Finite Group Databasebeta

← #31738237

Subgroups — #31738237

Order 17152.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574198C211yesmaximal, characteristic, complemented
2#22573201C211yesmaximal, characteristic, complemented
3#22573084C211yesmaximal, characteristic, complemented
4#22573036C211yesmaximal, characteristic, complemented
5#22572971C211yesmaximal, characteristic, complemented
6#22572588C211yesmaximal, characteristic, complemented
7#22572582C211yesmaximal, characteristic, complemented
8#22572566C211yesmaximal, characteristic, complemented
9#22572456C211yesmaximal, characteristic, complemented
10#22572425C211yesmaximal, characteristic, complemented
11#22572350C211yesmaximal, characteristic, complemented
12#22572290C211yesmaximal, characteristic, complemented
13#22572254C211yesmaximal, characteristic, complemented
14#22572194C211yesmaximal, characteristic, complemented
15#22571912C211yesmaximal, characteristic, complemented
16#22571912C211yesmaximal, characteristic, complemented
17D4×#11761616C211yesmaximal, characteristic, complemented
18#22570831C211yesmaximal, characteristic, complemented
19#22570820C211yesmaximal, characteristic, complemented
20#22570773C211yesmaximal, characteristic, complemented
21#22570432C211yesmaximal, characteristic, complemented
22#22570423C211yesmaximal, characteristic, complemented
23#22570402C211yesmaximal, characteristic, complemented
24#22570393C211yesmaximal, characteristic, complemented
25#22570376C211yesmaximal, characteristic, complemented
26#22570347C211yesmaximal, characteristic, complemented
27#22569185C211yesmaximal, characteristic, complemented
28#22569090C211yesmaximal, characteristic, complemented
29#22569066C211yesmaximal, characteristic, complemented
30C2×C4×#11761616C211yesmaximal, characteristic, complemented
31C67×#3513C211yesmaximal, characteristic, complemented
32C2×#14524063C2211yescharacteristic
33C22×#11761616C2211yescharacteristic
34C22×#11761616C2211yescharacteristic
35#16864124C2211yescharacteristic, complemented
36#16864119C2211yescharacteristic, complemented
37#16864113—21no—
38#16864103C2211yescharacteristic, complemented
39#16864100—21no—
40#16864092C2211yescharacteristic
41#16864089—21no—
42#16864086C2211yescharacteristic, complemented
43#16864082—21no—
44D4×Dic134C2211yescharacteristic
45#16864055C2211yescharacteristic, complemented
46#16864055C2211yescharacteristic, complemented
47#16864017C2211yescharacteristic, complemented
48#16864010—21no—
49#16864008C2211yescharacteristic, complemented
50#16864005—21no—
51#16863930C2211yescharacteristic, complemented
52#16863923—21no—
53#16863923—21no—
54#16863876C2211yescharacteristic, complemented
55#16863873C2211yescharacteristic, complemented
56C2×C4×Dic134C2211yescharacteristic, complemented
57#16863795C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863792C2211yescharacteristic, complemented
60#16863778C2211yescharacteristic, complemented
61#16863778C2211yescharacteristic, complemented
62#16863768C2211yescharacteristic
63#16863766C2211yescharacteristic, 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#16863726C2211yescharacteristic, complemented
74#16863726C2211yescharacteristic, complemented
75#16863720C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic
77#16863712C2211yescharacteristic
78#16863712C2211yescharacteristic, complemented
79#16863709C2211yescharacteristic, complemented
80#16863707C2211yescharacteristic, complemented
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#16863678C2211yescharacteristic, complemented
92#16863676C2211yescharacteristic
93#16863652C2211yescharacteristic, complemented
94#16863647C2211yescharacteristic
95#16863640C2211yescharacteristic, complemented
96#16863640C2211yescharacteristic, complemented
97#16863635C2211yescharacteristic, complemented
98#16863630C2211yescharacteristic
99#16863627C2211yescharacteristic, complemented
100#16863627C2211yescharacteristic, complemented
101#16863623C2211yescharacteristic
102#16863623C2211yescharacteristic
103#16863623C2211yescharacteristic, complemented
104#16863623C2211yescharacteristic, complemented
105#16863615C2211yescharacteristic, complemented
106#16863615C2211yescharacteristic, complemented
107#16863615C2211yescharacteristic, complemented
108#16863615C2211yescharacteristic, complemented
109#16863611C2211yescharacteristic
110#16863611C2211yescharacteristic
111#16863611C2211yescharacteristic, complemented
112#16863611C2211yescharacteristic, complemented
113#16863606C2211yescharacteristic, complemented
114#16863601C2211yescharacteristic
115#16863593C2211yescharacteristic
116#16863588C2211yescharacteristic
117#16863558C2211yescharacteristic
118#16863558C2211yescharacteristic
119#16863551C2211yescharacteristic, complemented
120#16863551C2211yescharacteristic, complemented
121#16863547C2211yescharacteristic
122#16863547C2211yescharacteristic
123#16863539C2211yescharacteristic, complemented
124#16863539C2211yescharacteristic, complemented
125#16863534C2211yescharacteristic
126#16863534C2211yescharacteristic
127#16863530C2211yescharacteristic
128#16863530C2211yescharacteristic
129#16863527C2211yescharacteristic, complemented
130Q8×C67⋊C8C2211yescharacteristic, complemented
131#16863506C2211yescharacteristic
132#16863506C2211yescharacteristic
133#16863506C2211yescharacteristic, complemented
134#16863501C2211yescharacteristic, complemented
135#16863501C2211yescharacteristic, complemented
136#16863501C2211yescharacteristic, complemented
137#16863496C2211yescharacteristic
138#16863496C2211yescharacteristic
139#16863496C2211yescharacteristic, complemented
140#16863496C2211yescharacteristic, complemented
141#16863496C2211yescharacteristic, complemented
142#16863496C2211yescharacteristic, complemented
143C4×#11761618C2211yescharacteristic, complemented
144C4×#11761615C2211yescharacteristic, complemented
145C4×#11761615C2211yescharacteristic, complemented
146C4×#11761616C2211yescharacteristic
147C4×#11761616C2211yescharacteristic
148C4×#11761616C2211yescharacteristic
149C4×#11761616C2211yescharacteristic
150C4×#11761616C2211yescharacteristic
151C4×#11761616C2211yescharacteristic
152C4×#11761616C2211yescharacteristic, complemented
153C4×#11761616C2211yescharacteristic, complemented
154C4×#11761616C2211yescharacteristic, complemented
155C4×#11761616C2211yescharacteristic, complemented
156C4×#11761616C2211yescharacteristic, complemented
157C4×#11761616C2211yescharacteristic, complemented
158C4×#11761613C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic, complemented
160#16863468C2211yescharacteristic
161#16863468C2211yescharacteristic, complemented
162D4×C67⋊C8C2211yescharacteristic
163D4×C67⋊C8C2211yescharacteristic, complemented
164D4×C67⋊C8C2211yescharacteristic, complemented
165#16863457C2211yescharacteristic, complemented
166#16863457C2211yescharacteristic, complemented
167#16863453C2211yescharacteristic, complemented
168#16863432C2211yescharacteristic, complemented
169C2×#14523974C2211yescharacteristic, complemented
170C2×#14523974C2211yescharacteristic, complemented
171#16863404C2211yescharacteristic, complemented
172#16863401C2211yescharacteristic
173#16863397C2211yescharacteristic
174#16863395C2211yescharacteristic, complemented
175C2×#14523966C2211yescharacteristic, complemented
176C2×#14523964C2211yescharacteristic
177#16863352C2211yescharacteristic, complemented
178#16863352C2211yescharacteristic, complemented
179C2×C4×C67⋊C8C2211yescharacteristic, 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
204C22×Dic134C2311yescharacteristic
205C22×Dic134C2311yescharacteristic
206#14524063—24no—
207C2×#11761618C2311yescharacteristic
208C2×#11761618C2311yescharacteristic
209C2×#11761618C2311yescharacteristic
210C2×#11761616—24no—
211C2×#11761616—24no—
212C2×#11761616C2311yescharacteristic
213C2×#11761616C2311yescharacteristic
214C2×#11761616C2311yescharacteristic
215C2×#11761616C2311yescharacteristic
216C2×#11761616C2311yescharacteristic
217C2×#11761616C2311yescharacteristic
218C2×#11761616C2311yescharacteristic
219C2×#11761616C2311yescharacteristic
220C2×#11761616C2311yescharacteristic
221C2×#11761615C2311yescharacteristic
222C2×#11761613C2311yescharacteristic
223C2×#11761613C2311yescharacteristic
224C2×#11761613C2311yescharacteristic
225C2×#11761612C2311yescharacteristic
226C2×#11761612C2311yescharacteristic
227C22×C67⋊C8C2311yescharacteristic
228C22×C67⋊C8C2311yescharacteristic
229C22×C67⋊C8C2311yescharacteristic
230C22×C67⋊C8C2311yescharacteristic
231#14524043C2311yescharacteristic
232#14524043C2311yescharacteristic
233#14524042—21no—
234#14524041—21no—
235#14524038—21no—
236#14524038—21no—
237#14524038—21no—
238#14524038—21no—
239#14524037—21no—
240#14524036—21no—
241#14524036—21no—
242#14524036—21no—
243#14524035C2311yescharacteristic
244#14524035C2311yescharacteristic
245#14524034—21no—
246#14524033—21no—
247#14524033—21no—
248#14524033—21no—
249#14524033—21no—
250#14524033—21no—
251#14524031C2311yescharacteristic
252#14524031C2311yescharacteristic
253#14524029—21no—
254#14524029—21no—
255#14524029—21no—
256#14524026—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#14524020—21no—
268#14524020—21no—
269#14524020—21no—
270#14524020—21no—
271#14524019—21no—
272#14524017C2311yescharacteristic
273#14524017C2311yescharacteristic
274#14524015—21no—
275#14524015—21no—
276#14524015—21no—
277C4×Dic134—21no—
278C4×Dic134—21no—
279C4×Dic134C2311yescharacteristic
280C4×Dic134C2311yescharacteristic
281C4×Dic134C2311yescharacteristic
282C4×Dic134C2311yescharacteristic
283C4×Dic134C2311yescharacteristic
284C4×Dic134C2311yescharacteristic
285C4×Dic134C2311yescharacteristic
286C4×Dic134C2311yescharacteristic
287#14524008—21no—
288#14524008—21no—
289#14524008—21no—
290C4×D268C2311yescharacteristic
291C4×D268C2311yescharacteristic
292D4×Dic67—21no—
293D4×Dic67—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#14524001—21no—
302#14524001—21no—
303#14524000—21no—
304#14523999—21no—
305#14523999—21no—
306#14523999—21no—
307C2×C4⋊Dic67C2311yescharacteristic
308C2×C4⋊Dic67C2311yescharacteristic
309C2×Dic67⋊C4—21no—
310C4⋊C4×D67—21no—
311C2×C4×Dic67—21no—
312#14523976C2311yescharacteristic
313#14523976C2311yescharacteristic
314#14523976C2311yescharacteristic
315#14523976C2311yescharacteristic
316#14523976C2311yescharacteristic
317#14523976C2311yescharacteristic
318#14523974C2311yescharacteristic
319#14523974C2311yescharacteristic
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#14523966C2311yescharacteristic
347#14523966C2311yescharacteristic
348#14523966C2311yescharacteristic
349#14523966C2311yescharacteristic
350#14523964C2311yescharacteristic
351#14523964C2311yescharacteristic
352#14523964C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523964C2311yescharacteristic
355#14523964C2311yescharacteristic
356#14523964C2311yescharacteristic
357#14523964C2311yescharacteristic
358#14523964C2311yescharacteristic
359#14523964C2311yescharacteristic
360#14523964C2311yescharacteristic
361#14523964C2311yescharacteristic
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—41no—
483C2×Dic134—22no—
484C2×Dic134—22no—
485C2×Dic134—21no—
486C2×Dic134—21no—
487C2×Dic134—21no—
488C2×Dic134—41no—
489C2×Dic134—41no—
490C2×Dic134C2411yescharacteristic
491C2×Dic134C2411yescharacteristic
492C2×Dic134C2411yescharacteristic
493C2×D268C2411yescharacteristic
494C2×C22⋊D67—21no—
495C2×C22⋊D67—21no—
496C2×C22⋊D67—21no—
497C22×Dic67—21no—
498C22×Dic67—21no—
499C22×Dic67—21no—
500C22×Dic67—21no—
501C2×C4×D67—21no—
502C2×C4×D67—21no—
503C2×C4×D67—21no—
504#11761618—22no—
505#11761618—41no—
506#11761618—41no—
507#11761616—22no—
508#11761616—22no—
509#11761616—22no—
510#11761616—22no—
511#11761616—22no—
512#11761616—22no—
513#11761616—41no—
514#11761616—41no—
515#11761616#4114yescomplemented
516#11761615—22no—
517#11761613—22no—
518#11761613—41no—
519#11761613—41no—
520#11761612—41no—
521#11761612—41no—
522C2×C67⋊C8—22no—
523C2×C67⋊C8—22no—
524C2×C67⋊C8—22no—
525C2×C67⋊C8—41no—
526C2×C67⋊C8C2411yescharacteristic
527C2×C67⋊C8C2411yescharacteristic
528C2×C67⋊C8C2411yescharacteristic
529C2×C67⋊C8C2411yescharacteristic
530C2×C67⋊C8C2411yescharacteristic
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C2×C67⋊C8C2411yescharacteristic
534C4⋊Dic67—21no—
535C4⋊Dic67—21no—
536C4⋊Dic67—21no—
537C4⋊Dic67—21no—
538C4⋊Dic67—21no—
539C4⋊Dic67C2411yescharacteristic
540C4⋊Dic67C2411yescharacteristic
541C4⋊Dic67C2411yescharacteristic
542C4⋊Dic67C2411yescharacteristic
543Dic67⋊C4—21no—
544Dic67⋊C4—21no—
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—
557Dic67⋊C4—21no—
558Dic67⋊C4—21no—
559C22⋊Dic67—21no—
560C22⋊Dic67—21no—
561C22⋊Dic67—21no—
562C22⋊Dic67—21no—
563C22⋊Dic67—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—
572C4×Dic67—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—
702Q8×C67—21no—
703Q8×C67—21no—
704Q8×C67—41no—
705Q8×C67—81no—
706D4×C67—22no—
707D4×C67—22no—
708D4×C67—21no—
709D4×C67—21no—
710D4×C67—21no—
711D4×C67—21no—
712D4×C67—21no—
713D4×C67—41no—
714D4×C67—42no—
715D4×C67—42no—
716D4×C67—42no—
717D4×C67—42no—
718D4×C67—81no—
719D4×C67—81no—
720D4×C67—81no—
721D4×C67—81no—
722D4×C67—81no—
723D4×C67C2×#4112yes—
724C2×C4×C67—22no—
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—42no—
738C2×C4×C67—42no—
739C2×C4×C67—81no—
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×C67C22×D411yescharacteristic
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×C67C2511yescharacteristic
760C22⋊D67—42no—
761C22⋊D67—42no—
762C22⋊D67—81no—
763C2×Dic67—21no—
764C2×Dic67—21no—
765C2×Dic67—21no—
766C2×Dic67—21no—
767C2×Dic67—21no—
768C2×Dic67—21no—
769C2×Dic67—21no—
770C2×Dic67—42no—
771C2×Dic67—42no—
772C2×Dic67—81no—
773C2×Dic67—81no—
774D268—21no—
775D268—21no—
776C4×D67—42no—
777C4×D67—81no—
778C4×D67—81no—
779Dic134—21no—
780Dic134—21no—
781Dic134—21no—
782Dic134—21no—
783Dic134—21no—
784Dic134—42no—
785Dic134—42no—
786Dic134—81no—
787Dic134C2×#4112yes—
788C67⋊C8—21no—
789C67⋊C8—21no—
790C67⋊C8—21no—
791C67⋊C8—21no—
792C67⋊C8—21no—
793C67⋊C8—21no—
794C67⋊C8—21no—
795C67⋊C8C2×#4112yes—
796C22×C67—21no—
797C22×C67—21no—
798C22×C67—21no—
799C22×C67—21no—
800C22×C67—21no—
801C22×C67—21no—
802C22×C67—22no—
803C22×C67—21no—
804C22×C67—21no—
805C22×C67—41no—
806C22×C67—41no—
807C22×C67—41no—
808C22×C67—41no—
809C22×C67—41no—
810C22×C67—41no—
811C22×C67—41no—
812C22×C67—41no—
813C22×C67—84no—
814C22×C67—162no—
815C22×C67#57712yes—
816C22×C67C23×D411yescharacteristic
817C2×D67—41no—
818C2×D67—41no—
819C2×D67—41no—
820C4×C67—21no—
821C4×C67—21no—
822C4×C67—21no—
823C4×C67—21no—
824C4×C67—21no—
825C4×C67—21no—
826C4×C67—21no—
827C4×C67—21no—
828C4×C67—21no—
829C4×C67—21no—
830C4×C67—21no—
831C4×C67—41no—
832C4×C67—41no—
833C4×C67—41no—
834C4×C67—41no—
835C4×C67—41no—
836C4×C67C22×#4111yescharacteristic
837C4×C67#58511yescharacteristic
838Dic67—22no—
839Dic67—41no—
840Dic67—41no—
841Dic67—41no—
842Dic67—41no—
843Dic67—41no—
844Dic67—41no—
845#61472—671nomaximal, Sylow
846C2×C67—22no—
847C2×C67—41no—
848C2×C67—41no—
849C2×C67—42no—
850C2×C67—81no—
851C2×C67—81no—
852C2×C67D4×#4111yescharacteristic
853C2×C67C2×#57711yescharacteristic
854C2×C67#358411yescharacteristic
855D67—81no—
856#3516—671no—
857#3513D6711yescharacteristic, complemented
858#3394—671no—
859#3381—671no—
860#3376—671no—
861#3371—671no—
862#3337—671no—
863#3337—671no—
864#3335—671no—
865#3326—671no—
866#3323—671no—
867#3318—671no—
868#3314—671no—
869#3312—671no—
870#3308—671no—
871#3282—671no—
872#3282—671no—
873D4×SD16—671no—
874#3174—671no—
875#3173—671no—
876#3168—671no—
877#3121—671no—
878#3120—671no—
879#3119—671no—
880#3118—671no—
881#3117—671no—
882#3114—671no—
883#2966—671no—
884#2952—671no—
885#2949—671no—
886C2×C4×SD16—671no—
887C67#6147211yescharacteristic, complemented, Sylow
888C2×#135—671no—
889C22×SD16—671no—
890C22×SD16—671no—
891#559C2×D6711yescharacteristic
892#557—671no—
893#556—671no—
894#556—1341no—
895#554—671no—
896#554—1341no—
897#554C2×D6711yescharacteristic
898#553—21no—
899#553—671no—
900#553—1341no—
901#553C2×D6711yescharacteristic
902#552—671no—
903#552—1341no—
904#552C2×D6711yescharacteristic
905#551—21no—
906#551—21no—
907D4×Q8—671no—
908#548—671no—
909#548—671no—
910#547C2×D6711yescharacteristic
911#546—21no—
912#546C2×D6711yescharacteristic
913#546C2×D6711yescharacteristic
914D42C2×D6711yescharacteristic
915#542—671no—
916#542—1341no—
917#542C2×D6711yescharacteristic
918#541—671no—
919#541—1341no—
920#540C2×D6711yescharacteristic
921#539—21no—
922#538—21no—
923#529—671no—
924#529—1341no—
925#529—1341no—
926#529C2×D6711yescharacteristic
927#529C2×D6711yescharacteristic
928#525—21no—
929C2×#123—21no—
930#520—671no—
931#520C2×D6711yescharacteristic
932#519—671no—
933#518C2×D6711yescharacteristic
934C2×C4×Q8—671no—
935C2×C4×D4C2×D6711yescharacteristic
936#499—671no—
937#499—671no—
938#498—671no—
939#495—671no—
940#495—671no—
941#492—671no—
942#491—671no—
943#490—671no—
944#489—671no—
945#489—671no—
946#488—671no—
947#488—671no—
948#485—671no—
949#485—671no—
950#484—671no—
951#484—671no—
952#483—671no—
953#483—671no—
954#482—671no—
955#482—671no—
956#481—671no—
957#481—671no—
958#480—671no—
959#480—671no—
960#479—671no—
961#479—671no—
962#479—671no—
963#479—671no—
964#478—671no—
965#478—671no—
966#478—671no—
967#478—671no—
968#477—671no—
969#476—671no—
970#475—671no—
971#474—671no—
972#470—671no—
973#469—671no—
974#468—671no—
975#468—671no—
976#467—671no—
977#466—671no—
978#465—671no—
979#465—671no—
980#465—671no—
981#465—671no—
982#465—671no—
983#465—671no—
984#464—671no—
985#464—671no—
986#464—671no—
987#464—671no—
988#463—671no—
989#463—671no—
990#463—671no—
991#463—671no—
992#462—671no—
993#461—671no—
994#460—671no—
995#459—671no—
996#452—671no—
997#452—671no—
998#451—671no—
999#451—671no—
1000#450—671no—
1001#450—671no—
1002#449—671no—
1003#449—671no—
1004#448—671no—
1005#448—671no—
1006#447—671no—
1007#447—671no—
1008#446—671no—
1009C8×Q8—671no—
1010#442—671no—
1011#442—671no—
1012#442—671no—
1013#441—671no—
1014#441—671no—
1015#441—671no—
1016#440—671no—
1017#440—671no—
1018#440—671no—
1019#440—671no—
1020#440—671no—
1021#440—671no—
1022C4×Q16—671no—
1023C4×SD16—671no—
1024C4×SD16—671no—
1025C4×SD16—671no—
1026C4×SD16—671no—
1027C4×SD16—671no—
1028C4×SD16—671no—
1029C4×SD16—671no—
1030C4×SD16—671no—
1031C4×SD16—671no—
1032C4×SD16—671no—
1033C4×SD16—671no—
1034C4×SD16—671no—
1035C4×SD16—671no—
1036C4×SD16—671no—
1037C4×D8—671no—
1038#436—671no—
1039#435—671no—
1040#435—671no—
1041C8×D4—671no—
1042C8×D4—671no—
1043C8×D4—671no—
1044#433—671no—
1045#433—671no—
1046#432—671no—
1047#427—671no—
1048C2×#106—671no—
1049C2×#106—671no—
1050#419—671no—
1051#418—671no—
1052#417—671no—
1053#417—671no—
1054C2×#103—671no—
1055C2×#102—671no—
1056#405—671no—
1057#405—671no—
1058C2×C4×C8—671no—
1059C2×#41—21no—
1060C2×#41—671no—
1061C2×#41C22×D6711yescharacteristic
1062C22×Q8—671no—
1063C22×Q8—671no—
1064C22×D4—21no—
1065C22×D4C22×D6711yescharacteristic
1066C22×D4C22×D6711yescharacteristic
1067C23×C4—21no—
1068#135—1344no—
1069C2×Q16—671no—
1070C2×Q16—671no—
1071C2×Q16—671no—
1072C2×SD16—671no—
1073C2×SD16—671no—
1074C2×SD16—671no—
1075C2×SD16—671no—
1076C2×SD16—671no—
1077C2×SD16—671no—
1078C2×SD16—671no—
1079C2×SD16—671no—
1080C2×SD16—671no—
1081C2×SD16—671no—
1082C2×SD16—1344no—
1083C2×SD16—1344no—
1084C2×D8—671no—
1085C2×D8—671no—
1086C2×D8—671no—
1087C2×M16—671no—
1088C2×M16—671no—
1089C22×C8—671no—
1090C22×C8—671no—
1091C22×C8—671no—
1092C22×C8—671no—
1093C4⋊Q8—671no—
1094C4⋊Q8—671no—
1095C4⋊Q8—1341no—
1096C4⋊Q8—1341no—
1097C4⋊Q8C22×D6711yescharacteristic
1098#127C22×D6711yescharacteristic
1099#126—21no—
1100#126—21no—
1101#126—21no—
1102#126—21no—
1103#126—1341no—
1104#126—1341no—
1105#126—1341no—
1106#126—1341no—
1107#126—1341no—
1108#126—1341no—
1109#126—1341no—
1110#126—1341no—
1111#126C22⋊D6711yescharacteristic
1112#126C22⋊D6711yescharacteristic
1113#125—21no—
1114#125—671no—
1115#125—671no—
1116#125—1341no—
1117#125—1341no—
1118#125—1341no—
1119#125—1341no—
1120#125—1341no—
1121#125—1341no—
1122#125C22⋊D6711yescharacteristic
1123#125C22×D6711yescharacteristic
1124#125C22×D6711yescharacteristic
1125#124—21no—
1126#124—21no—
1127#124—671no—
1128#124—671no—
1129#124—1341no—
1130#124—1341no—
1131#124—1341no—
1132#124C22⋊D6711yescharacteristic
1133#124C22×D6711yescharacteristic
1134#124C22×D6711yescharacteristic
1135#123—21no—
1136#123—21no—
1137#123—21no—
1138#123—21no—
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—1341no—
1148#123—1341no—
1149#123—1341no—
1150#123—1341no—
1151#123C22⋊D6711yescharacteristic
1152#123C22⋊D6711yescharacteristic
1153C22⋊Q8—21no—
1154C22⋊Q8—21no—
1155C22⋊Q8—21no—
1156C22⋊Q8—21no—
1157C22⋊Q8—21no—
1158C22⋊Q8—671no—
1159C22⋊Q8—671no—
1160C22⋊Q8—671no—
1161C22⋊Q8—671no—
1162C22⋊Q8—1341no—
1163C22⋊Q8—1341no—
1164C22⋊Q8—1341no—
1165C22⋊Q8—1341no—
1166C22⋊Q8—1341no—
1167C22⋊Q8—1341no—
1168C22⋊Q8—1341no—
1169C22⋊Q8—1341no—
1170C22⋊Q8C22⋊D6711yescharacteristic
1171C22⋊Q8C22×D6711yescharacteristic
1172C22⋊Q8C22×D6711yescharacteristic
1173#121—21no—
1174#121—21no—
1175#121—21no—
1176#121—21no—
1177#121—21no—
1178#121—21no—
1179#121—671no—
1180#121—671no—
1181#121—1341no—
1182#121—1341no—
1183#121—1341no—
1184#121C22⋊D6711yescharacteristic
1185#121C22×D6711yescharacteristic
1186#121C22×D6711yescharacteristic
1187#121C22×D6711yescharacteristic
1188#121C22×D6711yescharacteristic
1189#120—21no—
1190#120—21no—
1191#120—21no—
1192#120—21no—
1193C4×Q8—671no—
1194C4×Q8—671no—
1195C4×Q8—671no—
1196C4×Q8—671no—
1197C4×Q8—671no—
1198C4×Q8—671no—
1199C4×Q8—671no—
1200C4×Q8—671no—
1201C4×Q8—1341no—
1202C4×Q8—1341no—
1203C4×Q8—1341no—
1204C4×Q8—1341no—
1205C4×Q8—1341no—
1206C4×Q8C22×D6711yescharacteristic
1207C4×Q8C22×D6711yescharacteristic
1208C4×Q8C22×D6711yescharacteristic
1209C4×D4—21no—
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—671no—
1219C4×D4—671no—
1220C4×D4—1341no—
1221C4×D4—1341no—
1222C4×D4—1341no—
1223C4×D4—1341no—
1224C4×D4—1341no—
1225C4×D4—1341no—
1226C4×D4—1341no—
1227C4×D4—1341no—
1228C4×D4C22×D6711yescharacteristic
1229C4×D4C22×D6711yescharacteristic
1230C4×D4C22×D6711yescharacteristic
1231C4×D4C22×D6711yescharacteristic
1232C4×D4C22×D6711yescharacteristic
1233C4×D4C22×D6711yescharacteristic
1234C4×D4C22×D6711yescharacteristic
1235C4×D4C22×D6711yescharacteristic
1236C4×D4C22×D6711yescharacteristic
1237C4×D4C22×D6711yescharacteristic
1238C4×D4C22×D6711yescharacteristic
1239#117—21no—
1240#117—21no—
1241#117—21no—
1242#117—671no—
1243#117—1341no—
1244#117—1341no—
1245#117—1341no—
1246#117—1341no—
1247#117—1341no—
1248#117—1341no—
1249#117C22×D6711yescharacteristic
1250#117C22×D6711yescharacteristic
1251#117C22×D6711yescharacteristic
1252C2×C4⋊C4—21no—
1253C2×C4⋊C4—21no—
1254C2×C4⋊C4—671no—
1255C2×C4⋊C4—671no—
1256C2×C4⋊C4—1341no—
1257C2×C4⋊C4—1341no—
1258C2×C4⋊C4C22×D6711yescharacteristic
1259C2×C4⋊C4C22×D6711yescharacteristic
1260C2×C22⋊C4—21no—
1261C2×C22⋊C4—21no—
1262C2×C22⋊C4—21no—
1263C2×C22⋊C4—21no—
1264C2×C22⋊C4—21no—
1265C2×C42—1341no—
1266C2×C42C22×D6711yescharacteristic
1267#107—671no—
1268#107—671no—
1269#107—671no—
1270#107—671no—
1271#107—671no—
1272#107—671no—
1273#106—671no—
1274#106—671no—
1275#106—671no—
1276#106—671no—
1277#106—671no—
1278#106—671no—
1279#106—671no—
1280#106—671no—
1281#106—671no—
1282#106—671no—
1283C4⋊C8—671no—
1284C4⋊C8—671no—
1285C4⋊C8—671no—
1286C4⋊C8—671no—
1287C4⋊C8—671no—
1288C4⋊C8—671no—
1289#103—671no—
1290#103—671no—
1291#103—671no—
1292#103—671no—
1293#103—671no—
1294#103—671no—
1295#103—671no—
1296#103—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#102—671no—
1306#102—671no—
1307#102—671no—
1308#102—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—
1321C22⋊C8—671no—
1322C22⋊C8—671no—
1323C22⋊C8—671no—
1324C22⋊C8—671no—
1325C22⋊C8—671no—
1326C22⋊C8—671no—
1327#97—671no—
1328#97—671no—
1329#97—671no—
1330#97—671no—
1331C4×C8—671no—
1332C4×C8—671no—
1333C4×C8—671no—
1334C4×C8—671no—
1335C4×C8—671no—
1336C4×C8—671no—
1337C24—21no—
1338C24—21no—
1339#41—22no—
1340#41—41no—
1341#41—82no—
1342#41—2681no—
1343#41—1342no—
1344C2×Q8—21no—
1345C2×Q8—2681no—
1346C2×Q8—2681no—
1347C2×Q8—671no—
1348C2×Q8—671no—
1349C2×Q8—671no—
1350C2×Q8—1342no—
1351C2×Q8—1342no—
1352C2×Q8—1341no—
1353C2×Q8—1341no—
1354C2×Q8—1341no—
1355C2×Q8C2×C22⋊D6711yescharacteristic
1356C2×Q8C23×D6711yescharacteristic
1357C2×D4—22no—
1358C2×D4—22no—
1359C2×D4—21no—
1360C2×D4—21no—
1361C2×D4—21no—
1362C2×D4—21no—
1363C2×D4—21no—
1364C2×D4—21no—
1365C2×D4—21no—
1366C2×D4—21no—
1367C2×D4—21no—
1368C2×D4—41no—
1369C2×D4—41no—
1370C2×D4—82no—
1371C2×D4—671no—
1372C2×D4—1341no—
1373C2×D4—1341no—
1374C2×D4—1341no—
1375C2×D4C2×C22⋊D6711yescharacteristic
1376C2×D4C2×C22⋊D6711yescharacteristic
1377C2×D4C2×C22⋊D6711yescharacteristic
1378C2×D4C23×D6711yescharacteristic
1379C2×D4C23×D6711yescharacteristic
1380C2×D4C23×D6711yescharacteristic
1381C22×C4—21no—
1382C22×C4—21no—
1383C22×C4—21no—
1384C22×C4—21no—
1385C22×C4—21no—
1386C22×C4—21no—
1387C22×C4—21no—
1388C22×C4—21no—
1389C22×C4—21no—
1390C22×C4—21no—
1391C22×C4—21no—
1392C22×C4—82no—
1393C22×C4—1341no—
1394C22×C4—1341no—
1395C22×C4—1341no—
1396C22×C4—1341no—
1397C22×C4—1341no—
1398C22×C4—1341no—
1399C22×C4—1341no—
1400C22×C4C2×C22⋊D6711yescharacteristic
1401C22×C4C2×C22⋊D6711yescharacteristic
1402C22×C4C23×D6711yescharacteristic
1403C22×C4C23×D6711yescharacteristic
1404C22×C4C23×D6711yescharacteristic
1405Q16—2681no—
1406Q16—2681no—
1407Q16—1342no—
1408SD16—2681no—
1409SD16—2681no—
1410SD16—674no—
1411SD16—1342no—
1412SD16—1342no—
1413SD16—1342no—
1414SD16—1342no—
1415SD16—1342no—
1416SD16—1342no—
1417SD16—1342no—
1418D8—2681no—
1419D8—2681no—
1420D8—1342no—
1421M16—2681no—
1422M16—2681no—
1423C2×C8—2681no—
1424C2×C8—671no—
1425C2×C8—671no—
1426C2×C8—671no—
1427C2×C8—671no—
1428C2×C8—671no—
1429C2×C8—671no—
1430C2×C8—671no—
1431C2×C8—671no—
1432C2×C8—1342no—
1433C2×C8—1342no—
1434C2×C8—1342no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—21no—
1440C4⋊C4—21no—
1441C4⋊C4—21no—
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—21no—
1445C4⋊C4—21no—
1446C4⋊C4—671no—
1447C4⋊C4—671no—
1448C4⋊C4—671no—
1449C4⋊C4—671no—
1450C4⋊C4—1341no—
1451C4⋊C4—1341no—
1452C4⋊C4—1341no—
1453C4⋊C4—1341no—
1454C4⋊C4—1341no—
1455C4⋊C4—1341no—
1456C4⋊C4—1341no—
1457C4⋊C4—1341no—
1458C4⋊C4—1341no—
1459C4⋊C4—1341no—
1460C4⋊C4—1341no—
1461C4⋊C4—1341no—
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⋊C4C2×C22⋊D6711yescharacteristic
1472C4⋊C4C2×C22⋊D6711yescharacteristic
1473C4⋊C4C2×C22⋊D6711yescharacteristic
1474C4⋊C4C2×C22⋊D6711yescharacteristic
1475C4⋊C4C2×C22⋊D6711yescharacteristic
1476C4⋊C4C2×C22⋊D6711yescharacteristic
1477C4⋊C4C2×C22⋊D6711yescharacteristic
1478C4⋊C4C2×C22⋊D6711yescharacteristic
1479C4⋊C4C2×C22⋊D6711yescharacteristic
1480C4⋊C4C2×C22⋊D6711yescharacteristic
1481C4⋊C4C23×D6711yescharacteristic
1482C4⋊C4C23×D6711yescharacteristic
1483C4⋊C4C23×D6711yescharacteristic
1484C4⋊C4C23×D6711yescharacteristic
1485C22⋊C4—21no—
1486C22⋊C4—21no—
1487C22⋊C4—21no—
1488C22⋊C4—21no—
1489C22⋊C4—21no—
1490C22⋊C4—21no—
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—1341no—
1505C22⋊C4—1341no—
1506C22⋊C4—1341no—
1507C22⋊C4—1341no—
1508C22⋊C4—1341no—
1509C22⋊C4—1341no—
1510C22⋊C4—1341no—
1511C22⋊C4—1341no—
1512C22⋊C4—1341no—
1513C22⋊C4—1341no—
1514C22⋊C4—1341no—
1515C22⋊C4—1341no—
1516C22⋊C4—1341no—
1517C22⋊C4C2×C22⋊D6711yescharacteristic
1518C22⋊C4C2×C22⋊D6711yescharacteristic
1519C22⋊C4C2×C22⋊D6711yescharacteristic
1520C22⋊C4C2×C22⋊D6711yescharacteristic
1521C22⋊C4C2×C22⋊D6711yescharacteristic
1522C22⋊C4C2×C22⋊D6711yescharacteristic
1523C22⋊C4C2×C22⋊D6711yescharacteristic
1524C22⋊C4C2×C22⋊D6711yescharacteristic
1525C22⋊C4C2×C22⋊D6711yescharacteristic
1526C22⋊C4C2×C22⋊D6711yescharacteristic
1527C42—21no—
1528C42—21no—
1529C42—21no—
1530C42—1341no—
1531C42—1341no—
1532C42—1341no—
1533C42—1341no—
1534C42—1341no—
1535C42—1341no—
1536C42—1341no—
1537C42—1341no—
1538C42—1341no—
1539C42C2×C22⋊D6711yescharacteristic
1540C42C2×C22⋊D6711yescharacteristic
1541C42C23×D6711yescharacteristic
1542C42C23×D6711yescharacteristic
1543C42C23×D6711yescharacteristic
1544C42C23×D6711yescharacteristic
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—42no—
1549C23—42no—
1550C23—42no—
1551C23—81no—
1552C23—81no—
1553C23—81no—
1554C23—1341no—
1555C23C22×C22⋊D6711yescharacteristic
1556C23C22×C22⋊D6711yescharacteristic
1557C23C22×C22⋊D6711yescharacteristic
1558Q8—21no—
1559Q8—21no—
1560Q8—41no—
1561Q8—81no—
1562Q8—2682no—
1563Q8—2682no—
1564Q8—5361no—
1565Q8—672no—
1566Q8—1341no—
1567Q8—1341no—
1568Q8—1341no—
1569Q8—1341no—
1570Q8—1341no—
1571D4—22no—
1572D4—22no—
1573D4—21no—
1574D4—21no—
1575D4—21no—
1576D4—21no—
1577D4—21no—
1578D4—41no—
1579D4—42no—
1580D4—42no—
1581D4—42no—
1582D4—42no—
1583D4—81no—
1584D4—81no—
1585D4—81no—
1586D4—81no—
1587D4—81no—
1588D4—2682no—
1589D4—2682no—
1590D4—5361no—
1591D4—1341no—
1592D4—1341no—
1593D4#41×D6712yes—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—41no—
1607C2×C4—42no—
1608C2×C4—42no—
1609C2×C4—81no—
1610C2×C4—81no—
1611C2×C4—81no—
1612C2×C4—81no—
1613C2×C4—81no—
1614C2×C4—81no—
1615C2×C4—81no—
1616C2×C4—81no—
1617C2×C4—81no—
1618C2×C4—2682no—
1619C2×C4—2682no—
1620C2×C4—2682no—
1621C2×C4—5361no—
1622C2×C4—5361no—
1623C2×C4—5361no—
1624C2×C4—5361no—
1625C2×C4—1341no—
1626C2×C4—1341no—
1627C2×C4—1341no—
1628C2×C4—1341no—
1629C2×C4—1341no—
1630C2×C4—1341no—
1631C2×C4—1341no—
1632C2×C4C22×C22⋊D6711yescharacteristic
1633C2×C4C22×C22⋊D6711yescharacteristic
1634C2×C4C22×C22⋊D6711yescharacteristic
1635C2×C4C22×C22⋊D6711yescharacteristic
1636C2×C4C22×C22⋊D6711yescharacteristic
1637C2×C4C22×C22⋊D6711yescharacteristic
1638C2×C4C22×C22⋊D6711yescharacteristic
1639C2×C4C22×C22⋊D6711yescharacteristic
1640C2×C4C22×C22⋊D6711yescharacteristic
1641C2×C4C22×C22⋊D6711yescharacteristic
1642C2×C4C22×C22⋊D6711yescharacteristic
1643C2×C4C24×D6711yescharacteristic
1644C8—672no—
1645C8—1341no—
1646C8—1341no—
1647C8—1341no—
1648C8—1341no—
1649C8—1341no—
1650C8—1341no—
1651C8—1341no—
1652C22—21no—
1653C22—21no—
1654C22—21no—
1655C22—21no—
1656C22—21no—
1657C22—21no—
1658C22—22no—
1659C22—21no—
1660C22—21no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—84no—
1670C22—2681no—
1671C22—2681no—
1672C22—2681no—
1673C22—162no—
1674C22#1686420712yes—
1675C22C23×C22⋊D6711yescharacteristic
1676C4—21no—
1677C4—21no—
1678C4—21no—
1679C4—21no—
1680C4—21no—
1681C4—21no—
1682C4—21no—
1683C4—21no—
1684C4—21no—
1685C4—21no—
1686C4—21no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—2681no—
1693C4—2681no—
1694C4—2681no—
1695C4—2681no—
1696C4—2681no—
1697C4—2681no—
1698C4—1342no—
1699C4C2×#41×D6711yescharacteristic
1700C4#1686423211yescharacteristic
1701C2—22no—
1702C2—41no—
1703C2—41no—
1704C2—42no—
1705C2—81no—
1706C2—81no—
1707C2—5361no—
1708C2#41×C22⋊D6711yescharacteristic
1709C2C2×#1686420711yescharacteristic
1710C2#2257498011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3513C2
socleC22×C67C23×D4
hypercenter#3513D67
hypocenterC67#61472
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. #22574198C2semidirect
2. #22573201C2semidirect
3. #22573084C2semidirect
4. #22573036C2semidirect
5. #22572971C2semidirect
6. #22572588C2semidirect
7. #22572582C2semidirect
8. #22572566C2semidirect
9. #22572456C2semidirect
10. #22572425C2semidirect
11. #22572350C2semidirect
12. #22572290C2semidirect
13. #22572254C2semidirect
14. #22572194C2semidirect
15. #22571912C2semidirect
16. #22571912C2semidirect
17. D4×#11761616C2semidirect
18. #22570831C2semidirect
19. #22570820C2semidirect
20. #22570773C2semidirect
21. #22570432C2semidirect
22. #22570423C2semidirect
23. #22570402C2semidirect
24. #22570393C2semidirect
25. #22570376C2semidirect
26. #22570347C2semidirect
27. #22569185C2semidirect
28. #22569090C2semidirect
29. #22569066C2semidirect
30. C2×C4×#11761616C2semidirect
31. C67×#3513C2semidirect
35. #16864124C22semidirect
36. #16864119C22semidirect
38. #16864103C22semidirect
42. #16864086C22semidirect
45. #16864055C22semidirect
46. #16864055C22semidirect
47. #16864017C22semidirect
49. #16864008C22semidirect
51. #16863930C22semidirect
54. #16863876C22semidirect
55. #16863873C22semidirect
56. C2×C4×Dic134C22semidirect
57. #16863795C22semidirect
58. #16863795C22semidirect
59. #16863792C22semidirect
60. #16863778C22semidirect
61. #16863778C22semidirect
63. #16863766C22semidirect
65. #16863758C22semidirect
66. #16863755C22semidirect
67. #16863753C22semidirect
68. #16863750C22semidirect
69. #16863737C22semidirect
70. #16863734C22semidirect
71. #16863731C22semidirect
72. #16863729C22semidirect
73. #16863726C22semidirect
74. #16863726C22semidirect
75. #16863720C22semidirect
78. #16863712C22semidirect
79. #16863709C22semidirect
80. #16863707C22semidirect
81. #16863703C22semidirect
82. #16863700C22semidirect
83. #16863700C22semidirect
84. #16863700C22semidirect
87. #16863696C22semidirect
88. #16863693C22semidirect
89. #16863688C22semidirect
90. #16863686C22semidirect
91. #16863678C22semidirect
93. #16863652C22semidirect
95. #16863640C22semidirect
96. #16863640C22semidirect
97. #16863635C22semidirect
99. #16863627C22semidirect
100. #16863627C22semidirect
103. #16863623C22semidirect
104. #16863623C22semidirect
105. #16863615C22semidirect
106. #16863615C22semidirect
107. #16863615C22semidirect
108. #16863615C22semidirect
111. #16863611C22semidirect
112. #16863611C22semidirect
113. #16863606C22semidirect
119. #16863551C22semidirect
120. #16863551C22semidirect
123. #16863539C22semidirect
124. #16863539C22semidirect
129. #16863527C22semidirect
130. Q8×C67⋊C8C22semidirect
133. #16863506C22semidirect
134. #16863501C22semidirect
135. #16863501C22semidirect
136. #16863501C22semidirect
139. #16863496C22semidirect
140. #16863496C22semidirect
141. #16863496C22semidirect
142. #16863496C22semidirect
143. C4×#11761618C22semidirect
144. C4×#11761615C22semidirect
145. C4×#11761615C22semidirect
152. C4×#11761616C22semidirect
153. C4×#11761616C22semidirect
154. C4×#11761616C22semidirect
155. C4×#11761616C22semidirect
156. C4×#11761616C22semidirect
157. C4×#11761616C22semidirect
158. C4×#11761613C22semidirect
159. #16863474C22semidirect
161. #16863468C22semidirect
163. D4×C67⋊C8C22semidirect
164. D4×C67⋊C8C22semidirect
165. #16863457C22semidirect
166. #16863457C22semidirect
167. #16863453C22semidirect
168. #16863432C22semidirect
169. C2×#14523974C22semidirect
170. C2×#14523974C22semidirect
171. #16863404C22semidirect
174. #16863395C22semidirect
175. C2×#14523966C22semidirect
177. #16863352C22semidirect
178. #16863352C22semidirect
179. C2×C4×C67⋊C8C22semidirect
515. #11761616#41semidirect
857. #3513D67semidirect
887. C67#61472semidirect

Maximal subgroups

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

subgroupindex
#225741982
#225732012
#225730842
#225730362
#225729712
#225725882
#225725822
#225725662
#225724562
#225724252
#225723502
#225722902
#225722542
#225721942
#225719122
D4×#117616162
#225708312
#225708202
#225707732
#225704322
#225704232
#225704022
#225703932
#225703762
#225703472
#225691852
#225690902
#225690662
C2×C4×#117616162
C67×#35132
#6147267