Finite Group Databasebeta

← #11911031

Subgroups — #11911031

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#10596098C211yesmaximal, characteristic, complemented
2C3×#5647C212yesmaximal, complemented
3#10595438C211yesmaximal, characteristic, complemented
4#10595431C212yesmaximal, complemented
5#10595415C211yesmaximal, characteristic, complemented
6#10595090C212yesmaximal, complemented
7#10595081C211yesmaximal, characteristic, complemented
8#10595079C211yesmaximal, characteristic, complemented
9#10594653C212yesmaximal, complemented
10#10594633C212yesmaximal, complemented
11#10594611C212yesmaximal, complemented
12#10594610C211yesmaximal, characteristic, complemented
13#10594519C211yesmaximal, characteristic, complemented
14#10594461C212yesmaximal, complemented
15#10594338C212yesmaximal, complemented
16#10594306C212yesmaximal, complemented
17#10594284C212yesmaximal, complemented
18#10594282C212yesmaximal, complemented
19#10594151C212yesmaximal, complemented
20#87109—32nomaximal
21C2×#3832C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×#3811C2211yescharacteristic
24C2×#3811C2212yescomplemented
25C2×#3802C2211yescharacteristic, complemented
26C2×D3×D12C2212yescomplemented
27C2×D3×D12C2212yescomplemented
28C2×#3799C2212yescomplemented
29C32×C22⋊Q8C2211yescharacteristic, complemented
30#64155C2211yescharacteristic, complemented
31#64139C2211yescharacteristic, complemented
32#64104C2211yescharacteristic, complemented
33#64103C2212yescomplemented
34#64102C2212yescomplemented
35#64101C2211yescharacteristic, complemented
36#64091C2212yescomplemented
37#64090C2212yescomplemented
38C3×#947C2212yescomplemented
39C3×#946C2212yescomplemented
40C3×#930C2212yescomplemented
41C3×#929C2212yescomplemented
42C3×#897C2212yescomplemented
43C3×#896C2212yescomplemented
44C3×#895C2212yescomplemented
45C3×#894C2212yescomplemented
46C3×#894C2212yescomplemented
47C3×#889C2212yescomplemented
48C3×#885C2212yescomplemented
49C3×#884C2212yescomplemented
50C3×#884C2212yescomplemented
51C3×#883C2212yescomplemented
52#63983C2212yescomplemented
53#63980C2211yescharacteristic, complemented
54#63980C2211yescharacteristic, complemented
55#63979C2212yescomplemented
56#63974C2211yescharacteristic, complemented
57#63971C2212yescomplemented
58#63962C2212yescomplemented
59#63958C2212yescomplemented
60#63923C2212yescomplemented
61#63923C2212yescomplemented
62#63922C2212yes—
63#63922C2212yescomplemented
64#63922C2212yescomplemented
65#63922C2212yescomplemented
66#63921C2212yescomplemented
67#63921C2211yescharacteristic, complemented
68#63921C2211yescharacteristic, complemented
69#63921C2212yescomplemented
70D3×(C2×D3)⋊C4C2212yescomplemented
71#63916C2212yescomplemented
72#63916C2212yescomplemented
73#63912C2211yescharacteristic
74#63912C2211yescharacteristic, complemented
75#63910C2212yes—
76#63910C2212yescomplemented
77#63910C2212yescomplemented
78#63910C2212yescomplemented
79#63906C2212yescomplemented
80#63905C2212yescomplemented
81#63904C2212yescomplemented
82#63904C2212yescomplemented
83C4×#626C2212yescomplemented
84C4×#625C2212yescomplemented
85#63900C2211yescharacteristic, complemented
86#63894C2212yescomplemented
87#63891C2212yescomplemented
88#63888C2212yescomplemented
89#63888C2212yescomplemented
90#63886C2212yescomplemented
91#63885C2212yescomplemented
92#63883C2211yescharacteristic, complemented
93#63883C2211yescharacteristic, complemented
94#63880C2212yescomplemented
95#63878C2212yescomplemented
96#63863C2212yescomplemented
97#63862C2212yescomplemented
98#63861C2212yescomplemented
99#63859C2212yescomplemented
100#63854C2212yescomplemented
101#63854C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63850C2212yescomplemented
106#63848C2212yescomplemented
107#63847C2212yescomplemented
108C3×#562—32no—
109#5695—32no—
110#5692—32no—
111#5678—32no—
112#5678—32no—
113#5676—32no—
114#5676—32no—
115#5666—32no—
116#5663—32no—
117#5661—32no—
118#5659—32no—
119#5654—32no—
120#5653—32no—
121#5653—32no—
122D3×#123—32no—
123#5647D312yescomplemented
124#5638—32no—
125#5638—32no—
126#5637—32no—
127#5630—32no—
128#5630—32no—
129#5629—32no—
130#5627—32no—
131#5627—61no—
132#5620—32no—
133#5615—32no—
134#5613—32no—
135#5612—32no—
136#5609—32no—
137#5609—32no—
138#5605—32no—
139D3×#121—32no—
140C23×C3⋊D3C2311yescharacteristic
141C22×D32C2311yescharacteristic
142C22×D32C2312yes—
143C22×D32C2312yes—
144C2×C32×Q8C2311yescharacteristic
145C22×C32×C4C2311yescharacteristic
146C2×#638C2312yes—
147C22×C3⋊Dic3C2311yescharacteristic
148#3832—42no—
149C2×C4⋊(C3⋊D3)C2312yes—
150C2×C4⋊(C3⋊D3)C2312yes—
151C2×C4⋊(C3⋊D3)C2311yescharacteristic
152C2×C4×C3⋊D3—42no—
153C2×C4×C3⋊D3C2311yescharacteristic
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×C4×C3⋊D3C2312yes—
156C2×C4×C3⋊D3C2311yescharacteristic
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×D12C2312yes—
162C2×C3×D12C2312yes—
163C2×C3×D12C2312yes—
164C2×C3×C4×D3C2312yes—
165C2×C3×C4×D3C2312yes—
166C2×C3×C4×D3C2312yes—
167C2×C3×Dic6C2312yes—
168#3811—42no—
169#3811—44no—
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#626C2312yes—
173C2×#626C2312yes—
174C2×#626C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#625C2311yescharacteristic
178C2×#625C2311yescharacteristic
179C2×#625C2312yes—
180C2×#624C2311yescharacteristic
181C2×#624C2312yes—
182C2×#624C2311yescharacteristic
183C2×#624C2312yes—
184C2×#624C2311yescharacteristic
185C2×D3×Dic3C2312yes—
186#3802—42no—
187D3×D12—44no—
188D3×D12—44no—
189#3799—44no—
190C32×C4⋊C4C2312yes—
191C32×C4⋊C4C2311yescharacteristic
192C32×C22⋊C4C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3752C2312yes—
197C4⋊(C3⋊Dic3)C2311yescharacteristic
198#3750C2312yes—
199C4×C3⋊Dic3C2312yes—
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×C4⋊Dic3C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×C4×Dic3C2312yes—
218#3724C2311yescharacteristic
219#3724C2312yes—
220#3724C2311yescharacteristic
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C2×#239—32no—
237C2×#239—32no—
238C2×#239—61no—
239C2×D3×D4—32no—
240C2×D3×D4—32no—
241C2×D3×D4—32no—
242C2×D3×D4—32no—
243C2×D3×D4—32no—
244C2×D3×D4—32no—
245C2×#235—32no—
246C22×D12—32no—
247C22×D12—32no—
248C22×C4×D3—32no—
249C22×C4×D3—61no—
250C3×#125—32no—
251C3×#124—32no—
252C3×#124—32no—
253C3×#123—32no—
254C3×#123—32no—
255C3×#123—32no—
256C3×#123—32no—
257C3×C22⋊Q8—21no—
258C3×C22⋊Q8—32no—
259C3×C22⋊Q8—32no—
260C3×C22⋊Q8—32no—
261C3×C22⋊Q8C2×D312yescomplemented
262C3×#121—32no—
263C3×#121—32no—
264C3×#121—32no—
265C3×#121—32no—
266#947—32no—
267#947C2×D312yescomplemented
268#946—32no—
269#946—32no—
270#946—32no—
271#946—61no—
272#946C2×D312yescomplemented
273#940—32no—
274#940—32no—
275#939—32no—
276#939—32no—
277#939—32no—
278#939—32no—
279#939—32no—
280#938—32no—
281#938—32no—
282#938—32no—
283#937—32no—
284#937—32no—
285#937—32no—
286#937—32no—
287#937—32no—
288#937—32no—
289#936—32no—
290#935—32no—
291#930—32no—
292#930—32no—
293#930—61no—
294#930C2×D312yescomplemented
295#929—32no—
296#929—32no—
297#929C2×D312yescomplemented
298C4×#67—32no—
299C4×#67—32no—
300C4×#67—32no—
301C4×#67—32no—
302C4×#67—32no—
303C2×(C2×D3)⋊C4—32no—
304#898—32no—
305#898—32no—
306#898—32no—
307#898—32no—
308#897C2×D312yescomplemented
309#896—32no—
310#896—32no—
311#896C2×D312yescomplemented
312#895—32no—
313#895—32no—
314#895—32no—
315#895—32no—
316#895—32no—
317#895—32no—
318#895—32no—
319#895—32no—
320#895—61no—
321#895C2×D312yescomplemented
322#894—32no—
323#894—32no—
324#894—32no—
325#894—32no—
326#894—32no—
327#894—32no—
328#894—32no—
329#894—32no—
330#894—62no—
331#894C2×D312yescomplemented
332#894C2×D312yescomplemented
333#893—32no—
334#893—32no—
335#893—32no—
336#893—32no—
337#893—32no—
338#893—62no—
339#892—32no—
340#892—32no—
341#892—61no—
342D3×C4⋊C4—32no—
343D3×C4⋊C4—32no—
344D3×C4⋊C4—32no—
345#889—32no—
346#889—32no—
347#889C2×D312yescomplemented
348#886—32no—
349#886—32no—
350#885C2×D312yescomplemented
351#884—32no—
352#884—32no—
353#884—32no—
354#884—32no—
355#884—32no—
356#884—32no—
357#884—32no—
358#884—32no—
359#884—32no—
360#884—32no—
361#884C2×D312yescomplemented
362#884C2×D312yescomplemented
363#883—32no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883—32no—
368#883—32no—
369#883—32no—
370#883C2×D312yescomplemented
371#882—32no—
372#882—32no—
373#882—32no—
374#882—32no—
375#882—32no—
376#882—32no—
377#882—32no—
378#882—32no—
379#882—32no—
380#882—32no—
381#882—62no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—62no—
386D3×C22⋊C4—32no—
387D3×C22⋊C4—32no—
388D3×C22⋊C4—32no—
389D3×C22⋊C4—32no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—32no—
392D3×C22⋊C4—32no—
393D3×C22⋊C4—32no—
394#879—32no—
395#879—32no—
396#879—32no—
397#877—32no—
398#876—32no—
399C4×D12—32no—
400C4×D12—32no—
401C4×D12—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×D3C2412yes—
410C22×C3×D3C2412yes—
411C22×C3×D3C2412yes—
412C2×D32—22no—
413C2×D32—24no—
414C2×D32—42no—
415C2×D32—41no—
416C2×D32—42no—
417C2×D32—42no—
418C2×D32—42no—
419C2×D32—42no—
420C2×D32—41no—
421C32×Q8—41no—
422C2×C32×C4—41no—
423C2×C32×C4C2412yes—
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2411yescharacteristic
426C2×C32×C4C2412yes—
427#638—42no—
428C2×C3⋊Dic3—41no—
429C2×C3⋊Dic3C2412yes—
430C2×C3⋊Dic3C2411yescharacteristic
431C2×C3⋊Dic3C2411yescharacteristic
432C4⋊(C3⋊D3)—24no—
433C4⋊(C3⋊D3)—24no—
434C4⋊(C3⋊D3)—41no—
435C4×C3⋊D3—22no—
436C4×C3⋊D3—22no—
437C4×C3⋊D3—41no—
438C4×C3⋊D3—41no—
439C4×C3⋊D3—42no—
440C3×#67—42no—
441C3×#67—42no—
442C3×#67—42no—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2412yes—
447C2×C3×Dic3C2412yes—
448C3×D12—42no—
449C3×D12—42no—
450C3×D12—42no—
451C3×C4×D3—42no—
452C3×C4×D3—42no—
453C3×C4×D3—42no—
454C3×Dic6—42no—
455#626—24no—
456#626—24no—
457#626—24no—
458#626—42no—
459#626—42no—
460#626—42no—
461#626—42no—
462#625—41no—
463#625—41no—
464#625—42no—
465#624—22no—
466#624—42no—
467#624—41no—
468#624—42no—
469#624—41no—
470D3×Dic3—42no—
471#562—32no—
472#560—92no—
473#553—92no—
474#551—92no—
475#546—92no—
476#546—92no—
477#546—92no—
478D42—92no—
479#540—92no—
480#539—91no—
481#539—92no—
482#538—92no—
483#538—91no—
484#537—91no—
485#534—92no—
486#534—91no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C23×D3—32no—
491C23×D3—32no—
492C23×D3—32no—
493C23×D3—32no—
494C23×D3—32no—
495C23×D3—32no—
496C23×D3—61no—
497C2×C3×Q8—21no—
498C2×C3×Q8—32no—
499C2×C3×Q8C22×D312yes—
500C2×C3×D4—32no—
501C2×C3×D4—32no—
502C2×C3×D4—32no—
503C2×C3×D4—32no—
504C2×C3×D4—32no—
505C2×C3×D4—32no—
506C22×C3×C4—21no—
507C22×C3×C4—32no—
508C22×C3×C4—32no—
509C22×C3×C4—32no—
510C22×C3×C4C22×D312yes—
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×#67C22×D312yes—
526C2×#67C22×D312yes—
527C2×#67C22×D312yes—
528C22×Dic3—32no—
529C22×Dic3—32no—
530C22×Dic3—61no—
531#239—124no—
532#239—124no—
533#239—124no—
534D3×D4—124no—
535D3×D4—124no—
536D3×D4—124no—
537D3×D4—124no—
538D3×D4—124no—
539D3×D4—124no—
540#235—124no—
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—62no—
554C2×D12—62no—
555C2×D12—61no—
556C2×D12—124no—
557C2×D12—124no—
558C2×D12C22×D312yes—
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—32no—
574C2×C4×D3—32no—
575C2×C4×D3—61no—
576C2×C4×D3—62no—
577C2×C4×D3—61no—
578C2×C4×D3—61no—
579C2×C4×D3—61no—
580C2×C4×D3—124no—
581C2×C4×D3—124no—
582C2×C4×D3C22×D312yes—
583C2×C4×D3C22×D312yes—
584C2×C4×D3C22×D312yes—
585C2×Dic6C22×D312yes—
586C3×C4⋊C4—21no—
587C3×C4⋊C4—22no—
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⋊C4—32no—
595C3×C4⋊C4C22×D312yes—
596C3×C4⋊C4C22×D312yes—
597C3×C4⋊C4C22×D312yes—
598C3×C22⋊C4—22no—
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—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217C22×D312yes—
620(C2×D3)⋊C4—32no—
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—32no—
641(C2×D3)⋊C4—62no—
642(C2×D3)⋊C4—62no—
643(C2×D3)⋊C4—62no—
644(C2×D3)⋊C4—62no—
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—
654C4⋊Dic3—32no—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—61no—
659C4⋊Dic3C22×D312yes—
660C4⋊Dic3C22×D312yes—
661Dic3⋊C4—32no—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—62no—
671Dic3⋊C4C22×D312yes—
672Dic3⋊C4C22×D312yes—
673Dic3⋊C4C22×D312yes—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676C4×Dic3—32no—
677C4×Dic3—32no—
678C4×Dic3—32no—
679C4×Dic3—32no—
680C4×Dic3—62no—
681C4×Dic3C22×D312yes—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32C2511yescharacteristic
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—22no—
691C2×C3⋊D3—22no—
692C2×C3⋊D3—22no—
693C2×C3⋊D3—44no—
694C2×C3⋊D3H(5,𝔽2)12yes—
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—
705D32—82no—
706D32—84no—
707D32—84no—
708C32×C4—21no—
709C32×C4—22no—
710C32×C4—22no—
711C32×C4—21no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—22no—
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—92no—
730#126—92no—
731#126—92no—
732#126—92no—
733#125—32no—
734#125—92no—
735#124—32no—
736#124—32no—
737#124—92no—
738#123—32no—
739#123—32no—
740#123—32no—
741#123—32no—
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—32no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—91no—
758C22⋊Q8D3211yescharacteristic, complemented
759#121—32no—
760#121—32no—
761#121—32no—
762#121—32no—
763#121—91no—
764#121—91no—
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—91no—
777#121—91no—
778#121—91no—
779#121—91no—
780#120—92no—
781#120—92no—
782#120—92no—
783#120—92no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788C4×D4—92no—
789C4×D4—92no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796#117—92no—
797#117—91no—
798C2×C4⋊C4—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C22⋊C4—92no—
802C2×C22⋊C4—91no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—92no—
806C2×C22⋊C4—92no—
807C23×C3—21no—
808C23×C3—32no—
809C23×C3—32no—
810C23×C3—32no—
811C23×C3C23×D312yes—
812C22×D3—32no—
813C22×D3—32no—
814C22×D3—32no—
815C22×D3—32no—
816C22×D3—61no—
817C22×D3—61no—
818C22×D3—62no—
819C22×D3—64no—
820C22×D3—64no—
821C22×D3—64no—
822C22×D3—64no—
823C22×D3—64no—
824C22×D3—122no—
825C22×D3—122no—
826C22×D3—122no—
827C22×D3—122no—
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—42no—
844C3×Q8—42no—
845C3×Q8—122no—
846C3×D4—122no—
847C3×D4—122no—
848C3×D4—122no—
849C3×D4—122no—
850C3×D4—122no—
851C3×D4—122no—
852C2×C3×C4—21no—
853C2×C3×C4—22no—
854C2×C3×C4—22no—
855C2×C3×C4—21no—
856C2×C3×C4—32no—
857C2×C3×C4—32no—
858C2×C3×C4—32no—
859C2×C3×C4—32no—
860C2×C3×C4—32no—
861C2×C3×C4—42no—
862C2×C3×C4—42no—
863C2×C3×C4—122no—
864C2×C3×C4—122no—
865C2×C3×C4—122no—
866C2×C3×C4C23×D312yes—
867C2×C3×C4C23×D312yes—
868C2×C3×C4C23×D312yes—
869C2×C3×C4C23×D312yes—
870C2×C3×C4C23×D312yes—
871C2×C3×C4C23×D312yes—
872#67—42no—
873#67—42no—
874#67—42no—
875#67—64no—
876#67—64no—
877#67—64no—
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—
887#67—122no—
888#67—124no—
889C2×Dic3—32no—
890C2×Dic3—32no—
891C2×Dic3—32no—
892C2×Dic3—32no—
893C2×Dic3—61no—
894C2×Dic3—62no—
895C2×Dic3—61no—
896C2×Dic3—122no—
897C2×Dic3—122no—
898C2×Dic3—122no—
899C2×Dic3C23×D312yes—
900C2×Dic3C23×D312yes—
901C2×Dic3C23×D312yes—
902C2×Dic3C23×D312yes—
903C2×Dic3C23×D312yes—
904D12—42no—
905D12—42no—
906D12—42no—
907D12—64no—
908D12—64no—
909D12—64no—
910D12—64no—
911D12—64no—
912D12—64no—
913D12—64no—
914D12—124no—
915D12—124no—
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—64no—
927C4×D3—64no—
928C4×D3—64no—
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—
942C4×D3—122no—
943C4×D3—122no—
944Dic6—42no—
945C2×C32—41no—
946C2×C32C2×H(5,𝔽2)11yescharacteristic
947C2×C32C2×H(5,𝔽2)11yescharacteristic
948C2×C32#58511yescharacteristic
949C3⋊D3—22no—
950C3⋊D3—22no—
951C3⋊D3—42no—
952C3×D3—42no—
953C3×D3—42no—
954C3×D3—42no—
955C24—91no—
956C24—92no—
957C24—92no—
958C24—91no—
959#41—364no—
960#41—362no—
961C2×Q8—32no—
962C2×Q8C2×D3211yescharacteristic
963C2×D4—32no—
964C2×D4—32no—
965C2×D4—32no—
966C2×D4—32no—
967C2×D4—32no—
968C2×D4—32no—
969C2×D4—92no—
970C2×D4—92no—
971C2×D4—92no—
972C2×D4—92no—
973C2×D4—92no—
974C2×D4—92no—
975C2×D4—92no—
976C2×D4—92no—
977C2×D4—91no—
978C2×D4—91no—
979C2×D4—92no—
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—91no—
992C22×C4—91no—
993C22×C4—92no—
994C22×C4—92no—
995C22×C4—91no—
996C22×C4—92no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—91no—
1001C22×C4—91no—
1002C22×C4—92no—
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—32no—
1012C4⋊C4—92no—
1013C4⋊C4—91no—
1014C4⋊C4—91no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—91no—
1019C4⋊C4—92no—
1020C4⋊C4C2×D3211yescharacteristic
1021C4⋊C4C2×D3212yes—
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—92no—
1033C22⋊C4—92no—
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—
1049C42—92no—
1050C22×C3—22no—
1051C22×C3—22no—
1052C22×C3—22no—
1053C22×C3—22no—
1054C22×C3—21no—
1055C22×C3—41no—
1056C22×C3—41no—
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—62no—
1066C22×C3C24×D312yes—
1067C2×D3—22no—
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—34no—
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—121no—
1091C2×D3—121no—
1092C2×D3—121no—
1093C2×D3—121no—
1094C2×D3—122no—
1095C2×D3—122no—
1096C2×D3—122no—
1097C2×D3—128no—
1098C2×D3—128no—
1099C2×D3—244no—
1100C2×D3—244no—
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—41no—
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—62no—
1129Dic3—121no—
1130Dic3—122no—
1131C32#353411yescharacteristic, complemented, Sylow
1132C23—32no—
1133C23—32no—
1134C23—32no—
1135C23—91no—
1136C23—91no—
1137C23—92no—
1138C23—182no—
1139C23—182no—
1140C23—184no—
1141C23—182no—
1142C23—361no—
1143C23—362no—
1144C23—361no—
1145C23—362no—
1146C23—362no—
1147C23—362no—
1148C23—361no—
1149C23—362no—
1150C23C22×D3211yescharacteristic
1151Q8—41no—
1152Q8—122no—
1153D4—122no—
1154D4—122no—
1155D4—122no—
1156D4—122no—
1157D4—122no—
1158D4—122no—
1159D4—184no—
1160D4—184no—
1161D4—184no—
1162D4—184no—
1163D4—184no—
1164D4—361no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168D4—362no—
1169D4—362no—
1170D4—361no—
1171D4—361no—
1172D4—362no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—41no—
1179C2×C4—92no—
1180C2×C4—91no—
1181C2×C4—91no—
1182C2×C4—122no—
1183C2×C4—122no—
1184C2×C4—122no—
1185C2×C4—182no—
1186C2×C4—182no—
1187C2×C4—182no—
1188C2×C4—361no—
1189C2×C4—361no—
1190C2×C4—362no—
1191C2×C4—361no—
1192C2×C4—362no—
1193C2×C4—362no—
1194C2×C4—361no—
1195C2×C4—362no—
1196C2×C4—361no—
1197C2×C4C22×D3212yes—
1198C2×C4C22×D3212yes—
1199C2×C4C22×D3211yescharacteristic
1200C2×C4C22×D3211yescharacteristic
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—21no—
1204C2×C3—42no—
1205C2×C3—42no—
1206C2×C3—122no—
1207C2×C3—122no—
1208C2×C3—122no—
1209C2×C3D3×H(5,𝔽2)12yes—
1210C2×C3D3×H(5,𝔽2)12yes—
1211C2×C3#596812yes—
1212D3—42no—
1213D3—42no—
1214D3—42no—
1215D3—64no—
1216D3—64no—
1217D3—122no—
1218D3—122no—
1219D3—122no—
1220D3—122no—
1221D3—242no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—62no—
1230C22—62no—
1231C22—62no—
1232C22—62no—
1233C22—62no—
1234C22—92no—
1235C22—92no—
1236C22—181no—
1237C22—181no—
1238C22—181no—
1239C22—181no—
1240C22—182no—
1241C22—182no—
1242C22—182no—
1243C22—364no—
1244C22—722no—
1245C22—724no—
1246C22—724no—
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#8710912yescomplemented
1262C2—41no—
1263C2—122no—
1264C2—122no—
1265C2—122no—
1266C2—182no—
1267C2—182no—
1268C2—362no—
1269C2#1059667511yescharacteristic
1270C2#1059668911yescharacteristic
1271C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596098C2semidirect
2. C3×#5647C2semidirect
3. #10595438C2semidirect
4. #10595431C2semidirect
5. #10595415C2semidirect
6. #10595090C2semidirect
7. #10595081C2semidirect
8. #10595079C2semidirect
9. #10594653C2semidirect
10. #10594633C2semidirect
11. #10594611C2semidirect
12. #10594610C2semidirect
13. #10594519C2semidirect
14. #10594461C2semidirect
15. #10594338C2semidirect
16. #10594306C2semidirect
17. #10594284C2semidirect
18. #10594282C2semidirect
19. #10594151C2semidirect
21. C2×#3832C22semidirect
22. C22×C4×C3⋊D3C22semidirect
24. C2×#3811C22semidirect
25. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
27. C2×D3×D12C22semidirect
28. C2×#3799C22semidirect
29. C32×C22⋊Q8C22semidirect
30. #64155C22semidirect
31. #64139C22semidirect
32. #64104C22semidirect
33. #64103C22semidirect
34. #64102C22semidirect
35. #64101C22semidirect
36. #64091C22semidirect
37. #64090C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
40. C3×#930C22semidirect
41. C3×#929C22semidirect
42. C3×#897C22semidirect
43. C3×#896C22semidirect
44. C3×#895C22semidirect
45. C3×#894C22semidirect
46. C3×#894C22semidirect
47. C3×#889C22semidirect
48. C3×#885C22semidirect
49. C3×#884C22semidirect
50. C3×#884C22semidirect
51. C3×#883C22semidirect
52. #63983C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
55. #63979C22semidirect
56. #63974C22semidirect
57. #63971C22semidirect
58. #63962C22semidirect
59. #63958C22semidirect
60. #63923C22semidirect
61. #63923C22semidirect
63. #63922C22semidirect
64. #63922C22semidirect
65. #63922C22semidirect
66. #63921C22semidirect
67. #63921C22semidirect
68. #63921C22semidirect
69. #63921C22semidirect
70. D3×(C2×D3)⋊C4C22semidirect
71. #63916C22semidirect
72. #63916C22semidirect
74. #63912C22semidirect
76. #63910C22semidirect
77. #63910C22semidirect
78. #63910C22semidirect
79. #63906C22semidirect
80. #63905C22semidirect
81. #63904C22semidirect
82. #63904C22semidirect
83. C4×#626C22semidirect
84. C4×#625C22semidirect
85. #63900C22semidirect
86. #63894C22semidirect
87. #63891C22semidirect
88. #63888C22semidirect
89. #63888C22semidirect
90. #63886C22semidirect
91. #63885C22semidirect
92. #63883C22semidirect
93. #63883C22semidirect
94. #63880C22semidirect
95. #63878C22semidirect
96. #63863C22semidirect
97. #63862C22semidirect
98. #63861C22semidirect
99. #63859C22semidirect
100. #63854C22semidirect
101. #63854C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63850C22semidirect
106. #63848C22semidirect
107. #63847C22semidirect
123. #5647D3semidirect
261. C3×C22⋊Q8C2×D3semidirect
267. #947C2×D3semidirect
272. #946C2×D3semidirect
294. #930C2×D3semidirect
297. #929C2×D3semidirect
308. #897C2×D3semidirect
311. #896C2×D3semidirect
321. #895C2×D3semidirect
331. #894C2×D3semidirect
332. #894C2×D3semidirect
347. #889C2×D3semidirect
350. #885C2×D3semidirect
361. #884C2×D3semidirect
362. #884C2×D3semidirect
370. #883C2×D3semidirect
758. C22⋊Q8D32semidirect
1131. C32#3534semidirect
1261. C3#87109semidirect

Maximal subgroups

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

subgroupindex
#105960982
C3×#56472
#105954382
#105954312
#105954152
#105950902
#105950812
#105950792
#105946532
#105946332
#105946112
#105946102
#105945192
#105944612
#105943382
#105943062
#105942842
#105942822
#105941512
#871093