Finite Group Databasebeta

← #11860938

Subgroups — #11860938

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595353C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic
3#10594361C211yesmaximal, characteristic, complemented
4#10592502C211yesmaximal, characteristic, complemented
5C3×#4789C211yesmaximal, characteristic, complemented
6C3×#4788C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10#10590910C211yesmaximal, characteristic, complemented
11#10590792C211yesmaximal, characteristic, complemented
12#10590746C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590575C211yesmaximal, characteristic, complemented
15#10590458C211yesmaximal, characteristic, complemented
16#79832—31nomaximal
17#79650—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63950C418yescomplemented
29C4×#626—21no—
30#63900—21no—
31#63900C2211yescharacteristic
32#63894—21no—
33#63894—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63881—21no—
38#63877—21no—
39D3×Dic3⋊C4—21no—
40#63874—21no—
41#63874C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63662C2211yescharacteristic
48#63648C2211yescharacteristic
49#63636C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63573C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#919—31no—
63C2×#916—31no—
64#5574—31no—
65#5574—31no—
66#5574—31no—
67#5546—31no—
68C3×#441—31no—
69C3×C4×SD16—31no—
70#5184—31no—
71Dic3×SD16—31no—
72#5030—31no—
73C4×#215—31no—
74C4×#215—31no—
75#5014—31no—
76#4869—31no—
77D3×#106—31no—
78D3×#106—31no—
79#4852—31no—
80#4803—31no—
81#4803—31no—
82#4803—31no—
83#4803—61no—
84#4789D311yescharacteristic, complemented
85#4788—31no—
86#4788D311yescharacteristic, complemented
87#4785—31no—
88#4771—31no—
89#4711—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832C2×C414yescomplemented
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—22no—
118C3×#216C2×C414yescomplemented
119C3×#215C2×C414yescomplemented
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724D411yescharacteristic
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3714C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2952—91noSylow
147C2×#239—31no—
148C2×#239—31no—
149C2×#239—31no—
150C2×#239—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159Q8×Dic3C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161C2×#216C2×D311yescharacteristic
162C2×#215—31no—
163C2×#215C2×D311yescharacteristic
164D4×Dic3—31no—
165C2×#213—31no—
166C4×#67—61no—
167C2×Dic3⋊C4—61no—
168#919—38no—
169#916—38no—
170C2×D24—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—61no—
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177#893—31no—
178#893—31no—
179#893—61no—
180#893—61no—
181#893—61no—
182#893C2×D311yescharacteristic
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#877—61no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12—61no—
199C4×D12—61no—
200#872—31no—
201#872—31no—
202#872—61no—
203#872—61no—
204#872—61no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—61no—
219#832—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224#817—31no—
225#817—31no—
226#816C2×D311yescharacteristic
227#815—31no—
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic
239#808C2×D311yescharacteristic
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—24no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—24no—
256C4×C3⋊D3—81no—
257C4×C3⋊D3C22×C412yes—
258C4×C3⋊D3#4112yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6C22×C412yes—
271#626—24no—
272#624—81no—
273#624—81no—
274#624—81no—
275D3×Dic3—24no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8C22×C412yes—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—91no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—31no—
287#441—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305#239—34no—
306#239—34no—
307#239—34no—
308#239—64no—
309#239—62no—
310#239—62no—
311#239—62no—
312#239—122no—
313#237—34no—
314#237—62no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—121no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C2×Dic6C22×D311yescharacteristic
342C3×Q16—34no—
343C3×SD16—34no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42—61no—
363#217—61no—
364#216C4×D314yescomplemented
365#215—34no—
366#215C4×D314yescomplemented
367#213—34no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3—21no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—34no—
410#204—34no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—122no—
414D3×C8—34no—
415D3×C8—34no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3C4×D412yes—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C32×C4—22no—
427C32×C4—41no—
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3C4×D412yes—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C2×#41—91no—
441#135—98no—
442C2×Q16—31no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×M16—91no—
447C22×C8—91no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458C4×D4—181no—
459C4×D4—181no—
460#117—91no—
461#117—181no—
462#117—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—181no—
466C2×C4⋊C4—181no—
467#106—31no—
468#106—31no—
469#106—91no—
470#106—91no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103D3211yescharacteristic
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#97—31no—
480#97—91no—
481C4×C8—31no—
482C4×C8—91no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—22no—
494C3×Q8—32no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8C2×C4×D312yes—
498C3×Q8C2×C4×D312yes—
499C3×D4—32no—
500C3×D4—61no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—64no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—21no—
535D12—32no—
536D12—32no—
537D12—62no—
538D12—64no—
539D12—64no—
540D12—64no—
541D12—61no—
542D12—61no—
543D12—121no—
544D12—124no—
545D12C2×C4×D312yes—
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—64no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—81no—
556C4×D3—124no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—242no—
567Dic6—21no—
568Dic6C2×C4×D312yes—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—41no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8C2×C4×D312yes—
578C3⋊C8C2×C4×D312yes—
579C2×C32C2×C4×D411yescharacteristic
580C2×C32#57711yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—22no—
583C3⋊D3—42no—
584C3×D3—42no—
585#41—94no—
586#41—94no—
587#41—182no—
588#41—182no—
589C2×Q8—31no—
590C2×Q8C2×D3211yescharacteristic
591C2×D4—31no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604Q16—34no—
605SD16—34no—
606SD16—94no—
607D8—94no—
608M16—182no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—94no—
612C2×C8—91no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—31no—
633C42—31no—
634C42—61no—
635C42—61no—
636C42—61no—
637C42—181no—
638C22×C3—21no—
639C22×C3—62no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—22no—
645C2×D3—32no—
646C2×D3—32no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—62no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—122no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—42no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—62no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C22×C4×D311yescharacteristic
681C3×C4C22×C4×D311yescharacteristic
682C3×C4D3×#4111yescharacteristic
683C3×C4D3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—22no—
689Dic3—32no—
690Dic3—32no—
691Dic3—41no—
692Dic3—41no—
693Dic3—62no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#295211yescharacteristic, complemented, Sylow
698C23—61no—
699C23—91no—
700C23—181no—
701Q8—21no—
702Q8—32no—
703Q8—61no—
704Q8C4×D3212yes—
705D4—32no—
706D4—61no—
707D4—92no—
708D4—184no—
709D4—184no—
710D4—181no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—91no—
721C2×C4—92no—
722C2×C4—92no—
723C2×C4—184no—
724C2×C4—184no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—721no—
728C2×C4—721no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—32no—
735C8—32no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—122no—
741C2×C3C4×D3×D411yescharacteristic
742C2×C3C4×D3×D411yescharacteristic
743C2×C3#576211yescharacteristic
744C2×C3#577011yescharacteristic
745C2×C3#577811yescharacteristic
746C2×C3#577811yescharacteristic
747D3—42no—
748D3—62no—
749D3—62no—
750D3—122no—
751D3—122no—
752D3—122no—
753D3—242no—
754C22—62no—
755C22—92no—
756C22—121no—
757C22—121no—
758C22—181no—
759C22—181no—
760C22—182no—
761C22—361no—
762C22—361no—
763C22D32×D411yescharacteristic
764C4—22no—
765C4—41no—
766C4—61no—
767C4—61no—
768C4—62no—
769C4—61no—
770C4—61no—
771C4—92no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4C2×C4×D3211yescharacteristic
776C4#6431211yescharacteristic
777C3—21no—
778C3#7965011yescharacteristic, complemented
779C3#7983211yescharacteristic, complemented
780C2—122no—
781C2—182no—
782C2—362no—
783C2#1059425511yescharacteristic
784C2#1059475111yescharacteristic
785C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63950C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595353C2semidirect
3. #10594361C2semidirect
4. #10592502C2semidirect
5. C3×#4789C2semidirect
6. C3×#4788C2semidirect
7. #10591576C2semidirect
8. Dic3×#215C2semidirect
9. #10590957C2semidirect
10. #10590910C2semidirect
11. #10590792C2semidirect
12. #10590746C2semidirect
13. #10590589C2semidirect
14. #10590575C2semidirect
15. #10590458C2semidirect
28. #63950C4semidirect
84. #4789D3semidirect
86. #4788D3semidirect
95. #3832C2×C4semidirect
111. #3796C2×C4semidirect
118. C3×#216C2×C4semidirect
119. C3×#215C2×C4semidirect
143. #3717C2×C4semidirect
144. #3714C2×C4semidirect
145. #3710C2×C4semidirect
364. #216C4×D3semidirect
366. #215C4×D3semidirect
697. C32#2952semidirect
778. C3#79650semidirect
779. C3#79832semidirect

Maximal subgroups

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

subgroupindex
#105953532
C2×#639502
#105943612
#105925022
C3×#47892
C3×#47882
#105915762
Dic3×#2152
#105909572
#105909102
#105907922
#105907462
#105905892
#105905752
#105904582
#798323
#796503