Finite Group Databasebeta

← #11660479

Subgroups — #11660479

Order 768.

1818 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85802C211yesmaximal, characteristic
2C2×C3×#446C211yesmaximal, characteristic, complemented
3Q8×#208C211yesmaximal, characteristic, complemented
4#79949C214yesmaximal, complemented
5#79948C212yesmaximal, complemented
6#79947C212yesmaximal, complemented
7#79946C214yesmaximal, complemented
8#79945C212yesmaximal, complemented
9#79944C212yesmaximal, complemented
10#79012C211yesmaximal, characteristic, complemented
11#79012C212yesmaximal, complemented
12#79004C211yesmaximal, characteristic, complemented
13#79004C212yesmaximal, complemented
14#78491C212yesmaximal, complemented
15#78489C212yesmaximal, complemented
16#78458C211yesmaximal, characteristic, complemented
17#78455C211yesmaximal, characteristic, complemented
18#60275—31nomaximal, Sylow
19C2×C3×C4×Q8C2211yescharacteristic
20#5817C412yes—
21C2×#901C2212yes—
22C2×#901C2212yes—
23C2×#901C2212yes—
24#5585C411yescharacteristic
25#5585C412yes—
26#5584C412yes—
27#5584C411yescharacteristic
28#5580C2214yes—
29#5580C2212yes—
30#5577C411yescharacteristic
31C4×#239C2212yes—
32#5570C411yescharacteristic
33#5514C414yes—
34#5514C412yes—
35#5477C2211yescharacteristic
36#5477C2212yes—
37C4×#235C2211yescharacteristic
38C4×#235C2212yes—
39C3×#446C2211yescharacteristic
40C3×#446C2211yescharacteristic
41C3×#446C2212yes—
42C3×#446C2211yescharacteristic
43C3×#446C2211yescharacteristic
44C3×#446C2212yes—
45C2×C3×C4⋊C8C2212yes—
46C2×C3×C4⋊C8C2211yescharacteristic
47C2×C3×#97C2212yes—
48C2×C3×C4×C8C2211yescharacteristic
49#5110C2211yescharacteristic
50#5110C2211yescharacteristic
51#5110C2212yes—
52#5110C2212yes—
53#5102C2211yescharacteristic
54#5102C2211yescharacteristic
55#5102C2212yes—
56#5024C2212yes—
57#5024C2214yes—
58Q8×C3⋊C8C2212yes—
59#4924C2211yescharacteristic
60#4924C2212yes—
61C4×#208C2211yescharacteristic
62C4×#208C2212yes—
63#4839C2214yes—
64#4839C2214yes—
65#4839C2214yes—
66#4838C2212yes—
67#4838C2214yes—
68#4837C2214yes—
69#4837C2212yes—
70#4836C2214yes—
71#4836C2214yes—
72#4836C2214yes—
73#4834C2212yes—
74#4834C2214yes—
75D3×C4⋊C8C2212yes—
76D3×C4⋊C8C2214yes—
77#4709C2214yes—
78#4709C2214yes—
79#4706C2214yes—
80#4706C2214yes—
81#4706C2214yes—
82#4706C2214yes—
83#4705C2214yes—
84#4705C2214yes—
85#4690C2212yes—
86#4690C2212yes—
87#4688C2212yes—
88#4688C2212yes—
89C8×D12C2212yes—
90C8×D12C2212yes—
91#4685C2212yes—
92#4685C2212yes—
93#3480—31no—
94#2995—34no—
95#2994—32no—
96#2993—32no—
97#2992—34no—
98#2990—32no—
99#2989—32no—
100Q8×M16—31no—
101C2×#446D311yescharacteristic, complemented
102#2935—31no—
103#2935—32no—
104#2932—32no—
105#2931—31no—
106#2923—32no—
107#2922—31no—
108#2906—31no—
109#2906—32no—
110C22×C3×Q8C2×C411yescharacteristic
111C2×#239C2×C412yes—
112C2×#235C2311yescharacteristic
113C2×#235C2312yes—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2312yes—
116C22×C3×C8C2311yescharacteristic
117C3×C4×Q8C2×C411yescharacteristic
118C3×C4×Q8C2×C411yescharacteristic
119C3×C4×Q8C2×C412yes—
120C3×C4×Q8C2311yescharacteristic
121C3×C4×Q8C2311yescharacteristic
122C3×C4×Q8C2312yes—
123C2×C3×C4⋊C4C2×C411yescharacteristic
124C2×C3×C4⋊C4C2×C412yes—
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2312yes—
127#947C2×C412yes—
128#947C2×C414yes—
129#946C2×C412yes—
130#946C2×C414yes—
131Q8×Dic3C2×C412yes—
132#930C2×C412yes—
133#930C2×C414yes—
134#930C2×C412yes—
135#930C2×C414yes—
136C4×#67C2×C412yes—
137C4×#67C2×C414yes—
138C4×#67C2×C412yes—
139C4×#67C2×C414yes—
140#926C2311yescharacteristic
141C2×#208C2311yescharacteristic
142C2×#208C2311yescharacteristic
143C2×#208C2312yes—
144#901—44no—
145#901—44no—
146#901—44no—
147C2×ΓL(1,𝔽25)C2314yes—
148C2×ΓL(1,𝔽25)C2314yes—
149C2×ΓL(1,𝔽25)C2314yes—
150C2×D3×C8C2314yes—
151C2×D3×C8C2314yes—
152C2×D3×C8C2314yes—
153#898C2×C414yes—
154#898C2×C414yes—
155#898C2×C414yes—
156#895C2×C412yes—
157#895C2×C414yes—
158#894C2×C414yes—
159#894C2×C414yes—
160#894C2×C414yes—
161#893C2×C412yes—
162#893C2×C414yes—
163#892C2×C412yes—
164#892C2×C414yes—
165#890C2×C414yes—
166#890C2×C412yes—
167#875C2×C412yes—
168#875C2×C412yes—
169#875C2×C412yes—
170#874C2×C411yescharacteristic
171#874C2×C412yes—
172C4×D12C2×C411yescharacteristic
173C4×D12C2×C412yes—
174C4×D12C2×C411yescharacteristic
175C4×D12C2×C412yes—
176C4×D12C2312yes—
177C4×D12C2312yes—
178C4×D12C2314yes—
179C4×D12C2314yes—
180#872C2312yes—
181#872C2314yes—
182C42×D3C2312yes—
183C42×D3C2314yes—
184#869C2×C411yescharacteristic
185#869C2×C412yes—
186C4×Dic6C2×C411yescharacteristic
187C4×Dic6C2×C412yes—
188C4×Dic6C2×C411yescharacteristic
189C4×Dic6C2×C412yes—
190C3×C4⋊C8C2312yes—
191C3×C4⋊C8C2311yescharacteristic
192C3×C4⋊C8C2311yescharacteristic
193C3×C4⋊C8C2312yes—
194C3×C4⋊C8C2312yes—
195C3×C4⋊C8C2312yes—
196C3×C4⋊C8C2312yes—
197C3×#97C2312yes—
198C3×#97C2312yes—
199C3×#97C2312yes—
200C3×#97C2312yes—
201C3×C4×C8C2311yescharacteristic
202C3×C4×C8C2311yescharacteristic
203C3×C4×C8C2311yescharacteristic
204C3×C4×C8C2311yescharacteristic
205(C2×D3)⋊C8C2312yes—
206(C2×D3)⋊C8C2312yes—
207(C2×D3)⋊C8C2312yes—
208(C2×D3)⋊C8C2312yes—
209(C2×D3)⋊C8C2314yes—
210(C2×D3)⋊C8C2314yes—
211(C2×D3)⋊C8C2314yes—
212(C2×D3)⋊C8C2314yes—
213Dic3⋊C8C2312yes—
214Dic3⋊C8C2312yes—
215Dic3⋊C8C2312yes—
216Dic3⋊C8C2312yes—
217Dic3⋊C8C2314yes—
218Dic3⋊C8C2314yes—
219C4⋊(C3⋊C8)C2312yes—
220C4⋊(C3⋊C8)C2312yes—
221C4⋊(C3⋊C8)C2314yes—
222C4⋊(C3⋊C8)C2314yes—
223#803C2312yes—
224#803C2314yes—
225C4×C3⋊C8C2312yes—
226C4×C3⋊C8C2314yes—
227C2×#131—32no—
228C2×#131—32no—
229C2×#131—32no—
230#559—31no—
231#559—32no—
232#557—31no—
233#556—31no—
234#556—32no—
235#553—32no—
236#553—34no—
237#550—31no—
238#548—32no—
239#532—31no—
240#532—32no—
241#529—34no—
242#529—32no—
243C4×#41—32no—
244C4×#41—31no—
245C4×#41—32no—
246C2×C4×Q8C2×D311yescharacteristic
247#446—32no—
248#446—34no—
249#446C2×D311yescharacteristic
250#446C2×D311yescharacteristic
251#446C2×D312yes—
252#446C2×D311yescharacteristic
253#446C2×D311yescharacteristic
254#446C2×D312yes—
255C8×Q8—32no—
256#436—32no—
257#436—34no—
258#436—32no—
259#436—32no—
260#435—34no—
261#435—34no—
262#435—34no—
263#435—34no—
264#435—34no—
265#435—34no—
266#435—34no—
267C8×D4—32no—
268C8×D4—34no—
269C8×D4—32no—
270C8×D4—32no—
271#433—34no—
272#433—34no—
273#433—32no—
274#433—32no—
275#432—34no—
276#432—34no—
277#431—32no—
278#431—32no—
279#424—31no—
280#424—32no—
281#424—31no—
282#424—34no—
283#424—34no—
284#424—34no—
285#423—31no—
286#423—32no—
287#423—34no—
288#423—32no—
289C2×C4⋊C8—32no—
290C2×C4⋊C8—34no—
291C2×C4⋊C8C2×D312yes—
292C2×C4⋊C8C2×D311yescharacteristic
293#408—31no—
294#408—31no—
295#408—32no—
296#408—32no—
297C4×M16—31no—
298C4×M16—32no—
299C2×#97C2×D312yes—
300C2×C4×C8C2×D311yescharacteristic
301C2×C3×Q8—42no—
302C2×C3×Q8C22×C411yescharacteristic
303C2×C3×Q8C22×C411yescharacteristic
304C2×C3×Q8C22×C412yes—
305C22×C3×C4C22×C411yescharacteristic
306C22×C3×C4C22×C411yescharacteristic
307C22×C3×C4C22×C412yes—
308C22×C3×C4C22×C412yes—
309C22×C3×C4C2411yescharacteristic
310C2×#67C22×C412yes—
311C2×#67C22×C414yes—
312#239—44no—
313#235—24no—
314#235—22no—
315#235—22no—
316#235—24no—
317C2×D12C22×C411yescharacteristic
318C2×D12C22×C412yes—
319C2×D12C22×C412yes—
320C2×D12C22×C414yes—
321C2×D12C22×C412yes—
322C2×D12C22×C414yes—
323C2×C4×D3C22×C412yes—
324C2×C4×D3C22×C414yes—
325C2×C4×D3C22×C412yes—
326C2×C4×D3C22×C414yes—
327C2×C4×D3C2412yes—
328C2×C4×D3C2414yes—
329C2×Dic6C22×C411yescharacteristic
330C2×Dic6C22×C412yes—
331C2×C3×C8—22no—
332C2×C3×C8—24no—
333C2×C3×C8—22no—
334C2×C3×C8C2411yescharacteristic
335C2×C3×C8C2411yescharacteristic
336C2×C3×C8C2411yescharacteristic
337C2×C3×C8C2411yescharacteristic
338C2×C3×C8C2412yes—
339C2×C3×C8C2412yes—
340C3×C4⋊C4C22×C412yes—
341C3×C4⋊C4C22×C411yescharacteristic
342C3×C4⋊C4C22×C412yes—
343C3×C4⋊C4C22×C411yescharacteristic
344C3×C4⋊C4C22×C412yes—
345C3×C4⋊C4C22×C412yes—
346C3×C4⋊C4C22×C412yes—
347C3×C42C22×C412yes—
348C3×C42C22×C411yescharacteristic
349C3×C42C22×C411yescharacteristic
350C3×C42C22×C412yes—
351C3×C42C2411yescharacteristic
352C3×C42C2412yes—
353C3×C42C2411yescharacteristic
354C3×C42C2412yes—
355#217C22×C412yes—
356(C2×D3)⋊C4C22×C412yes—
357(C2×D3)⋊C4C22×C414yes—
358(C2×D3)⋊C4C22×C412yes—
359(C2×D3)⋊C4C22×C414yes—
360(C2×D3)⋊C4C22×C414yes—
361(C2×D3)⋊C4C22×C414yes—
362(C2×D3)⋊C4C22×C414yes—
363(C2×D3)⋊C4C22×C414yes—
364(C2×D3)⋊C4C22×C414yes—
365(C2×D3)⋊C4C22×C414yes—
366C4⋊Dic3C22×C411yescharacteristic
367C4⋊Dic3C22×C411yescharacteristic
368C4⋊Dic3C22×C412yes—
369C4⋊Dic3C22×C414yes—
370C4⋊Dic3C22×C414yes—
371C4⋊Dic3C22×C412yes—
372Dic3⋊C4C22×C412yes—
373Dic3⋊C4C22×C414yes—
374Dic3⋊C4C22×C412yes—
375Dic3⋊C4C22×C414yes—
376C4×Dic3C22×C414yes—
377C4×Dic3C22×C412yes—
378C4×Dic3C22×C412yes—
379C4×Dic3C22×C414yes—
380C4×Dic3C2412yes—
381#208—24no—
382#208—22no—
383#208—22no—
384C2×C3⋊C8C2412yes—
385C2×C3⋊C8C2412yes—
386C2×C3⋊C8C2414yes—
387ΓL(1,𝔽25)—44no—
388ΓL(1,𝔽25)—44no—
389ΓL(1,𝔽25)—44no—
390D3×C8—44no—
391D3×C8—44no—
392D3×C8—44no—
393C2×#41—32no—
394C2×#41—31no—
395C2×#41—32no—
396C22×Q8C4×D311yescharacteristic
397#131—124no—
398#131—124no—
399#131—124no—
400C2×M16—32no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—34no—
404C2×M16—34no—
405C2×M16—34no—
406C22×C8—34no—
407C22×C8—34no—
408C22×C8—34no—
409C22×C8C22×D311yescharacteristic
410C22×C8C22×D312yes—
411C22×C8C22×D311yescharacteristic
412C4⋊Q8—31no—
413C4⋊Q8—32no—
414#127—31no—
415#127—32no—
416#126—34no—
417#126—34no—
418#126—34no—
419#125—34no—
420#125—32no—
421#124—32no—
422#124—34no—
423#124—32no—
424#124—32no—
425#124—32no—
426#123—34no—
427#123—34no—
428#123—34no—
429C22⋊Q8—32no—
430C22⋊Q8—34no—
431#121—32no—
432#121—34no—
433#121—32no—
434#121—34no—
435#121—32no—
436#121—34no—
437C4×Q8—32no—
438C4×Q8—31no—
439C4×Q8—32no—
440C4×Q8—31no—
441C4×Q8—32no—
442C4×Q8C4×D311yescharacteristic
443C4×Q8C4×D311yescharacteristic
444C4×Q8C4×D312yes—
445C4×Q8C22×D311yescharacteristic
446C4×Q8C22×D311yescharacteristic
447C4×Q8C22×D312yes—
448C4×D4—32no—
449C4×D4—34no—
450C4×D4—32no—
451C4×D4—34no—
452C4×D4—32no—
453C4×D4—34no—
454C4×D4—31no—
455C4×D4—32no—
456C4×D4—31no—
457C4×D4—32no—
458C4×D4—32no—
459C4×D4—34no—
460C4×D4—34no—
461C4×D4—32no—
462#117—31no—
463#117—32no—
464#117—34no—
465#117—34no—
466#117—32no—
467C2×C4⋊C4C4×D311yescharacteristic
468C2×C4⋊C4C4×D312yes—
469C2×C42—32no—
470C2×C42—34no—
471C2×C42C22×D311yescharacteristic
472C2×C42C22×D312yes—
473C4⋊C8—32no—
474C4⋊C8—34no—
475C4⋊C8—34no—
476C4⋊C8—32no—
477C4⋊C8—32no—
478C4⋊C8—32no—
479C4⋊C8—32no—
480C4⋊C8—34no—
481C4⋊C8—32no—
482C4⋊C8—34no—
483C4⋊C8C22×D312yes—
484C4⋊C8C22×D311yescharacteristic
485C4⋊C8C22×D311yescharacteristic
486C4⋊C8C22×D312yes—
487C4⋊C8C22×D312yes—
488C4⋊C8C22×D312yes—
489C4⋊C8C22×D312yes—
490C22⋊C8—32no—
491C22⋊C8—32no—
492C22⋊C8—32no—
493C22⋊C8—32no—
494C22⋊C8—34no—
495C22⋊C8—34no—
496C22⋊C8—34no—
497C22⋊C8—34no—
498#97—34no—
499#97—32no—
500#97C22×D312yes—
501#97C22×D312yes—
502#97C22×D312yes—
503#97C22×D312yes—
504C4×C8—32no—
505C4×C8—34no—
506C4×C8C22×D311yescharacteristic
507C4×C8C22×D311yescharacteristic
508C4×C8C22×D311yescharacteristic
509C4×C8C22×D311yescharacteristic
510C23×C3C23×C411yescharacteristic
511C22×D3C23×C412yes—
512C22×D3C23×C414yes—
513C3×Q8—22no—
514C3×Q8—22no—
515C3×Q8—42no—
516C2×C3×C4—22no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4C23×C412yes—
521C2×C3×C4C23×C411yescharacteristic
522C2×C3×C4C23×C412yes—
523C2×C3×C4C23×C412yes—
524C2×C3×C4C23×C411yescharacteristic
525C2×C3×C4C23×C411yescharacteristic
526C2×C3×C4C23×C412yes—
527C2×C3×C4C23×C411yescharacteristic
528C2×C3×C4C23×C411yescharacteristic
529C2×C3×C4H(5,𝔽2)12yes—
530C2×C3×C42−1+412yes—
531C2×C3×C4C2511yescharacteristic
532#67—24no—
533#67—28no—
534C2×Dic3C23×C412yes—
535C2×Dic3C23×C412yes—
536C2×Dic3C23×C414yes—
537C2×Dic3C23×C412yes—
538D12—22no—
539D12—24no—
540D12—24no—
541D12—42no—
542D12—44no—
543D12—44no—
544C4×D3—24no—
545C4×D3—24no—
546C4×D3—22no—
547C4×D3—22no—
548C4×D3—24no—
549C4×D3—42no—
550C4×D3—44no—
551C4×D3—44no—
552Dic6—22no—
553Dic6—24no—
554C3×C8—21no—
555C3×C8—22no—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3⋊C8—24no—
561C3⋊C8—22no—
562C3⋊C8—22no—
563#41—62no—
564#41—64no—
565#41—64no—
566#41—62no—
567#41—124no—
568C2×Q8—31no—
569C2×Q8—32no—
570C2×Q8—42no—
571C2×Q8C2×C4×D311yescharacteristic
572C2×Q8C2×C4×D311yescharacteristic
573C2×Q8C2×C4×D312yes—
574C2×D4—32no—
575C2×D4—34no—
576C2×D4—32no—
577C2×D4—31no—
578C2×D4—32no—
579C2×D4—34no—
580C2×D4—34no—
581C2×D4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—32no—
587C22×C4—34no—
588C22×C4C2×C4×D311yescharacteristic
589C22×C4C2×C4×D311yescharacteristic
590C22×C4C2×C4×D312yes—
591C22×C4C2×C4×D312yes—
592C22×C4C23×D311yescharacteristic
593M16—62no—
594M16—64no—
595M16—62no—
596M16—124no—
597M16—124no—
598M16—124no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—24no—
602C2×C8—32no—
603C2×C8—32no—
604C2×C8—34no—
605C2×C8—124no—
606C2×C8—124no—
607C2×C8—124no—
608C2×C8C23×D311yescharacteristic
609C2×C8C23×D311yescharacteristic
610C2×C8C23×D311yescharacteristic
611C2×C8C23×D311yescharacteristic
612C2×C8C23×D312yes—
613C2×C8C23×D312yes—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—34no—
617C4⋊C4—32no—
618C4⋊C4—32no—
619C4⋊C4—34no—
620C4⋊C4—34no—
621C4⋊C4—32no—
622C4⋊C4—34no—
623C4⋊C4—32no—
624C4⋊C4C2×C4×D312yes—
625C4⋊C4C2×C4×D311yescharacteristic
626C4⋊C4C2×C4×D312yes—
627C4⋊C4C2×C4×D311yescharacteristic
628C4⋊C4C2×C4×D312yes—
629C4⋊C4C2×C4×D312yes—
630C4⋊C4C2×C4×D312yes—
631C22⋊C4—32no—
632C22⋊C4—34no—
633C22⋊C4—32no—
634C22⋊C4—34no—
635C22⋊C4—34no—
636C22⋊C4—34no—
637C22⋊C4—32no—
638C22⋊C4—34no—
639C22⋊C4—34no—
640C22⋊C4—34no—
641C22⋊C4—34no—
642C42—32no—
643C42—34no—
644C42—34no—
645C42—32no—
646C42—32no—
647C42C2×C4×D311yescharacteristic
648C42C2×C4×D312yes—
649C42C2×C4×D312yes—
650C42C2×C4×D311yescharacteristic
651C42C23×D311yescharacteristic
652C42C23×D312yes—
653C42C23×D311yescharacteristic
654C42C23×D312yes—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3#52012yes—
658C22×C3C24×C411yescharacteristic
659C2×D3—22no—
660C2×D3—24no—
661C2×D3—22no—
662C2×D3—24no—
663C2×D3—22no—
664C2×D3—24no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4#52012yes—
673C3×C4#56812yes—
674C3×C4C2×H(5,𝔽2)11yescharacteristic
675C3×C4C2×2−1+411yescharacteristic
676Dic3—24no—
677Dic3—22no—
678Dic3—22no—
679Dic3—22no—
680C23—32no—
681C23—34no—
682C23C22×C4×D311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—62no—
687Q8—64no—
688D4—64no—
689D4—68no—
690D4—64no—
691D4—62no—
692D4—64no—
693D4—124no—
694D4—124no—
695D4—122no—
696C2×C4—22no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—34no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—62no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—124no—
710C2×C4—122no—
711C2×C4—124no—
712C2×C4C22×C4×D311yescharacteristic
713C2×C4C22×C4×D312yes—
714C2×C4C22×C4×D312yes—
715C2×C4C22×C4×D311yescharacteristic
716C2×C4C22×C4×D312yes—
717C2×C4C22×C4×D312yes—
718C2×C4C22×C4×D311yescharacteristic
719C2×C4C22×C4×D311yescharacteristic
720C2×C4C22×C4×D311yescharacteristic
721C2×C4#100712yes—
722C2×C4#100912yes—
723C2×C4C24×D311yescharacteristic
724C8—21no—
725C8—21no—
726C8—21no—
727C8—22no—
728C8—22no—
729C8—21no—
730C8—62no—
731C8—62no—
732C8—64no—
733C2×C3—22no—
734C2×C3C2×#52011yescharacteristic
735C2×C3C2×#56811yescharacteristic
736C2×C3#357311yescharacteristic
737D3—42no—
738D3—44no—
739C22—21no—
740C22—21no—
741C22—62no—
742C22—64no—
743C22—62no—
744C22—64no—
745C22—62no—
746C22—64no—
747C22#557412yes—
748C22C23×C4×D311yescharacteristic
749C4—21no—
750C4—22no—
751C4—22no—
752C4—21no—
753C4—22no—
754C4—22no—
755C4—21no—
756C4—62no—
757C4—64no—
758C4—62no—
759C4—62no—
760C4#557412yes—
761C4#574512yes—
762C4C2×#100711yescharacteristic
763C4C2×#100911yescharacteristic
764C3#6027511yescharacteristic, complemented, Sylow
765C2—22no—
766C2—122no—
767C2—124no—
768C2C2×#557411yescharacteristic
769C2C2×#574511yescharacteristic
770C2#8716011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC2×C3×#446C2
prime radical#85802C2
cosocleC2×C3×C4C25
hypercenterC2×#446D3
hypocenterC3#60275
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×C3×#446C2semidirect
3. Q8×#208C2semidirect
4. #79949C2semidirect
5. #79948C2semidirect
6. #79947C2semidirect
7. #79946C2semidirect
8. #79945C2semidirect
9. #79944C2semidirect
10. #79012C2semidirect
11. #79012C2semidirect
12. #79004C2semidirect
13. #79004C2semidirect
14. #78491C2semidirect
15. #78489C2semidirect
16. #78458C2semidirect
17. #78455C2semidirect
101. C2×#446D3semidirect
764. C3#60275semidirect

Maximal subgroups

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

subgroupindex
#858022
C2×C3×#4462
Q8×#2082
#799492
#799482
#799472
#799462
#799452
#799442
#790122
#790042
#784912
#784892
#784582
#784552
#602753