Finite Group Databasebeta

← #11910867

Subgroups — #11910867

Order 1152.

2287 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596186C211yesmaximal, characteristic, complemented
2C3×#5719C212yesmaximal, complemented
3#10595312C211yesmaximal, characteristic, complemented
4#10595310C212yesmaximal, complemented
5#10595308C211yesmaximal, characteristic, complemented
6#10595296C212yesmaximal, complemented
7#10595263C212yesmaximal, complemented
8#10595255C212yesmaximal, complemented
9#10595212C211yesmaximal, characteristic, complemented
10#10595203C212yesmaximal, complemented
11#10595196C212yesmaximal, complemented
12#10595169C211yesmaximal, characteristic, complemented
13#10595162C212yesmaximal, complemented
14#10595138C212yesmaximal, complemented
15#10595127C212yesmaximal, complemented
16#10595118C212yesmaximal, complemented
17#10594014C211yesmaximal, characteristic, complemented
18#10593872C212yesmaximal, complemented
19#10593857C211yesmaximal, characteristic, complemented
20#86489—32nomaximal
21C2×#3830C2211yescharacteristic, complemented
22C2×D4×C3⋊D3C2211yescharacteristic
23C2×#3811C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×#3804C2212yes—
26C32×#127C2211yescharacteristic, complemented
27#64149C2211yescharacteristic
28#64148C2212yes—
29#64148C2212yescomplemented
30#64146C2212yes—
31#64146C2212yescomplemented
32#64145C2211yescharacteristic, complemented
33#64084C2211yescharacteristic
34#64081C2211yescharacteristic, complemented
35C3×#939C2212yes—
36C3×#939C2212yescomplemented
37C3×#939C2212yescomplemented
38C3×#939C2212yescomplemented
39C3×#938C2212yescomplemented
40C3×#938C2212yescomplemented
41C3×#935C2212yescomplemented
42C3×#935C2212yescomplemented
43C3×#935C2212yescomplemented
44C3×#935C2212yescomplemented
45C3×D4×Dic3C2212yescomplemented
46C3×D4×Dic3C2212yescomplemented
47C3×#872C2212yescomplemented
48C3×#870C2212yescomplemented
49#63983C2211yescharacteristic
50#63983C2212yescomplemented
51#63982C2212yescomplemented
52#63981C2212yes—
53#63978C2212yes—
54#63978C2212yescomplemented
55#63975C2211yescharacteristic
56#63975C2212yescomplemented
57#63975C2211yescharacteristic, complemented
58#63975C2211yescharacteristic, complemented
59#63974C2212yes—
60#63974C2211yescharacteristic, complemented
61#67⋊Dic3C2212yescomplemented
62Dic3×#67C2212yescomplemented
63#63969C2212yescomplemented
64#63966C2212yes—
65#63966C2212yescomplemented
66C2×Dic3⋊Dic3C2212yescomplemented
67#63964C2212yescomplemented
68#63964C2212yescomplemented
69C2×#3722C2211yescharacteristic
70#63962C2212yescomplemented
71#63959C2212yescomplemented
72#63959C2212yescomplemented
73#63958C2212yes—
74#63958C2212yescomplemented
75#63956C2212yescomplemented
76#63955C2212yescomplemented
77#63953C2212yescomplemented
78#63953C2212yescomplemented
79#63952C2212yescomplemented
80#63952C2212yescomplemented
81#63952C2212yescomplemented
82#63923C2211yescharacteristic
83D3×(C2×D3)⋊C4C2212yescomplemented
84#63904C2212yes—
85#63897C2211yescharacteristic
86#63897C2211yescharacteristic
87#63897C2211yescharacteristic
88#63896C2212yescomplemented
89#63895C2212yescomplemented
90#63895C2212yescomplemented
91#63895C2212yescomplemented
92#63883C2212yescomplemented
93#63880C2212yescomplemented
94#63868C2212yescomplemented
95#63867C2212yescomplemented
96#63862C2212yescomplemented
97#63858C2212yescomplemented
98#63854C2212yes—
99#63853C2212yes—
100#63851C2212yescomplemented
101#63850C2212yescomplemented
102#63848C2212yescomplemented
103#63848C2212yescomplemented
104#63846C2212yescomplemented
105#63840C2212yescomplemented
106#63838C2212yescomplemented
107#63836C2212yescomplemented
108C3×#540—32no—
109#5719D312yescomplemented
110#5715—32no—
111#5715—61no—
112#5699—32no—
113#5693—32no—
114#5667—32no—
115#5665—32no—
116#5664—32no—
117#5662—32no—
118#5658—32no—
119#5657—32no—
120#5655—32no—
121D3×#123—32no—
122#5621—32no—
123#5620—32no—
124#5617—32no—
125#5613—32no—
126#5613—32no—
127#5612—32no—
128#5611—32no—
129#5610—32no—
130#5606—32no—
131#5605—32no—
132#5603—32no—
133#5601—32no—
134#5565—32no—
135#5564—32no—
136#5556—32no—
137#5547—32no—
138#5529—32no—
139#5527—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C22×D32C2311yescharacteristic
143C2×C32×D4C2312yes—
144C2×C32×D4C2312yes—
145C2×C32×D4C2311yescharacteristic
146C2×C32×D4C2311yescharacteristic
147C2×#638C2312yes—
148C2×#638C2311yescharacteristic
149C2×#638C2311yescharacteristic
150C2×#638C2312yes—
151C2×#638C2312yes—
152C22×C3⋊Dic3C2312yes—
153#3830—42no—
154D4×C3⋊D3—42no—
155C2×C4⋊(C3⋊D3)C2311yescharacteristic
156C2×C4×C3⋊D3C2311yescharacteristic
157C2×#634C2311yescharacteristic
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C22×C3×Dic3C2312yes—
163C22×C3×Dic3C2312yes—
164C22×C3×Dic3C2312yes—
165C22×C3×Dic3C2312yes—
166C2×C3×C4×D3C2312yes—
167#3811—42no—
168C2×#627C2312yes—
169C2×#627C2312yes—
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#624—42no—
173C2×#624C2312yes—
174C2×#624C2311yescharacteristic
175C2×#624C2311yescharacteristic
176C2×#624C2311yescharacteristic
177C2×#624C2312yes—
178#3804—44no—
179C2×D3×Dic3C2312yes—
180C32×C42C2311yescharacteristic
181#3757C2312yes—
182#3757C2312yes—
183#3752C2312yes—
184#3752C2312yes—
185#3752C2312yes—
186#3750C2312yes—
187C4×C3⋊Dic3C2311yescharacteristic
188C3×#217C2312yes—
189C3×#217C2312yes—
190C3×#217C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×#217C2312yes—
195C3×#217C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×C4×Dic3C2312yes—
207#3724C2312yes—
208#3724C2312yes—
209Dic3⋊Dic3C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217#3722C2312yes—
218#3722C2311yescharacteristic
219#3722C2311yescharacteristic
220#3722C2312yes—
221#3722C2312yes—
222#3722C2311yescharacteristic
223#3722C2311yescharacteristic
224#3722C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2312yes—
230Dic32C2312yes—
231Dic32C2312yes—
232#3533—91noSylow
233C2×#237—32no—
234C2×#237—32no—
235C2×#237—61no—
236C2×D3×D4—32no—
237C2×D3×D4—32no—
238C2×D3×D4—61no—
239C2×#235—32no—
240C22×C4×D3—32no—
241C3×#127—21no—
242C3×#127C2×D312yescomplemented
243C3×#125—32no—
244C3×#123—32no—
245C3×#123—32no—
246C3×#123—32no—
247C3×#123—32no—
248C3×#121—32no—
249C3×#121—32no—
250C3×#121—32no—
251C3×#121—32no—
252C3×#121—32no—
253C3×#121—32no—
254C3×C4×D4—32no—
255C3×C4×D4—32no—
256C3×#117—32no—
257#940—32no—
258#940—61no—
259#939—32no—
260#939—32no—
261#939—32no—
262#939—32no—
263#939—32no—
264#939—32no—
265#939—62no—
266#939—62no—
267#939C2×D312yes—
268#939C2×D312yescomplemented
269#939C2×D312yescomplemented
270#939C2×D312yescomplemented
271#938—32no—
272#938—32no—
273#938C2×D312yescomplemented
274#938C2×D312yescomplemented
275#937—32no—
276#937—32no—
277#937—32no—
278#937—32no—
279#937—32no—
280#937—32no—
281#937—32no—
282#937—32no—
283#937—62no—
284#937—62no—
285#936—32no—
286#936—32no—
287#936—32no—
288#936—61no—
289#935—32no—
290#935—32no—
291#935C2×D312yescomplemented
292#935C2×D312yescomplemented
293#935C2×D312yescomplemented
294#935C2×D312yescomplemented
295D4×Dic3—32no—
296D4×Dic3—32no—
297D4×Dic3C2×D312yescomplemented
298D4×Dic3C2×D312yescomplemented
299#930—32no—
300#930—32no—
301#929—32no—
302#929—32no—
303#929—32no—
304C4×#67—32no—
305C4×#67—32no—
306C4×#67—32no—
307C4×#67—32no—
308C4×#67—32no—
309C2×(C2×D3)⋊C4—32no—
310C2×(C2×D3)⋊C4—32no—
311#926—32no—
312C2×C4⋊Dic3—32no—
313#924—32no—
314#924—32no—
315#924—32no—
316C2×Dic3⋊C4—32no—
317#898—32no—
318#898—32no—
319#898—32no—
320#898—32no—
321#898—32no—
322#898—32no—
323#898—32no—
324#897—32no—
325#897—32no—
326#897—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#896—32no—
331#896—32no—
332#894—32no—
333#894—32no—
334#894—32no—
335#894—32no—
336#894—32no—
337#894—32no—
338#893—32no—
339#892—32no—
340D3×C4⋊C4—32no—
341D3×C4⋊C4—32no—
342#890—32no—
343#889—32no—
344#889—32no—
345#888—32no—
346#888—32no—
347#887—32no—
348#887—32no—
349#886—32no—
350#886—32no—
351#886—32no—
352#885—32no—
353#885—32no—
354#885—32no—
355#885—32no—
356#885—32no—
357#885—32no—
358#884—32no—
359#884—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#883—32no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883—32no—
368#882—32no—
369#882—32no—
370#67⋊C4—32no—
371#67⋊C4—32no—
372#67⋊C4—32no—
373#67⋊C4—32no—
374#67⋊C4—32no—
375D3×C22⋊C4—32no—
376D3×C22⋊C4—32no—
377D3×C22⋊C4—32no—
378D3×C22⋊C4—32no—
379#879—32no—
380#879—32no—
381#879—32no—
382#879—32no—
383#878—32no—
384#878—32no—
385#878—32no—
386#878—32no—
387#878—32no—
388#877—32no—
389#876—32no—
390#875—32no—
391#875—61no—
392C4×D12—32no—
393#872—32no—
394#872—32no—
395#872—61no—
396#872C2×D312yescomplemented
397#870—32no—
398#870C2×D312yescomplemented
399C23×C32C2411yescharacteristic
400C23×C32C2411yescharacteristic
401C23×C32C2412yes—
402C22×C3⋊D3—22no—
403C22×C3⋊D3—22no—
404C22×C3⋊D3—42no—
405C22×C3⋊D3—42no—
406C22×C3⋊D3C2411yescharacteristic
407C22×C3⋊D3C2411yescharacteristic
408C22×C3⋊D3C2411yescharacteristic
409C22×C3×D3C2412yes—
410C2×D32—42no—
411C2×D32—41no—
412C32×D4—41no—
413C32×D4—41no—
414C32×D4—42no—
415C32×D4—42no—
416C2×C32×C4C2412yes—
417C2×C32×C4C2411yescharacteristic
418#638—24no—
419#638—41no—
420#638—41no—
421#638—42no—
422#638—42no—
423C2×C3⋊Dic3—42no—
424C2×C3⋊Dic3C2412yes—
425C2×C3⋊Dic3C2412yes—
426C2×C3⋊Dic3C2411yescharacteristic
427C4⋊(C3⋊D3)—41no—
428C4×C3⋊D3—22no—
429#634—41no—
430C3×#67—42no—
431C3×#67—42no—
432C3×#67—42no—
433C3×#67—42no—
434C2×C3×Dic3—42no—
435C2×C3×Dic3—42no—
436C2×C3×Dic3—42no—
437C2×C3×Dic3—42no—
438C2×C3×Dic3C2412yes—
439C2×C3×Dic3C2412yes—
440C2×C3×Dic3C2412yes—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C3×C4×D3—42no—
446#627—42no—
447#627—42no—
448#626—24no—
449#626—42no—
450#624—24no—
451#624—41no—
452#624—41no—
453#624—42no—
454#624—41no—
455D3×Dic3—42no—
456#563—91no—
457#562—92no—
458#560—91no—
459#559—91no—
460#553—92no—
461#552—92no—
462#551—91no—
463#551—92no—
464#547—92no—
465#546—92no—
466#542—92no—
467#540—32no—
468#539—92no—
469#538—92no—
470#538—92no—
471#535—91no—
472#534—91no—
473#525—92no—
474C2×#123—91no—
475C23×D3—32no—
476C23×D3—32no—
477C23×D3—32no—
478C23×D3—61no—
479C23×D3—61no—
480C2×C3×D4—21no—
481C2×C3×D4—21no—
482C2×C3×D4—22no—
483C2×C3×D4—22no—
484C2×C3×D4—32no—
485C2×C3×D4—32no—
486C2×C3×D4—32no—
487C2×C3×D4—32no—
488C2×C3×D4C22×D312yes—
489C2×C3×D4C22×D312yes—
490C2×C3×D4C22×D312yes—
491C2×C3×D4C22×D312yes—
492C2×C3×D4C22×D312yes—
493C2×C3×D4C22×D312yes—
494C22×C3×C4—32no—
495C22×C3×C4—32no—
496C22×C3×C4—32no—
497C22×C3×C4—32no—
498C22×C3×C4—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—32no—
504C2×#67—32no—
505C2×#67—32no—
506C2×#67—32no—
507C2×#67—32no—
508C2×#67—32no—
509C2×#67—62no—
510C2×#67—61no—
511C2×#67—61no—
512C2×#67—62no—
513C2×#67—62no—
514C2×#67C22×D312yes—
515C2×#67C22×D312yes—
516C2×#67C22×D312yes—
517C2×#67C22×D312yes—
518C22×Dic3—32no—
519C22×Dic3—32no—
520C22×Dic3—32no—
521C22×Dic3—62no—
522C22×Dic3C22×D312yes—
523C22×Dic3C22×D312yes—
524C22×Dic3C22×D312yes—
525C22×Dic3C22×D312yes—
526#237—124no—
527#237—124no—
528#237—124no—
529D3×D4—124no—
530D3×D4—124no—
531D3×D4—124no—
532#235—124no—
533C2×D12—32no—
534C2×D12—32no—
535C2×D12—32no—
536C2×D12—61no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—61no—
547C2×C4×D3—124no—
548C2×C4×D3C22×D312yes—
549C2×Dic6—32no—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—32no—
553C2×Dic6—32no—
554C2×Dic6—61no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4—32no—
562C3×C4⋊C4—32no—
563C3×C22⋊C4—32no—
564C3×C22⋊C4—32no—
565C3×C22⋊C4—32no—
566C3×C22⋊C4—32no—
567C3×C22⋊C4—32no—
568C3×C22⋊C4—32no—
569C3×C22⋊C4—32no—
570C3×C22⋊C4—32no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4—32no—
573C3×C42—21no—
574C3×C42—32no—
575C3×C42C22×D312yes—
576#217—32no—
577#217—32no—
578#217—32no—
579#217—32no—
580#217—32no—
581#217—32no—
582#217—32no—
583#217—32no—
584#217—62no—
585#217—62no—
586#217C22×D312yes—
587#217C22×D312yes—
588#217C22×D312yes—
589#217C22×D312yes—
590#217C22×D312yes—
591#217C22×D312yes—
592#217C22×D312yes—
593#217C22×D312yes—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—62no—
617(C2×D3)⋊C4—62no—
618(C2×D3)⋊C4—62no—
619(C2×D3)⋊C4C22×D312yes—
620(C2×D3)⋊C4C22×D312yes—
621C4⋊Dic3—32no—
622C4⋊Dic3—32no—
623C4⋊Dic3—32no—
624C4⋊Dic3—32no—
625C4⋊Dic3—32no—
626C4⋊Dic3—32no—
627C4⋊Dic3—32no—
628C4⋊Dic3—32no—
629C4⋊Dic3C22×D312yes—
630C4⋊Dic3C22×D312yes—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4—62no—
646Dic3⋊C4C22×D312yes—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652C4×Dic3—32no—
653C4×Dic3—32no—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—61no—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—21no—
664C22×C32—22no—
665C22×C32—22no—
666C22×C32—22no—
667C22×C32—22no—
668C22×C32C2511yescharacteristic
669C2×C3⋊D3—22no—
670C2×C3⋊D3—21no—
671C2×C3⋊D3—21no—
672C2×C3⋊D3—22no—
673C2×C3⋊D3—22no—
674C2×C3⋊D3—44no—
675C2×C3⋊D3—82no—
676C2×C3⋊D3H(5,𝔽2)12yes—
677C2×C3×D3—22no—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680D32—82no—
681C32×C4—21no—
682C32×C4—22no—
683C3⋊Dic3—21no—
684C3⋊Dic3—22no—
685C3⋊Dic3—22no—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C2×#41—92no—
694C2×#41—91no—
695C22×D4—91no—
696C22×D4—91no—
697C23×C4—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127D3211yescharacteristic, complemented
701#126—92no—
702#126—92no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—32no—
708#125—92no—
709#125—92no—
710#124—92no—
711#124—92no—
712#124—92no—
713#124—92no—
714#124—91no—
715#124—91no—
716#123—32no—
717#123—32no—
718#123—32no—
719#123—32no—
720#123—91no—
721#123—91no—
722#123—92no—
723#123—91no—
724#123—92no—
725#123—92no—
726#123—92no—
727#123—92no—
728#123—92no—
729#123—92no—
730#123—91no—
731#123—91no—
732#123—91no—
733#123—92no—
734C22⋊Q8—92no—
735C22⋊Q8—92no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742#121—32no—
743#121—32no—
744#121—32no—
745#121—32no—
746#121—32no—
747#121—32no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#120—91no—
755#120—92no—
756#120—91no—
757#120—92no—
758#120—92no—
759#120—92no—
760C4×Q8—92no—
761C4×D4—32no—
762C4×D4—32no—
763C4×D4—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770#117—32no—
771#117—92no—
772#117—92no—
773#117—91no—
774C2×C4⋊C4—92no—
775C2×C4⋊C4—92no—
776C2×C22⋊C4—91no—
777C2×C22⋊C4—92no—
778C2×C22⋊C4—92no—
779C2×C22⋊C4—91no—
780C23×C3—21no—
781C23×C3—21no—
782C23×C3—22no—
783C23×C3—32no—
784C23×C3C23×D312yes—
785C23×C3C23×D312yes—
786C23×C3C23×D312yes—
787C23×C3C23×D312yes—
788C22×D3—32no—
789C22×D3—32no—
790C22×D3—32no—
791C22×D3—61no—
792C22×D3—61no—
793C22×D3—61no—
794C22×D3—64no—
795C22×D3—64no—
796C22×D3—122no—
797C22×D3—122no—
798C22×D3—122no—
799C22×D3—122no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3—122no—
804C22×D3—122no—
805C22×D3—242no—
806C22×D3—242no—
807C22×D3C23×D312yes—
808C3×D4—42no—
809C3×D4—42no—
810C3×D4—42no—
811C3×D4—42no—
812C3×D4—42no—
813C3×D4—42no—
814C3×D4—42no—
815C3×D4—42no—
816C3×D4—82no—
817C3×D4—82no—
818C3×D4—122no—
819C3×D4—122no—
820C3×D4—122no—
821C3×D4—122no—
822C2×C3×C4—21no—
823C2×C3×C4—22no—
824C2×C3×C4—32no—
825C2×C3×C4—32no—
826C2×C3×C4—32no—
827C2×C3×C4—32no—
828C2×C3×C4—32no—
829C2×C3×C4—32no—
830C2×C3×C4—32no—
831C2×C3×C4—122no—
832C2×C3×C4—122no—
833C2×C3×C4—122no—
834C2×C3×C4—122no—
835C2×C3×C4—122no—
836C2×C3×C4C23×D312yes—
837C2×C3×C4C23×D312yes—
838C2×C3×C4C23×D312yes—
839#67—42no—
840#67—42no—
841#67—42no—
842#67—42no—
843#67—64no—
844#67—64no—
845#67—64no—
846#67—124no—
847#67—122no—
848#67—122no—
849#67—122no—
850#67—122no—
851#67—122no—
852#67—122no—
853#67—122no—
854#67—122no—
855#67—122no—
856#67—242no—
857#67—242no—
858C2×Dic3—32no—
859C2×Dic3—32no—
860C2×Dic3—32no—
861C2×Dic3—32no—
862C2×Dic3—32no—
863C2×Dic3—42no—
864C2×Dic3—42no—
865C2×Dic3—42no—
866C2×Dic3—42no—
867C2×Dic3—61no—
868C2×Dic3—62no—
869C2×Dic3—62no—
870C2×Dic3—122no—
871C2×Dic3—122no—
872C2×Dic3—122no—
873C2×Dic3—124no—
874C2×Dic3C23×D312yes—
875C2×Dic3C23×D312yes—
876C2×Dic3C23×D312yes—
877C2×Dic3C23×D312yes—
878C2×Dic3C23×D312yes—
879C2×Dic3C23×D312yes—
880C2×Dic3C23×D312yes—
881D12—64no—
882D12—122no—
883D12—122no—
884D12—122no—
885C4×D3—42no—
886C4×D3—64no—
887C4×D3—64no—
888C4×D3—64no—
889C4×D3—64no—
890C4×D3—122no—
891C4×D3—122no—
892C4×D3—122no—
893C4×D3—122no—
894C4×D3—122no—
895C4×D3—122no—
896Dic6—122no—
897Dic6—122no—
898Dic6—122no—
899Dic6—122no—
900Dic6—122no—
901Dic6—122no—
902C2×C32—41no—
903C2×C32—41no—
904C2×C32—42no—
905C2×C32C2×H(5,𝔽2)11yescharacteristic
906C2×C32#58512yes—
907C3⋊D3—22no—
908C3⋊D3—41no—
909C3⋊D3—41no—
910C3×D3—42no—
911C24—91no—
912C24—91no—
913C24—91no—
914#41—364no—
915#41—362no—
916C2×Q8—92no—
917C2×Q8—92no—
918C2×Q8—91no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—32no—
922C2×D4—32no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—92no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—91no—
931C2×D4—362no—
932C2×D4—362no—
933C2×D4C2×D3212yes—
934C2×D4C2×D3212yes—
935C2×D4C2×D3211yescharacteristic
936C2×D4C2×D3211yescharacteristic
937C22×C4—32no—
938C22×C4—32no—
939C22×C4—32no—
940C22×C4—32no—
941C22×C4—32no—
942C22×C4—92no—
943C22×C4—92no—
944C22×C4—91no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—92no—
948C22×C4—92no—
949C22×C4—91no—
950C22×C4—362no—
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—32no—
957C4⋊C4—32no—
958C4⋊C4—32no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4—92no—
965C4⋊C4—92no—
966C4⋊C4—92no—
967C4⋊C4—92no—
968C4⋊C4—92no—
969C4⋊C4—92no—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—32no—
975C22⋊C4—32no—
976C22⋊C4—32no—
977C22⋊C4—32no—
978C22⋊C4—32no—
979C22⋊C4—32no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—92no—
983C22⋊C4—91no—
984C22⋊C4—91no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4—92no—
990C22⋊C4—92no—
991C22⋊C4—92no—
992C22⋊C4—92no—
993C22⋊C4—92no—
994C22⋊C4—92no—
995C22⋊C4—92no—
996C22⋊C4—92no—
997C42—32no—
998C42—92no—
999C42—92no—
1000C42—92no—
1001C42—91no—
1002C42C2×D3211yescharacteristic
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—22no—
1013C22×C3—22no—
1014C22×C3—22no—
1015C22×C3—21no—
1016C22×C3—42no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—42no—
1020C22×C3—42no—
1021C22×C3—42no—
1022C22×C3—42no—
1023C22×C3—62no—
1024C22×C3—62no—
1025C22×C3—62no—
1026C22×C3C24×D312yes—
1027C2×D3—22no—
1028C2×D3—22no—
1029C2×D3—22no—
1030C2×D3—34no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—62no—
1038C2×D3—62no—
1039C2×D3—62no—
1040C2×D3—122no—
1041C2×D3—121no—
1042C2×D3—121no—
1043C2×D3—122no—
1044C2×D3—122no—
1045C2×D3—128no—
1046C2×D3—244no—
1047C2×D3—244no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C3×C4—22no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—22no—
1054C3×C4—42no—
1055C3×C4—62no—
1056C3×C4—62no—
1057C3×C4—62no—
1058C3×C4—62no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4—62no—
1062Dic3—22no—
1063Dic3—22no—
1064Dic3—22no—
1065Dic3—22no—
1066Dic3—22no—
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—62no—
1070Dic3—62no—
1071Dic3—62no—
1072Dic3—62no—
1073Dic3—62no—
1074Dic3—62no—
1075Dic3—122no—
1076Dic3—122no—
1077C32#353311yescharacteristic, complemented, Sylow
1078C23—32no—
1079C23—91no—
1080C23—91no—
1081C23—91no—
1082C23—182no—
1083C23—182no—
1084C23—362no—
1085C23—362no—
1086C23—361no—
1087C23—362no—
1088C23C22×D3211yescharacteristic
1089C23C22×D3211yescharacteristic
1090C23C22×D3212yes—
1091Q8—361no—
1092Q8—362no—
1093Q8—362no—
1094D4—41no—
1095D4—41no—
1096D4—42no—
1097D4—42no—
1098D4—122no—
1099D4—122no—
1100D4—122no—
1101D4—122no—
1102D4—184no—
1103D4—184no—
1104D4—361no—
1105D4—362no—
1106D4—361no—
1107D4—361no—
1108D4—362no—
1109D4—362no—
1110C2×C4—32no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—32no—
1116C2×C4—32no—
1117C2×C4—92no—
1118C2×C4—92no—
1119C2×C4—91no—
1120C2×C4—122no—
1121C2×C4—122no—
1122C2×C4—122no—
1123C2×C4—122no—
1124C2×C4—122no—
1125C2×C4—182no—
1126C2×C4—184no—
1127C2×C4—361no—
1128C2×C4—361no—
1129C2×C4—361no—
1130C2×C4—362no—
1131C2×C4—362no—
1132C2×C4—362no—
1133C2×C4C22×D3212yes—
1134C2×C4C22×D3211yescharacteristic
1135C2×C3—21no—
1136C2×C3—22no—
1137C2×C3—42no—
1138C2×C3—42no—
1139C2×C3—42no—
1140C2×C3—42no—
1141C2×C3—81no—
1142C2×C3—81no—
1143C2×C3—82no—
1144C2×C3—122no—
1145C2×C3#596412yes—
1146C2×C3D3×H(5,𝔽2)12yes—
1147C2×C3#596612yes—
1148D3—42no—
1149D3—64no—
1150D3—122no—
1151D3—122no—
1152D3—122no—
1153D3—241no—
1154D3—241no—
1155C22—21no—
1156C22—22no—
1157C22—21no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—22no—
1162C22—62no—
1163C22—62no—
1164C22—62no—
1165C22—92no—
1166C22—182no—
1167C22—181no—
1168C22—181no—
1169C22—182no—
1170C22—182no—
1171C22—364no—
1172C22—722no—
1173C22—722no—
1174C22C23×D3211yescharacteristic
1175C4—21no—
1176C4—22no—
1177C4—62no—
1178C4—62no—
1179C4—62no—
1180C4—62no—
1181C4—62no—
1182C4—62no—
1183C4—62no—
1184C4—181no—
1185C4—182no—
1186C4—182no—
1187C3—21no—
1188C3#8648912yescomplemented
1189C2—41no—
1190C2—41no—
1191C2—42no—
1192C2—122no—
1193C2—182no—
1194C2—361no—
1195C2—361no—
1196C2#1059667511yescharacteristic
1197C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596186C2semidirect
2. C3×#5719C2semidirect
3. #10595312C2semidirect
4. #10595310C2semidirect
5. #10595308C2semidirect
6. #10595296C2semidirect
7. #10595263C2semidirect
8. #10595255C2semidirect
9. #10595212C2semidirect
10. #10595203C2semidirect
11. #10595196C2semidirect
12. #10595169C2semidirect
13. #10595162C2semidirect
14. #10595138C2semidirect
15. #10595127C2semidirect
16. #10595118C2semidirect
17. #10594014C2semidirect
18. #10593872C2semidirect
19. #10593857C2semidirect
21. C2×#3830C22semidirect
24. C22×#624C22semidirect
26. C32×#127C22semidirect
29. #64148C22semidirect
31. #64146C22semidirect
32. #64145C22semidirect
34. #64081C22semidirect
36. C3×#939C22semidirect
37. C3×#939C22semidirect
38. C3×#939C22semidirect
39. C3×#938C22semidirect
40. C3×#938C22semidirect
41. C3×#935C22semidirect
42. C3×#935C22semidirect
43. C3×#935C22semidirect
44. C3×#935C22semidirect
45. C3×D4×Dic3C22semidirect
46. C3×D4×Dic3C22semidirect
47. C3×#872C22semidirect
48. C3×#870C22semidirect
50. #63983C22semidirect
51. #63982C22semidirect
54. #63978C22semidirect
56. #63975C22semidirect
57. #63975C22semidirect
58. #63975C22semidirect
60. #63974C22semidirect
61. #67⋊Dic3C22semidirect
62. Dic3×#67C22semidirect
63. #63969C22semidirect
65. #63966C22semidirect
66. C2×Dic3⋊Dic3C22semidirect
67. #63964C22semidirect
68. #63964C22semidirect
70. #63962C22semidirect
71. #63959C22semidirect
72. #63959C22semidirect
74. #63958C22semidirect
75. #63956C22semidirect
76. #63955C22semidirect
77. #63953C22semidirect
78. #63953C22semidirect
79. #63952C22semidirect
80. #63952C22semidirect
81. #63952C22semidirect
83. D3×(C2×D3)⋊C4C22semidirect
88. #63896C22semidirect
89. #63895C22semidirect
90. #63895C22semidirect
91. #63895C22semidirect
92. #63883C22semidirect
93. #63880C22semidirect
94. #63868C22semidirect
95. #63867C22semidirect
96. #63862C22semidirect
97. #63858C22semidirect
100. #63851C22semidirect
101. #63850C22semidirect
102. #63848C22semidirect
103. #63848C22semidirect
104. #63846C22semidirect
105. #63840C22semidirect
106. #63838C22semidirect
107. #63836C22semidirect
109. #5719D3semidirect
242. C3×#127C2×D3semidirect
268. #939C2×D3semidirect
269. #939C2×D3semidirect
270. #939C2×D3semidirect
273. #938C2×D3semidirect
274. #938C2×D3semidirect
291. #935C2×D3semidirect
292. #935C2×D3semidirect
293. #935C2×D3semidirect
294. #935C2×D3semidirect
297. D4×Dic3C2×D3semidirect
298. D4×Dic3C2×D3semidirect
396. #872C2×D3semidirect
398. #870C2×D3semidirect
700. #127D32semidirect
1077. C32#3533semidirect
1188. C3#86489semidirect

Maximal subgroups

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

subgroupindex
#105961862
C3×#57192
#105953122
#105953102
#105953082
#105952962
#105952632
#105952552
#105952122
#105952032
#105951962
#105951692
#105951622
#105951382
#105951272
#105951182
#105940142
#105938722
#105938572
#864893