Finite Group Databasebeta

← #11860239

Subgroups — #11860239

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595386C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic
3#10594360C211yesmaximal, characteristic, complemented
4#10592503C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4789C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590746C211yesmaximal, characteristic, complemented
12#10590668C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590574C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#79828—31nomaximal
17#79772—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63950C418yescomplemented
29#63904—21no—
30#63894—21no—
31#63894—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35C4×#624—21no—
36C4×#624C2211yescharacteristic
37#63880—21no—
38#63878—21no—
39C4×D3×Dic3—21no—
40#63849—21no—
41#63849C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63662C2211yescharacteristic
48#63648C2211yescharacteristic
49#63636C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61#63554C2211yescharacteristic
62C2×#919—31no—
63C2×#916—31no—
64C4×#239—31no—
65C4×#239—31no—
66C4×#239—31no—
67C4×#237—31no—
68C3×#441—31no—
69C3×#440—31no—
70#5184—31no—
71#5164—31no—
72#5030—31no—
73#5026—31no—
74#5026—31no—
75#5014—31no—
76#4889—31no—
77#4880—31no—
78#4869—31no—
79#4860—31no—
80#4817—31no—
81#4817D311yescharacteristic, complemented
82#4804—31no—
83#4804—31no—
84#4804—31no—
85#4804—61no—
86#4789D311yescharacteristic, complemented
87#4785—31no—
88#4772—31no—
89#4711—31no—
90#4710—31no—
91D3×#97—31no—
92D3×#97—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⋊D3C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×#624D411yescharacteristic
107C2×#624D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—22no—
119C3×#216C2×C414yescomplemented
120C3×#215C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3717C2×C414yescomplemented
144#3714C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2943—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×C4×Dic3—61no—
168#919—38no—
169#916—38no—
170C2×D24—31no—
171C2×#204—31no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177#893—31no—
178#893—31no—
179#893—61no—
180#893—61no—
181#893—61no—
182#893C2×D311yescharacteristic
183#892—31no—
184#892—31no—
185#892—31no—
186#892—31no—
187#892—61no—
188#892—61no—
189#892—61no—
190#892—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—
200C42×D3—31no—
201C42×D3—31no—
202C42×D3—61no—
203C42×D3—61no—
204C42×D3—61no—
205C4×Dic6—31no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#97—31no—
214C3×#97—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#818—31no—
225#817—31no—
226#816C2×D311yescharacteristic
227#815—31no—
228#815—31no—
229#815C2×D311yescharacteristic
230#815C2×D311yescharacteristic
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#808—31no—
237#808C2×D311yescharacteristic
238#807—31no—
239#807C2×D311yescharacteristic
240#803—31no—
241#803—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⋊D3C22×C412yes—
257C4×C3⋊D3#4112yes—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6C22×C412yes—
270#626—24no—
271#624—41no—
272#624—41no—
273#624—42no—
274#624—42no—
275D3×Dic3—24no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8C22×C412yes—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282C4×#41—91no—
283C4×#41—91no—
284#442—91no—
285#442—91no—
286#441—31no—
287#441—91no—
288#440—31no—
289#440—91no—
290#440—91no—
291#440—91no—
292#427—91no—
293#416—91no—
294#416—91no—
295C2×#97—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—31no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
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×Dic6C22×D311yescharacteristic
341C3×Q16—34no—
342C3×SD16—34no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362#217—61no—
363#216C4×D314yescomplemented
364#215—34no—
365#215C4×D314yescomplemented
366#213—34no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
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—61no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
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—
411D3×C8—34no—
412D3×C8—34no—
413D3×C8—62no—
414D3×C8—62no—
415D3×C8—122no—
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—
446C22×C8—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—91no—
462#117—181no—
463#117—181no—
464C2×C42—91no—
465C2×C42—181no—
466C2×C42—181no—
467#107—31no—
468#107—91no—
469#106—31no—
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—31no—
481#97—91no—
482#97—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—122no—
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—122no—
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—42no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—64no—
556C4×D3—124no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—122no—
566Dic6—21no—
567Dic6C2×C4×D312yes—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—32no—
571C3×C8—32no—
572C3×C8—41no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—121no—
576C3⋊C8C2×C4×D312yes—
577C3⋊C8C2×C4×D312yes—
578C2×C32C2×C4×D411yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57511yescharacteristic
581C3⋊D3—22no—
582C3⋊D3—42no—
583C3×D3—42no—
584#41—94no—
585#41—94no—
586#41—182no—
587#41—182no—
588C2×Q8—31no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—181no—
593C2×D4—181no—
594C22×C4—61no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603Q16—34no—
604SD16—34no—
605SD16—94no—
606D8—94no—
607C2×C8—31no—
608C2×C8—31no—
609C2×C8—94no—
610C2×C8—91no—
611C2×C8—182no—
612C2×C8C2×D3211yescharacteristic
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—61no—
630C42—61no—
631C42—61no—
632C42—91no—
633C42—91no—
634C42—181no—
635C42—181no—
636C42—181no—
637C22×C3—21no—
638C22×C3—62no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—22no—
644C2×D3—32no—
645C2×D3—32no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—62no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—62no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C22×C4×D311yescharacteristic
680C3×C4C22×C4×D311yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—22no—
688Dic3—32no—
689Dic3—32no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696C32#294311yescharacteristic, complemented, Sylow
697C23—61no—
698C23—91no—
699C23—181no—
700Q8—21no—
701Q8—32no—
702Q8—61no—
703Q8C4×D3212yes—
704D4—32no—
705D4—61no—
706D4—92no—
707D4—184no—
708D4—184no—
709D4—181no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—92no—
722C2×C4—122no—
723C2×C4—184no—
724C2×C4—184no—
725C2×C4—181no—
726C2×C4—361no—
727C2×C4—361no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—32no—
734C8—32no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—122no—
740C2×C3C4×D3×D411yescharacteristic
741C2×C3C4×D3×D411yescharacteristic
742C2×C3#577311yescharacteristic
743C2×C3#577711yescharacteristic
744C2×C3#577711yescharacteristic
745C2×C3#577711yescharacteristic
746D3—42no—
747D3—62no—
748D3—62no—
749D3—122no—
750D3—122no—
751D3—122no—
752D3—242no—
753C22—62no—
754C22—92no—
755C22—121no—
756C22—121no—
757C22—181no—
758C22—181no—
759C22—182no—
760C22—361no—
761C22—361no—
762C22D32×D411yescharacteristic
763C4—22no—
764C4—41no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—62no—
770C4—92no—
771C4—121no—
772C4—121no—
773C4—361no—
774C4C2×C4×D3211yescharacteristic
775C4#6431211yescharacteristic
776C3—21no—
777C3#7977211yescharacteristic, complemented
778C3#7982811yescharacteristic, complemented
779C2—122no—
780C2—182no—
781C2—362no—
782C2#1059425511yescharacteristic
783C2#1059474411yescharacteristic
784C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63950C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2943
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. #10595386C2semidirect
3. #10594360C2semidirect
4. #10592503C2semidirect
5. C3×#4817C2semidirect
6. C3×#4789C2semidirect
7. #10591576C2semidirect
8. #10591566C2semidirect
9. #10590956C2semidirect
10. #10590795C2semidirect
11. #10590746C2semidirect
12. #10590668C2semidirect
13. #10590589C2semidirect
14. #10590574C2semidirect
15. #10590457C2semidirect
28. #63950C4semidirect
81. #4817D3semidirect
86. #4789D3semidirect
95. #3832C2×C4semidirect
111. #3796C2×C4semidirect
119. C3×#216C2×C4semidirect
120. C3×#215C2×C4semidirect
143. #3717C2×C4semidirect
144. #3714C2×C4semidirect
145. #3710C2×C4semidirect
363. #216C4×D3semidirect
365. #215C4×D3semidirect
696. C32#2943semidirect
777. C3#79772semidirect
778. C3#79828semidirect

Maximal subgroups

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

subgroupindex
#105953862
C2×#639502
#105943602
#105925032
C3×#48172
C3×#47892
#105915762
#105915662
#105909562
#105907952
#105907462
#105906682
#105905892
#105905742
#105904572
#798283
#797723