Finite Group Databasebeta

← #11660520

Subgroups — #11660520

Order 768.

1806 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86257C211yesmaximal, characteristic
2C3×#2985C211yesmaximal, characteristic, complemented
3#83331C211yesmaximal, characteristic, complemented
4#79947C212yesmaximal, complemented
5#79946C214yesmaximal, complemented
6#79938C212yesmaximal, complemented
7#79938C214yesmaximal, complemented
8#79908C212yesmaximal, complemented
9C8×#239C212yesmaximal, complemented
10#79376C214yesmaximal, complemented
11#79372C214yesmaximal, complemented
12#79338C211yesmaximal, characteristic, complemented
13#79331C211yesmaximal, characteristic, complemented
14#79290C211yesmaximal, characteristic, complemented
15D3×#431C211yesmaximal, characteristic, complemented
16#60279—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18#5728C411yescharacteristic
19#5728C411yescharacteristic
20#5725C411yescharacteristic
21#5725C411yescharacteristic
22#5691C412yes—
23#5691C412yes—
24#5627C412yes—
25#5627C412yes—
26#5624C412yes—
27#5624C412yes—
28#5580C2212yes—
29#5580C2212yes—
30C4×#239C2212yes—
31C4×#239C2212yes—
32#5524C2212yes—
33#5522C2212yes—
34#5477C2211yescharacteristic
35C2×C42×D3C2211yescharacteristic
36C3×#446C2214yescomplemented
37C3×#446C2212yescomplemented
38C3×C8×Q8C2212yescomplemented
39C3×#433C2214yes—
40C3×#432C2211yescharacteristic
41C3×#431C2211yescharacteristic
42#5024C2212yescomplemented
43#5024C2214yescomplemented
44Q8×C3⋊C8C2212yescomplemented
45#5000C2214yes—
46#4926C2211yescharacteristic
47#4925C2211yescharacteristic
48#4839C2214yescomplemented
49#4839C2214yescomplemented
50#4838C2214yes—
51#4838C2212yescomplemented
52#4837C2212yes—
53#4836C2214yes—
54#4836C2214yes—
55#4836C2214yescomplemented
56#4834C2214yes—
57#4834C2212yescomplemented
58#4833C2212yes—
59#4833C2212yes—
60#4833C2214yescomplemented
61#4833C2214yescomplemented
62D3×C4⋊C8C2212yes—
63#4727C2214yes—
64#4727C2214yes—
65#4726C2212yes—
66D3×C22⋊C8C2212yes—
67#4718C2212yes—
68#4718C2212yes—
69#4709C2214yescomplemented
70#4707C2212yes—
71#4707C2214yescomplemented
72#4706C2214yes—
73#4706C2214yes—
74#4706C2214yescomplemented
75#4705C2212yes—
76#4690C2214yescomplemented
77#4688C2214yes—
78#4688C2212yescomplemented
79C8×D12C2214yes—
80C8×D12C2212yescomplemented
81#4685C2211yescharacteristic
82#4685C2211yescharacteristic
83C4×D3×C8C2211yescharacteristic
84C4×D3×C8C2211yescharacteristic
85C4×D3×C8C2214yescomplemented
86#3444—31no—
87#2993—32no—
88#2993—32no—
89#2992—34no—
90#2985—31no—
91#2985D311yescharacteristic, complemented
92#2981—31no—
93#2981—31no—
94#2976—34no—
95#2965—32no—
96#2965—34no—
97C8×#41—32no—
98#2922—34no—
99#2920—31no—
100C2×#431—31no—
101C2×#239C2×C412yes—
102C2×#239C2×C412yes—
103C2×#235C2312yes—
104C22×C4×D3C2×C411yescharacteristic
105C22×C4×D3C2×C411yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C3×C4⋊Q8C2×C411yescharacteristic
108C3×C4⋊Q8C2×C411yescharacteristic
109C3×#125C2×C412yes—
110C3×C22⋊Q8C2×C412yes—
111C3×C22⋊Q8C2×C412yes—
112C3×C4×Q8C2312yes—
113C3×C4×Q8C2312yes—
114C3×#117C2312yes—
115C2×C3×C42C2311yescharacteristic
116#947C2×C412yes—
117#947C2×C412yes—
118#946C2×C412yes—
119#946C2×C412yes—
120Q8×Dic3C2×C412yes—
121Q8×Dic3C2×C412yes—
122#930C2×C412yes—
123#930C2×C412yes—
124C2×C4×Dic3C2×C411yescharacteristic
125C2×C4×Dic3C2×C411yescharacteristic
126C2×C4×Dic3C2311yescharacteristic
127C2×ΓL(1,𝔽25)C2314yes—
128C2×ΓL(1,𝔽25)C2314yes—
129C2×ΓL(1,𝔽25)C2314yes—
130C2×D3×C8C2312yes—
131C2×D3×C8C2312yes—
132C2×D3×C8C2314yes—
133C2×D3×C8C2314yes—
134#898C2×C414yes—
135#898C2×C414yes—
136#897C2×C412yes—
137#897C2×C412yes—
138#895C2×C412yes—
139#895C2×C412yes—
140#895C2×C412yes—
141#895C2×C412yes—
142#894C2×C414yes—
143#894C2×C414yes—
144#893C2×C412yes—
145#893C2×C412yes—
146#893C2×C414yes—
147#893C2×C414yes—
148#893C2×C412yes—
149#893C2×C412yes—
150#892C2×C414yes—
151#892C2×C414yes—
152#892C2×C412yes—
153#892C2×C412yes—
154#890C2×C412yes—
155#890C2×C412yes—
156#887C2×C412yes—
157#887C2×C412yes—
158#886C2×C414yes—
159#882C2×C414yes—
160#67⋊C4C2×C414yes—
161#67⋊C4C2×C414yes—
162#875C2×C412yes—
163#874C2×C411yescharacteristic
164C4×D12C2314yes—
165C4×D12C2312yes—
166C4×D12C2314yes—
167C4×D12C2312yes—
168#872C2314yes—
169C42×D3C2×C411yescharacteristic
170C42×D3C2×C411yescharacteristic
171C42×D3C2×C411yescharacteristic
172C42×D3C2×C411yescharacteristic
173C42×D3C2311yescharacteristic
174C42×D3C2314yes—
175C42×D3C2311yescharacteristic
176C42×D3C2311yescharacteristic
177C42×D3C2311yescharacteristic
178#869C2×C411yescharacteristic
179C3×C4⋊C8C2312yes—
180C3×C4⋊C8C2312yes—
181C3×C4⋊C8C2314yes—
182C3×C4⋊C8C2314yes—
183C3×C22⋊C8C2312yes—
184C3×C22⋊C8C2312yes—
185C3×#97C2312yes—
186C3×#97C2314yes—
187C3×C4×C8C2311yescharacteristic
188C3×C4×C8C2311yescharacteristic
189C3×C4×C8C2314yes—
190#830C2312yes—
191#830C2312yes—
192(C2×D3)⋊C8C2312yes—
193(C2×D3)⋊C8C2312yes—
194(C2×D3)⋊C8C2314yes—
195(C2×D3)⋊C8C2314yes—
196(C2×D3)⋊C8C2314yes—
197(C2×D3)⋊C8C2314yes—
198(C2×D3)⋊C8C2314yes—
199Dic3⋊C8C2312yes—
200Dic3⋊C8C2312yes—
201Dic3⋊C8C2314yes—
202C8×Dic3C2312yes—
203C8×Dic3C2312yes—
204C8×Dic3C2314yes—
205C4⋊(C3⋊C8)C2312yes—
206C4⋊(C3⋊C8)C2312yes—
207C4⋊(C3⋊C8)C2314yes—
208C4⋊(C3⋊C8)C2314yes—
209#803C2312yes—
210#803C2314yes—
211C4×C3⋊C8C2311yescharacteristic
212C4×C3⋊C8C2311yescharacteristic
213C4×C3⋊C8C2314yes—
214#533—31no—
215#533—31no—
216#533C2×D311yescharacteristic
217#532—31no—
218#532—31no—
219#532—31no—
220#529—32no—
221#529—32no—
222#529—32no—
223#529—32no—
224#529—32no—
225#529—32no—
226#525—32no—
227#525—32no—
228#525—32no—
229C4×#41—32no—
230C4×#41—32no—
231C4×#41—32no—
232C22×C42—31no—
233#446—34no—
234#446—32no—
235#446C2×D314yescomplemented
236#446C2×D312yescomplemented
237C8×Q8—32no—
238C8×Q8C2×D312yescomplemented
239#436—34no—
240#436—32no—
241#436—34no—
242#436—32no—
243#435—34no—
244#435—34no—
245#435—34no—
246#435—34no—
247#435—34no—
248#435—34no—
249C8×D4—34no—
250C8×D4—32no—
251C8×D4—34no—
252C8×D4—32no—
253#433—34no—
254#433—34no—
255#433—34no—
256#433C2×D314yes—
257#432—31no—
258#432—32no—
259#432C2×D311yescharacteristic
260#431—31no—
261#431—32no—
262#431—32no—
263#431—34no—
264#431—34no—
265#431—32no—
266#431—32no—
267#431—31no—
268#431—31no—
269#431C2×D311yescharacteristic
270#424—34no—
271#424—34no—
272#423—32no—
273C2×C4⋊C8—32no—
274#408—34no—
275#408—34no—
276#407—32no—
277C2×C22⋊C8—32no—
278C4×M16—32no—
279C4×M16—34no—
280C2×C4×C8—31no—
281C2×C4×C8—31no—
282C2×C4×C8—34no—
283C23×D3C22×C411yescharacteristic
284C2×C3×Q8C22×C412yes—
285C2×C3×Q8C22×C412yes—
286C22×C3×C4C22×C411yescharacteristic
287C22×C3×C4C22×C411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C2×#67C22×C414yes—
290C22×Dic3C22×C411yescharacteristic
291C22×Dic3C22×C411yescharacteristic
292C22×Dic3C22×C411yescharacteristic
293#239—28no—
294#239—44no—
295#235—44no—
296C2×D12C22×C412yes—
297C2×D12C22×C414yes—
298C2×D12C22×C412yes—
299C2×D12C22×C414yes—
300C2×D12C22×C412yes—
301C2×C4×D3—24no—
302C2×C4×D3—42no—
303C2×C4×D3—42no—
304C2×C4×D3C22×C411yescharacteristic
305C2×C4×D3C22×C411yescharacteristic
306C2×C4×D3C22×C411yescharacteristic
307C2×C4×D3C22×C411yescharacteristic
308C2×C4×D3C22×C411yescharacteristic
309C2×C4×D3C22×C414yes—
310C2×C4×D3C22×C414yes—
311C2×C4×D3C22×C411yescharacteristic
312C2×C4×D3C22×C411yescharacteristic
313C2×C4×D3C22×C411yescharacteristic
314C2×C4×D3C22×C411yescharacteristic
315C2×C4×D3C22×C411yescharacteristic
316C2×C4×D3C2411yescharacteristic
317C2×C4×D3C2411yescharacteristic
318C2×C4×D3C2414yes—
319C2×Dic6C22×C412yes—
320C2×C3×C8C2412yes—
321C2×C3×C8C2412yes—
322C2×C3×C8C2414yes—
323C3×C4⋊C4C22×C412yes—
324C3×C4⋊C4C22×C412yes—
325C3×C4⋊C4C22×C412yes—
326C3×C4⋊C4C22×C412yes—
327C3×C4⋊C4C22×C414yes—
328C3×C4⋊C4C22×C414yes—
329C3×C22⋊C4C22×C414yes—
330C3×C42C22×C411yescharacteristic
331C3×C42C22×C411yescharacteristic
332C3×C42C2411yescharacteristic
333C3×C42C2414yes—
334C3×C42C2411yescharacteristic
335(C2×D3)⋊C4C22×C414yes—
336(C2×D3)⋊C4C22×C414yes—
337(C2×D3)⋊C4C22×C414yes—
338(C2×D3)⋊C4C22×C414yes—
339(C2×D3)⋊C4C22×C414yes—
340(C2×D3)⋊C4C22×C414yes—
341(C2×D3)⋊C4C22×C414yes—
342(C2×D3)⋊C4C22×C414yes—
343C4⋊Dic3C22×C412yes—
344C4⋊Dic3C22×C412yes—
345C4⋊Dic3C22×C414yes—
346C4⋊Dic3C22×C414yes—
347Dic3⋊C4C22×C414yes—
348Dic3⋊C4C22×C414yes—
349C4×Dic3C22×C411yescharacteristic
350C4×Dic3C22×C411yescharacteristic
351C4×Dic3C22×C411yescharacteristic
352C4×Dic3C22×C411yescharacteristic
353C4×Dic3C22×C411yescharacteristic
354C4×Dic3C22×C411yescharacteristic
355C4×Dic3C22×C411yescharacteristic
356C4×Dic3C22×C411yescharacteristic
357C4×Dic3C22×C411yescharacteristic
358C4×Dic3C22×C411yescharacteristic
359C4×Dic3C22×C414yes—
360C4×Dic3C22×C414yes—
361C4×Dic3C2411yescharacteristic
362C4×Dic3C2411yescharacteristic
363C2×C3⋊C8C2412yes—
364C2×C3⋊C8C2412yes—
365C2×C3⋊C8C2414yes—
366ΓL(1,𝔽25)—44no—
367ΓL(1,𝔽25)—44no—
368ΓL(1,𝔽25)—44no—
369D3×C8—42no—
370D3×C8—44no—
371D3×C8—44no—
372D3×C8—42no—
373C2×#41—32no—
374C2×#41—32no—
375C2×#41—32no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C2×M16—34no—
380C2×M16—34no—
381C2×M16—34no—
382C22×C8—32no—
383C22×C8—32no—
384C22×C8—34no—
385C22×C8—34no—
386C4⋊Q8—31no—
387C4⋊Q8C4×D311yescharacteristic
388C4⋊Q8C4×D311yescharacteristic
389#127—31no—
390#126—34no—
391#126—34no—
392#125—32no—
393#125—32no—
394#125C4×D312yes—
395#124—32no—
396#124—32no—
397#124—32no—
398#123—34no—
399#123—34no—
400#123—34no—
401C22⋊Q8—32no—
402C22⋊Q8—32no—
403C22⋊Q8—32no—
404C22⋊Q8—32no—
405C22⋊Q8C4×D312yes—
406C22⋊Q8C4×D312yes—
407#121—32no—
408#121—32no—
409#121—32no—
410#121—32no—
411#121—32no—
412#121—32no—
413#120—34no—
414C4×Q8—32no—
415C4×Q8—32no—
416C4×Q8—32no—
417C4×Q8—32no—
418C4×Q8C22×D312yes—
419C4×Q8C22×D312yes—
420C4×D4—34no—
421C4×D4—34no—
422C4×D4—32no—
423C4×D4—32no—
424C4×D4—32no—
425C4×D4—32no—
426C4×D4—34no—
427C4×D4—34no—
428C4×D4—34no—
429C4×D4—34no—
430C4×D4—32no—
431C4×D4—32no—
432#117—32no—
433#117—32no—
434#117—34no—
435#117—34no—
436#117—34no—
437#117C22×D312yes—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—31no—
445C2×C42—34no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42C22×D311yescharacteristic
451C4⋊C8—32no—
452C4⋊C8—32no—
453C4⋊C8—34no—
454C4⋊C8—32no—
455C4⋊C8—32no—
456C4⋊C8—34no—
457C4⋊C8—34no—
458C4⋊C8C22×D312yes—
459C4⋊C8C22×D312yes—
460C4⋊C8C22×D314yes—
461C4⋊C8C22×D314yes—
462C22⋊C8—32no—
463C22⋊C8—32no—
464C22⋊C8—32no—
465C22⋊C8—32no—
466C22⋊C8—34no—
467C22⋊C8—34no—
468C22⋊C8—34no—
469C22⋊C8—34no—
470C22⋊C8—34no—
471C22⋊C8C22×D312yes—
472C22⋊C8C22×D312yes—
473#97—32no—
474#97—34no—
475#97C22×D312yes—
476#97C22×D314yes—
477C4×C8—32no—
478C4×C8—32no—
479C4×C8—34no—
480C4×C8—31no—
481C4×C8—31no—
482C4×C8—34no—
483C4×C8C22×D311yescharacteristic
484C4×C8C22×D311yescharacteristic
485C4×C8C22×D314yes—
486C23×C3C23×C411yescharacteristic
487C22×D3—22no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3C23×C414yes—
491C22×D3C23×C411yescharacteristic
492C22×D3C23×C411yescharacteristic
493C3×Q8—24no—
494C3×Q8—42no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—41no—
498C2×C3×C4C23×C411yescharacteristic
499C2×C3×C4C23×C411yescharacteristic
500C2×C3×C4C23×C411yescharacteristic
501C2×C3×C4C23×C411yescharacteristic
502C2×C3×C4C23×C414yes—
503C2×C3×C4C23×C414yes—
504C2×C3×C4C23×C411yescharacteristic
505C2×C3×C4C2511yescharacteristic
506#67—44no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—41no—
510C2×Dic3C23×C411yescharacteristic
511C2×Dic3C23×C411yescharacteristic
512C2×Dic3C23×C411yescharacteristic
513C2×Dic3C23×C411yescharacteristic
514C2×Dic3C23×C414yes—
515C2×Dic3C23×C411yescharacteristic
516C2×Dic3C23×C411yescharacteristic
517D12—28no—
518D12—24no—
519D12—42no—
520D12—42no—
521D12—44no—
522C4×D3—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—24no—
526C4×D3—24no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—28no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—28no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3#13114yes—
538Dic6—42no—
539C3×C8—22no—
540C3×C8—24no—
541C3×C8—22no—
542C3⋊C8—22no—
543C3⋊C8—24no—
544C3⋊C8—22no—
545C24—31no—
546#41—68no—
547#41—124no—
548#41—124no—
549C2×Q8—32no—
550C2×Q8C2×C4×D312yes—
551C2×Q8C2×C4×D312yes—
552C2×D4—34no—
553C2×D4—34no—
554C2×D4—32no—
555C2×D4—34no—
556C2×D4—32no—
557C2×D4—32no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—34no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—64no—
577C22×C4—122no—
578C22×C4—122no—
579C22×C4C2×C4×D311yescharacteristic
580C22×C4C2×C4×D311yescharacteristic
581C22×C4C23×D311yescharacteristic
582M16—124no—
583M16—124no—
584M16—124no—
585C2×C8—32no—
586C2×C8—32no—
587C2×C8—34no—
588C2×C8—122no—
589C2×C8—124no—
590C2×C8—124no—
591C2×C8—122no—
592C2×C8C23×D312yes—
593C2×C8C23×D312yes—
594C2×C8C23×D314yes—
595C4⋊C4—32no—
596C4⋊C4—32no—
597C4⋊C4—34no—
598C4⋊C4—34no—
599C4⋊C4—34no—
600C4⋊C4—34no—
601C4⋊C4C2×C4×D312yes—
602C4⋊C4C2×C4×D312yes—
603C4⋊C4C2×C4×D314yes—
604C4⋊C4C2×C4×D314yes—
605C4⋊C4C2×C4×D312yes—
606C4⋊C4C2×C4×D312yes—
607C22⋊C4—34no—
608C22⋊C4—34no—
609C22⋊C4—34no—
610C22⋊C4—34no—
611C22⋊C4—34no—
612C22⋊C4—34no—
613C22⋊C4—34no—
614C22⋊C4—34no—
615C22⋊C4C2×C4×D314yes—
616C42—31no—
617C42—31no—
618C42—31no—
619C42—31no—
620C42—31no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—31no—
626C42—34no—
627C42—34no—
628C42—31no—
629C42—31no—
630C42C2×C4×D311yescharacteristic
631C42C2×C4×D311yescharacteristic
632C42C23×D311yescharacteristic
633C42C23×D314yes—
634C42C23×D311yescharacteristic
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3C24×C411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—24no—
643C2×D3—21no—
644C2×D3—24no—
645C2×D3—21no—
646C2×D3—24no—
647C2×D3—44no—
648C2×D3C2×#13112yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—24no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—24no—
655C3×C4C2×#13112yes—
656C3×C4#58512yes—
657Dic3—24no—
658Dic3—21no—
659Dic3—21no—
660Dic3—21no—
661Dic3—21no—
662Dic3C2×#13112yes—
663Dic3#56812yes—
664C23—31no—
665C23—34no—
666C23—31no—
667C23—62no—
668C23—121no—
669C23—121no—
670C23C22×C4×D311yescharacteristic
671Q8—24no—
672Q8—42no—
673Q8—122no—
674D4—68no—
675D4—64no—
676D4—122no—
677D4—122no—
678D4—124no—
679D4—124no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—34no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—34no—
690C2×C4—41no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—68no—
695C2×C4—68no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4C22×C4×D311yescharacteristic
710C2×C4C22×C4×D311yescharacteristic
711C2×C4C22×C4×D311yescharacteristic
712C2×C4C22×C4×D311yescharacteristic
713C2×C4C22×C4×D314yes—
714C2×C4C22×C4×D314yes—
715C2×C4C22×C4×D311yescharacteristic
716C2×C4C24×D311yescharacteristic
717C8—22no—
718C8—24no—
719C8—22no—
720C8—62no—
721C8—62no—
722C8—64no—
723C2×C3—41no—
724C2×C3#342811yescharacteristic
725C2×C3C22×#13111yescharacteristic
726C2×C3C2×#56811yescharacteristic
727D3—22no—
728D3—44no—
729D3—41no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—32no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—64no—
738C22—61no—
739C22—64no—
740C22—61no—
741C22—64no—
742C22—124no—
743C22C23×C4×D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—24no—
747C4—21no—
748C4—21no—
749C4—24no—
750C4—32no—
751C4—32no—
752C4—61no—
753C4—61no—
754C4—64no—
755C4—61no—
756C4—61no—
757C4D3×#13112yes—
758C4#596812yes—
759C3#6027911yescharacteristic, complemented, Sylow
760C2—41no—
761C2—62no—
762C2—121no—
763C2—124no—
764C2#8587211yescharacteristic
765C2C2×D3×#13111yescharacteristic
766C2D3×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2985C2
prime radical#86257C2
cosocleC2×C3×C4C25
hypercenter#2985D3
hypocenterC3#60279
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2985

Complements

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

NH ≅ G/Ntype
2. C3×#2985C2semidirect
3. #83331C2semidirect
4. #79947C2semidirect
5. #79946C2semidirect
6. #79938C2semidirect
7. #79938C2semidirect
8. #79908C2semidirect
9. C8×#239C2semidirect
10. #79376C2semidirect
11. #79372C2semidirect
12. #79338C2semidirect
13. #79331C2semidirect
14. #79290C2semidirect
15. D3×#431C2semidirect
36. C3×#446C22semidirect
37. C3×#446C22semidirect
38. C3×C8×Q8C22semidirect
42. #5024C22semidirect
43. #5024C22semidirect
44. Q8×C3⋊C8C22semidirect
48. #4839C22semidirect
49. #4839C22semidirect
51. #4838C22semidirect
55. #4836C22semidirect
57. #4834C22semidirect
60. #4833C22semidirect
61. #4833C22semidirect
69. #4709C22semidirect
71. #4707C22semidirect
74. #4706C22semidirect
76. #4690C22semidirect
78. #4688C22semidirect
80. C8×D12C22semidirect
85. C4×D3×C8C22semidirect
91. #2985D3semidirect
235. #446C2×D3semidirect
236. #446C2×D3semidirect
238. C8×Q8C2×D3semidirect
759. C3#60279semidirect

Maximal subgroups

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

subgroupindex
#862572
C3×#29852
#833312
#799472
#799462
#799382
#799082
C8×#2392
#793762
#793722
#793382
#793312
#792902
D3×#4312
#602793