Finite Group Databasebeta

← #11660475

Subgroups — #11660475

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#85825C211yesmaximal, characteristic
2C3×#2922C211yesmaximal, characteristic, complemented
3#82512C211yesmaximal, characteristic, complemented
4#79382C214yesmaximal, complemented
5#79379C214yesmaximal, complemented
6#79296C212yesmaximal, complemented
7#79295C212yesmaximal, complemented
8#79293C212yesmaximal, complemented
9#79292C212yesmaximal, complemented
10#79081C212yesmaximal, complemented
11#79071C212yesmaximal, complemented
12#78660C212yesmaximal, complemented
13#78658C212yesmaximal, complemented
14#78522C211yesmaximal, characteristic, complemented
15M16×Dic6C211yesmaximal, characteristic, complemented
16#78458C211yesmaximal, characteristic, complemented
17C2×#4679C211yesmaximal, characteristic, complemented
18#60275—31nomaximal, Sylow
19C3×C4×#41C2211yescharacteristic
20#5832C2212yes—
21C2×#948C2212yes—
22C2×#907C2212yes—
23C2×#901C2212yes—
24#5585C411yescharacteristic
25#5568C412yes—
26#5567C411yescharacteristic
27#5565C412yes—
28#5559C412yes—
29#5553C411yescharacteristic
30#5552C412yes—
31#5542C411yescharacteristic
32#5540C414yes—
33#5528C2214yes—
34#5522C2212yes—
35#5479C2212yes—
36#5477C2211yescharacteristic
37C4×#235C2212yes—
38C2×C4×Dic6C2211yescharacteristic
39C3×#433C2212yes—
40C3×#433C2212yes—
41C3×#431C2212yes—
42C3×#431C2212yes—
43C3×#424C2211yescharacteristic
44C3×#424C2211yescharacteristic
45C3×#408C2211yescharacteristic
46C3×#408C2211yescharacteristic
47C3×C4×M16C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49#5129C2212yes—
50#5118C2212yes—
51Dic3×M16C2212yes—
52#5110C2212yes—
53C2×#815C2212yes—
54C2×Dic3⋊C8C2212yes—
55#4999C2214yes—
56#4999C2212yes—
57#4924C2211yescharacteristic
58#4924C2212yes—
59C2×C4⋊(C3⋊C8)C2211yescharacteristic
60C2×C4⋊(C3⋊C8)C2212yes—
61#4840C2214yes—
62#4840C2214yes—
63#4839C2214yes—
64#4839C2214yes—
65#4837C2214yes—
66#4835C2214yes—
67#4835C2214yes—
68D3×C4⋊C8C2214yes—
69#4730C2214yes—
70#4730C2214yes—
71#4730C2214yes—
72#4729C2214yes—
73#4728C2214yes—
74#4728C2214yes—
75#4728C2214yes—
76#67⋊C8C2214yes—
77#4706C2214yes—
78#4701C2214yes—
79#4688C2212yes—
80#4688C2212yes—
81#4688C2212yes—
82C8×D12C2212yes—
83C8×D12C2212yes—
84C8×D12C2212yes—
85#4679C2212yes—
86#4679C2212yes—
87#4679C2211yescharacteristic
88#4679C2211yescharacteristic
89#4679C2211yescharacteristic
90#4679C2211yescharacteristic
91#4679C2212yes—
92C8×Dic6C2212yes—
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×#446—31no—
102#2935—32no—
103#2935—31no—
104#2932—32no—
105#2931—31no—
106#2923—32no—
107#2922D311yescharacteristic, complemented
108#2906—32no—
109#2906—31no—
110C2×C3×#41C2311yescharacteristic
111C2×#235C2×C412yes—
112C2×#235C2312yes—
113C22×Dic6C2×C411yescharacteristic
114C2×C3×M16C2311yescharacteristic
115C2×C3×M16C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C3×C4×Q8C2×C411yescharacteristic
119C3×C4×Q8C2×C411yescharacteristic
120C3×C4×D4C2×C412yes—
121C3×C4×D4C2×C411yescharacteristic
122C3×C4×D4C2×C412yes—
123C3×C4×D4C2×C411yescharacteristic
124C3×#117C2311yescharacteristic
125C3×#117C2312yes—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2312yes—
128#948—44no—
129#947C2×C412yes—
130#944C2×C412yes—
131#940C2×C412yes—
132#939C2×C414yes—
133#939C2×C414yes—
134#936C2×C412yes—
135#930C2×C412yes—
136#930C2×C412yes—
137#930C2×C412yes—
138#929C2×C414yes—
139C4×#67C2×C414yes—
140C4×#67C2314yes—
141C4×#67C2314yes—
142#926C2×C412yes—
143C2×C4⋊Dic3C2×C411yescharacteristic
144#924C2×C412yes—
145C2×Dic3⋊C4C2×C412yes—
146C2×C4×Dic3C2312yes—
147C2×#208C2312yes—
148C2×#208C2314yes—
149C22×C3⋊C8C2312yes—
150C22×C3⋊C8C2314yes—
151#907—44no—
152#901—44no—
153C2×ΓL(1,𝔽25)C2314yes—
154C2×ΓL(1,𝔽25)C2314yes—
155C2×D3×C8C2314yes—
156C2×D3×C8C2314yes—
157#898C2×C414yes—
158#896C2×C414yes—
159#894C2×C414yes—
160#893C2×C412yes—
161#893C2×C412yes—
162#889C2×C414yes—
163#887C2×C412yes—
164#887C2×C412yes—
165#885C2×C414yes—
166#884C2×C414yes—
167#883C2×C414yes—
168#67⋊C4C2×C414yes—
169#67⋊C4C2×C414yes—
170#879C2×C414yes—
171#876C2×C414yes—
172#875C2×C412yes—
173#875C2×C412yes—
174#874C2×C411yescharacteristic
175C4×D12C2×C412yes—
176C4×D12C2312yes—
177C4×D12C2312yes—
178#872C2×C414yes—
179#872C2314yes—
180C42×D3C2314yes—
181#870C2×C412yes—
182#869C2×C411yescharacteristic
183C4×Dic6C2×C411yescharacteristic
184C4×Dic6C2×C411yescharacteristic
185C4×Dic6C2×C412yes—
186C4×Dic6C2×C412yes—
187C4×Dic6C2311yescharacteristic
188C4×Dic6C2311yescharacteristic
189C4×Dic6C2312yes—
190C3×C4⋊C8C2312yes—
191C3×C4⋊C8C2312yes—
192C3×C4⋊C8C2312yes—
193C3×C4⋊C8C2312yes—
194C3×C22⋊C8C2312yes—
195C3×C22⋊C8C2312yes—
196C3×C22⋊C8C2312yes—
197C3×C22⋊C8C2312yes—
198C3×#97C2312yes—
199C3×C4×C8C2312yes—
200C3×C4×C8C2311yescharacteristic
201C3×C4×C8C2311yescharacteristic
202C3×C4×C8C2311yescharacteristic
203C3×C4×C8C2311yescharacteristic
204(C2×D3)⋊C8C2314yes—
205(C2×D3)⋊C8C2314yes—
206(C2×D3)⋊C8C2314yes—
207(C2×D3)⋊C8C2314yes—
208#815C2312yes—
209#815C2312yes—
210#815C2312yes—
211#815C2312yes—
212#815C2314yes—
213Dic3⋊C8C2314yes—
214Dic3⋊C8C2312yes—
215Dic3⋊C8C2312yes—
216Dic3⋊C8C2312yes—
217Dic3⋊C8C2312yes—
218Dic3⋊C8C2314yes—
219C8×Dic3C2314yes—
220C4⋊(C3⋊C8)C2311yescharacteristic
221C4⋊(C3⋊C8)C2312yes—
222C4⋊(C3⋊C8)C2311yescharacteristic
223C4⋊(C3⋊C8)C2312yes—
224C4⋊(C3⋊C8)C2314yes—
225C4⋊(C3⋊C8)C2312yes—
226C4⋊(C3⋊C8)C2314yes—
227C2×#131—32no—
228C2×#131—32no—
229C2×#131—32no—
230#559—31no—
231#559—32no—
232#557—31no—
233#556—32no—
234#556—31no—
235#553—34no—
236#553—32no—
237#550—31no—
238#548—32no—
239#532—32no—
240#532—31no—
241#529—34no—
242#529—32no—
243C4×#41—32no—
244C4×#41—32no—
245C4×#41C2×D311yescharacteristic
246C2×C4×Q8—31no—
247#446—34no—
248#446—31no—
249#446—31no—
250#446—32no—
251#446—31no—
252#446—31no—
253#446—32no—
254#446—32no—
255C8×Q8—32no—
256#436—34no—
257#436—32no—
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—34no—
268C8×D4—32no—
269C8×D4—32no—
270C8×D4—32no—
271#433—34no—
272#433—34no—
273#433C2×D312yes—
274#433C2×D312yes—
275#432—34no—
276#432—34no—
277#431C2×D312yes—
278#431C2×D312yes—
279#424—32no—
280#424—34no—
281#424—34no—
282#424—34no—
283#424C2×D311yescharacteristic
284#424C2×D311yescharacteristic
285#423—32no—
286#423—31no—
287#423—32no—
288#423—34no—
289C2×C4⋊C8—32no—
290C2×C4⋊C8—31no—
291C2×C4⋊C8—32no—
292C2×C4⋊C8—34no—
293#408—32no—
294#408—32no—
295#408C2×D311yescharacteristic
296#408C2×D311yescharacteristic
297C4×M16—32no—
298C4×M16C2×D311yescharacteristic
299C2×#97—32no—
300C2×C4×C8C2×D311yescharacteristic
301C3×#41—22no—
302C3×#41—22no—
303C2×C3×Q8C22×C411yescharacteristic
304C2×C3×D4C22×C411yescharacteristic
305C2×C3×D4C22×C412yes—
306C22×C3×C4C22×C412yes—
307C22×C3×C4C22×C411yescharacteristic
308C22×C3×C4C22×C411yescharacteristic
309C22×C3×C4C22×C412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2411yescharacteristic
312C2×#67C22×C414yes—
313C2×#67C22×C414yes—
314C2×#67C22×C414yes—
315C22×Dic3C22×C412yes—
316C22×Dic3C22×C412yes—
317#235—24no—
318#235—24no—
319#235—44no—
320C2×D12C22×C412yes—
321C2×D12C22×C412yes—
322C2×D12C22×C412yes—
323C2×C4×D3C22×C414yes—
324C2×C4×D3C22×C414yes—
325C2×C4×D3C2414yes—
326C2×Dic6—42no—
327C2×Dic6C22×C411yescharacteristic
328C2×Dic6C22×C411yescharacteristic
329C2×Dic6C22×C412yes—
330C2×Dic6C22×C412yes—
331C3×M16—22no—
332C3×M16—22no—
333C2×C3×C8—22no—
334C2×C3×C8—22no—
335C2×C3×C8C2412yes—
336C2×C3×C8C2411yescharacteristic
337C2×C3×C8C2411yescharacteristic
338C2×C3×C8C2412yes—
339C2×C3×C8C2411yescharacteristic
340C2×C3×C8C2411yescharacteristic
341C3×C4⋊C4C22×C411yescharacteristic
342C3×C4⋊C4C22×C411yescharacteristic
343C3×C4⋊C4C22×C412yes—
344C3×C4⋊C4C22×C412yes—
345C3×C22⋊C4C22×C412yes—
346C3×C22⋊C4C22×C412yes—
347C3×C22⋊C4C22×C412yes—
348C3×C42C22×C411yescharacteristic
349C3×C42C22×C411yescharacteristic
350C3×C42C22×C412yes—
351C3×C42C22×C412yes—
352C3×C42C2411yescharacteristic
353C3×C42C2411yescharacteristic
354C3×C42C2412yes—
355#217C22×C414yes—
356#217C22×C414yes—
357(C2×D3)⋊C4C22×C414yes—
358(C2×D3)⋊C4C22×C414yes—
359(C2×D3)⋊C4C22×C414yes—
360(C2×D3)⋊C4C22×C414yes—
361(C2×D3)⋊C4C22×C414yes—
362(C2×D3)⋊C4C22×C414yes—
363C4⋊Dic3C22×C411yescharacteristic
364C4⋊Dic3C22×C411yescharacteristic
365C4⋊Dic3C22×C412yes—
366C4⋊Dic3C22×C412yes—
367C4⋊Dic3C22×C412yes—
368Dic3⋊C4C22×C412yes—
369Dic3⋊C4C22×C412yes—
370Dic3⋊C4C22×C412yes—
371Dic3⋊C4C22×C412yes—
372Dic3⋊C4C22×C414yes—
373Dic3⋊C4C22×C414yes—
374Dic3⋊C4C22×C414yes—
375Dic3⋊C4C22×C414yes—
376C4×Dic3C22×C412yes—
377C4×Dic3C22×C412yes—
378C4×Dic3C22×C414yes—
379C4×Dic3C22×C414yes—
380C4×Dic3C2412yes—
381C4×Dic3C2412yes—
382#208—24no—
383#208—44no—
384C2×C3⋊C8—24no—
385C2×C3⋊C8—44no—
386C2×C3⋊C8C2414yes—
387C2×C3⋊C8C2412yes—
388C2×C3⋊C8C2412yes—
389ΓL(1,𝔽25)—44no—
390ΓL(1,𝔽25)—44no—
391D3×C8—44no—
392D3×C8—44no—
393C2×#41—32no—
394C2×#41—32no—
395C2×#41C22×D311yescharacteristic
396C22×Q8—31no—
397#131—124no—
398#131—124no—
399#131—124no—
400C2×M16—32no—
401C2×M16—34no—
402C2×M16—34no—
403C2×M16—34no—
404C2×M16C22×D311yescharacteristic
405C2×M16C22×D311yescharacteristic
406C22×C8—32no—
407C22×C8—34no—
408C22×C8—34no—
409C22×C8—34no—
410C22×C8C22×D311yescharacteristic
411C22×C8C22×D311yescharacteristic
412C4⋊Q8—32no—
413C4⋊Q8—31no—
414#127—32no—
415#127—31no—
416#126—34no—
417#126—34no—
418#126—34no—
419#125—34no—
420#125—32no—
421#124—32no—
422#124—32no—
423#124—34no—
424#124—32no—
425#124—32no—
426#123—34no—
427#123—34no—
428#123—34no—
429C22⋊Q8—32no—
430C22⋊Q8—34no—
431#121—34no—
432#121—34no—
433#121—32no—
434#121—32no—
435#121—32no—
436#121—34no—
437C4×Q8—32no—
438C4×Q8—32no—
439C4×Q8—31no—
440C4×Q8—31no—
441C4×Q8—32no—
442C4×Q8—32no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—32no—
446C4×Q8C4×D311yescharacteristic
447C4×Q8C4×D311yescharacteristic
448C4×D4—34no—
449C4×D4—34no—
450C4×D4—34no—
451C4×D4—32no—
452C4×D4—32no—
453C4×D4—34no—
454C4×D4—34no—
455C4×D4—32no—
456C4×D4—32no—
457C4×D4—32no—
458C4×D4C4×D312yes—
459C4×D4C4×D311yescharacteristic
460C4×D4C4×D312yes—
461C4×D4C4×D311yescharacteristic
462#117—32no—
463#117—34no—
464#117—34no—
465#117C22×D311yescharacteristic
466#117C22×D312yes—
467C2×C4⋊C4—32no—
468C2×C4⋊C4—31no—
469C2×C42—32no—
470C2×C42—34no—
471C2×C42C22×D311yescharacteristic
472C2×C42C22×D312yes—
473C4⋊C8—32no—
474C4⋊C8—34no—
475C4⋊C8—32no—
476C4⋊C8—32no—
477C4⋊C8—32no—
478C4⋊C8—34no—
479C4⋊C8—31no—
480C4⋊C8—31no—
481C4⋊C8—32no—
482C4⋊C8—34no—
483C4⋊C8—34no—
484C4⋊C8—32no—
485C4⋊C8—32no—
486C4⋊C8C22×D312yes—
487C4⋊C8C22×D312yes—
488C4⋊C8C22×D312yes—
489C4⋊C8C22×D312yes—
490C22⋊C8—34no—
491C22⋊C8—34no—
492C22⋊C8—34no—
493C22⋊C8—34no—
494C22⋊C8C22×D312yes—
495C22⋊C8C22×D312yes—
496C22⋊C8C22×D312yes—
497C22⋊C8C22×D312yes—
498#97—32no—
499#97—32no—
500#97—32no—
501#97—32no—
502#97—34no—
503#97C22×D312yes—
504C4×C8—34no—
505C4×C8C22×D311yescharacteristic
506C4×C8C22×D311yescharacteristic
507C4×C8C22×D311yescharacteristic
508C4×C8C22×D311yescharacteristic
509C4×C8C22×D312yes—
510C23×C3C23×C412yes—
511C23×C3C23×C411yescharacteristic
512C22×D3C23×C414yes—
513C3×Q8—22no—
514C3×D4—24no—
515C3×D4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—24no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—42no—
521C2×C3×C4—41no—
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×C4C23×C411yescharacteristic
530C2×C3×C4H(5,𝔽2)12yes—
531C2×C3×C42−1+412yes—
532C2×C3×C4C2511yescharacteristic
533#67—28no—
534#67—44no—
535#67—44no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3C23×C412yes—
539C2×Dic3C23×C412yes—
540C2×Dic3C23×C414yes—
541C2×Dic3C23×C412yes—
542C2×Dic3C23×C412yes—
543D12—24no—
544D12—24no—
545D12—42no—
546C4×D3—24no—
547C4×D3—24no—
548C4×D3—44no—
549C4×D3—44no—
550Dic6—24no—
551Dic6—22no—
552Dic6—22no—
553Dic6—42no—
554C3×C8—21no—
555C3×C8—22no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—22no—
560C3⋊C8—22no—
561C3⋊C8—24no—
562C3⋊C8—22no—
563#41—22no—
564#41—22no—
565#41—64no—
566#41—64no—
567#41—124no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—32no—
571C2×Q8—32no—
572C2×Q8—122no—
573C2×Q8C2×C4×D311yescharacteristic
574C2×D4—34no—
575C2×D4—34no—
576C2×D4—34no—
577C2×D4—32no—
578C2×D4—32no—
579C2×D4—32no—
580C2×D4C2×C4×D312yes—
581C2×D4C2×C4×D311yescharacteristic
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—34no—
587C22×C4C2×C4×D311yescharacteristic
588C22×C4C2×C4×D312yes—
589C22×C4C2×C4×D311yescharacteristic
590C22×C4C2×C4×D312yes—
591C22×C4C23×D312yes—
592C22×C4C23×D311yescharacteristic
593M16—22no—
594M16—22no—
595M16—64no—
596M16—124no—
597M16—124no—
598M16—124no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—34no—
602C2×C8—32no—
603C2×C8—32no—
604C2×C8—64no—
605C2×C8—124no—
606C2×C8—124no—
607C2×C8—124no—
608C2×C8C23×D312yes—
609C2×C8C23×D311yescharacteristic
610C2×C8C23×D311yescharacteristic
611C2×C8C23×D311yescharacteristic
612C2×C8C23×D311yescharacteristic
613C2×C8C23×D312yes—
614C4⋊C4—32no—
615C4⋊C4—31no—
616C4⋊C4—32no—
617C4⋊C4—31no—
618C4⋊C4—32no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—34no—
622C4⋊C4—32no—
623C4⋊C4—34no—
624C4⋊C4—34no—
625C4⋊C4—34no—
626C4⋊C4—32no—
627C4⋊C4C2×C4×D311yescharacteristic
628C4⋊C4C2×C4×D311yescharacteristic
629C4⋊C4C2×C4×D312yes—
630C4⋊C4C2×C4×D312yes—
631C22⋊C4—34no—
632C22⋊C4—34no—
633C22⋊C4—34no—
634C22⋊C4—34no—
635C22⋊C4—34no—
636C22⋊C4—34no—
637C22⋊C4—34no—
638C22⋊C4—34no—
639C22⋊C4C2×C4×D312yes—
640C22⋊C4C2×C4×D312yes—
641C22⋊C4C2×C4×D312yes—
642C42—34no—
643C42—34no—
644C42—32no—
645C42—32no—
646C42—32no—
647C42—32no—
648C42C2×C4×D312yes—
649C42C2×C4×D312yes—
650C42C2×C4×D311yescharacteristic
651C42C2×C4×D311yescharacteristic
652C42C23×D311yescharacteristic
653C42C23×D311yescharacteristic
654C42C23×D312yes—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3#52012yes—
661C22×C3C24×C411yescharacteristic
662C2×D3—24no—
663C2×D3—24no—
664C2×D3—24no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4#52012yes—
672C3×C4#56812yes—
673C3×C4C2×H(5,𝔽2)11yescharacteristic
674C3×C4C2×2−1+411yescharacteristic
675Dic3—24no—
676Dic3—22no—
677Dic3—22no—
678Dic3—22no—
679Dic3—22no—
680C23—34no—
681C23C22×C4×D312yes—
682C23C22×C4×D311yescharacteristic
683Q8—22no—
684Q8—62no—
685Q8—62no—
686Q8—64no—
687Q8—122no—
688D4—24no—
689D4—22no—
690D4—68no—
691D4—64no—
692D4—64no—
693D4—122no—
694D4—124no—
695D4—124no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—34no—
704C2×C4—32no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—124no—
710C2×C4—124no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4C22×C4×D312yes—
714C2×C4C22×C4×D312yes—
715C2×C4C22×C4×D311yescharacteristic
716C2×C4C22×C4×D312yes—
717C2×C4C22×C4×D311yescharacteristic
718C2×C4C22×C4×D311yescharacteristic
719C2×C4C22×C4×D311yescharacteristic
720C2×C4C22×C4×D311yescharacteristic
721C2×C4#100912yes—
722C2×C4#101012yes—
723C2×C4C24×D311yescharacteristic
724C8—21no—
725C8—21no—
726C8—22no—
727C8—21no—
728C8—21no—
729C8—22no—
730C8—62no—
731C8—62no—
732C8—64no—
733C2×C3—22no—
734C2×C3—42no—
735C2×C3C2×#52011yescharacteristic
736C2×C3C2×#56811yescharacteristic
737C2×C3#357311yescharacteristic
738D3—44no—
739C22—21no—
740C22—21no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—64no—
745C22—64no—
746C22—64no—
747C22#552312yes—
748C22C23×C4×D311yescharacteristic
749C4—22no—
750C4—21no—
751C4—21no—
752C4—22no—
753C4—21no—
754C4—22no—
755C4—62no—
756C4—62no—
757C4—62no—
758C4—62no—
759C4—64no—
760C4#552312yes—
761C4#575012yes—
762C4C2×#100911yescharacteristic
763C4C2×#101011yescharacteristic
764C3#6027511yescharacteristic, complemented, Sylow
765C2—22no—
766C2—42no—
767C2—124no—
768C2C2×#552311yescharacteristic
769C2C2×#575011yescharacteristic
770C2#8716011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2922C2
prime radical#85825C2
cosocleC2×C3×C4C25
hypercenter#2922D3
hypocenterC3#60275
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. C3×#2922C2semidirect
3. #82512C2semidirect
4. #79382C2semidirect
5. #79379C2semidirect
6. #79296C2semidirect
7. #79295C2semidirect
8. #79293C2semidirect
9. #79292C2semidirect
10. #79081C2semidirect
11. #79071C2semidirect
12. #78660C2semidirect
13. #78658C2semidirect
14. #78522C2semidirect
15. M16×Dic6C2semidirect
16. #78458C2semidirect
17. C2×#4679C2semidirect
107. #2922D3semidirect
764. C3#60275semidirect

Maximal subgroups

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

subgroupindex
#858252
C3×#29222
#825122
#793822
#793792
#792962
#792952
#792932
#792922
#790812
#790712
#786602
#786582
#785222
M16×Dic62
#784582
C2×#46792
#602753