Finite Group Databasebeta

← #11633823

Subgroups — #11633823

Order 768.

2458 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic, complemented
2C2×#5551C211yesmaximal, characteristic, complemented
3C3×#2563C211yesmaximal, characteristic, complemented
4#83260C211yesmaximal, characteristic, complemented
5C4×#938C211yesmaximal, characteristic, complemented
6#76826C214yesmaximal, complemented
7#76785C214yesmaximal, complemented
8#76449C212yesmaximal, complemented
9#76438C212yesmaximal, complemented
10#74229C212yesmaximal, complemented
11#74163C212yesmaximal, complemented
12#74015C212yesmaximal, complemented
13#73934C212yesmaximal, complemented
14#73892C212yesmaximal, complemented
15#73877C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic, complemented
17#73650C211yesmaximal, characteristic, complemented
18#59034—31nomaximal, Sylow
19C22×#235C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2212yes—
23C2×Q8×Dic3C2212yes—
24C2×#938C2212yes—
25C2×#938C2211yescharacteristic
26C2×C4×#67C2212yes—
27C2×#924C2212yes—
28#5728—28no—
29#5551—28no—
30C2×#897C2212yes—
31C2×#895C2211yescharacteristic
32C2×#892C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×#890C2212yes—
35C2×#887C2212yes—
36C2×#887C2212yes—
37C2×#883C2214yes—
38C2×C4×D12C2211yescharacteristic
39C2×C4×D12C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×#869C2211yescharacteristic
42C3×#393C2214yes—
43C3×#390C2212yes—
44C3×#382C2212yes—
45C3×#380C2212yes—
46C3×#380C2212yes—
47C3×C4×C4⋊C4C2211yescharacteristic
48#5231C2214yes—
49#5221C2211yescharacteristic
50C4×#217C2212yes—
51#4988C2211yescharacteristic
52#4988C2212yes—
53#4987C2211yescharacteristic
54#4987C2212yes—
55#4987C2212yes—
56#4987C2211yescharacteristic
57#4984C2211yescharacteristic
58#4977C2212yes—
59#4973C2212yes—
60#4972C2211yescharacteristic
61#4961C2214yes—
62#4960C2214yes—
63#4959C2214yes—
64#4957C2214yes—
65#4957C2214yes—
66#4956C2212yes—
67#4952C2214yes—
68#4951C2214yes—
69#4951C2214yes—
70#4944C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72C4×C4⋊Dic3C2211yescharacteristic
73C4×C4⋊Dic3C2212yes—
74#4928C2212yes—
75#4670C2212yes—
76#4669C2214yes—
77#4668C2214yes—
78#4667C2214yes—
79#4666C2214yes—
80#4665C2212yes—
81#4665C2214yes—
82#4658C2214yes—
83#4657C2214yes—
84#4654C2214yes—
85#4653C2214yes—
86C2×#547—31no—
87C2×#533—31no—
88#2696—34no—
89#2563—31no—
90#2563D311yescharacteristic, complemented
91#2536—32no—
92#2490—32no—
93#2458—34no—
94#2442—32no—
95#2421—32no—
96#2414—32no—
97#2407—32no—
98#2365—31no—
99#2352—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2314yes—
107C22×#67C2312yes—
108C2×#235—28no—
109C2×#235—28no—
110C2×#235—44no—
111C22×D12C2312yes—
112C22×D12C2311yescharacteristic
113C22×C4×D3C2312yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2314yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4⋊Q8—24no—
120C3×C4×D4—24no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C42C2312yes—
130C2×C3×C42C2311yescharacteristic
131C2×#217C2312yes—
132C2×#217C2314yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135#946—28no—
136Q8×Dic3—28no—
137#938—24no—
138#938—28no—
139C4×#67—44no—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156#924—28no—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2312yes—
161C2×C4×Dic3C2314yes—
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2314yes—
167#897—28no—
168#895—24no—
169#892—28no—
170D3×C4⋊C4—28no—
171#890—28no—
172#887—28no—
173#887—44no—
174#883—216no—
175C4×D12—28no—
176C4×D12—24no—
177C42×D3—24no—
178#869D418yescomplemented
179C3×#95C2312yes—
180C3×#95C2314yes—
181C3×#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C22×#41—32no—
192#547—68no—
193#533—68no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125—32no—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×#121—31no—
202C2×#121—32no—
203C2×#121—31no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×D4—32no—
208C2×C4×D4—31no—
209C2×C4×D4—32no—
210C2×C4×D4C2×D311yescharacteristic
211C2×#117—32no—
212C22×C4⋊C4—32no—
213C22×C42—31no—
214#400—34no—
215#398—34no—
216#397—34no—
217#394—34no—
218#394—34no—
219#393—34no—
220#393C2×D314yes—
221#392—34no—
222#391—32no—
223#390—31no—
224#390—32no—
225#390—31no—
226#390—34no—
227#390—34no—
228#390C2×D312yes—
229#389—31no—
230#389—31no—
231#389—32no—
232#388—32no—
233#388—34no—
234#388—34no—
235#388—34no—
236#388—32no—
237#387—34no—
238#387—34no—
239#386—32no—
240#386—34no—
241#386—32no—
242#385—34no—
243#382—32no—
244#382C2×D312yes—
245#380—32no—
246#380—32no—
247#380—31no—
248#380—31no—
249#380—34no—
250#380C2×D312yes—
251#380C2×D312yes—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—32no—
254C4×C4⋊C4C2×D311yescharacteristic
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—34no—
258C24×C3C2412yes—
259C23×D3C2411yescharacteristic
260C23×D3C2412yes—
261C2×C3×Q8—24no—
262C2×C3×Q8—42no—
263C2×C3×Q8—42no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2414yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—28no—
279C2×#67—28no—
280C2×#67—42no—
281C2×#67—44no—
282C2×#67—42no—
283C22×Dic3C2412yes—
284C22×Dic3C2412yes—
285C22×Dic3C2412yes—
286C22×Dic3C2411yescharacteristic
287C22×Dic3C2411yescharacteristic
288C22×Dic3C2414yes—
289C22×Dic3C2411yescharacteristic
290#235—432no—
291C2×D12—22no—
292C2×D12—22no—
293C2×D12—24no—
294C2×D12—24no—
295C2×D12—42no—
296C2×D12#4114yes—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—28no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—24no—
307C2×C4×D3—28no—
308C2×C4×D3—41no—
309C2×C4×D3—41no—
310C2×C4×D3—44no—
311C2×C4×D3#4114yescomplemented
312C2×Dic6—24no—
313C2×Dic6—24no—
314C2×Dic6C2×D418yes—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—22no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—44no—
322C3×C22⋊C4—44no—
323C3×C42—24no—
324C3×C42C2×D414yes—
325#217—28no—
326#217—24no—
327#217—42no—
328#217—42no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—42no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3—22no—
341C4⋊Dic3—28no—
342C4⋊Dic3—24no—
343C4⋊Dic3C2×D418yes—
344C4⋊Dic3C2×D418yes—
345Dic3⋊C4—28no—
346Dic3⋊C4—28no—
347Dic3⋊C4—44no—
348Dic3⋊C4—42no—
349C4×Dic3—22no—
350C4×Dic3—22no—
351C4×Dic3—22no—
352C4×Dic3—24no—
353C4×Dic3—28no—
354C4×Dic3—44no—
355C2×#41—68no—
356C2×#41—68no—
357C2×#41—124no—
358C22×Q8—32no—
359C22×Q8C22×D312yes—
360C22×D4—34no—
361C22×D4—32no—
362C22×D4—31no—
363C22×D4—32no—
364C22×D4C22×D311yescharacteristic
365C23×C4—31no—
366C23×C4—32no—
367C23×C4—31no—
368C23×C4—34no—
369C23×C4—31no—
370C23×C4C22×D312yes—
371C4⋊Q8—24no—
372C4⋊Q8—38no—
373#125—68no—
374#123—616no—
375C22⋊Q8—68no—
376C22⋊Q8—68no—
377C22⋊Q8—68no—
378#121—64no—
379#121—68no—
380#121—64no—
381C4×Q8—68no—
382C4×Q8—68no—
383C4×Q8—124no—
384C4×D4—24no—
385C4×D4—68no—
386C4×D4—64no—
387C4×D4—124no—
388#117—68no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—68no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D312yes—
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4C22×D312yes—
420C2×C22⋊C4C22×D314yes—
421C2×C22⋊C4C22×D314yes—
422C2×C42—34no—
423C2×C42—32no—
424C2×C42—31no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—34no—
428C2×C42—64no—
429C2×C42C22×D312yes—
430C2×C42C22×D311yescharacteristic
431#95—32no—
432#95—32no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—34no—
437#95—34no—
438#95—34no—
439#95—34no—
440#95C22×D314yes—
441#95C22×D312yes—
442#95C22×D314yes—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3C2511yescharacteristic
451C22×D3—21no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—22no—
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3C2×#4112yes—
464C22×D3C2×#4114yes—
465C3×Q8—48no—
466C3×D4—44no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—24no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—48no—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4H(5,𝔽2)12yes—
488C2×C3×C42−1+412yes—
489#67—416no—
490#67—48no—
491C2×Dic3—21no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3C22×D418yes—
511C2×Dic3C2×#4112yes—
512D12—28no—
513D12—48no—
514C4×D3—28no—
515C4×D3—416no—
516C4×D3—44no—
517C4×D3—44no—
518C4×D3—48no—
519Dic6—216no—
520C24—31no—
521C24—32no—
522C24C23×D312yes—
523#41—1232no—
524C2×Q8—24no—
525C2×Q8—38no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—64no—
529C2×Q8—64no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—34no—
534C2×D4—64no—
535C2×D4—64no—
536C2×D4—68no—
537C2×D4—64no—
538C2×D4—68no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—124no—
544C2×D4—122no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—31no—
549C22×C4—34no—
550C22×C4—34no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—68no—
557C22×C4—68no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—124no—
568C22×C4—121no—
569C22×C4—121no—
570C22×C4C23×D312yes—
571C22×C4C23×D312yes—
572C22×C4C23×D314yes—
573C22×C4C23×D312yes—
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—38no—
583C4⋊C4—38no—
584C4⋊C4—68no—
585C4⋊C4—64no—
586C4⋊C4—68no—
587C4⋊C4—68no—
588C4⋊C4—62no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—122no—
592C4⋊C4—124no—
593C22⋊C4—24no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—68no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—68no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—124no—
606C22⋊C4—124no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C42—24no—
610C42—68no—
611C42—62no—
612C42—62no—
613C42—62no—
614C42—64no—
615C42—124no—
616C42D3×D414yes—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3C23×D411yescharacteristic
625C22×C3C22×#4111yescharacteristic
626C22×C3C22×#4111yescharacteristic
627C22×C3C2×H(5,𝔽2)11yescharacteristic
628C22×C3C2×2−1+411yescharacteristic
629C22×C3#58511yescharacteristic
630C22×C3#58511yescharacteristic
631C2×D3—24no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—24no—
635C2×D3—22no—
636C2×D3—24no—
637C2×D3—41no—
638C2×D3—42no—
639C2×D3—41no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—42no—
645C3×C4—22no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—44no—
649C3×C4—42no—
650C3×C4#54614yes—
651C3×C4#54814yes—
652Dic3—28no—
653Dic3—22no—
654Dic3—41no—
655Dic3—42no—
656Dic3—41no—
657Dic3—42no—
658Dic3—42no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—32no—
667C23—34no—
668C23—61no—
669C23—62no—
670C23—62no—
671C23—61no—
672C23—62no—
673C23—61no—
674C23—61no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—61no—
679C23—61no—
680C23C24×D311yescharacteristic
681Q8—48no—
682Q8—616no—
683D4—44no—
684D4—68no—
685D4—128no—
686D4—1216no—
687D4—128no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—38no—
703C2×C4—32no—
704C2×C4—48no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—68no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—62no—
725C2×C4—124no—
726C2×C4—1216no—
727C2×C4—128no—
728C2×C4—124no—
729C2×C4C2×D3×D412yes—
730C2×C4C2×D3×D412yes—
731C2×C4C2×D3×D412yes—
732C2×C4#100712yes—
733C2×C4D3×#4112yes—
734C2×C4D3×#4112yes—
735C2×C4#100912yes—
736C2×C3—82no—
737C2×C3C2×#54611yescharacteristic
738C2×C3C2×#54811yescharacteristic
739C2×C3#347511yescharacteristic
740C2×C3#348711yescharacteristic
741C2×C3#350611yescharacteristic
742C2×C3#351511yescharacteristic
743C2×C3#354711yescharacteristic
744D3—44no—
745D3—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—64no—
754C22—64no—
755C22—62no—
756C22—64no—
757C22—62no—
758C22—62no—
759C22—121no—
760C22—122no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22C22×D3×D411yescharacteristic
768C22C2×#100711yescharacteristic
769C22C2×D3×#4111yescharacteristic
770C22C2×D3×#4111yescharacteristic
771C22C2×#100911yescharacteristic
772C22#596611yescharacteristic
773C22#596611yescharacteristic
774C4—22no—
775C4—44no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—68no—
780C4—62no—
781C4—121no—
782C4—121no—
783C4—122no—
784C4—122no—
785C4—122no—
786C4#563314yes—
787C4#567614yes—
788C3#5903411yescharacteristic, complemented, Sylow
789C2—82no—
790C2—124no—
791C2—122no—
792C2C2×#563311yescharacteristic
793C2C2×#567611yescharacteristic
794C2#8631511yescharacteristic
795C2#8693111yescharacteristic
796C2#8695411yescharacteristic
797C2#8695811yescharacteristic
798C2#8697311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2563C2
hypercenter#2563D3
hypocenterC3#59034
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×#5551C2semidirect
3. C3×#2563C2semidirect
4. #83260C2semidirect
5. C4×#938C2semidirect
6. #76826C2semidirect
7. #76785C2semidirect
8. #76449C2semidirect
9. #76438C2semidirect
10. #74229C2semidirect
11. #74163C2semidirect
12. #74015C2semidirect
13. #73934C2semidirect
14. #73892C2semidirect
15. #73877C2semidirect
16. C4×#895C2semidirect
17. #73650C2semidirect
90. #2563D3semidirect
178. #869D4semidirect
311. C2×C4×D3#41semidirect
788. C3#59034semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×#55512
C3×#25632
#832602
C4×#9382
#768262
#767852
#764492
#764382
#742292
#741632
#740152
#739342
#738922
#738772
C4×#8952
#736502
#590343