Finite Group Databasebeta

← #10967461

Subgroups — #10967461

Order 768.

2698 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5680C211yesmaximal, characteristic, complemented
2C2×C4×#237C211yesmaximal, characteristic, complemented
3C3×#2540C211yesmaximal, characteristic, complemented
4#82976C211yesmaximal, characteristic, complemented
5#82752C212yesmaximal, complemented
6Dic3×C22⋊Q8C212yesmaximal, complemented
7#82641C212yesmaximal, complemented
8Dic3×#121C212yesmaximal, complemented
9#82383C211yesmaximal, characteristic, complemented
10#78106C212yesmaximal, complemented
11#78018C212yesmaximal, complemented
12#76757C212yesmaximal, complemented
13#76666C212yesmaximal, complemented
14#76369C214yesmaximal, complemented
15#76291C214yesmaximal, complemented
16C4×D3×C4⋊C4C211yesmaximal, characteristic, complemented
17#73727C211yesmaximal, characteristic, complemented
18#34964—31nomaximal, Sylow
19C22×#237C2211yescharacteristic
20C2×C3×#124C2211yescharacteristic
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×#121C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×#938C2214yes—
27C2×#938C2211yescharacteristic
28C2×D4×Dic3C2211yescharacteristic
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2214yes—
31C2×C4×#67C2212yes—
32C22×C4×Dic3C2212yes—
33#5680—28no—
34C4×#237—28no—
35C2×#892C2211yescharacteristic
36C2×D3×C4⋊C4C2212yes—
37C2×#887C2211yescharacteristic
38C2×#883C2212yes—
39C2×#67⋊C4C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#879C2212yes—
42C2×#877C2212yes—
43C2×#877C2212yes—
44C2×C42×D3C2212yes—
45C2×C42×D3C2211yescharacteristic
46C2×#870C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48C3×#399C2212yes—
49C3×#392C2212yes—
50C3×#390C2214yes—
51C3×C4×C4⋊C4C2211yescharacteristic
52#5229C2212yes—
53#5222C2214yes—
54#5222C2212yes—
55#5221C2212yes—
56#5220C2214yes—
57#5212C2212yes—
58#5212C2212yes—
59#4987C2214yes—
60#4985C2212yes—
61#4984C2212yes—
62#4984C2212yes—
63#4983C2214yes—
64#4980C2214yes—
65Dic3×C4⋊C4C2214yes—
66Dic3×C4⋊C4C2212yes—
67#4956C2214yes—
68#4956C2214yes—
69#4953C2212yes—
70#4951C2214yes—
71#4950C2214yes—
72#4948C2214yes—
73#4948C2214yes—
74#4947C2212yes—
75#4945C2214yes—
76#4945C2214yes—
77Dic3×C22⋊C4C2214yes—
78Dic3×C22⋊C4C2214yes—
79C4×C4⋊Dic3C2211yescharacteristic
80C4×Dic3⋊C4C2212yes—
81#4928C2214yes—
82D3×#95C2212yes—
83#4661C2212yes—
84#4656C2212yes—
85#4649C2212yes—
86C2×#529—31no—
87C2×C4×#41—31no—
88#2601—34no—
89#2592—31no—
90#2584—31no—
91#2562—31no—
92#2540D311yescharacteristic, complemented
93#2498—32no—
94#2430—32no—
95#2417—32no—
96#2416—32no—
97#2396—32no—
98#2392—32no—
99C4×C22⋊Q8—32no—
100C4×#121—34no—
101C4×#121—32no—
102C2×C4×C4⋊C4—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C22×C3×D4C2314yes—
107C23×C3×C4C2312yes—
108C22×#67C2312yes—
109C22×#67C2312yes—
110C23×Dic3C2312yes—
111C23×Dic3C2312yes—
112C23×Dic3C2312yes—
113C2×#237—28no—
114C2×#237—24no—
115C22×C4×D3C2314yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×Dic6C2311yescharacteristic
120C3×#124—24no—
121C3×C22⋊Q8—28no—
122C3×#121—28no—
123C3×C4×D4—24no—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141#946—24no—
142Q8×Dic3—24no—
143#938—216no—
144#938—24no—
145D4×Dic3—24no—
146D4×Dic3—24no—
147D4×Dic3—48no—
148C4×#67—28no—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×C4⋊Dic3C2314yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×C4×Dic3—28no—
165C2×C4×Dic3C2314yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2311yescharacteristic
174#892—24no—
175D3×C4⋊C4—28no—
176#887—24no—
177#883—28no—
178#67⋊C4—28no—
179#67⋊C4—28no—
180#879—28no—
181#877—28no—
182#877—28no—
183C42×D3—44no—
184C42×D3D418yescomplemented
185#870—24no—
186C4×Dic6—24no—
187C3×#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C22×#41—31no—
197#529—68no—
198C2×#126—32no—
199C2×#125—31no—
200C2×#124C2×D311yescharacteristic
201C2×#123—32no—
202C2×C22⋊Q8—31no—
203C2×C22⋊Q8C2×D312yes—
204C2×#121—31no—
205C2×#121—34no—
206C2×#121C2×D312yes—
207C4×#41—68no—
208C2×C4×Q8—31no—
209C2×C4×Q8—31no—
210C2×C4×Q8—31no—
211C2×C4×D4—31no—
212C2×C4×D4—31no—
213C2×C4×D4—32no—
214C2×C4×D4—34no—
215C2×C4×D4—32no—
216C2×C4×D4—32no—
217C2×C4×D4C2×D311yescharacteristic
218C2×#117—31no—
219C2×#117—32no—
220C2×#117—32no—
221C22×C4⋊C4—32no—
222C22×C42—31no—
223C22×C42—32no—
224C22×C42—32no—
225#400—32no—
226#399C2×D312yes—
227#398—34no—
228#398—32no—
229#397—32no—
230#396—34no—
231#396—34no—
232#395—32no—
233#394—32no—
234#394—34no—
235#393—32no—
236#392C2×D312yes—
237#391—32no—
238#390—32no—
239#390C2×D314yes—
240#389—32no—
241#389—32no—
242#389—34no—
243#388—34no—
244#388—34no—
245#388—34no—
246#387—34no—
247#386—34no—
248#386—34no—
249#386—34no—
250#385—34no—
251#380—32no—
252#380—32no—
253#380—34no—
254C4×C4⋊C4—34no—
255C4×C4⋊C4—32no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4—32no—
258C4×C4⋊C4—32no—
259C4×C4⋊C4C2×D311yescharacteristic
260C4×C22⋊C4—34no—
261C4×C22⋊C4—34no—
262C2×#95—32no—
263C24×C3C2412yes—
264C24×C3C2412yes—
265C23×D3C2411yescharacteristic
266C2×C3×Q8—22no—
267C2×C3×Q8—24no—
268C2×C3×D4—24no—
269C2×C3×D4—28no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—28no—
273C2×C3×D4—24no—
274C2×C3×D4—44no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2414yes—
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—28no—
288C2×#67#4118yes—
289C22×Dic3—24no—
290C22×Dic3—24no—
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—24no—
295C22×Dic3—24no—
296C22×Dic3—24no—
297C22×Dic3—24no—
298C22×Dic3C2414yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2411yescharacteristic
304C22×Dic3C2412yes—
305C22×Dic3C2411yescharacteristic
306#237—232no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—28no—
312C2×C4×D3—28no—
313C2×C4×D3—44no—
314C2×C4×D3C2×D414yes—
315C2×C4×D3C2×D414yes—
316C2×C4×D3C2×D414yes—
317C2×Dic6—22no—
318C2×Dic6—24no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—28no—
321C3×C4⋊C4#4118yescomplemented
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327C3×C42—42no—
328C3×C42C2×D414yes—
329#217—28no—
330#217—24no—
331#217—24no—
332#217—24no—
333#217—28no—
334#217—44no—
335#217—44no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3—22no—
341C4⋊Dic3—24no—
342C4⋊Dic3—24no—
343C4⋊Dic3—28no—
344C4⋊Dic3—44no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—28no—
349Dic3⋊C4—24no—
350Dic3⋊C4—24no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—24no—
355C4×Dic3—28no—
356C4×Dic3—42no—
357C4×Dic3C2×D414yes—
358C4×Dic3C2×D414yes—
359C4×Dic3C2×D414yes—
360C2×#41—64no—
361C2×#41—68no—
362C22×Q8—31no—
363C22×Q8C22×D311yescharacteristic
364C22×D4—32no—
365C22×D4—32no—
366C22×D4C22×D311yescharacteristic
367C22×D4C22×D311yescharacteristic
368C22×D4C22×D314yes—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—32no—
373C23×C4—32no—
374C23×C4—32no—
375C23×C4—34no—
376C23×C4C22×D312yes—
377#126—68no—
378#125—64no—
379#124—24no—
380#123—68no—
381C22⋊Q8—28no—
382C22⋊Q8—64no—
383#121—28no—
384#121—64no—
385#121—616no—
386C4×Q8—64no—
387C4×Q8—64no—
388C4×Q8—64no—
389C4×D4—24no—
390C4×D4—64no—
391C4×D4—64no—
392C4×D4—68no—
393C4×D4—68no—
394C4×D4—68no—
395C4×D4—128no—
396#117—68no—
397#117—68no—
398#117—64no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—68no—
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D314yes—
415C2×C4⋊C4C22×D312yes—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4C22×D312yes—
426C2×C22⋊C4C22×D312yes—
427C2×C22⋊C4C22×D312yes—
428C2×C22⋊C4C22×D314yes—
429C2×C22⋊C4C22×D314yes—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—31no—
433C2×C42—38no—
434C2×C42—32no—
435C2×C42—32no—
436C2×C42—32no—
437C2×C42—32no—
438C2×C42—34no—
439C2×C42—32no—
440C2×C42—68no—
441C2×C42—124no—
442C2×C42C22×D312yes—
443C2×C42C22×D311yescharacteristic
444#95—34no—
445#95—32no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95C22×D312yes—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—24no—
461C23×C3—24no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3C2×#4114yes—
465C23×C3C2511yescharacteristic
466C22×D3—22no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3C22×D412yes—
470C22×D3C2×#4114yes—
471C3×Q8—44no—
472C3×D4—28no—
473C3×D4—416no—
474C3×D4—44no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—48no—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C2×#4118yes—
490C2×C3×C4C2×#4114yes—
491#67—216no—
492#67—48no—
493C2×Dic3—216no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—48no—
510C2×Dic3—48no—
511C2×Dic3C22×D412yes—
512C2×Dic3C22×D412yes—
513C2×Dic3C22×D412yes—
514C2×Dic3C2×#4114yes—
515C2×Dic3H(5,𝔽2)12yes—
516C2×Dic32−1+412yes—
517C4×D3—28no—
518C4×D3—28no—
519C4×D3—28no—
520C4×D3—416no—
521Dic6—28no—
522C24—31no—
523C24C23×D312yes—
524C24C23×D312yes—
525#41—632no—
526C2×Q8—22no—
527C2×Q8—24no—
528C2×Q8—64no—
529C2×Q8—62no—
530C2×D4—24no—
531C2×D4—28no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—28no—
535C2×D4—24no—
536C2×D4—38no—
537C2×D4—44no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—68no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—31no—
549C22×C4—34no—
550C22×C4—34no—
551C22×C4—34no—
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—64no—
559C22×C4—68no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—68no—
571C22×C4—124no—
572C22×C4C23×D312yes—
573C22×C4C23×D312yes—
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D314yes—
577C22×C4C23×D311yescharacteristic
578C4⋊C4—22no—
579C4⋊C4—28no—
580C4⋊C4—64no—
581C4⋊C4—64no—
582C4⋊C4—64no—
583C4⋊C4—68no—
584C4⋊C4—64no—
585C4⋊C4—62no—
586C4⋊C4—64no—
587C4⋊C4—62no—
588C4⋊C4—64no—
589C4⋊C4—62no—
590C4⋊C4—68no—
591C4⋊C4—64no—
592C4⋊C4—124no—
593C4⋊C4#23718yescomplemented
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—68no—
605C22⋊C4—68no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C42—34no—
609C42—34no—
610C42—34no—
611C42—42no—
612C42—64no—
613C42—64no—
614C42—68no—
615C42—64no—
616C42—64no—
617C42—122no—
618C42D3×D414yes—
619C22×C3—24no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3C23×D411yescharacteristic
632C22×C3C22×#4112yes—
633C22×C3C22×#4112yes—
634C22×C3C2×H(5,𝔽2)11yescharacteristic
635C22×C3C2×2−1+411yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—24no—
639C2×D3—24no—
640C2×D3#52514yes—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—28no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4#53214yes—
647Dic3—24no—
648Dic3—22no—
649Dic3—22no—
650Dic3—42no—
651Dic3—42no—
652Dic3—42no—
653Dic3—44no—
654Dic3#53714yes—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—32no—
667C23—34no—
668C23—62no—
669C23—61no—
670C23—61no—
671C23D3×#4114yes—
672C23C24×D311yescharacteristic
673Q8—44no—
674Q8—68no—
675D4—28no—
676D4—416no—
677D4—44no—
678D4—616no—
679D4—128no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—34no—
696C2×C4—48no—
697C2×C4—68no—
698C2×C4—68no—
699C2×C4—616no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—68no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—1216no—
717C2×C4—128no—
718C2×C4—128no—
719C2×C4C2×D3×D412yes—
720C2×C4C2×D3×D412yes—
721C2×C4C2×D3×D412yes—
722C2×C4C2×#23718yes—
723C2×C4C2×#23714yes—
724C2×C3—44no—
725C2×C3—82no—
726C2×C3C2×#52511yescharacteristic
727C2×C3C2×#53211yescharacteristic
728C2×C3C2×#53711yescharacteristic
729C2×C3#348112yes—
730C2×C3#348212yes—
731D3—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—34no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—64no—
746C22—62no—
747C22—62no—
748C22—64no—
749C22C22×D3×D411yescharacteristic
750C22C22×#23712yes—
751C22C2×D3×#4112yes—
752C22D3×H(5,𝔽2)11yescharacteristic
753C22D3×2−1+411yescharacteristic
754C4—22no—
755C4—28no—
756C4—22no—
757C4—34no—
758C4—42no—
759C4—42no—
760C4—62no—
761C4—64no—
762C4—62no—
763C4—122no—
764C4—124no—
765C4—122no—
766C4—122no—
767C4#571614yes—
768C3#3496411yescharacteristic, complemented, Sylow
769C2—44no—
770C2—64no—
771C2—82no—
772C2D3×#52511yescharacteristic
773C2C2×#571611yescharacteristic
774C2D3×#53711yescharacteristic
775C2#8662812yes—
776C2#8671212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2540C2
hypercenter#2540D3
hypocenterC3#34964
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#5680C2semidirect
2. C2×C4×#237C2semidirect
3. C3×#2540C2semidirect
4. #82976C2semidirect
5. #82752C2semidirect
6. Dic3×C22⋊Q8C2semidirect
7. #82641C2semidirect
8. Dic3×#121C2semidirect
9. #82383C2semidirect
10. #78106C2semidirect
11. #78018C2semidirect
12. #76757C2semidirect
13. #76666C2semidirect
14. #76369C2semidirect
15. #76291C2semidirect
16. C4×D3×C4⋊C4C2semidirect
17. #73727C2semidirect
92. #2540D3semidirect
184. C42×D3D4semidirect
321. C3×C4⋊C4#41semidirect
593. C4⋊C4#237semidirect
768. C3#34964semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×C4×#2372
C3×#25402
#829762
#827522
Dic3×C22⋊Q82
#826412
Dic3×#1212
#823832
#781062
#780182
#767572
#766662
#763692
#762912
C4×D3×C4⋊C42
#737272
#349643