Finite Group Databasebeta

← #11660478

Subgroups — #11660478

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#86220C211yesmaximal, characteristic
2C3×#2931C211yesmaximal, characteristic, complemented
3#83788C212yesmaximal, complemented
4#83783C212yesmaximal, complemented
5#83277C211yesmaximal, characteristic, complemented
6#79528C214yesmaximal, complemented
7#79526C212yesmaximal, complemented
8#79523C212yesmaximal, complemented
9#79410C212yesmaximal, complemented
10#79407C214yesmaximal, complemented
11#79406C212yesmaximal, complemented
12#79049C211yesmaximal, characteristic, complemented
13#79046C211yesmaximal, characteristic, complemented
14#78658C212yesmaximal, complemented
15#78649C212yesmaximal, complemented
16#78455C211yesmaximal, characteristic, complemented
17C2×#4679C211yesmaximal, characteristic, complemented
18#60275—31nomaximal, Sylow
19C2×C3×#131C2212yes—
20C3×#532C2211yescharacteristic
21#5832C2212yes—
22Dic3×#41C2212yes—
23C2×#948C2212yes—
24C2×#907C2212yes—
25#5732C411yescharacteristic
26#5721C411yescharacteristic
27#5718C411yescharacteristic
28#5713C411yescharacteristic
29#5681C412yes—
30#5671C412yes—
31#5618C412yes—
32#5601C414yes—
33#5598C412yes—
34#5557C2212yes—
35#5538C2214yes—
36C4×#237C2212yes—
37C4×#235C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C3×#436C2212yes—
40C3×#436C2212yes—
41C3×C8×D4C2212yes—
42C3×C8×D4C2212yes—
43C3×#423C2211yescharacteristic
44C3×#408C2212yes—
45C2×C3×C4×C8C2211yescharacteristic
46#5234C2212yes—
47#5128C2214yes—
48#5127C2214yes—
49#5119C2212yes—
50#5119C2214yes—
51#5118C2212yes—
52#5118C2214yes—
53Dic3×M16C2212yes—
54#5111C2214yes—
55#5110C2211yescharacteristic
56#5110C2211yescharacteristic
57C8×#67C2214yes—
58#5102C2214yes—
59#5102C2211yescharacteristic
60#5102C2211yescharacteristic
61C2×#815C2212yes—
62C2×Dic3⋊C8C2214yes—
63C2×Dic3⋊C8C2212yes—
64#5012C2212yes—
65#5011C2214yes—
66D4×C3⋊C8C2212yes—
67C2×C4⋊(C3⋊C8)C2211yescharacteristic
68C4×#208C2211yescharacteristic
69#4839C2214yes—
70#4837C2212yes—
71D3×C4⋊C8C2212yes—
72#4831C2212yes—
73#4830C2212yes—
74#4828C2214yes—
75#4730C2214yes—
76#4730C2214yes—
77#4728C2214yes—
78#4728C2214yes—
79#4720C2214yes—
80#4720C2214yes—
81#4719C2214yes—
82#4719C2214yes—
83#4690C2212yes—
84#4690C2212yes—
85#4685C2212yes—
86#4685C2212yes—
87#4679C2211yescharacteristic
88#4679C2212yes—
89#4679C2211yescharacteristic
90#4679C2211yescharacteristic
91#4679C2211yescharacteristic
92#4679C2212yes—
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#2931D311yescharacteristic, complemented
106#2923—32no—
107#2922—31no—
108#2906—31no—
109#2906—32no—
110C2×C3×#41C2312yes—
111C2×#237C2×C412yes—
112C2×#235C2311yescharacteristic
113C22×Dic6C2×C411yescharacteristic
114C3×#131—44no—
115C2×C3×M16C2312yes—
116C2×C3×M16C2314yes—
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2314yes—
120C3×C4⋊Q8C2×C411yescharacteristic
121C3×#127C2×C411yescharacteristic
122C3×#124C2×C412yes—
123C3×#121C2×C412yes—
124C3×#121C2×C412yes—
125C3×C4×D4C2312yes—
126C3×C4×D4C2312yes—
127C2×C3×C42C2311yescharacteristic
128#948—44no—
129#947C2×C412yes—
130Q8×Dic3C2×C412yes—
131Q8×Dic3C2×C412yes—
132#944C2×C412yes—
133#940C2×C412yes—
134#939C2×C414yes—
135#939C2×C414yes—
136#939C2×C414yes—
137#938C2×C412yes—
138#936C2×C412yes—
139#936C2×C412yes—
140#935C2×C414yes—
141D4×Dic3C2×C412yes—
142D4×Dic3C2×C412yes—
143D4×Dic3C2×C412yes—
144D4×Dic3C2×C414yes—
145D4×Dic3C2×C414yes—
146C4×#67C2×C412yes—
147C4×#67C2×C412yes—
148C4×#67C2314yes—
149C4×#67C2314yes—
150#926C2311yescharacteristic
151#926C2314yes—
152C2×C4⋊Dic3C2×C411yescharacteristic
153C2×Dic3⋊C4C2×C412yes—
154C2×C4×Dic3C2312yes—
155C2×C4×Dic3C2314yes—
156C2×#208C2311yescharacteristic
157C2×#208C2311yescharacteristic
158C2×#208C2314yes—
159C22×C3⋊C8C2312yes—
160C22×C3⋊C8C2314yes—
161#907—44no—
162C2×ΓL(1,𝔽25)C2314yes—
163C2×D3×C8C2314yes—
164#898C2×C414yes—
165#897C2×C412yes—
166#892C2×C412yes—
167#890C2×C412yes—
168#889C2×C414yes—
169#887C2×C412yes—
170#886C2×C414yes—
171#885C2×C414yes—
172#883C2×C414yes—
173#67⋊C4C2×C414yes—
174#879C2×C414yes—
175#879C2×C414yes—
176#878C2×C414yes—
177#877C2×C414yes—
178C4×D12C2×C411yescharacteristic
179C4×D12C2×C411yescharacteristic
180#872C2312yes—
181C42×D3C2312yes—
182C4×Dic6C2×C411yescharacteristic
183C4×Dic6C2×C412yes—
184C4×Dic6C2×C411yescharacteristic
185C4×Dic6C2×C411yescharacteristic
186C4×Dic6C2×C411yescharacteristic
187C4×Dic6C2311yescharacteristic
188C4×Dic6C2312yes—
189C4×Dic6C2311yescharacteristic
190C3×C4⋊C8C2312yes—
191C3×C4⋊C8C2312yes—
192C3×C22⋊C8C2314yes—
193C3×C22⋊C8C2314yes—
194C3×C4×C8C2311yescharacteristic
195C3×C4×C8C2311yescharacteristic
196C3×C4×C8C2311yescharacteristic
197C3×C4×C8C2311yescharacteristic
198#830C2314yes—
199#830C2314yes—
200(C2×D3)⋊C8C2312yes—
201(C2×D3)⋊C8C2312yes—
202(C2×D3)⋊C8C2312yes—
203(C2×D3)⋊C8C2312yes—
204#815C2314yes—
205#815C2312yes—
206#815C2312yes—
207#815C2312yes—
208#815C2312yes—
209Dic3⋊C8C2312yes—
210Dic3⋊C8C2312yes—
211Dic3⋊C8C2312yes—
212Dic3⋊C8C2312yes—
213Dic3⋊C8C2312yes—
214Dic3⋊C8C2312yes—
215Dic3⋊C8C2312yes—
216Dic3⋊C8C2312yes—
217Dic3⋊C8C2314yes—
218Dic3⋊C8C2314yes—
219Dic3⋊C8C2314yes—
220Dic3⋊C8C2314yes—
221C8×Dic3C2314yes—
222C4⋊(C3⋊C8)C2311yescharacteristic
223C4⋊(C3⋊C8)C2312yes—
224C4⋊(C3⋊C8)C2311yescharacteristic
225#803C2312yes—
226C4×C3⋊C8C2312yes—
227C2×#131—32no—
228C2×#131—32no—
229C2×#131C2×D312yes—
230#559—31no—
231#559—32no—
232#557—31no—
233#556—31no—
234#556—32no—
235#553—34no—
236#553—32no—
237#550—31no—
238#548—32no—
239#532—32no—
240#532C2×D311yescharacteristic
241#529—34no—
242#529—32no—
243C4×#41—32no—
244C4×#41—32no—
245C4×#41—31no—
246C2×C4×Q8—31no—
247#446—32no—
248#446—34no—
249#446—31no—
250#446—31no—
251#446—32no—
252#446—31no—
253#446—31no—
254#446—32no—
255C8×Q8—32no—
256#436—34no—
257#436—32no—
258#436C2×D312yes—
259#436C2×D312yes—
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×D4C2×D312yes—
270C8×D4C2×D312yes—
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—32no—
280#424—34no—
281#424—31no—
282#424—34no—
283#424—31no—
284#424—34no—
285#423—32no—
286#423—34no—
287#423—32no—
288#423C2×D311yescharacteristic
289C2×C4⋊C8—32no—
290C2×C4⋊C8—34no—
291C2×C4⋊C8—31no—
292C2×C4⋊C8—32no—
293#408—32no—
294#408—31no—
295#408—31no—
296#408C2×D312yes—
297C4×M16—32no—
298C4×M16—31no—
299C2×#97—32no—
300C2×C4×C8C2×D311yescharacteristic
301C3×#41—24no—
302C3×#41—24no—
303C2×C3×Q8C22×C412yes—
304C2×C3×D4C22×C412yes—
305C2×C3×D4C22×C414yes—
306C2×C3×D4C22×C412yes—
307C2×C3×D4C22×C412yes—
308C22×C3×C4C22×C411yescharacteristic
309C22×C3×C4C22×C411yescharacteristic
310C22×C3×C4C2414yes—
311C22×C3×C4C2411yescharacteristic
312C2×#67C22×C412yes—
313C2×#67C22×C414yes—
314C2×#67C22×C414yes—
315C22×Dic3C22×C414yes—
316C22×Dic3C22×C414yes—
317C22×Dic3C22×C412yes—
318C22×Dic3C22×C412yes—
319#237—44no—
320#235—22no—
321#235—22no—
322C2×D12C22×C411yescharacteristic
323C2×C4×D3C22×C412yes—
324C2×C4×D3C22×C412yes—
325C2×C4×D3C2412yes—
326C2×Dic6—42no—
327C2×Dic6C22×C411yescharacteristic
328C2×Dic6C22×C411yescharacteristic
329C2×Dic6C22×C411yescharacteristic
330C2×Dic6C22×C412yes—
331C3×M16—24no—
332C3×M16—44no—
333C2×C3×C8—22no—
334C2×C3×C8—22no—
335C2×C3×C8—44no—
336C2×C3×C8C2414yes—
337C2×C3×C8C2411yescharacteristic
338C2×C3×C8C2411yescharacteristic
339C2×C3×C8C2411yescharacteristic
340C2×C3×C8C2411yescharacteristic
341C3×C4⋊C4C22×C412yes—
342C3×C4⋊C4C22×C412yes—
343C3×C22⋊C4C22×C414yes—
344C3×C22⋊C4C22×C414yes—
345C3×C42C22×C411yescharacteristic
346C3×C42C22×C411yescharacteristic
347C3×C42C2411yescharacteristic
348C3×C42C2411yescharacteristic
349#217C22×C414yes—
350#217C22×C414yes—
351#217C22×C414yes—
352#217C22×C414yes—
353#217C22×C412yes—
354(C2×D3)⋊C4C22×C412yes—
355(C2×D3)⋊C4C22×C412yes—
356(C2×D3)⋊C4C22×C414yes—
357(C2×D3)⋊C4C22×C414yes—
358C4⋊Dic3C22×C412yes—
359C4⋊Dic3C22×C411yescharacteristic
360C4⋊Dic3C22×C411yescharacteristic
361C4⋊Dic3C22×C411yescharacteristic
362C4⋊Dic3C22×C411yescharacteristic
363C4⋊Dic3C22×C414yes—
364C4⋊Dic3C22×C414yes—
365Dic3⋊C4C22×C412yes—
366Dic3⋊C4C22×C412yes—
367Dic3⋊C4C22×C412yes—
368Dic3⋊C4C22×C412yes—
369Dic3⋊C4C22×C412yes—
370Dic3⋊C4C22×C412yes—
371Dic3⋊C4C22×C414yes—
372Dic3⋊C4C22×C414yes—
373C4×Dic3C22×C412yes—
374C4×Dic3C22×C412yes—
375C4×Dic3C22×C412yes—
376C4×Dic3C22×C412yes—
377C4×Dic3C22×C414yes—
378C4×Dic3C22×C414yes—
379C4×Dic3C2412yes—
380C4×Dic3C2412yes—
381C4×Dic3C2412yes—
382#208—22no—
383#208—22no—
384#208—44no—
385C2×C3⋊C8—24no—
386C2×C3⋊C8—44no—
387C2×C3⋊C8C2412yes—
388C2×C3⋊C8C2412yes—
389C2×C3⋊C8C2412yes—
390C2×C3⋊C8C2412yes—
391ΓL(1,𝔽25)—44no—
392D3×C8—44no—
393C2×#41—32no—
394C2×#41—31no—
395C2×#41C22×D312yes—
396C22×Q8—31no—
397#131—44no—
398#131—124no—
399#131—124no—
400C2×M16—31no—
401C2×M16—31no—
402C2×M16—34no—
403C2×M16—34no—
404C2×M16C22×D312yes—
405C2×M16C22×D314yes—
406C22×C8—32no—
407C22×C8—34no—
408C22×C8—34no—
409C22×C8C22×D311yescharacteristic
410C22×C8C22×D311yescharacteristic
411C22×C8C22×D314yes—
412C4⋊Q8—32no—
413C4⋊Q8C4×D311yescharacteristic
414#127—32no—
415#127C4×D311yescharacteristic
416#126—34no—
417#126—34no—
418#126—34no—
419#125—34no—
420#125—32no—
421#124—32no—
422#124—32no—
423#124—32no—
424#124—34no—
425#124C4×D312yes—
426#123—34no—
427#123—34no—
428#123—34no—
429C22⋊Q8—32no—
430C22⋊Q8—34no—
431#121—32no—
432#121—34no—
433#121—34no—
434#121—34no—
435#121C4×D312yes—
436#121C4×D312yes—
437C4×Q8—32no—
438C4×Q8—32no—
439C4×Q8—32no—
440C4×Q8—31no—
441C4×Q8—31no—
442C4×Q8—32no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—32no—
448C4×D4—34no—
449C4×D4—32no—
450C4×D4—34no—
451C4×D4—32no—
452C4×D4—32no—
453C4×D4—32no—
454C4×D4—32no—
455C4×D4—34no—
456C4×D4—34no—
457C4×D4—34no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4C22×D312yes—
461C4×D4C22×D312yes—
462#117—31no—
463#117—34no—
464#117—32no—
465#117—34no—
466#117—32no—
467C2×C4⋊C4—32no—
468C2×C4⋊C4—31no—
469C2×C42—32no—
470C2×C42—34no—
471C2×C42—32no—
472C2×C42C22×D311yescharacteristic
473C4⋊C8—32no—
474C4⋊C8—32no—
475C4⋊C8—34no—
476C4⋊C8—32no—
477C4⋊C8—34no—
478C4⋊C8—34no—
479C4⋊C8—32no—
480C4⋊C8—32no—
481C4⋊C8—32no—
482C4⋊C8—34no—
483C4⋊C8—32no—
484C4⋊C8—32no—
485C4⋊C8—31no—
486C4⋊C8—31no—
487C4⋊C8—32no—
488C4⋊C8C22×D312yes—
489C4⋊C8C22×D312yes—
490C22⋊C8—34no—
491C22⋊C8—34no—
492C22⋊C8—32no—
493C22⋊C8—32no—
494C22⋊C8—32no—
495C22⋊C8—32no—
496C22⋊C8C22×D314yes—
497C22⋊C8C22×D314yes—
498#97—32no—
499#97—32no—
500#97—32no—
501#97—32no—
502#97—34no—
503#97—32no—
504C4×C8—34no—
505C4×C8—32no—
506C4×C8C22×D311yescharacteristic
507C4×C8C22×D311yescharacteristic
508C4×C8C22×D311yescharacteristic
509C4×C8C22×D311yescharacteristic
510C23×C3C23×C414yes—
511C23×C3C23×C411yescharacteristic
512C22×D3C23×C412yes—
513C3×Q8—24no—
514C3×D4—28no—
515C3×D4—24no—
516C3×D4—24no—
517C3×D4—42no—
518C2×C3×C4—22no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—41no—
522C2×C3×C4C23×C411yescharacteristic
523C2×C3×C4C23×C414yes—
524C2×C3×C4C23×C411yescharacteristic
525C2×C3×C4C23×C411yescharacteristic
526C2×C3×C4C23×C411yescharacteristic
527C2×C3×C4C23×C411yescharacteristic
528C2×C3×C4H(5,𝔽2)12yes—
529C2×C3×C42−1+412yes—
530C2×C3×C4C2511yescharacteristic
531#67—24no—
532#67—44no—
533#67—44no—
534C2×Dic3—42no—
535C2×Dic3—44no—
536C2×Dic3—44no—
537C2×Dic3—42no—
538C2×Dic3C23×C412yes—
539C2×Dic3C23×C412yes—
540C2×Dic3C23×C412yes—
541C2×Dic3C23×C412yes—
542C2×Dic3C23×C412yes—
543C2×Dic3C23×C412yes—
544C2×Dic3C23×C412yes—
545D12—22no—
546C4×D3—24no—
547C4×D3—22no—
548C4×D3—22no—
549C4×D3—42no—
550Dic6—22no—
551Dic6—22no—
552Dic6—22no—
553Dic6—42no—
554C3×C8—24no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3⋊C8—22no—
560C3⋊C8—22no—
561C3⋊C8—22no—
562C3⋊C8—22no—
563#41—24no—
564#41—24no—
565#41—62no—
566#41—62no—
567#41—124no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—32no—
572C2×Q8—122no—
573C2×Q8C2×C4×D312yes—
574C2×D4—32no—
575C2×D4—34no—
576C2×D4—34no—
577C2×D4—31no—
578C2×D4C2×C4×D314yes—
579C2×D4C2×C4×D312yes—
580C2×D4C2×C4×D312yes—
581C2×D4C2×C4×D312yes—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4C2×C4×D311yescharacteristic
590C22×C4C2×C4×D311yescharacteristic
591C22×C4C23×D314yes—
592C22×C4C23×D311yescharacteristic
593M16—24no—
594M16—44no—
595M16—62no—
596M16—62no—
597M16—124no—
598M16—124no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—32no—
602C2×C8—32no—
603C2×C8—32no—
604C2×C8—32no—
605C2×C8—44no—
606C2×C8—64no—
607C2×C8—124no—
608C2×C8—124no—
609C2×C8C23×D314yes—
610C2×C8C23×D311yescharacteristic
611C2×C8C23×D311yescharacteristic
612C2×C8C23×D311yescharacteristic
613C2×C8C23×D311yescharacteristic
614C4⋊C4—32no—
615C4⋊C4—31no—
616C4⋊C4—32no—
617C4⋊C4—31no—
618C4⋊C4—32no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—34no—
624C4⋊C4—32no—
625C4⋊C4—34no—
626C4⋊C4—32no—
627C4⋊C4—34no—
628C4⋊C4—34no—
629C4⋊C4C2×C4×D312yes—
630C4⋊C4C2×C4×D312yes—
631C22⋊C4—32no—
632C22⋊C4—34no—
633C22⋊C4—34no—
634C22⋊C4—34no—
635C22⋊C4—34no—
636C22⋊C4—32no—
637C22⋊C4—34no—
638C22⋊C4—32no—
639C22⋊C4—34no—
640C22⋊C4C2×C4×D314yes—
641C22⋊C4C2×C4×D314yes—
642C42—34no—
643C42—32no—
644C42—34no—
645C42—32no—
646C42—32no—
647C42—32no—
648C42—32no—
649C42—32no—
650C42—32no—
651C42C2×C4×D311yescharacteristic
652C42C2×C4×D311yescharacteristic
653C42C23×D311yescharacteristic
654C42C23×D311yescharacteristic
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3#52012yes—
661C22×C3C24×C411yescharacteristic
662C2×D3—22no—
663C2×D3—22no—
664C2×D3—22no—
665C3×C4—24no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4#52012yes—
670C3×C4#56812yes—
671C3×C4C2×H(5,𝔽2)11yescharacteristic
672C3×C4C2×2−1+411yescharacteristic
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—22no—
677Dic3—22no—
678Dic3—22no—
679Dic3—22no—
680C23—32no—
681C23C22×C4×D314yes—
682C23C22×C4×D311yescharacteristic
683Q8—24no—
684Q8—62no—
685Q8—62no—
686Q8—62no—
687Q8—122no—
688D4—28no—
689D4—24no—
690D4—24no—
691D4—42no—
692D4—64no—
693D4—62no—
694D4—124no—
695D4—124no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—41no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—64no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—124no—
713C2×C4—124no—
714C2×C4—122no—
715C2×C4C22×C4×D311yescharacteristic
716C2×C4C22×C4×D314yes—
717C2×C4C22×C4×D311yescharacteristic
718C2×C4C22×C4×D311yescharacteristic
719C2×C4C22×C4×D311yescharacteristic
720C2×C4C22×C4×D311yescharacteristic
721C2×C4#100412yes—
722C2×C4#101012yes—
723C2×C4C24×D311yescharacteristic
724C8—21no—
725C8—21no—
726C8—24no—
727C8—21no—
728C8—21no—
729C8—62no—
730C8—62no—
731C8—62no—
732C8—62no—
733C2×C3—22no—
734C2×C3—44no—
735C2×C3C2×#52011yescharacteristic
736C2×C3C2×#56811yescharacteristic
737C2×C3#357311yescharacteristic
738D3—42no—
739C22—21no—
740C22—21no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22#554612yes—
748C22C23×C4×D311yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—24no—
753C4—62no—
754C4—62no—
755C4—62no—
756C4—62no—
757C4—62no—
758C4—62no—
759C4—62no—
760C4#554612yes—
761C4#575012yes—
762C4C2×#100411yescharacteristic
763C4C2×#101011yescharacteristic
764C3#6027511yescharacteristic, complemented, Sylow
765C2—22no—
766C2—44no—
767C2—122no—
768C2C2×#554611yescharacteristic
769C2C2×#575011yescharacteristic
770C2#8716011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2931C2
prime radical#86220C2
cosocleC2×C3×C4C25
hypercenter#2931D3
hypocenterC3#60275
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. C3×#2931C2semidirect
3. #83788C2semidirect
4. #83783C2semidirect
5. #83277C2semidirect
6. #79528C2semidirect
7. #79526C2semidirect
8. #79523C2semidirect
9. #79410C2semidirect
10. #79407C2semidirect
11. #79406C2semidirect
12. #79049C2semidirect
13. #79046C2semidirect
14. #78658C2semidirect
15. #78649C2semidirect
16. #78455C2semidirect
17. C2×#4679C2semidirect
105. #2931D3semidirect
764. C3#60275semidirect

Maximal subgroups

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

subgroupindex
#862202
C3×#29312
#837882
#837832
#832772
#795282
#795262
#795232
#794102
#794072
#794062
#790492
#790462
#786582
#786492
#784552
C2×#46792
#602753