4—21no—
563(C2×D67)⋊C4—21no—
564C4×Dic67—21no—
565C4×Dic67—21no—
566C4×Dic67—21no—
567C4×Dic67—21no—
568C4×Dic67—21no—
569C4×Dic67—21no—
570#41×C67—82no—
571#41×C67—82no—
572C2×Q8×C67—21no—
573C2×Q8×C67—21no—
574C2×Q8×C67—21no—
575C2×Q8×C67—21no—
576C2×Q8×C67—21no—
577C2×Q8×C67—82no—
578C2×Q8×C67C2×D411yescharacteristic
579C2×D4×C67—21no—
580C2×D4×C67—21no—
581C2×D4×C67—21no—
582C2×D4×C67—21no—
583C2×D4×C67—21no—
584C2×D4×C67—21no—
585C2×D4×C67—21no—
586C2×D4×C67—21no—
587C2×D4×C67C2×D411yescharacteristic
588C2×D4×C67C2×D411yescharacteristic
589C2×D4×C67C2×D411yescharacteristic
590C2×D4×C67C2411yescharacteristic
591C2×D4×C67C2411yescharacteristic
592C22×C4×C67—21no—
593C22×C4×C67—21no—
594C22×C4×C67—21no—
595C22×C4×C67—21no—
596C22×C4×C67—21no—
597C22×C4×C67—21no—
598C22×C4×C67—21no—
599C22×C4×C67—21no—
600C22×C4×C67C2×D411yescharacteristic
601C22×C4×C67C2×D411yescharacteristic
602C22×C4×C67C2411yescharacteristic
603C22×C4×C67C2411yescharacteristic
604C22×C4×C67C2411yescharacteristic
605C4⋊C4×C67—21no—
606C4⋊C4×C67—21no—
607C4⋊C4×C67—21no—
608C4⋊C4×C67—21no—
609C4⋊C4×C67—21no—
610C4⋊C4×C67—21no—
611C4⋊C4×C67—21no—
612C4⋊C4×C67—21no—
613C4⋊C4×C67—21no—
614C4⋊C4×C67—21no—
615C4⋊C4×C67—21no—
616C4⋊C4×C67—21no—
617C4⋊C4×C67—21no—
618C4⋊C4×C67—21no—
619C4⋊C4×C67—21no—
620C4⋊C4×C67C2×D411yescharacteristic
621C4⋊C4×C67C2×D411yescharacteristic
622C4⋊C4×C67C2×D411yescharacteristic
623C4⋊C4×C67C2×D411yescharacteristic
624C4⋊C4×C67C2×D411yescharacteristic
625C4⋊C4×C67C2×D411yescharacteristic
626C4⋊C4×C67C2×D411yescharacteristic
627C4⋊C4×C67C2×D411yescharacteristic
628C4⋊C4×C67C2×D411yescharacteristic
629C4⋊C4×C67C2×D411yescharacteristic
630C4⋊C4×C67C2411yescharacteristic
631C4⋊C4×C67C2411yescharacteristic
632C4⋊C4×C67C2411yescharacteristic
633C4⋊C4×C67C2411yescharacteristic
634C4⋊C4×C67C2411yescharacteristic
635C4⋊C4×C67C2411yescharacteristic
636C22⋊C4×C67—21no—
637C22⋊C4×C67—21no—
638C22⋊C4×C67—21no—
639C22⋊C4×C67—21no—
640C22⋊C4×C67—21no—
641C22⋊C4×C67—21no—
642C22⋊C4×C67—21no—
643C22⋊C4×C67—21no—
644C22⋊C4×C67—21no—
645C22⋊C4×C67—21no—
646C22⋊C4×C67—21no—
647C22⋊C4×C67—21no—
648C22⋊C4×C67—21no—
649C22⋊C4×C67—21no—
650C22⋊C4×C67—21no—
651C22⋊C4×C67—21no—
652C22⋊C4×C67C2×D411yescharacteristic
653C22⋊C4×C67C2×D411yescharacteristic
654C22⋊C4×C67C2×D411yescharacteristic
655C22⋊C4×C67C2×D411yescharacteristic
656C22⋊C4×C67C2×D411yescharacteristic
657C22⋊C4×C67C2×D411yescharacteristic
658C22⋊C4×C67C2×D411yescharacteristic
659C22⋊C4×C67C2×D411yescharacteristic
660C22⋊C4×C67C2×D411yescharacteristic
661C22⋊C4×C67C2×D411yescharacteristic
662C42×C67—21no—
663C42×C67—21no—
664C42×C67—21no—
665C42×C67—21no—
666C42×C67C2×D411yescharacteristic
667C42×C67C2×D411yescharacteristic
668C42×C67C2411yescharacteristic
669C42×C67C2411yescharacteristic
670C42×C67C2411yescharacteristic
671C42×C67C2411yescharacteristic
672C23×C67—21no—
673C23×C67—21no—
674C23×C67C22×D411yescharacteristic
675C23×C67C22×D411yescharacteristic
676C23×C67C22×D411yescharacteristic
677C22×D67—21no—
678C22×D67—21no—
679C22×D67—42no—
680C22×D67—81no—
681C22×D67—81no—
682Q8×C67—41no—
683Q8×C67—42no—
684Q8×C67—81no—
685Q8×C67—81no—
686Q8×C67—81no—
687Q8×C67—81no—
688D4×C67—21no—
689D4×C67—21no—
690D4×C67—21no—
691D4×C67—21no—
692D4×C67—41no—
693D4×C67—41no—
694D4×C67—41no—
695D4×C67—81no—
696D4×C67—81no—
697D4×C67—81no—
698D4×C67—81no—
699D4×C67—81no—
700D4×C67—81no—
701D4×C67—81no—
702D4×C67—81no—
703C2×C4×C67—21no—
704C2×C4×C67—21no—
705C2×C4×C67—21no—
706C2×C4×C67—21no—
707C2×C4×C67—21no—
708C2×C4×C67—21no—
709C2×C4×C67—21no—
710C2×C4×C67—21no—
711C2×C4×C67—21no—
712C2×C4×C67—21no—
713C2×C4×C67—21no—
714C2×C4×C67—21no—
715C2×C4×C67—41no—
716C2×C4×C67—41no—
717C2×C4×C67—42no—
718C2×C4×C67—42no—
719C2×C4×C67—81no—
720C2×C4×C67—81no—
721C2×C4×C67—81no—
722C2×C4×C67—81no—
723C2×C4×C67—81no—
724C2×C4×C67—81no—
725C2×C4×C67C22×D411yescharacteristic
726C2×C4×C67C22×D411yescharacteristic
727C2×C4×C67C22×D411yescharacteristic
728C2×C4×C67C22×D411yescharacteristic
729C2×C4×C67C22×D411yescharacteristic
730C2×C4×C67C22×D411yescharacteristic
731C2×C4×C67C22×D411yescharacteristic
732C2×C4×C67C22×D411yescharacteristic
733C2×C4×C67C22×D411yescharacteristic
734C2×C4×C67C22×D411yescharacteristic
735C2×C4×C67C22×D411yescharacteristic
736C2×C4×C67C2511yescharacteristic
737C22⋊D67—42no—
738C22⋊D67—42no—
739C22⋊D67—81no—
740C22⋊D67—81no—
741C2×Dic67—21no—
742C2×Dic67—21no—
743C2×Dic67—21no—
744C2×Dic67—21no—
745C2×Dic67—21no—
746C2×Dic67—21no—
747C2×Dic67—81no—
748D268—21no—
749D268—21no—
750D268—21no—
751D268—42no—
752D2682−1+412yes—
753C4×D67—42no—
754C4×D67—42no—
755C4×D67—81no—
756C4×D67—81no—
757C4×D67—81no—
758C4×D67—81no—
759C4×D67—81no—
760C4×D67—81no—
761Dic134—21no—
762Dic134—21no—
763Dic134—21no—
764Dic134—21no—
765Dic134—81no—
766C67⋊C8—21no—
767C67⋊C8—21no—
768C67⋊C8—21no—
769C67⋊C8—21no—
770C67⋊C8—21no—
771C67⋊C8—21no—
772C67⋊C8—21no—
773C67⋊C8—21no—
774C22×C67—21no—
775C22×C67—21no—
776C22×C67—21no—
777C22×C67—21no—
778C22×C67—21no—
779C22×C67—21no—
780C22×C67—21no—
781C22×C67—21no—
782C22×C67—21no—
783C22×C67—41no—
784C22×C67—41no—
785C22×C67—41no—
786C22×C67—41no—
787C22×C67—41no—
788C22×C67—41no—
789C22×C67C23×D411yescharacteristic
790C2×D67—22no—
791C2×D67—41no—
792C2×D67—41no—
793C2×D67—41no—
794C2×D67—41no—
795C2×D67—41no—
796C2×D67—162no—
797C4×C67—21no—
798C4×C67—21no—
799C4×C67—21no—
800C4×C67—21no—
801C4×C67—21no—
802C4×C67—21no—
803C4×C67—21no—
804C4×C67—21no—
805C4×C67—21no—
806C4×C67—21no—
807C4×C67—21no—
808C4×C67—41no—
809C4×C67—41no—
810C4×C67—41no—
811C4×C67—41no—
812C4×C67—41no—
813C4×C67—41no—
814C4×C67C2×2−1+411yescharacteristic
815C4×C67#58511yescharacteristic
816Dic67—41no—
817Dic67—41no—
818Dic67—41no—
819Dic67—41no—
820Dic67—41no—
821Dic67—41no—
822#62171—671nomaximal, Sylow
823C2×C67—41no—
824C2×C67—41no—
825C2×C67—41no—
826C2×C67—81no—
827C2×C67—81no—
828C2×C67#348911yescharacteristic
829C2×C67#358411yescharacteristic
830C2×C67#358511yescharacteristic
831D67—42no—
832D67—81no—
833#3547D6711yescharacteristic, complemented
834#3521—671no—
835#3389—671no—
836#3384—671no—
837#3376—671no—
838#3367—671no—
839#3350—671no—
840#3348—671no—
841#3347—671no—
842#3343—671no—
843#3340—671no—
844#3339—671no—
845#3319—671no—
846#3319—671no—
847#3307—671no—
848#3306—671no—
849#3303—671no—
850#3297—671no—
851#3260—671no—
852#3257—671no—
853#3247—671no—
854#3244—671no—
855#3242—671no—
856#3240—671no—
857#3122—671no—
858#3119—671no—
859#3115—671no—
860#3083—671no—
861#3081—671no—
862#3076—671no—
863#2992—671no—
864C67#6217111yescharacteristic, complemented, Sylow
865#562—21no—
866#562—21no—
867#556—671no—
868#556—671no—
869#555C2×D6711yescharacteristic
870#555C2×D6711yescharacteristic
871#555C2×D6711yescharacteristic, complemented
872#554—671no—
873#554C2×D6711yescharacteristic, complemented
874#553—671no—
875#553—1341no—
876#553C2×D6711yescharacteristic
877#553C2×D6711yescharacteristic, complemented
878#552—21no—
879#552—671no—
880#552—1341no—
881#551—1341no—
882#551—1341no—
883D4×Q8C2×D6711yescharacteristic, complemented
884#548—21no—
885#547—671no—
886#547C2×D6711yescharacteristic
887#546—671no—
888#546—671no—
889#544C2×D6711yescharacteristic
890#544C2×D6711yescharacteristic, complemented
891#542—21no—
892#542—21no—
893#542—671no—
894#541—671no—
895#540C2×D6711yescharacteristic
896#540C2×D6711yescharacteristic, complemented
897#539—1341no—
898#538—1341no—
899#537—21no—
900#536—21no—
901#533C2×D6711yescharacteristic, complemented
902#532C2×D6711yescharacteristic, complemented
903#529—671no—
904#529—1341no—
905#529C2×D6711yescharacteristic
906C2×#126—1341no—
907#520—671no—
908#518—671no—
909C4×#41—671no—
910#501—671no—
911#501—671no—
912#501—671no—
913#501—671no—
914#499—671no—
915#498—671no—
916#491—671no—
917#489—671no—
918#489—671no—
919#489—671no—
920#488—671no—
921#487—671no—
922#485—671no—
923#485—671no—
924#485—671no—
925#485—671no—
926#485—671no—
927#484—671no—
928#483—671no—
929#483—671no—
930#482—671no—
931#482—671no—
932#482—671no—
933#482—671no—
934#482—671no—
935#482—671no—
936#482—671no—
937#481—671no—
938#481—671no—
939#480—671no—
940#479—671no—
941#479—671no—
942#479—671no—
943#479—671no—
944#479—671no—
945#478—671no—
946#478—671no—
947#478—671no—
948#478—671no—
949#478—671no—
950#478—671no—
951#478—671no—
952#478—671no—
953#478—671no—
954#478—671no—
955#478—671no—
956#477—671no—
957#477—671no—
958#477—671no—
959#476—671no—
960#476—671no—
961#476—671no—
962#476—671no—
963#475—671no—
964#475—671no—
965#474—671no—
966#474—671no—
967#474—671no—
968#474—671no—
969#474—671no—
970#469—671no—
971#468—671no—
972#468—671no—
973#468—671no—
974#466—671no—
975#466—671no—
976#466—671no—
977#465—671no—
978#465—671no—
979#465—671no—
980#465—671no—
981#465—671no—
982#463—671no—
983#463—671no—
984#463—671no—
985#463—671no—
986#461—671no—
987#461—671no—
988#460—671no—
989#460—671no—
990#459—671no—
991#459—671no—
992#449—671no—
993#449—671no—
994#449—671no—
995#449—671no—
996#447—671no—
997#447—671no—
998#446—671no—
999#446—671no—
1000#442—671no—
1001#442—671no—
1002#442—671no—
1003#442—671no—
1004#442—671no—
1005#440—671no—
1006#440—671no—
1007#440—671no—
1008C4×SD16—671no—
1009C4×D8—671no—
1010C4×D8—671no—
1011C4×D8—671no—
1012#435—671no—
1013#435—671no—
1014#435—671no—
1015#435—671no—
1016C8×D4—671no—
1017C8×D4—671no—
1018#433—671no—
1019#433—671no—
1020#432—671no—
1021#428—671no—
1022#428—671no—
1023#427—671no—
1024#427—671no—
1025#427—671no—
1026C2×#107—671no—
1027#424—671no—
1028#424—671no—
1029C2×C4⋊C8—671no—
1030#418—671no—
1031#417—671no—
1032#416—671no—
1033#416—671no—
1034#416—671no—
1035C2×#102—671no—
1036C2×#41—21no—
1037C2×#41—21no—
1038C2×#41—671no—
1039C2×#41—671no—
1040C22×Q8—21no—
1041C22×D4—671no—
1042C2×SD16—671no—
1043C2×SD16—671no—
1044C2×SD16—671no—
1045C2×SD16—671no—
1046C2×D8—671no—
1047C2×D8—671no—
1048C2×D8—671no—
1049C2×D8—671no—
1050C2×M16—671no—
1051C2×M16—671no—
1052C22×C8—671no—
1053C22×C8—671no—
1054C22×C8—671no—
1055C22×C8—671no—
1056C4⋊Q8—21no—
1057C4⋊Q8—21no—
1058C4⋊Q8—671no—
1059C4⋊Q8—671no—
1060C4⋊Q8C22×D6711yescharacteristic
1061C4⋊Q8C22×D6711yescharacteristic
1062C4⋊Q8C22×D6711yescharacteristic
1063C4⋊Q8C22×D6711yescharacteristic
1064C4⋊Q8C22×D6711yescharacteristic
1065#127C22×D6711yescharacteristic
1066#126—21no—
1067#126—21no—
1068#126—1341no—
1069#126—1341no—
1070#126—1341no—
1071#126—1341no—
1072#126—1341no—
1073#126—1341no—
1074#126—1341no—
1075#126—1341no—
1076#126—1341no—
1077#126—1341no—
1078#126C22⋊D6711yescharacteristic
1079#126C22⋊D6711yescharacteristic
1080#125—21no—
1081#125—21no—
1082#125—671no—
1083#125—671no—
1084#125—1341no—
1085#125—1341no—
1086#125—1341no—
1087#125C22⋊D6711yescharacteristic
1088#125C22×D6711yescharacteristic
1089#125C22×D6711yescharacteristic
1090#125C22×D6711yescharacteristic
1091#125C22×D6711yescharacteristic
1092#124—21no—
1093#124—21no—
1094#124—21no—
1095#124—21no—
1096#124—21no—
1097#124—21no—
1098#124—21no—
1099#124—671no—
1100#124—671no—
1101#124—1341no—
1102#124—1341no—
1103#124C22⋊D6711yescharacteristic
1104#123—21no—
1105#123—21no—
1106#123—21no—
1107#123—21no—
1108#123—21no—
1109#123—21no—
1110#123—21no—
1111#123—21no—
1112#123—1341no—
1113#123—1341no—
1114#123—1341no—
1115#123—1341no—
1116#123—1341no—
1117#123—1341no—
1118#123—1341no—
1119#123—1341no—
1120#123C22⋊D6711yescharacteristic
1121#123C22⋊D6711yescharacteristic
1122C22⋊Q8—21no—
1123C22⋊Q8—21no—
1124C22⋊Q8—21no—
1125C22⋊Q8—21no—
1126C22⋊Q8—21no—
1127C22⋊Q8—21no—
1128C22⋊Q8—21no—
1129C22⋊Q8—21no—
1130C22⋊Q8—21no—
1131C22⋊Q8—21no—
1132C22⋊Q8—21no—
1133C22⋊Q8—21no—
1134C22⋊Q8—21no—
1135C22⋊Q8—671no—
1136C22⋊Q8—671no—
1137C22⋊Q8—671no—
1138C22⋊Q8—671no—
1139C22⋊Q8—1341no—
1140C22⋊Q8—1341no—
1141C22⋊Q8—1341no—
1142C22⋊Q8—1341no—
1143C22⋊Q8—1341no—
1144C22⋊Q8C22⋊D6711yescharacteristic
1145#121—21no—
1146#121—21no—
1147#121—21no—
1148#121—21no—
1149#121—21no—
1150#121—21no—
1151#121—21no—
1152#121—21no—
1153#121—21no—
1154#121—21no—
1155#121—671no—
1156#121—671no—
1157#121—1341no—
1158#121—1341no—
1159#121—1341no—
1160#121—1341no—
1161#121C22⋊D6711yescharacteristic
1162#121C22×D6711yescharacteristic
1163#121C22×D6711yescharacteristic
1164#121C22×D6711yescharacteristic
1165#121C22×D6711yescharacteristic
1166#121C22×D6711yescharacteristic
1167#121C22×D6711yescharacteristic
1168#120—1341no—
1169#120—1341no—
1170C4×Q8—21no—
1171C4×Q8—21no—
1172C4×Q8—671no—
1173C4×Q8—671no—
1174C4×Q8—671no—
1175C4×Q8—671no—
1176C4×Q8—1341no—
1177C4×Q8C22×D6711yescharacteristic
1178C4×D4—21no—
1179C4×D4—21no—
1180C4×D4—21no—
1181C4×D4—671no—
1182C4×D4—671no—
1183C4×D4—671no—
1184C4×D4—671no—
1185C4×D4—671no—
1186C4×D4—671no—
1187C4×D4—1341no—
1188C4×D4—1341no—
1189C4×D4—1341no—
1190C4×D4—1341no—
1191C4×D4—1341no—
1192C4×D4—1341no—
1193C4×D4—1341no—
1194C4×D4—1341no—
1195C4×D4C22×D6711yescharacteristic
1196C4×D4C22×D6711yescharacteristic
1197C4×D4C22×D6711yescharacteristic
1198C4×D4C22×D6711yescharacteristic
1199C4×D4C22×D6711yescharacteristic
1200C4×D4C22×D6711yescharacteristic
1201C4×D4C22×D6711yescharacteristic
1202C4×D4C22×D6711yescharacteristic
1203C4×D4C22×D6711yescharacteristic
1204#117—21no—
1205#117—21no—
1206#117—21no—
1207#117—671no—
1208#117—671no—
1209#117—1341no—
1210#117—1341no—
1211#117—1341no—
1212#117—1341no—
1213#117—1341no—
1214#117C22×D6711yescharacteristic
1215#117C22×D6711yescharacteristic
1216#117C22×D6711yescharacteristic
1217#117C22×D6711yescharacteristic
1218#117C22×D6711yescharacteristic
1219#117C22×D6711yescharacteristic
1220C2×C4⋊C4—21no—
1221C2×C4⋊C4—671no—
1222C2×C4⋊C4—1341no—
1223C2×C4⋊C4—1341no—
1224C2×C4⋊C4—1341no—
1225C2×C4⋊C4C22×D6711yescharacteristic
1226C2×C4⋊C4C22×D6711yescharacteristic
1227C2×C22⋊C4—1341no—
1228C2×C22⋊C4—1341no—
1229C2×C22⋊C4—1341no—
1230C2×C22⋊C4—1341no—
1231C2×C42—1341no—
1232C2×C42C22×D6711yescharacteristic
1233#107—671no—
1234#107—671no—
1235#107—671no—
1236#107—671no—
1237#107—671no—
1238#107—671no—
1239#107—671no—
1240#107—671no—
1241#107—671no—
1242#107—671no—
1243#107—671no—
1244#107—671no—
1245#106—671no—
1246#106—671no—
1247#106—671no—
1248#106—671no—
1249#106—671no—
1250#106—671no—
1251#106—671no—
1252#106—671no—
1253#106—671no—
1254#106—671no—
1255#106—671no—
1256#106—671no—
1257C4⋊C8—671no—
1258C4⋊C8—671no—
1259C4⋊C8—671no—
1260C4⋊C8—671no—
1261C4⋊C8—671no—
1262C4⋊C8—671no—
1263C4⋊C8—671no—
1264C4⋊C8—671no—
1265C4⋊C8—671no—
1266C4⋊C8—671no—
1267#103—671no—
1268#103—671no—
1269#103—671no—
1270#103—671no—
1271#103—671no—
1272#103—671no—
1273#103—671no—
1274#103—671no—
1275#103—671no—
1276#103—671no—
1277#103—671no—
1278#103—671no—
1279#102—671no—
1280#102—671no—
1281#102—671no—
1282#102—671no—
1283#102—671no—
1284#102—671no—
1285#102—671no—
1286#102—671no—
1287#102—671no—
1288#102—671no—
1289#102—671no—
1290#102—671no—
1291#102—671no—
1292#102—671no—
1293#102—671no—
1294#102—671no—
1295#102—671no—
1296#102—671no—
1297#102—671no—
1298#102—671no—
1299C22⋊C8—671no—
1300C22⋊C8—671no—
1301C22⋊C8—671no—
1302C22⋊C8—671no—
1303C22⋊C8—671no—
1304C22⋊C8—671no—
1305#97—671no—
1306#97—671no—
1307#97—671no—
1308#97—671no—
1309C4×C8—671no—
1310C4×C8—671no—
1311C24—1341no—
1312#41—82no—
1313#41—82no—
1314#41—2681no—
1315#41—2681no—
1316#41—1342no—
1317#41—1342no—
1318C2×Q8—21no—
1319C2×Q8—21no—
1320C2×Q8—21no—
1321C2×Q8—21no—
1322C2×Q8—21no—
1323C2×Q8—82no—
1324C2×Q8—671no—
1325C2×Q8—671no—
1326C2×Q8—1341no—
1327C2×Q8C2×C22⋊D6711yescharacteristic
1328C2×D4—21no—
1329C2×D4—21no—
1330C2×D4—21no—
1331C2×D4—21no—
1332C2×D4—21no—
1333C2×D4—21no—
1334C2×D4—21no—
1335C2×D4—21no—
1336C2×D4—2681no—
1337C2×D4—671no—
1338C2×D4—671no—
1339C2×D4—1342no—
1340C2×D4—1341no—
1341C2×D4—1341no—
1342C2×D4—1341no—
1343C2×D4—1341no—
1344C2×D4—1341no—
1345C2×D4C2×C22⋊D6711yescharacteristic
1346C2×D4C2×C22⋊D6711yescharacteristic
1347C2×D4C2×C22⋊D6711yescharacteristic
1348C2×D4C23×D6711yescharacteristic
1349C2×D4C23×D6711yescharacteristic
1350C22×C4—21no—
1351C22×C4—21no—
1352C22×C4—21no—
1353C22×C4—21no—
1354C22×C4—21no—
1355C22×C4—21no—
1356C22×C4—21no—
1357C22×C4—21no—
1358C22×C4—1341no—
1359C22×C4—1341no—
1360C22×C4—1341no—
1361C22×C4—1341no—
1362C22×C4—1341no—
1363C22×C4—1341no—
1364C22×C4—1341no—
1365C22×C4—1341no—
1366C22×C4—1341no—
1367C22×C4C2×C22⋊D6711yescharacteristic
1368C22×C4C2×C22⋊D6711yescharacteristic
1369C22×C4C23×D6711yescharacteristic
1370C22×C4C23×D6711yescharacteristic
1371C22×C4C23×D6711yescharacteristic
1372SD16—2681no—
1373SD16—2681no—
1374SD16—2681no—
1375SD16—2681no—
1376D8—2681no—
1377D8—2681no—
1378D8—1342no—
1379D8—1342no—
1380M16—2681no—
1381M16—2681no—
1382C2×C8—2681no—
1383C2×C8—2681no—
1384C2×C8—2681no—
1385C2×C8—2681no—
1386C2×C8—671no—
1387C2×C8—671no—
1388C2×C8—671no—
1389C2×C8—671no—
1390C2×C8—671no—
1391C2×C8—671no—
1392C2×C8—671no—
1393C2×C8—671no—
1394C4⋊C4—21no—
1395C4⋊C4—21no—
1396C4⋊C4—21no—
1397C4⋊C4—21no—
1398C4⋊C4—21no—
1399C4⋊C4—21no—
1400C4⋊C4—21no—
1401C4⋊C4—21no—
1402C4⋊C4—21no—
1403C4⋊C4—21no—
1404C4⋊C4—21no—
1405C4⋊C4—21no—
1406C4⋊C4—21no—
1407C4⋊C4—21no—
1408C4⋊C4—21no—
1409C4⋊C4—671no—
1410C4⋊C4—671no—
1411C4⋊C4—671no—
1412C4⋊C4—671no—
1413C4⋊C4—1341no—
1414C4⋊C4—1341no—
1415C4⋊C4—1341no—
1416C4⋊C4—1341no—
1417C4⋊C4—1341no—
1418C4⋊C4—1341no—
1419C4⋊C4—1341no—
1420C4⋊C4—1341no—
1421C4⋊C4—1341no—
1422C4⋊C4—1341no—
1423C4⋊C4—1341no—
1424C4⋊C4—1341no—
1425C4⋊C4—1341no—
1426C4⋊C4—1341no—
1427C4⋊C4—1341no—
1428C4⋊C4—1341no—
1429C4⋊C4C2×C22⋊D6711yescharacteristic
1430C4⋊C4C2×C22⋊D6711yescharacteristic
1431C4⋊C4C2×C22⋊D6711yescharacteristic
1432C4⋊C4C2×C22⋊D6711yescharacteristic
1433C4⋊C4C2×C22⋊D6711yescharacteristic
1434C4⋊C4C2×C22⋊D6711yescharacteristic
1435C4⋊C4C2×C22⋊D6711yescharacteristic
1436C4⋊C4C2×C22⋊D6711yescharacteristic
1437C4⋊C4C2×C22⋊D6711yescharacteristic
1438C4⋊C4C2×C22⋊D6711yescharacteristic
1439C4⋊C4C23×D6711yescharacteristic
1440C4⋊C4C23×D6711yescharacteristic
1441C4⋊C4C23×D6711yescharacteristic
1442C4⋊C4C23×D6711yescharacteristic
1443C4⋊C4C23×D6711yescharacteristic
1444C4⋊C4C23×D6711yescharacteristic
1445C22⋊C4—21no—
1446C22⋊C4—21no—
1447C22⋊C4—21no—
1448C22⋊C4—21no—
1449C22⋊C4—21no—
1450C22⋊C4—21no—
1451C22⋊C4—21no—
1452C22⋊C4—21no—
1453C22⋊C4—21no—
1454C22⋊C4—21no—
1455C22⋊C4—21no—
1456C22⋊C4—21no—
1457C22⋊C4—21no—
1458C22⋊C4—21no—
1459C22⋊C4—21no—
1460C22⋊C4—21no—
1461C22⋊C4—1341no—
1462C22⋊C4—1341no—
1463C22⋊C4—1341no—
1464C22⋊C4—1341no—
1465C22⋊C4—1341no—
1466C22⋊C4—1341no—
1467C22⋊C4—1341no—
1468C22⋊C4—1341no—
1469C22⋊C4—1341no—
1470C22⋊C4—1341no—
1471C22⋊C4—1341no—
1472C22⋊C4—1341no—
1473C22⋊C4—1341no—
1474C22⋊C4—1341no—
1475C22⋊C4—1341no—
1476C22⋊C4—1341no—
1477C22⋊C4—1341no—
1478C22⋊C4—1341no—
1479C22⋊C4C2×C22⋊D6711yescharacteristic
1480C22⋊C4C2×C22⋊D6711yescharacteristic
1481C22⋊C4C2×C22⋊D6711yescharacteristic
1482C22⋊C4C2×C22⋊D6711yescharacteristic
1483C22⋊C4C2×C22⋊D6711yescharacteristic
1484C22⋊C4C2×C22⋊D6711yescharacteristic
1485C22⋊C4C2×C22⋊D6711yescharacteristic
1486C22⋊C4C2×C22⋊D6711yescharacteristic
1487C22⋊C4C2×C22⋊D6711yescharacteristic
1488C22⋊C4C2×C22⋊D6711yescharacteristic
1489C42—21no—
1490C42—21no—
1491C42—21no—
1492C42—21no—
1493C42—1341no—
1494C42—1341no—
1495C42—1341no—
1496C42—1341no—
1497C42—1341no—
1498C42—1341no—
1499C42C2×C22⋊D6711yescharacteristic
1500C42C2×C22⋊D6711yescharacteristic
1501C42C23×D6711yescharacteristic
1502C42C23×D6711yescharacteristic
1503C42C23×D6711yescharacteristic
1504C42C23×D6711yescharacteristic
1505C23—21no—
1506C23—21no—
1507C23—2682no—
1508C23—5361no—
1509C23—5361no—
1510C23—1341no—
1511C23—1341no—
1512C23C22×C22⋊D6711yescharacteristic
1513C23C22×C22⋊D6711yescharacteristic
1514C23C22×C22⋊D6711yescharacteristic
1515Q8—41no—
1516Q8—42no—
1517Q8—81no—
1518Q8—81no—
1519Q8—81no—
1520Q8—81no—
1521Q8—5361no—
1522Q8—1341no—
1523Q8—1341no—
1524Q8—1341no—
1525Q8—1341no—
1526D4—21no—
1527D4—21no—
1528D4—21no—
1529D4—21no—
1530D4—41no—
1531D4—41no—
1532D4—41no—
1533D4—81no—
1534D4—81no—
1535D4—81no—
1536D4—81no—
1537D4—81no—
1538D4—81no—
1539D4—81no—
1540D4—81no—
1541D4—2682no—
1542D4—2682no—
1543D4—2682no—
1544D4—5361no—
1545D4—5361no—
1546D4—672no—
1547D4—1341no—
1548D4—1341no—
1549D4—1341no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—41no—
1563C2×C4—41no—
1564C2×C4—42no—
1565C2×C4—42no—
1566C2×C4—81no—
1567C2×C4—81no—
1568C2×C4—81no—
1569C2×C4—81no—
1570C2×C4—81no—
1571C2×C4—81no—
1572C2×C4—2682no—
1573C2×C4—2682no—
1574C2×C4—5361no—
1575C2×C4—5361no—
1576C2×C4—5361no—
1577C2×C4—5361no—
1578C2×C4—5361no—
1579C2×C4—5361no—
1580C2×C4—5361no—
1581C2×C4—1341no—
1582C2×C4—1341no—
1583C2×C4—1341no—
1584C2×C4—1341no—
1585C2×C4—1341no—
1586C2×C4—1341no—
1587C2×C4C22×C22⋊D6711yescharacteristic
1588C2×C4C22×C22⋊D6711yescharacteristic
1589C2×C4C22×C22⋊D6711yescharacteristic
1590C2×C4C22×C22⋊D6711yescharacteristic
1591C2×C4C22×C22⋊D6711yescharacteristic
1592C2×C4C22×C22⋊D6711yescharacteristic
1593C2×C4C22×C22⋊D6711yescharacteristic
1594C2×C4C22×C22⋊D6711yescharacteristic
1595C2×C4C22×C22⋊D6711yescharacteristic
1596C2×C4C22×C22⋊D6711yescharacteristic
1597C2×C4C22×C22⋊D6711yescharacteristic
1598C2×C4C24×D6711yescharacteristic
1599C8—1341no—
1600C8—1341no—
1601C8—1341no—
1602C8—1341no—
1603C8—1341no—
1604C8—1341no—
1605C8—1341no—
1606C8—1341no—
1607C22—21no—
1608C22—21no—
1609C22—21no—
1610C22—21no—
1611C22—21no—
1612C22—21no—
1613C22—21no—
1614C22—21no—
1615C22—21no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—2681no—
1623C22—2681no—
1624C22—2681no—
1625C22—2681no—
1626C22—2681no—
1627C22—10722no—
1628C22—1342no—
1629C22C23×C22⋊D6711yescharacteristic
1630C4—21no—
1631C4—21no—
1632C4—21no—
1633C4—21no—
1634C4—21no—
1635C4—21no—
1636C4—21no—
1637C4—21no—
1638C4—21no—
1639C4—21no—
1640C4—21no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—2681no—
1648C4—2681no—
1649C4—2681no—
1650C4—2681no—
1651C4—2681no—
1652C4—2681no—
1653C42−1+4×D6711yescharacteristic
1654C4#1686423311yescharacteristic
1655C2—41no—
1656C2—41no—
1657C2—41no—
1658C2—81no—
1659C2—81no—
1660C2—2682no—
1661C2—5361no—
1662C2#2257388211yescharacteristic
1663C2#2257498011yescharacteristic
1664C2#2257498911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3547C2
socleC22×C67C23×D4
hypercenter#3547D67
hypocenterC67#62171
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #529 ◁ #3547

Complements

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

NH ≅ G/Ntype
1. #22574281C2semidirect
2. #22573163C2semidirect
3. #22573104C2semidirect
4. #22573036C2semidirect
5. #22572927C2semidirect
6. #22572748C2semidirect
7. #22572724C2semidirect
8. #22572709C2semidirect
9. #22572643C2semidirect
10. #22572622C2semidirect
11. #22572605C2semidirect
12. #22572359C2semidirect
13. #22572359C2semidirect
14. #22572179C2semidirect
15. #22572164C2semidirect
16. #22572131C2semidirect
17. #22572053C2semidirect
18. #22571655C2semidirect
19. #22571614C2semidirect
20. #22571529C2semidirect
21. #22571507C2semidirect
22. #22571477C2semidirect
23. #22571449C2semidirect
24. #22570447C2semidirect
25. #22570402C2semidirect
26. #22570354C2semidirect
27. #22570056C2semidirect
28. #22570034C2semidirect
29. #22569991C2semidirect
30. #22569348C2semidirect
31. C67×#3547C2semidirect
54. #16863806C22semidirect
55. #16863802C22semidirect
56. #16863802C22semidirect
57. #16863802C22semidirect
58. #16863795C22semidirect
59. #16863792C22semidirect
60. #16863766C22semidirect
65. #16863748C22semidirect
68. #16863737C22semidirect
69. #16863737C22semidirect
70. #16863737C22semidirect
73. #16863726C22semidirect
79. #16863717C22semidirect
80. #16863717C22semidirect
82. #16863712C22semidirect
83. #16863707C22semidirect
84. #16863700C22semidirect
85. #16863700C22semidirect
86. #16863700C22semidirect
87. #16863700C22semidirect
88. #16863700C22semidirect
89. #16863696C22semidirect
90. #16863696C22semidirect
91. #16863696C22semidirect
92. #16863696C22semidirect
100. #16863688C22semidirect
101. #16863688C22semidirect
102. #16863688C22semidirect
103. #16863686C22semidirect
107. #16863678C22semidirect
108. #16863678C22semidirect
109. #16863676C22semidirect
117. #16863640C22semidirect
123. #16863623C22semidirect
124. #16863623C22semidirect
125. #16863623C22semidirect
130. #16863601C22semidirect
131. #16863601C22semidirect
132. #16863593C22semidirect
133. #16863593C22semidirect
142. #16863527C22semidirect
143. #16863527C22semidirect
149. #16863496C22semidirect
150. #16863496C22semidirect
151. #16863496C22semidirect
152. C4×#11761616C22semidirect
159. #16863468C22semidirect
161. D4×C67⋊C8C22semidirect
163. #16863457C22semidirect
164. #16863453C22semidirect
165. #16863439C22semidirect
168. #16863432C22semidirect
169. #16863432C22semidirect
170. C2×#14523976C22semidirect
172. #16863423C22semidirect
173. C2×C4⋊(C67⋊C8)C22semidirect
184. #555×C67C22semidirect
185. #554×C67C22semidirect
187. #553×C67C22semidirect
189. D4×Q8×C67C22semidirect
193. #544×C67C22semidirect
197. #540×C67C22semidirect
200. #533×C67C22semidirect
201. #532×C67C22semidirect
833. #3547D67semidirect
864. C67#62171semidirect
871. #555C2×D67semidirect
873. #554C2×D67semidirect
877. #553C2×D67semidirect
883. D4×Q8C2×D67semidirect
890. #544C2×D67semidirect
896. #540C2×D67semidirect
901. #533C2×D67semidirect
902. #532C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225742812
#225731632
#225731042
#225730362
#225729272
#225727482
#225727242
#225727092
#225726432
#225726222
#225726052
#225723592
#225721792
#225721642
#225721312
#225720532
#225716552
#225716142
#225715292
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