Finite Group Databasebeta

← #11860972

Subgroups — #11860972

Order 1152.

1034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595222C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic
3#10594327C211yesmaximal, characteristic, complemented
4#10592484C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic, complemented
6C3×#4758C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590908C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590791C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590477C211yesmaximal, characteristic, complemented
16#79650—31nomaximal
17#78869—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30C2×Dic3⋊Dic3—21no—
31#63955—21no—
32#63935C418yescomplemented
33#63904—21no—
34C4×#626—21no—
35#63894C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63883—21no—
38#63855C2211yescharacteristic
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3718C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63574C2211yescharacteristic
57#63573C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63554C2211yescharacteristic
61#63553C2211yescharacteristic
62#5827—31no—
63C2×#950—31no—
64C2×#916—31no—
65#5574—31no—
66#5546—31no—
67#5504—31no—
68C3×C4×SD16—31no—
69C3×#417—31no—
70Dic3×SD16—31no—
71#5133—31no—
72#5122—31no—
73#5030—31no—
74#5014—31no—
75C2×#808—31no—
76D3×#106—31no—
77#4852—31no—
78#4803—31no—
79#4789—31no—
80#4789—31no—
81#4789—31no—
82#4788—31no—
83#4788—31no—
84#4785—31no—
85#4785—31no—
86#4785—31no—
87#4785—61no—
88#4771D311yescharacteristic, complemented
89#4758—31no—
90#4758D311yescharacteristic, complemented
91C4×#204—31no—
92#4689—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237C2×C414yescomplemented
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115#3753C2×C414yescomplemented
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#214C2×C414yescomplemented
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3718C2×C414yescomplemented
144#3717C2×C414yescomplemented
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#239—31no—
149C2×#237C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156#950—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—61no—
176#926—31no—
177#926—61no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×Dic3⋊C4—61no—
181C22×C3⋊C8—31no—
182#916—38no—
183C2×#204—31no—
184C2×ΓL(1,𝔽25)C2×D311yescharacteristic
185C2×D3×C8—31no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—61no—
190#893—61no—
191#892—61no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4—61no—
195D3×C4⋊C4C2×D311yescharacteristic
196#887—31no—
197#887—31no—
198#887C2×D311yescharacteristic
199#67⋊C4—61no—
200#877—61no—
201C4×D12—31no—
202C4×D12—61no—
203#872—31no—
204#872—61no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×C4×C8—31no—
215#835—31no—
216#832C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808—61no—
240#808C2×D311yescharacteristic
241#803—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—81no—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—81no—
267C3×C4×D3C22×C412yes—
268C3×C4×D3#4112yes—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6C22×C412yes—
272C3×Dic6C22×C412yes—
273#626—24no—
274#624—24no—
275#624—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—91no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—31no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—61no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316#239—34no—
317#239—62no—
318#237—22no—
319#237C4×D314yescomplemented
320#235—34no—
321#235—62no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×C4×D3—21no—
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—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C3×SD16—34no—
339C3×M16—62no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—21no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—121no—
361#216—34no—
362#216—34no—
363#215—34no—
364#214C4×D314yescomplemented
365#213—34no—
366#213—34no—
367#213—64no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—21no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—34no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412ΓL(1,𝔽25)—22no—
413D3×C8—34no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3C4×D412yes—
424C32×C4—41no—
425C32×C4C23×C411yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×M16—31no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4—181no—
458#117—91no—
459#117—181no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102D3211yescharacteristic
477#97—91no—
478#97—91no—
479C4×C8—31no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3D3×D411yescharacteristic
489C3×Q8—32no—
490C3×Q8—32no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—41no—
497C3×D4—64no—
498C3×D4C2×C4×D312yes—
499C3×D4C2×C4×D312yes—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—24no—
519#67—64no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—24no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—81no—
534C2×Dic3—121no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—242no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—32no—
543D12—32no—
544D12—62no—
545D12—64no—
546D12—61no—
547D12—61no—
548D12—121no—
549C4×D3—64no—
550C4×D3—64no—
551C4×D3—81no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—242no—
557C4×D3—241no—
558C4×D3C2×C4×D312yes—
559C4×D3#23712yes—
560Dic6—21no—
561Dic6—21no—
562Dic6C2×C4×D312yes—
563Dic6C2×C4×D312yes—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—32no—
567C3×C8—41no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—32no—
571C3⋊C8—32no—
572C3⋊C8—62no—
573C3⋊C8C2×C4×D312yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32#57711yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—42no—
579C3×D3—22no—
580#41—34no—
581#41—62no—
582#41—94no—
583#41—182no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4C2×D3211yescharacteristic
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—94no—
600SD16—34no—
601SD16—94no—
602D8—94no—
603M16—62no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—94no—
607C2×C8—91no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—61no—
629C42—91no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—241no—
658C2×D3—241no—
659C2×D3#67⋊C412yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—62no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—62no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C22×C4×D311yescharacteristic
673C3×C4C22×C4×D311yescharacteristic
674C3×C4C2×#23711yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—22no—
677Dic3—21no—
678Dic3—21no—
679Dic3—22no—
680Dic3—41no—
681Dic3—41no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3#67⋊C412yes—
692C32#295211yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—181no—
696Q8—32no—
697Q8—32no—
698Q8—61no—
699Q8—61no—
700D4—21no—
701D4—64no—
702D4—92no—
703D4—184no—
704D4—181no—
705D4C4×D3212yes—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—64no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—184no—
720C2×C4—181no—
721C2×C4—241no—
722C2×C4—241no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—32no—
730C8—61no—
731C8—92no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3C2×#67⋊C411yescharacteristic
740C2×C3C4×D3×D411yescharacteristic
741C2×C3#576211yescharacteristic
742C2×C3#577011yescharacteristic
743C2×C3#577511yescharacteristic
744C2×C3#577811yescharacteristic
745D3—22no—
746D3—122no—
747D3—122no—
748D3—242no—
749C22—22no—
750C22—32no—
751C22—41no—
752C22—41no—
753C22—61no—
754C22—61no—
755C22—182no—
756C22—361no—
757C22—361no—
758C22D32×D411yescharacteristic
759C4—32no—
760C4—41no—
761C4—61no—
762C4—61no—
763C4—62no—
764C4—62no—
765C4—121no—
766C4—121no—
767C4—181no—
768C4—181no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23711yescharacteristic
772C3—21no—
773C3#7886911yescharacteristic, complemented
774C3#7965011yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—362no—
778C2D3×#67⋊C411yescharacteristic
779C2#1059473611yescharacteristic
780C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63935C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595222C2semidirect
3. #10594327C2semidirect
4. #10592484C2semidirect
5. C3×#4771C2semidirect
6. C3×#4758C2semidirect
7. #10591445C2semidirect
8. #10591404C2semidirect
9. #10590908C2semidirect
10. #10590792C2semidirect
11. #10590791C2semidirect
12. #10590671C2semidirect
13. D3×#808C2semidirect
14. #10590483C2semidirect
15. #10590477C2semidirect
32. #63935C4semidirect
88. #4771D3semidirect
90. #4758D3semidirect
101. C3×#237C2×C4semidirect
111. #3799C2×C4semidirect
115. #3753C2×C4semidirect
121. C3×#214C2×C4semidirect
143. #3718C2×C4semidirect
144. #3717C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
319. #237C4×D3semidirect
364. #214C4×D3semidirect
692. C32#2952semidirect
773. C3#78869semidirect
774. C3#79650semidirect

Maximal subgroups

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

subgroupindex
#105952222
C2×#639352
#105943272
#105924842
C3×#47712
C3×#47582
#105914452
#105914042
#105909082
#105907922
#105907912
#105906712
D3×#8082
#105904832
#105904772
#796503
#788693