Finite Group Databasebeta

← #11911088

Subgroups — #11911088

Order 1152.

2497 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595995C211yesmaximal, characteristic, complemented
2C3×#5527C212yesmaximal, complemented
3#10595079C211yesmaximal, characteristic, complemented
4#10595077C212yesmaximal, complemented
5C2×#63912C211yesmaximal, characteristic, complemented
6#10594663C212yesmaximal, complemented
7#10594659C211yesmaximal, characteristic, complemented
8#10594610C211yesmaximal, characteristic, complemented
9#10594590C212yesmaximal, complemented
10#10594519C211yesmaximal, characteristic, complemented
11#10594491C211yesmaximal, characteristic, complemented
12#10594290C212yesmaximal, complemented
13#10594277C212yesmaximal, complemented
14#10594241C212yesmaximal, complemented
15#10594187C212yesmaximal, complemented
16#10594019C212yesmaximal, complemented
17#10594007C212yesmaximal, complemented
18#10593986C212yesmaximal, complemented
19#10593937C212yesmaximal, complemented
20#86801—32nomaximal
21C2×#3828C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×#3811C2211yescharacteristic
24C2×D3×#67C2212yescomplemented
25C22×#626C2212yescomplemented
26C22×#625C2211yescharacteristic, complemented
27C2×D3×D12C2212yescomplemented
28C2×#3799C2212yescomplemented
29C32×#117C2211yescharacteristic, complemented
30#64106C2211yescharacteristic, complemented
31#64106C2211yescharacteristic, complemented
32#64104C2211yescharacteristic, complemented
33#64104C2211yescharacteristic, complemented
34#64095C2212yescomplemented
35#64091C2212yescomplemented
36C4×C4⋊(C3⋊D3)C2212yescomplemented
37C4×C4⋊(C3⋊D3)C2212yescomplemented
38C3×#929C2212yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40C3×#898C2212yescomplemented
41C3×#896C2212yescomplemented
42C3×#894C2212yescomplemented
43C3×#894C2212yescomplemented
44C3×#882C2212yes—
45C3×#67⋊C4C2212yescomplemented
46C3×D3×C22⋊C4C2212yescomplemented
47C3×#878C2212yescomplemented
48C3×#876C2212yescomplemented
49C3×#875C2212yescomplemented
50C3×C4×D12C2212yescomplemented
51C3×#872C2212yescomplemented
52#63978C2212yes—
53#63977C2212yescomplemented
54#63974C2211yescharacteristic, complemented
55C2×#3724C2211yescharacteristic, complemented
56#63962C2212yescomplemented
57#63952C2212yescomplemented
58#63923C2212yescomplemented
59#63923C2212yescomplemented
60#63922C2212yescomplemented
61#63922C2212yescomplemented
62#63922C2212yescomplemented
63#63921C2212yescomplemented
64#63921C2211yescharacteristic, complemented
65#63921C2211yescharacteristic, complemented
66#63913C2212yescomplemented
67#63912C2211yescharacteristic
68#63912C2212yescomplemented
69#63912C2212yescomplemented
70#63912C2211yescharacteristic, complemented
71#63912C2212yescomplemented
72#63912C2211yescharacteristic, complemented
73#63912C2211yescharacteristic, complemented
74#63911C2212yescomplemented
75#63910C2212yescomplemented
76#63910C2212yescomplemented
77#63910C2212yescomplemented
78#63910C2212yescomplemented
79#63909C2212yescomplemented
80#63908C2212yescomplemented
81#63908C2212yescomplemented
82#63907C2212yescomplemented
83#63906C2212yescomplemented
84#63906C2212yescomplemented
85#63906C2212yescomplemented
86#63904C2212yescomplemented
87#63896C2212yescomplemented
88#63891C2212yescomplemented
89#63891C2212yescomplemented
90#63888C2212yescomplemented
91#63886C2212yescomplemented
92#63883C2211yescharacteristic, complemented
93#63883C2211yescharacteristic, complemented
94#63881C2212yescomplemented
95#63880C2212yescomplemented
96#63869C2212yescomplemented
97#63868C2212yescomplemented
98#63861C2212yescomplemented
99#63856C2212yescomplemented
100#63854C2212yescomplemented
101#63854C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63850C2212yescomplemented
106#63850C2212yescomplemented
107#63845C2212yescomplemented
108C3×#551—32no—
109#5711—32no—
110#5709—32no—
111#5707—32no—
112#5704—32no—
113#5678—32no—
114#5676—32no—
115#5667—32no—
116#5666—32no—
117#5657—32no—
118#5654—32no—
119#5653—32no—
120D3×#123—32no—
121#5647—32no—
122#5645—32no—
123#5630—32no—
124#5629—32no—
125#5590—32no—
126#5589—32no—
127#5564—32no—
128#5562—32no—
129#5550—32no—
130D4×D12—32no—
131#5535—32no—
132#5530—32no—
133#5527D312yescomplemented
134#5524—32no—
135#5524—61no—
136#5493—32no—
137#5490—32no—
138#5490—32no—
139C2×#884—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3×D3C2312yes—
142C22×D32C2311yescharacteristic
143C22×D32C2312yes—
144C22×C32×C4C2311yescharacteristic
145C2×#638C2312yes—
146C22×C3⋊Dic3C2311yescharacteristic
147#3828—42no—
148C2×C4⋊(C3⋊D3)C2312yes—
149C2×C4⋊(C3⋊D3)C2312yes—
150C2×C4⋊(C3⋊D3)C2311yescharacteristic
151C2×C4×C3⋊D3—42no—
152C2×C4×C3⋊D3C2311yescharacteristic
153C2×C4×C3⋊D3C2311yescharacteristic
154C2×C4×C3⋊D3C2312yes—
155C2×C4×C3⋊D3C2311yescharacteristic
156C2×C4×C3⋊D3C2311yescharacteristic
157C2×#634C2311yescharacteristic
158C2×C3×#67C2312yes—
159C22×C3×Dic3C2312yes—
160C2×C3×D12C2312yes—
161C2×C3×D12C2312yes—
162C2×C3×C4×D3C2312yes—
163C2×C3×C4×D3C2312yes—
164C2×C3×C4×D3C2312yes—
165C2×C3×Dic6C2312yes—
166#3811—42no—
167D3×#67—44no—
168C2×#626—44no—
169C2×#626C2312yes—
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#626C2312yes—
173C2×#626C2312yes—
174C2×#626C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#625—42no—
179C2×#625C2311yescharacteristic
180C2×#625C2312yes—
181C2×#625C2311yescharacteristic
182C2×#625C2312yes—
183C2×#624C2311yescharacteristic
184C2×#624C2312yes—
185C2×#624C2311yescharacteristic
186C2×#624C2311yescharacteristic
187C2×D3×Dic3C2312yes—
188D3×D12—44no—
189#3799—44no—
190C32×C4⋊C4C2311yescharacteristic
191C32×C4⋊C4C2311yescharacteristic
192C32×C22⋊C4C2312yes—
193C32×C42C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3752C2312yes—
197#3752C2312yes—
198C4⋊(C3⋊Dic3)C2312yes—
199C4⋊(C3⋊Dic3)C2312yes—
200C3×#217C2312yes—
201C3×(C2×D3)⋊C4C2312yes—
202C3×(C2×D3)⋊C4C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×C4⋊Dic3C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×Dic3⋊C4C2312yes—
218C3×C4×Dic3C2312yes—
219#3724C2312yes—
220#3724C2311yescharacteristic
221#3724C2312yes—
222#3724C2311yescharacteristic
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228#3722C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C22×#67—32no—
237C22×#67—32no—
238C22×#67—32no—
239C2×#239—32no—
240C2×D3×D4—32no—
241C2×D3×D4—32no—
242C2×D3×D4—32no—
243C2×#235—32no—
244C2×#235—32no—
245C2×#235—61no—
246C22×D12—32no—
247C22×D12—32no—
248C22×C4×D3—32no—
249C22×C4×D3—61no—
250C3×#126—32no—
251C3×#126—32no—
252C3×#124—32no—
253C3×#123—32no—
254C3×#123—32no—
255C3×#123—32no—
256C3×C22⋊Q8—32no—
257C3×C22⋊Q8—32no—
258C3×#120—32no—
259C3×C4×D4—32no—
260C3×C4×D4—32no—
261C3×#117—21no—
262C3×#117—32no—
263C3×#117C2×D312yescomplemented
264C2×C3×C22⋊C4—32no—
265C2×C3×C22⋊C4—32no—
266#953—32no—
267#947—32no—
268#946—32no—
269#946—32no—
270#940—32no—
271#939—32no—
272#939—32no—
273#938—32no—
274#938—32no—
275#937—32no—
276#937—32no—
277#937—32no—
278#935—32no—
279#930—32no—
280#930—32no—
281#930—32no—
282#930—32no—
283#930—32no—
284#930—32no—
285#930—32no—
286#929—32no—
287#929—32no—
288#929C2×D312yescomplemented
289C4×#67—32no—
290C4×#67—32no—
291C2×(C2×D3)⋊C4C2×D312yescomplemented
292#924—32no—
293C2×Dic3⋊C4—32no—
294#898—32no—
295#898—32no—
296#898C2×D312yescomplemented
297#897—32no—
298#897—32no—
299#897—61no—
300#897—61no—
301#896—32no—
302#896—32no—
303#896C2×D312yescomplemented
304#895—32no—
305#895—32no—
306#895—32no—
307#895—32no—
308#895—32no—
309#895—32no—
310#895—32no—
311#895—32no—
312#895—61no—
313#895—61no—
314#894—32no—
315#894—32no—
316#894—32no—
317#894—32no—
318#894—32no—
319#894—32no—
320#894—32no—
321#894C2×D312yescomplemented
322#894C2×D312yescomplemented
323#893—32no—
324#893—32no—
325D3×C4⋊C4—32no—
326D3×C4⋊C4—32no—
327#890—32no—
328#890—32no—
329#889—32no—
330#886—32no—
331#886—32no—
332#886—32no—
333#886—32no—
334#886—32no—
335#886—62no—
336#885—32no—
337#885—32no—
338#885—32no—
339#884—32no—
340#884—32no—
341#884—32no—
342#884—32no—
343#884—32no—
344#884—32no—
345#884—32no—
346#884—32no—
347#884—32no—
348#884—32no—
349#884—32no—
350#884—32no—
351#884—32no—
352#884—32no—
353#884—32no—
354#884—32no—
355#884—32no—
356#883—32no—
357#883—32no—
358#883—32no—
359#883—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#882—32no—
364#882—32no—
365#882—32no—
366#882—32no—
367#882—32no—
368#882—32no—
369#882—32no—
370#882—32no—
371#882—32no—
372#882—32no—
373#882—62no—
374#882C2×D312yes—
375#67⋊C4—32no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4C2×D312yescomplemented
379D3×C22⋊C4—32no—
380D3×C22⋊C4—32no—
381D3×C22⋊C4—32no—
382D3×C22⋊C4—32no—
383D3×C22⋊C4—32no—
384D3×C22⋊C4C2×D312yescomplemented
385#879—32no—
386#878—32no—
387#878C2×D312yescomplemented
388#876—32no—
389#876C2×D312yescomplemented
390#875C2×D312yescomplemented
391#874—32no—
392C4×D12—32no—
393C4×D12—32no—
394C4×D12—32no—
395C4×D12—32no—
396C4×D12—32no—
397C4×D12—62no—
398C4×D12—62no—
399C4×D12C2×D312yescomplemented
400#872C2×D312yescomplemented
401#870—32no—
402C23×C32C2411yescharacteristic
403C22×C3⋊D3—22no—
404C22×C3⋊D3—22no—
405C22×C3⋊D3—41no—
406C22×C3⋊D3C2412yes—
407C22×C3⋊D3C2411yescharacteristic
408C22×C3⋊D3C2411yescharacteristic
409C22×C3×D3—24no—
410C22×C3×D3—42no—
411C22×C3×D3—42no—
412C22×C3×D3C2412yes—
413C22×C3×D3C2412yes—
414C22×C3×D3C2412yes—
415C2×D32—22no—
416C2×D32—41no—
417C2×D32—42no—
418C2×D32—42no—
419C2×D32—42no—
420C2×D32—41no—
421C2×C32×C4—22no—
422C2×C32×C4C2412yes—
423C2×C32×C4C2411yescharacteristic
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2412yes—
426#638—24no—
427C2×C3⋊Dic3—22no—
428C2×C3⋊Dic3C2412yes—
429C2×C3⋊Dic3C2411yescharacteristic
430C2×C3⋊Dic3C2411yescharacteristic
431C4⋊(C3⋊D3)—24no—
432C4⋊(C3⋊D3)—42no—
433C4⋊(C3⋊D3)—41no—
434C4×C3⋊D3—41no—
435C4×C3⋊D3—41no—
436C4×C3⋊D3—41no—
437C4×C3⋊D3—41no—
438C4×C3⋊D3—42no—
439#634—41no—
440C3×#67—24no—
441C2×C3×Dic3—42no—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2412yes—
447C3×D12—42no—
448C3×D12—42no—
449C3×C4×D3—42no—
450C3×C4×D3—42no—
451C3×C4×D3—42no—
452C3×Dic6—42no—
453#626—24no—
454#626—24no—
455#626—42no—
456#626—42no—
457#626—42no—
458#626—42no—
459#626—42no—
460#626—42no—
461#626—42no—
462#625—41no—
463#625—42no—
464#625—41no—
465#625—42no—
466#624—22no—
467#624—42no—
468#624—41no—
469#624—41no—
470D3×Dic3—42no—
471#562—92no—
472#560—92no—
473#553—92no—
474#551—32no—
475#546—92no—
476#546—92no—
477#546—92no—
478D42—92no—
479#540—92no—
480#539—92no—
481#539—91no—
482#538—91no—
483#538—92no—
484#537—91no—
485#534—92no—
486#534—91no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C24×C3—32no—
491C23×D3—32no—
492C23×D3—32no—
493C23×D3—32no—
494C23×D3—32no—
495C23×D3—61no—
496C23×D3C22×D312yes—
497C2×C3×Q8—32no—
498C2×C3×D4—32no—
499C2×C3×D4—32no—
500C2×C3×D4—32no—
501C22×C3×C4—21no—
502C22×C3×C4—32no—
503C22×C3×C4—32no—
504C22×C3×C4—32no—
505C22×C3×C4—32no—
506C22×C3×C4C22×D312yes—
507C2×#67—32no—
508C2×#67—32no—
509C2×#67—32no—
510C2×#67—32no—
511C2×#67—32no—
512C2×#67—32no—
513C2×#67—32no—
514C2×#67—32no—
515C2×#67—32no—
516C2×#67—32no—
517C2×#67—32no—
518C2×#67—32no—
519C2×#67—32no—
520C2×#67—32no—
521C2×#67—32no—
522C2×#67—32no—
523C2×#67—32no—
524C2×#67—62no—
525C2×#67—124no—
526C2×#67—124no—
527C2×#67—124no—
528C2×#67C22×D312yes—
529C22×Dic3—32no—
530C22×Dic3—32no—
531C22×Dic3—61no—
532C22×Dic3C22×D312yes—
533#239—124no—
534D3×D4—124no—
535D3×D4—124no—
536D3×D4—124no—
537#235—124no—
538#235—124no—
539#235—124no—
540C2×D12—32no—
541C2×D12—32no—
542C2×D12—32no—
543C2×D12—32no—
544C2×D12—32no—
545C2×D12—32no—
546C2×D12—32no—
547C2×D12—32no—
548C2×D12—32no—
549C2×D12—32no—
550C2×D12—32no—
551C2×D12—32no—
552C2×D12—32no—
553C2×D12—32no—
554C2×D12—62no—
555C2×D12—62no—
556C2×D12—61no—
557C2×D12—124no—
558C2×D12—124no—
559C2×D12C22×D312yes—
560C2×D12C22×D312yes—
561C2×C4×D3—32no—
562C2×C4×D3—32no—
563C2×C4×D3—32no—
564C2×C4×D3—32no—
565C2×C4×D3—32no—
566C2×C4×D3—32no—
567C2×C4×D3—32no—
568C2×C4×D3—32no—
569C2×C4×D3—32no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—61no—
574C2×C4×D3—61no—
575C2×C4×D3—62no—
576C2×C4×D3—61no—
577C2×C4×D3—61no—
578C2×C4×D3—124no—
579C2×C4×D3—124no—
580C2×C4×D3C22×D312yes—
581C2×C4×D3C22×D312yes—
582C2×C4×D3C22×D312yes—
583C2×Dic6—32no—
584C2×Dic6—61no—
585C2×Dic6C22×D312yes—
586C3×C4⋊C4—21no—
587C3×C4⋊C4—21no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—32no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4C22×D312yes—
595C3×C4⋊C4C22×D312yes—
596C3×C22⋊C4—22no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4C22×D312yes—
610C3×C22⋊C4C22×D312yes—
611C3×C42—22no—
612C3×C42—32no—
613C3×C42C22×D312yes—
614C3×C42C22×D312yes—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217—32no—
620#217C22×D312yes—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—62no—
641(C2×D3)⋊C4—62no—
642(C2×D3)⋊C4—62no—
643(C2×D3)⋊C4—62no—
644(C2×D3)⋊C4C22×D312yes—
645(C2×D3)⋊C4C22×D312yes—
646(C2×D3)⋊C4C22×D312yes—
647(C2×D3)⋊C4C22×D312yes—
648(C2×D3)⋊C4C22×D312yes—
649(C2×D3)⋊C4C22×D312yes—
650(C2×D3)⋊C4C22×D312yes—
651(C2×D3)⋊C4C22×D312yes—
652(C2×D3)⋊C4C22×D312yes—
653(C2×D3)⋊C4C22×D312yes—
654(C2×D3)⋊C4C22×D312yes—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—32no—
659C4⋊Dic3—32no—
660C4⋊Dic3—32no—
661C4⋊Dic3—32no—
662C4⋊Dic3—62no—
663C4⋊Dic3—62no—
664C4⋊Dic3C22×D312yes—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676Dic3⋊C4C22×D312yes—
677Dic3⋊C4C22×D312yes—
678Dic3⋊C4C22×D312yes—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3C22×D312yes—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32H(5,𝔽2)12yes—
685C22×C32C2511yescharacteristic
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—22no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—22no—
693C2×C3⋊D3—22no—
694C2×C3⋊D3—44no—
695C2×C3⋊D3H(5,𝔽2)12yes—
696C2×C3×D3—22no—
697C2×C3×D3—22no—
698C2×C3×D3—22no—
699C2×C3×D3—22no—
700C2×C3×D3—22no—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—84no—
706D32—82no—
707D32—84no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—22no—
711C32×C4—22no—
712C3⋊Dic3—22no—
713C3⋊Dic3—21no—
714C3⋊Dic3—21no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C2×#41—92no—
721C2×#41—91no—
722C22×D4—92no—
723C22×D4—92no—
724C22×D4—91no—
725C22×D4—92no—
726C22×D4—91no—
727C23×C4—91no—
728#127—92no—
729#126—32no—
730#126—32no—
731#126—92no—
732#126—92no—
733#125—92no—
734#125—92no—
735#124—32no—
736#124—92no—
737#124—92no—
738#123—32no—
739#123—32no—
740#123—32no—
741#123—92no—
742#123—92no—
743#123—92no—
744#123—92no—
745#123—92no—
746#123—92no—
747#123—92no—
748#123—92no—
749#123—92no—
750#123—92no—
751#123—92no—
752C22⋊Q8—32no—
753C22⋊Q8—32no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—91no—
758C22⋊Q8—91no—
759#121—91no—
760#121—91no—
761#121—91no—
762#121—91no—
763#121—92no—
764#121—92no—
765#121—92no—
766#121—92no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—92no—
774#121—92no—
775#121—92no—
776#121—92no—
777#121—92no—
778#121—91no—
779#121—91no—
780#120—32no—
781#120—92no—
782#120—92no—
783#120—92no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788C4×D4—32no—
789C4×D4—32no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796#117—32no—
797#117D3211yescharacteristic, complemented
798C2×C4⋊C4—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C22⋊C4—32no—
802C2×C22⋊C4—32no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—91no—
806C2×C22⋊C4—92no—
807C23×C3—21no—
808C23×C3—32no—
809C23×C3—32no—
810C23×C3—32no—
811C23×C3—64no—
812C23×C3—122no—
813C23×C3—122no—
814C23×C3C23×D312yes—
815C22×D3—24no—
816C22×D3—32no—
817C22×D3—32no—
818C22×D3—32no—
819C22×D3—32no—
820C22×D3—42no—
821C22×D3—42no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—62no—
825C22×D3—64no—
826C22×D3—64no—
827C22×D3—64no—
828C22×D3—122no—
829C22×D3—122no—
830C22×D3—122no—
831C22×D3—122no—
832C22×D3—122no—
833C22×D3—122no—
834C22×D3—122no—
835C22×D3—122no—
836C22×D3—122no—
837C22×D3—122no—
838C22×D3—122no—
839C22×D3—122no—
840C22×D3C23×D312yes—
841C22×D3C23×D312yes—
842C22×D3C23×D312yes—
843C3×Q8—122no—
844C3×D4—64no—
845C3×D4—122no—
846C3×D4—122no—
847C2×C3×C4—24no—
848C2×C3×C4—24no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—22no—
852C2×C3×C4—22no—
853C2×C3×C4—32no—
854C2×C3×C4—32no—
855C2×C3×C4—32no—
856C2×C3×C4—32no—
857C2×C3×C4—32no—
858C2×C3×C4—122no—
859C2×C3×C4—122no—
860C2×C3×C4—122no—
861C2×C3×C4—122no—
862C2×C3×C4C23×D312yes—
863C2×C3×C4C23×D312yes—
864C2×C3×C4C23×D312yes—
865C2×C3×C4C23×D312yes—
866C2×C3×C4C23×D312yes—
867C2×C3×C4C23×D312yes—
868#67—24no—
869#67—64no—
870#67—64no—
871#67—64no—
872#67—64no—
873#67—124no—
874#67—122no—
875#67—122no—
876#67—122no—
877#67—122no—
878#67—122no—
879#67—122no—
880#67—122no—
881#67—122no—
882#67—122no—
883#67—122no—
884#67—122no—
885#67—122no—
886#67—122no—
887C2×Dic3—32no—
888C2×Dic3—32no—
889C2×Dic3—32no—
890C2×Dic3—32no—
891C2×Dic3—42no—
892C2×Dic3—62no—
893C2×Dic3—61no—
894C2×Dic3—61no—
895C2×Dic3—64no—
896C2×Dic3—122no—
897C2×Dic3—122no—
898C2×Dic3C23×D312yes—
899C2×Dic3C23×D312yes—
900C2×Dic3C23×D312yes—
901C2×Dic3C23×D312yes—
902C2×Dic3C23×D312yes—
903D12—42no—
904D12—42no—
905D12—64no—
906D12—64no—
907D12—64no—
908D12—64no—
909D12—124no—
910D12—122no—
911D12—122no—
912D12—122no—
913D12—122no—
914D12—124no—
915D12—122no—
916D12—122no—
917D12—122no—
918D12—122no—
919D12—122no—
920D12—122no—
921D12—122no—
922C4×D3—42no—
923C4×D3—42no—
924C4×D3—42no—
925C4×D3—64no—
926C4×D3—122no—
927C4×D3—122no—
928C4×D3—122no—
929C4×D3—122no—
930C4×D3—122no—
931C4×D3—122no—
932C4×D3—122no—
933C4×D3—122no—
934C4×D3—122no—
935C4×D3—122no—
936C4×D3—122no—
937C4×D3—122no—
938C4×D3—122no—
939C4×D3—122no—
940C4×D3—122no—
941C4×D3—124no—
942Dic6—42no—
943Dic6—122no—
944Dic6—122no—
945C2×C32—22no—
946C2×C32C2×H(5,𝔽2)11yescharacteristic
947C2×C32C2×H(5,𝔽2)11yescharacteristic
948C2×C32#58511yescharacteristic
949C3⋊D3—22no—
950C3⋊D3—41no—
951C3⋊D3—42no—
952C3×D3—42no—
953C3×D3—42no—
954C3×D3—42no—
955C24—32no—
956C24—91no—
957C24—92no—
958C24—91no—
959#41—362no—
960#41—364no—
961C2×Q8—32no—
962C2×Q8—91no—
963C2×D4—32no—
964C2×D4—32no—
965C2×D4—32no—
966C2×D4—92no—
967C2×D4—92no—
968C2×D4—92no—
969C2×D4—92no—
970C2×D4—92no—
971C2×D4—92no—
972C2×D4—92no—
973C2×D4—92no—
974C2×D4—92no—
975C2×D4—92no—
976C2×D4—91no—
977C2×D4—92no—
978C2×D4—92no—
979C2×D4—91no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—91no—
983C2×D4—364no—
984C2×D4—364no—
985C2×D4—362no—
986C2×D4—362no—
987C2×D4—364no—
988C22×C4—32no—
989C22×C4—32no—
990C22×C4—32no—
991C22×C4—32no—
992C22×C4—91no—
993C22×C4—91no—
994C22×C4—92no—
995C22×C4—91no—
996C22×C4—92no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—92no—
1001C22×C4—91no—
1002C22×C4—91no—
1003C22×C4—362no—
1004C22×C4C2×D3211yescharacteristic
1005C4⋊C4—32no—
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—91no—
1012C4⋊C4—92no—
1013C4⋊C4—91no—
1014C4⋊C4—92no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4C2×D3211yescharacteristic
1021C4⋊C4C2×D3211yescharacteristic
1022C22⋊C4—32no—
1023C22⋊C4—32no—
1024C22⋊C4—32no—
1025C22⋊C4—32no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4C2×D3212yes—
1047C42—32no—
1048C42—92no—
1049C42C2×D3212yes—
1050C22×C3—22no—
1051C22×C3—22no—
1052C22×C3—22no—
1053C22×C3—21no—
1054C22×C3—41no—
1055C22×C3—41no—
1056C22×C3—62no—
1057C22×C3—62no—
1058C22×C3—62no—
1059C22×C3—62no—
1060C22×C3—62no—
1061C22×C3—62no—
1062C22×C3—62no—
1063C22×C3—62no—
1064C22×C3—62no—
1065C22×C3—244no—
1066C22×C3#100914yes—
1067C22×C3C24×D312yes—
1068C2×D3—22no—
1069C2×D3—22no—
1070C2×D3—22no—
1071C2×D3—22no—
1072C2×D3—22no—
1073C2×D3—22no—
1074C2×D3—22no—
1075C2×D3—22no—
1076C2×D3—22no—
1077C2×D3—34no—
1078C2×D3—62no—
1079C2×D3—62no—
1080C2×D3—62no—
1081C2×D3—62no—
1082C2×D3—62no—
1083C2×D3—62no—
1084C2×D3—62no—
1085C2×D3—62no—
1086C2×D3—62no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—84no—
1092C2×D3—121no—
1093C2×D3—121no—
1094C2×D3—121no—
1095C2×D3—121no—
1096C2×D3—122no—
1097C2×D3—122no—
1098C2×D3—122no—
1099C2×D3—128no—
1100C2×D3—128no—
1101C2×D3—244no—
1102C2×D3—244no—
1103C2×D3—244no—
1104C3×C4—22no—
1105C3×C4—22no—
1106C3×C4—22no—
1107C3×C4—22no—
1108C3×C4—22no—
1109C3×C4—22no—
1110C3×C4—22no—
1111C3×C4—22no—
1112C3×C4—42no—
1113C3×C4—42no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—62no—
1117C3×C4—62no—
1118C3×C4—62no—
1119Dic3—22no—
1120Dic3—22no—
1121Dic3—22no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—62no—
1125Dic3—62no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—122no—
1129Dic3—121no—
1130Dic3—121no—
1131C32#353411yescharacteristic, complemented, Sylow
1132C23—32no—
1133C23—32no—
1134C23—32no—
1135C23—64no—
1136C23—91no—
1137C23—91no—
1138C23—92no—
1139C23—122no—
1140C23—122no—
1141C23—182no—
1142C23—182no—
1143C23—182no—
1144C23—361no—
1145C23—362no—
1146C23—361no—
1147C23—362no—
1148C23—361no—
1149C23—362no—
1150C23C22×D3211yescharacteristic
1151Q8—122no—
1152Q8—361no—
1153D4—64no—
1154D4—122no—
1155D4—122no—
1156D4—184no—
1157D4—184no—
1158D4—184no—
1159D4—184no—
1160D4—361no—
1161D4—362no—
1162D4—362no—
1163D4—362no—
1164D4—362no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168D4—362no—
1169D4—361no—
1170D4—362no—
1171D4—361no—
1172D4—362no—
1173C2×C4—22no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—92no—
1180C2×C4—91no—
1181C2×C4—91no—
1182C2×C4—122no—
1183C2×C4—122no—
1184C2×C4—122no—
1185C2×C4—122no—
1186C2×C4—182no—
1187C2×C4—182no—
1188C2×C4—361no—
1189C2×C4—361no—
1190C2×C4—361no—
1191C2×C4—361no—
1192C2×C4—362no—
1193C2×C4—361no—
1194C2×C4—362no—
1195C2×C4—361no—
1196C2×C4—362no—
1197C2×C4C22×D3212yes—
1198C2×C4C22×D3211yescharacteristic
1199C2×C4C22×D3212yes—
1200C2×C4C22×D3211yescharacteristic
1201C2×C3—24no—
1202C2×C3—21no—
1203C2×C3—21no—
1204C2×C3—21no—
1205C2×C3—42no—
1206C2×C3—122no—
1207C2×C3—122no—
1208C2×C3—122no—
1209C2×C3C2×#100912yes—
1210C2×C3#596412yes—
1211C2×C3D3×H(5,𝔽2)12yes—
1212D3—42no—
1213D3—42no—
1214D3—42no—
1215D3—64no—
1216D3—122no—
1217D3—122no—
1218D3—122no—
1219D3—122no—
1220D3—122no—
1221D3—242no—
1222C22—21no—
1223C22—21no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—62no—
1230C22—62no—
1231C22—62no—
1232C22—62no—
1233C22—92no—
1234C22—181no—
1235C22—181no—
1236C22—181no—
1237C22—182no—
1238C22—182no—
1239C22—181no—
1240C22—181no—
1241C22—182no—
1242C22—244no—
1243C22—364no—
1244C22—722no—
1245C22—724no—
1246C22#6430812yes—
1247C22C23×D3211yescharacteristic
1248C4—21no—
1249C4—21no—
1250C4—22no—
1251C4—22no—
1252C4—62no—
1253C4—62no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—181no—
1258C4—181no—
1259C4—182no—
1260C3—21no—
1261C3#8680112yescomplemented
1262C2—22no—
1263C2—122no—
1264C2—122no—
1265C2—122no—
1266C2—182no—
1267C2—361no—
1268C2—362no—
1269C2C2×#6430811yescharacteristic
1270C2#1059669211yescharacteristic
1271C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595995C2semidirect
2. C3×#5527C2semidirect
3. #10595079C2semidirect
4. #10595077C2semidirect
5. C2×#63912C2semidirect
6. #10594663C2semidirect
7. #10594659C2semidirect
8. #10594610C2semidirect
9. #10594590C2semidirect
10. #10594519C2semidirect
11. #10594491C2semidirect
12. #10594290C2semidirect
13. #10594277C2semidirect
14. #10594241C2semidirect
15. #10594187C2semidirect
16. #10594019C2semidirect
17. #10594007C2semidirect
18. #10593986C2semidirect
19. #10593937C2semidirect
21. C2×#3828C22semidirect
22. C22×C4×C3⋊D3C22semidirect
24. C2×D3×#67C22semidirect
25. C22×#626C22semidirect
26. C22×#625C22semidirect
27. C2×D3×D12C22semidirect
28. C2×#3799C22semidirect
29. C32×#117C22semidirect
30. #64106C22semidirect
31. #64106C22semidirect
32. #64104C22semidirect
33. #64104C22semidirect
34. #64095C22semidirect
35. #64091C22semidirect
36. C4×C4⋊(C3⋊D3)C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×#929C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C3×#898C22semidirect
41. C3×#896C22semidirect
42. C3×#894C22semidirect
43. C3×#894C22semidirect
45. C3×#67⋊C4C22semidirect
46. C3×D3×C22⋊C4C22semidirect
47. C3×#878C22semidirect
48. C3×#876C22semidirect
49. C3×#875C22semidirect
50. C3×C4×D12C22semidirect
51. C3×#872C22semidirect
53. #63977C22semidirect
54. #63974C22semidirect
55. C2×#3724C22semidirect
56. #63962C22semidirect
57. #63952C22semidirect
58. #63923C22semidirect
59. #63923C22semidirect
60. #63922C22semidirect
61. #63922C22semidirect
62. #63922C22semidirect
63. #63921C22semidirect
64. #63921C22semidirect
65. #63921C22semidirect
66. #63913C22semidirect
68. #63912C22semidirect
69. #63912C22semidirect
70. #63912C22semidirect
71. #63912C22semidirect
72. #63912C22semidirect
73. #63912C22semidirect
74. #63911C22semidirect
75. #63910C22semidirect
76. #63910C22semidirect
77. #63910C22semidirect
78. #63910C22semidirect
79. #63909C22semidirect
80. #63908C22semidirect
81. #63908C22semidirect
82. #63907C22semidirect
83. #63906C22semidirect
84. #63906C22semidirect
85. #63906C22semidirect
86. #63904C22semidirect
87. #63896C22semidirect
88. #63891C22semidirect
89. #63891C22semidirect
90. #63888C22semidirect
91. #63886C22semidirect
92. #63883C22semidirect
93. #63883C22semidirect
94. #63881C22semidirect
95. #63880C22semidirect
96. #63869C22semidirect
97. #63868C22semidirect
98. #63861C22semidirect
99. #63856C22semidirect
100. #63854C22semidirect
101. #63854C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63850C22semidirect
106. #63850C22semidirect
107. #63845C22semidirect
133. #5527D3semidirect
263. C3×#117C2×D3semidirect
288. #929C2×D3semidirect
291. C2×(C2×D3)⋊C4C2×D3semidirect
296. #898C2×D3semidirect
303. #896C2×D3semidirect
321. #894C2×D3semidirect
322. #894C2×D3semidirect
378. #67⋊C4C2×D3semidirect
384. D3×C22⋊C4C2×D3semidirect
387. #878C2×D3semidirect
389. #876C2×D3semidirect
390. #875C2×D3semidirect
399. C4×D12C2×D3semidirect
400. #872C2×D3semidirect
797. #117D32semidirect
1131. C32#3534semidirect
1261. C3#86801semidirect

Maximal subgroups

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

subgroupindex
#105959952
C3×#55272
#105950792
#105950772
C2×#639122
#105946632
#105946592
#105946102
#105945902
#105945192
#105944912
#105942902
#105942772
#105942412
#105941872
#105940192
#105940072
#105939862
#105939372
#868013