Finite Group Databasebeta

← #11633822

Subgroups — #11633822

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×#5551C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×#121C211yesmaximal, characteristic, complemented
4#82704C212yesmaximal, complemented
5#82402C212yesmaximal, complemented
6#82384C211yesmaximal, characteristic, complemented
7#82375C212yesmaximal, complemented
8C4×#930C211yesmaximal, characteristic, complemented
9#76450C212yesmaximal, complemented
10#76002C212yesmaximal, complemented
11#75506C214yesmaximal, complemented
12#74808C214yesmaximal, complemented
13#74012C212yesmaximal, complemented
14#73807C211yesmaximal, characteristic, complemented
15#73651C211yesmaximal, characteristic, complemented
16#73483C212yesmaximal, complemented
17#73454C212yesmaximal, complemented
18#59034—31nomaximal, Sylow
19C22×#235C2212yes—
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×#938C2212yes—
25C2×#930C2211yescharacteristic
26C2×C4×#67C2212yes—
27C2×#926C2212yes—
28C2×#924C2212yes—
29C2×#924C2212yes—
30C2×#924C2212yes—
31#5551—28no—
32C2×D3×C4⋊C4C2212yes—
33C2×#883C2214yes—
34C2×C4×D12C2211yescharacteristic
35#5470—28no—
36C2×#870C2212yes—
37C2×#869C2211yescharacteristic
38C2×#869C2211yescharacteristic
39C2×C4×Dic6C2212yes—
40C2×C4×Dic6C2212yes—
41C2×C4×Dic6C2212yes—
42C3×#390C2211yescharacteristic
43C3×#389C2211yescharacteristic
44C3×#388C2212yes—
45C3×#386C2212yes—
46C3×#380C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C22⋊C4C2212yes—
49#5223C2214yes—
50#5222C2214yes—
51#5221C2212yes—
52#5213C2212yes—
53#5212C2212yes—
54#5212C2211yescharacteristic
55#5212C2212yes—
56#4989C2214yes—
57#4987C2212yes—
58#4987C2212yes—
59#4983C2214yes—
60#4977C2212yes—
61Dic3×C4⋊C4C2212yes—
62#4972C2212yes—
63#4959C2214yes—
64#4957C2214yes—
65#4957C2214yes—
66#4956C2214yes—
67#4952C2214yes—
68#4947C2214yes—
69#4945C2214yes—
70#4944C2214yes—
71#4944C2214yes—
72#4940C2212yes—
73#4939C2212yes—
74#4939C2211yescharacteristic
75C4×(C2×D3)⋊C4C2212yes—
76#4936C2212yes—
77C4×C4⋊Dic3C2211yescharacteristic
78#4929C2212yes—
79#4928C2211yescharacteristic
80#4673C2214yes—
81#4667C2214yes—
82#4666C2214yes—
83#4658C2214yes—
84#4654C2214yes—
85#4652C2214yes—
86C2×#547—31no—
87C2×#533—31no—
88#2696—34no—
89#2563—31no—
90#2563—31no—
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×#121D311yescharacteristic, complemented
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2312yes—
105C23×C3×C4C2312yes—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C22×#67C2314yes—
110C22×#67C2312yes—
111C2×#235—28no—
112C2×#235—28no—
113C2×#235—44no—
114C22×D12C2311yescharacteristic
115C22×C4×D3C2312yes—
116C22×C4×D3C2314yes—
117C22×Dic6C2312yes—
118C22×Dic6C2312yes—
119C3×#121—24no—
120C3×C4×D4—24no—
121C3×C4×D4—44no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C42—24no—
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2312yes—
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142#938—28no—
143#930—24no—
144C4×#67—28no—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151#926—28no—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159#924—28no—
160#924—28no—
161#924—28no—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×C4×Dic3C2314yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2314yes—
170D3×C4⋊C4—28no—
171#883—216no—
172C4×D12—24no—
173#870—28no—
174#869—24no—
175#869D418yescomplemented
176C4×Dic6—28no—
177C4×Dic6—28no—
178C4×Dic6—44no—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C22×#41—32no—
192#547—68no—
193#533—68no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8—31no—
196C2×#125—32no—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×#121—32no—
202C2×#121—31no—
203C2×#121C2×D311yescharacteristic
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×D4—32no—
208C2×C4×D4—31no—
209C2×C4×D4C2×D311yescharacteristic
210C2×C4×D4C2×D312yes—
211C2×#117—32no—
212C22×C4⋊C4—32no—
213C22×C42C2×D311yescharacteristic
214#400—34no—
215#398—34no—
216#397—34no—
217#394—34no—
218#394—34no—
219#393—34no—
220#393—34no—
221#392—34no—
222#391—32no—
223#390—32no—
224#390—34no—
225#390—34no—
226#390—32no—
227#390—31no—
228#390C2×D311yescharacteristic
229#389—32no—
230#389—31no—
231#389C2×D311yescharacteristic
232#388—34no—
233#388—34no—
234#388—34no—
235#388—32no—
236#388C2×D312yes—
237#387—34no—
238#387—34no—
239#386—32no—
240#386—34no—
241#386C2×D312yes—
242#385—34no—
243#382—32no—
244#382—32no—
245#380—32no—
246#380—32no—
247#380—31no—
248#380—32no—
249#380—32no—
250#380—34no—
251#380C2×D311yescharacteristic
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4C2×D311yescharacteristic
255C4×C22⋊C4—32no—
256C4×C22⋊C4—34no—
257C4×C22⋊C4C2×D312yes—
258C24×C3C2412yes—
259C24×C3C2411yescharacteristic
260C23×D3C2412yes—
261C2×C3×D4—24no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—41no—
277C22×C3×C4—41no—
278C22×C3×C4#4114yescomplemented
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—42no—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2414yes—
298C22×Dic3C2414yes—
299#235—432no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12#4114yes—
303C2×C4×D3—28no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—28no—
308C2×C4×D3—44no—
309C2×Dic6—24no—
310C2×Dic6—24no—
311C2×Dic6—24no—
312C2×Dic6—42no—
313C2×Dic6—42no—
314C2×Dic6C2×D418yes—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—42no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C42—22no—
325C3×C42—22no—
326C3×C42—22no—
327C3×C42—24no—
328C3×C42C2×D414yes—
329#217—24no—
330#217—28no—
331#217—28no—
332#217—44no—
333#217—44no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340C4⋊Dic3—24no—
341C4⋊Dic3—24no—
342C4⋊Dic3—22no—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3C2×D418yes—
346C4⋊Dic3C2×D418yes—
347Dic3⋊C4—24no—
348Dic3⋊C4—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—28no—
351Dic3⋊C4—44no—
352C4×Dic3—24no—
353C4×Dic3—28no—
354C4×Dic3—44no—
355C2×#41—68no—
356C2×#41—68no—
357C2×#41—124no—
358C22×Q8—32no—
359C22×Q8—32no—
360C22×D4—32no—
361C22×D4—34no—
362C22×D4—31no—
363C22×D4C22×D311yescharacteristic
364C22×D4C22×D312yes—
365C23×C4—32no—
366C23×C4—34no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D312yes—
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C4⋊Q8—38no—
372C4⋊Q8—64no—
373#125—68no—
374#123—616no—
375C22⋊Q8—68no—
376C22⋊Q8—68no—
377C22⋊Q8—68no—
378#121—24no—
379#121—68no—
380#121—64no—
381C4×Q8—68no—
382C4×Q8—68no—
383C4×Q8—124no—
384C4×D4—24no—
385C4×D4—44no—
386C4×D4—68no—
387C4×D4—64no—
388#117—68no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—68no—
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C4⋊C4C22×D312yes—
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—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4C22×D312yes—
418C2×C22⋊C4C22×D312yes—
419C2×C22⋊C4C22×D312yes—
420C2×C22⋊C4C22×D312yes—
421C2×C22⋊C4C22×D312yes—
422C2×C42—24no—
423C2×C42—34no—
424C2×C42—32no—
425C2×C42—34no—
426C2×C42C22×D312yes—
427C2×C42C22×D311yescharacteristic
428C2×C42C22×D311yescharacteristic
429C2×C42C22×D311yescharacteristic
430C2×C42C22×D311yescharacteristic
431#95—34no—
432#95—32no—
433#95—32no—
434#95—32no—
435#95—34no—
436#95—34no—
437#95—34no—
438#95—34no—
439#95—34no—
440#95C22×D312yes—
441#95C22×D312yes—
442#95C22×D312yes—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3C2×#4112yes—
457C23×C3C2511yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C2×#4114yes—
465C3×D4—48no—
466C3×D4—44no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—28no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—44no—
488C2×C3×C4—48no—
489C2×C3×C4—44no—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C2×#4112yes—
494C2×C3×C4C2×#4112yes—
495C2×C3×C4C2×#4112yes—
496C2×C3×C4H(5,𝔽2)12yes—
497C2×C3×C42−1+412yes—
498#67—416no—
499#67—48no—
500C2×Dic3—24no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—24no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3C22×D418yes—
515D12—28no—
516C4×D3—416no—
517C4×D3—48no—
518Dic6—216no—
519Dic6—48no—
520C24—32no—
521C24C23×D312yes—
522C24C23×D311yescharacteristic
523#41—1232no—
524C2×Q8—38no—
525C2×Q8—64no—
526C2×Q8—64no—
527C2×Q8—64no—
528C2×Q8—122no—
529C2×Q8—122no—
530C2×D4—24no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—34no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—68no—
538C2×D4—64no—
539C2×D4—68no—
540C2×D4—64no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—124no—
544C2×D4—122no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—34no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—34no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—68no—
562C22×C4—68no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—124no—
567C22×C4#23514yescomplemented
568C22×C4C23×D312yes—
569C22×C4C23×D312yes—
570C22×C4C23×D312yes—
571C22×C4C23×D311yescharacteristic
572C22×C4C23×D311yescharacteristic
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—38no—
581C4⋊C4—38no—
582C4⋊C4—42no—
583C4⋊C4—68no—
584C4⋊C4—68no—
585C4⋊C4—68no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—62no—
589C4⋊C4—64no—
590C4⋊C4—62no—
591C4⋊C4—62no—
592C4⋊C4—124no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—64no—
599C22⋊C4—68no—
600C22⋊C4—68no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—124no—
605C22⋊C4—122no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C22⋊C4—124no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—24no—
613C42—68no—
614C42—64no—
615C42—124no—
616C42D3×D414yes—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3C23×D411yescharacteristic
632C22×C3C22×#4111yescharacteristic
633C22×C3C22×#4111yescharacteristic
634C22×C3C2×H(5,𝔽2)11yescharacteristic
635C22×C3C2×2−1+411yescharacteristic
636C22×C3#58511yescharacteristic
637C22×C3#58511yescharacteristic
638C2×D3—24no—
639C2×D3—24no—
640C2×D3—24no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4#54614yes—
653C3×C4#54814yes—
654Dic3—28no—
655Dic3—42no—
656Dic3—42no—
657Dic3—44no—
658Dic3—42no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—34no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23C2×#23512yes—
680C23C24×D311yescharacteristic
681Q8—616no—
682Q8—128no—
683D4—48no—
684D4—44no—
685D4—68no—
686D4—1216no—
687D4—128no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—38no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—44no—
712C2×C4—64no—
713C2×C4—64no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—1216no—
727C2×C4—128no—
728C2×C4C2×#23512yes—
729C2×C4C2×#23512yes—
730C2×C4C2×D3×D412yes—
731C2×C4C2×D3×D412yes—
732C2×C4C2×D3×D412yes—
733C2×C4#100412yes—
734C2×C4D3×#4112yes—
735C2×C4#101012yes—
736C2×C3—42no—
737C2×C3—82no—
738C2×C3C2×#54611yescharacteristic
739C2×C3C2×#54811yescharacteristic
740C2×C3#347511yescharacteristic
741C2×C3#348711yescharacteristic
742C2×C3#350611yescharacteristic
743C2×C3#351511yescharacteristic
744C2×C3#354711yescharacteristic
745D3—44no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—64no—
761C22—64no—
762C22—64no—
763C22—122no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22C22×#23511yescharacteristic
768C22C22×D3×D411yescharacteristic
769C22C2×#100411yescharacteristic
770C22C2×D3×#4111yescharacteristic
771C22C2×#101011yescharacteristic
772C22#596411yescharacteristic
773C22#596411yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—68no—
782C4—124no—
783C4—122no—
784C4—122no—
785C4—122no—
786C4#555214yes—
787C4#561214yes—
788C3#5903411yescharacteristic, complemented, Sylow
789C2—42no—
790C2—82no—
791C2—124no—
792C2C2×#555211yescharacteristic
793C2#8578811yescharacteristic
794C2#8584011yescharacteristic
795C2C2×#561211yescharacteristic
796C2#8602311yescharacteristic
797C2#8616511yescharacteristic
798C2#8623011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#59034
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5551C2semidirect
2. C2×#5470C2semidirect
3. C3×C4×#121C2semidirect
4. #82704C2semidirect
5. #82402C2semidirect
6. #82384C2semidirect
7. #82375C2semidirect
8. C4×#930C2semidirect
9. #76450C2semidirect
10. #76002C2semidirect
11. #75506C2semidirect
12. #74808C2semidirect
13. #74012C2semidirect
14. #73807C2semidirect
15. #73651C2semidirect
16. #73483C2semidirect
17. #73454C2semidirect
102. C4×#121D3semidirect
175. #869D4semidirect
278. C22×C3×C4#41semidirect
567. C22×C4#235semidirect
788. C3#59034semidirect

Maximal subgroups

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

subgroupindex
C2×#55512
C2×#54702
C3×C4×#1212
#827042
#824022
#823842
#823752
C4×#9302
#764502
#760022
#755062
#748082
#740122
#738072
#736512
#734832
#734542
#590343