Finite Group Databasebeta

← #11860939

Subgroups — #11860939

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595394C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic
3#10594359C211yesmaximal, characteristic, complemented
4#10592488C211yesmaximal, characteristic, complemented
5C3×#4803C211yesmaximal, characteristic, complemented
6C3×#4788C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10590908C211yesmaximal, characteristic, complemented
10#10590744C211yesmaximal, characteristic, complemented
11#10590741C211yesmaximal, characteristic, complemented
12#10590670C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#79650—31nomaximal
17#78869—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63947C418yescomplemented
29C4×#625—21no—
30#63898—21no—
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic
33Dic3×D12—21no—
34Dic3×D12C2211yescharacteristic
35D3×C4⋊Dic3—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63855—21no—
41#63855C2211yescharacteristic
42#63844C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63643C2211yescharacteristic
48#63642C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63574C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63563C2211yescharacteristic
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#4803D311yescharacteristic, complemented
79#4789—31no—
80#4789—31no—
81#4789—31no—
82#4789—61no—
83#4788—31no—
84#4788D311yescharacteristic, complemented
85#4785—31no—
86#4785—31no—
87#4785—31no—
88#4771—31no—
89#4758—31no—
90#4758—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yescomplemented
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3756C2×C414yescomplemented
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—22no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3713C2×C414yescomplemented
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×#237—31no—
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—61no—
160Q8×Dic3C2×D311yescharacteristic
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—61no—
164C2×#215C2×D311yescharacteristic
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#213—31no—
172C2×#213—31no—
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—61no—
189#893C2×D311yescharacteristic
190#892—61no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—61no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4C2×D311yescharacteristic
195#887—31no—
196#887—31no—
197#887—31no—
198#887—61no—
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—21no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C2×D311yescharacteristic
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C4×C8—31no—
215#835C2×D311yescharacteristic
216#832—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220#817—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#815—31no—
226#815—31no—
227#815—31no—
228#815—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic
232#810—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808—61no—
240#808C2×D311yescharacteristic
241#803—31no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—21no—
255#634C22×C412yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×D12C22×C412yes—
266C3×C4×D3—24no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271#625—24no—
272D3×Dic3—24no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275D3×Dic3—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—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—22no—
316#239C4×D314yescomplemented
317#237—34no—
318#237—62no—
319#235—34no—
320#235—62no—
321C2×D12—21no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
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×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C3×SD16—34no—
337C3×M16—62no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C42—31no—
352C3×C42—61no—
353#217—31no—
354#217—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#216—34no—
359#216—34no—
360#216—64no—
361#215C4×D314yescomplemented
362#214—34no—
363#213—34no—
364#213—34no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—121no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392C4×Dic3—21no—
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—61no—
402C4×Dic3—121no—
403C4×Dic3—121no—
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×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4—41no—
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—22no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
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—91no—
471#103—91no—
472#103D3211yescharacteristic
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#97—91no—
478#97—91no—
479C4×C8—31no—
480C4×C8—91no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3D3×D411yescharacteristic
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—22no—
490C3×Q8—41no—
491C3×Q8C2×C4×D312yes—
492C3×Q8C2×C4×D312yes—
493C3×D4—32no—
494C3×D4—32no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
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—41no—
510C2×C3×C4—64no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518#67—64no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—64no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541D12—24no—
542D12—21no—
543D12—21no—
544D12C2×C4×D312yes—
545D12C2×C4×D312yes—
546C4×D3—24no—
547C4×D3—64no—
548C4×D3—81no—
549C4×D3—81no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3C2×C4×D312yes—
555C4×D3#23712yes—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—32no—
565C3×C8—41no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—32no—
569C3⋊C8—32no—
570C3⋊C8—62no—
571C3⋊C8C2×C4×D312yes—
572C2×C32C2×C4×D411yescharacteristic
573C2×C32#57711yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—22no—
576C3×D3—42no—
577C3×D3—42no—
578#41—34no—
579#41—62no—
580#41—94no—
581#41—182no—
582C2×Q8—91no—
583C2×Q8C2×D3211yescharacteristic
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—94no—
598SD16—34no—
599SD16—94no—
600D8—94no—
601M16—62no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42—181no—
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3#67⋊C412yes—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C22×C4×D311yescharacteristic
666C3×C4C22×C4×D311yescharacteristic
667C3×C4C2×#23711yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—62no—
679Dic3—122no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685Dic3#67⋊C412yes—
686C32#295211yescharacteristic, complemented, Sylow
687C23—31no—
688C23—61no—
689C23—61no—
690Q8—21no—
691Q8—92no—
692Q8—181no—
693Q8C4×D3212yes—
694D4—32no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4—61no—
699D4—184no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—64no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—184no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—32no—
724C8—61no—
725C8—92no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—62no—
730C2×C3—122no—
731C2×C3—122no—
732C2×C3C2×#67⋊C411yescharacteristic
733C2×C3C4×D3×D411yescharacteristic
734C2×C3#576211yescharacteristic
735C2×C3#577011yescharacteristic
736C2×C3#577511yescharacteristic
737C2×C3#577811yescharacteristic
738D3—22no—
739D3—42no—
740D3—42no—
741C22—32no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—62no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22D32×D411yescharacteristic
751C4—22no—
752C4—32no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—181no—
759C4—182no—
760C4—181no—
761C4—361no—
762C4C2×C4×D3211yescharacteristic
763C4D3×#23711yescharacteristic
764C3—21no—
765C3#7886911yescharacteristic, complemented
766C3#7965011yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—122no—
770C2D3×#67⋊C411yescharacteristic
771C2#1059474911yescharacteristic
772C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63947C2
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. #10595394C2semidirect
3. #10594359C2semidirect
4. #10592488C2semidirect
5. C3×#4803C2semidirect
6. C3×#4788C2semidirect
7. #10591571C2semidirect
8. #10591541C2semidirect
9. #10590908C2semidirect
10. #10590744C2semidirect
11. #10590741C2semidirect
12. #10590670C2semidirect
13. D3×#808C2semidirect
14. #10590460C2semidirect
15. #10590455C2semidirect
28. #63947C4semidirect
78. #4803D3semidirect
84. #4788D3semidirect
96. C3×#239C2×C4semidirect
111. #3795C2×C4semidirect
114. #3756C2×C4semidirect
122. C3×#215C2×C4semidirect
143. #3716C2×C4semidirect
144. #3713C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
316. #239C4×D3semidirect
361. #215C4×D3semidirect
686. C32#2952semidirect
765. C3#78869semidirect
766. C3#79650semidirect

Maximal subgroups

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

subgroupindex
#105953942
C2×#639472
#105943592
#105924882
C3×#48032
C3×#47882
#105915712
#105915412
#105909082
#105907442
#105907412
#105906702
D3×#8082
#105904602
#105904552
#796503
#788693