Finite Group Databasebeta

← #11633818

Subgroups — #11633818

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×#5726C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3C3×#2365C211yesmaximal, characteristic, complemented
4#82499C212yesmaximal, complemented
5#82457C212yesmaximal, complemented
6#76622C212yesmaximal, complemented
7#76618C212yesmaximal, complemented
8#76209C212yesmaximal, complemented
9#76003C212yesmaximal, complemented
10#75325C214yesmaximal, complemented
11#75152C214yesmaximal, complemented
12#73807C211yesmaximal, characteristic, complemented
13#73807C211yesmaximal, characteristic, complemented
14#73787C212yesmaximal, complemented
15#73771C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic, complemented
17C4×#895C211yesmaximal, characteristic, complemented
18#59034—31nomaximal, Sylow
19C22×#239C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2212yes—
22C2×#946C2212yes—
23C2×#946C2212yes—
24C2×Q8×Dic3C2212yes—
25#5728—28no—
26#5726—28no—
27C2×#897C2212yes—
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#895C2212yes—
31C2×#894C2214yes—
32C2×#892C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×#890C2212yes—
35C2×#887C2212yes—
36C2×C4×D12C2212yes—
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2211yescharacteristic
39C2×C4×D12C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×#869C2211yescharacteristic
42C3×#391C2212yes—
43C3×#389C2212yes—
44C3×#387C2214yes—
45C3×C4×C4⋊C4C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2212yes—
48#4991C2214yes—
49#4988C2211yescharacteristic
50#4988C2214yes—
51#4988C2211yescharacteristic
52#4987C2212yes—
53#4987C2214yes—
54#4987C2211yescharacteristic
55#4987C2211yescharacteristic
56#4987C2212yes—
57#4987C2212yes—
58#4987C2212yes—
59#4984C2211yescharacteristic
60#4984C2211yescharacteristic
61#4981C2214yes—
62#4940C2214yes—
63#4940C2214yes—
64#4939C2214yes—
65#4939C2212yes—
66#4939C2212yes—
67C4×(C2×D3)⋊C4C2212yes—
68C4×(C2×D3)⋊C4C2214yes—
69C4×(C2×D3)⋊C4C2212yes—
70#4936C2212yes—
71#4936C2212yes—
72#4674C2214yes—
73#4673C2214yes—
74#4673C2214yes—
75#4672C2214yes—
76#4671C2214yes—
77#4670C2212yes—
78#4670C2212yes—
79#4670C2214yes—
80#4668C2214yes—
81#4665C2212yes—
82#4665C2212yes—
83#4665C2214yes—
84#4659C2214yes—
85#4653C2214yes—
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#2365D311yescharacteristic, complemented
99#2352—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C2×#239—28no—
105C2×#239—28no—
106C2×#239—44no—
107C22×D12C2311yescharacteristic
108C22×D12C2312yes—
109C22×D12C2314yes—
110C22×D12C2311yescharacteristic
111C22×D12C2312yes—
112C22×C4×D3C2312yes—
113C22×C4×D3C2312yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2314yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4⋊Q8D418yescomplemented
120C3×C4×Q8—44no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C42C2312yes—
129C2×C3×C42C2312yes—
130C2×C3×C42C2314yes—
131C2×C3×C42C2311yescharacteristic
132#946—28no—
133#946—28no—
134Q8×Dic3—28no—
135C2×(C2×D3)⋊C4C2312yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×C4×Dic3C2314yes—
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164#897—28no—
165#895—24no—
166#895—24no—
167#895—28no—
168#894—216no—
169#892—28no—
170D3×C4⋊C4—28no—
171#890—28no—
172#887—28no—
173C4×D12—28no—
174C4×D12—24no—
175C4×D12—24no—
176C4×D12—44no—
177C42×D3—24no—
178#869—24no—
179C3×#95C2314yes—
180C3×#95C2314yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
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—31no—
203C2×#121—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8C2×D312yes—
207C2×C4×D4—31no—
208C2×C4×D4—31no—
209C2×C4×D4—32no—
210C2×C4×D4—32no—
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#393—34no—
221#392—34no—
222#391C2×D312yes—
223#390—31no—
224#390—34no—
225#390—31no—
226#390—32no—
227#390—32no—
228#390—34no—
229#389—31no—
230#389—31no—
231#389C2×D312yes—
232#388—34no—
233#388—34no—
234#388—34no—
235#388—32no—
236#388—32no—
237#387—34no—
238#387C2×D314yes—
239#386—34no—
240#386—32no—
241#386—32no—
242#385—34no—
243#382—32no—
244#382—32no—
245#380—32no—
246#380—32no—
247#380—32no—
248#380—32no—
249#380—34no—
250#380—31no—
251#380—31no—
252C4×C4⋊C4C2×D311yescharacteristic
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C4⋊C4C2×D312yes—
255C4×C22⋊C4—34no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C23×D3C2412yes—
259C23×D3C2411yescharacteristic
260C23×D3C2412yes—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8C2×D418yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2414yes—
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C22×Dic3C2412yes—
273C22×Dic3C2412yes—
274C22×Dic3C2411yescharacteristic
275C22×Dic3C2414yes—
276C22×Dic3C2411yescharacteristic
277C22×Dic3C2411yescharacteristic
278#239—432no—
279C2×D12—22no—
280C2×D12—22no—
281C2×D12—24no—
282C2×D12—24no—
283C2×D12—24no—
284C2×D12—28no—
285C2×D12—22no—
286C2×D12—28no—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—42no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—44no—
293C2×D12#4114yes—
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3—28no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—28no—
302C2×C4×D3—24no—
303C2×C4×D3—22no—
304C2×C4×D3—24no—
305C2×C4×D3—22no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—41no—
309C2×C4×D3—41no—
310C2×C4×D3—44no—
311C2×C4×D3#4114yescomplemented
312C2×Dic6—24no—
313C2×Dic6—42no—
314C2×Dic6—42no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—44no—
320C3×C4⋊C4C2×D418yes—
321C3×C4⋊C4C2×D418yes—
322C3×C42—24no—
323C3×C42—24no—
324C3×C42—44no—
325C3×C42C2×D414yes—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—42no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342C4⋊Dic3—24no—
343C4⋊Dic3—24no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—28no—
347C4⋊Dic3—24no—
348C4⋊Dic3—42no—
349Dic3⋊C4—28no—
350Dic3⋊C4—28no—
351C4×Dic3—22no—
352C4×Dic3—22no—
353C4×Dic3—22no—
354C4×Dic3—28no—
355C2×#41—68no—
356C2×#41—68no—
357C2×#41—124no—
358C22×Q8—32no—
359C22×Q8C22×D312yes—
360C22×D4—31no—
361C22×D4—31no—
362C22×D4—32no—
363C22×D4—34no—
364C22×D4—32no—
365C23×C4—31no—
366C23×C4—32no—
367C23×C4—31no—
368C23×C4—32no—
369C23×C4—34no—
370C23×C4—31no—
371C4⋊Q8—64no—
372C4⋊Q8D1218yescomplemented
373#125—68no—
374#123—616no—
375C22⋊Q8—68no—
376C22⋊Q8—68no—
377C22⋊Q8—68no—
378#121—64no—
379#121—64no—
380#121—68no—
381C4×Q8—44no—
382C4×Q8—68no—
383C4×Q8—68no—
384C4×D4—68no—
385C4×D4—64no—
386C4×D4—64no—
387C4×D4—124no—
388#117—68no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—68no—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D314yes—
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D312yes—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
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—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C42—34no—
423C2×C42—31no—
424C2×C42—31no—
425C2×C42—31no—
426C2×C42—64no—
427C2×C42C22×D312yes—
428C2×C42C22×D312yes—
429C2×C42C22×D314yes—
430C2×C42C22×D311yescharacteristic
431#95—32no—
432#95—34no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—34no—
437#95—34no—
438#95—34no—
439#95C22×D314yes—
440#95C22×D312yes—
441#95C22×D312yes—
442#95C22×D314yes—
443C23×C3C2511yescharacteristic
444C22×D3—21no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—22no—
450C22×D3—21no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3C2×#4112yes—
464C22×D3C2×#4114yes—
465C3×Q8—216no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
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—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4C22×D418yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4H(5,𝔽2)12yes—
489C2×C3×C42−1+412yes—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—24no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3C2×#4112yes—
508D12—28no—
509D12—416no—
510D12—48no—
511D12—48no—
512D12—44no—
513C4×D3—28no—
514C4×D3—416no—
515C4×D3—44no—
516C4×D3—44no—
517C4×D3—48no—
518C4×D3—48no—
519Dic6—48no—
520C24—31no—
521C24—32no—
522C24—32no—
523#41—1232no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—64no—
527C2×Q8—122no—
528C2×Q8—122no—
529C2×Q8C2×D1218yes—
530C2×D4—34no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—68no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—68no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—122no—
542C2×D4—124no—
543C2×D4—122no—
544C2×D4—122no—
545C22×C4—31no—
546C22×C4—34no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—31no—
550C22×C4—34no—
551C22×C4—31no—
552C22×C4—68no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—64no—
558C22×C4—68no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—62no—
565C22×C4—64no—
566C22×C4—124no—
567C22×C4—121no—
568C22×C4—121no—
569C22×C4C23×D312yes—
570C22×C4C23×D312yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D314yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—44no—
582C4⋊C4—64no—
583C4⋊C4—62no—
584C4⋊C4—68no—
585C4⋊C4—64no—
586C4⋊C4—62no—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—64no—
590C4⋊C4—122no—
591C4⋊C4C2×D1218yes—
592C4⋊C4C2×D1218yes—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—68no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—68no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—124no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C22⋊C4—124no—
609C42—24no—
610C42—24no—
611C42—44no—
612C42—62no—
613C42—62no—
614C42—62no—
615C42—68no—
616C42C2×D1214yes—
617C22×C3C23×D411yescharacteristic
618C22×C3C22×#4111yescharacteristic
619C22×C3C22×#4111yescharacteristic
620C22×C3C2×H(5,𝔽2)11yescharacteristic
621C22×C3C2×2−1+411yescharacteristic
622C22×C3#58511yescharacteristic
623C22×C3#58511yescharacteristic
624C2×D3—24no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—24no—
628C2×D3—22no—
629C2×D3—24no—
630C2×D3—41no—
631C2×D3—42no—
632C2×D3—41no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C3×C4—28no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4#54614yes—
652C3×C4#54814yes—
653Dic3—22no—
654Dic3—42no—
655Dic3—41no—
656Dic3—42no—
657Dic3—44no—
658Dic3—41no—
659C23—32no—
660C23—34no—
661C23—61no—
662C23—62no—
663C23—61no—
664C23—62no—
665C23—61no—
666C23—62no—
667C23—62no—
668C23—61no—
669C23—62no—
670C23—62no—
671C23—61no—
672C23—61no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23C24×D311yescharacteristic
681Q8—216no—
682Q8—128no—
683D4—68no—
684D4—1216no—
685D4—128no—
686D4—128no—
687D4—124no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—21no—
691C2×C4—21no—
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—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—32no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—68no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—64no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—1216no—
724C2×C4—124no—
725C2×C4—128no—
726C2×C4—124no—
727C2×C4—128no—
728C2×C4C22×D1212yes—
729C2×C4C22×D1218yes—
730C2×C4C22×D1212yes—
731C2×C4C22×D1212yes—
732C2×C4#100412yes—
733C2×C4#100712yes—
734C2×C4D3×#4112yes—
735C2×C4D3×#4112yes—
736C2×C3C2×#54611yescharacteristic
737C2×C3C2×#54811yescharacteristic
738C2×C3#347511yescharacteristic
739C2×C3#348711yescharacteristic
740C2×C3#350611yescharacteristic
741C2×C3#351511yescharacteristic
742C2×C3#354711yescharacteristic
743D3—44no—
744D3—42no—
745D3—82no—
746C22—64no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—64no—
751C22—64no—
752C22—121no—
753C22—122no—
754C22—121no—
755C22—122no—
756C22—122no—
757C22—121no—
758C22—122no—
759C22—121no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22C23×D1211yescharacteristic
768C22C2×#100411yescharacteristic
769C22C2×#100711yescharacteristic
770C22C2×D3×#4111yescharacteristic
771C22C2×D3×#4111yescharacteristic
772C22#596811yescharacteristic
773C22#596811yescharacteristic
774C4—28no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—62no—
781C4—122no—
782C4—121no—
783C4—122no—
784C4—121no—
785C4—124no—
786C4#555414yes—
787C4#557614yes—
788C3#5903411yescharacteristic, complemented, Sylow
789C2—124no—
790C2—122no—
791C2—242no—
792C2C2×#555411yescharacteristic
793C2C2×#557611yescharacteristic
794C2#8587411yescharacteristic
795C2#8670311yescharacteristic
796C2#8676311yescharacteristic
797C2#8697911yescharacteristic
798C2#8702111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2365C2
hypercenter#2365D3
hypocenterC3#59034
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#5726C2semidirect
2. C2×#5728C2semidirect
3. C3×#2365C2semidirect
4. #82499C2semidirect
5. #82457C2semidirect
6. #76622C2semidirect
7. #76618C2semidirect
8. #76209C2semidirect
9. #76003C2semidirect
10. #75325C2semidirect
11. #75152C2semidirect
12. #73807C2semidirect
13. #73807C2semidirect
14. #73787C2semidirect
15. #73771C2semidirect
16. C4×#895C2semidirect
17. C4×#895C2semidirect
98. #2365D3semidirect
119. C3×C4⋊Q8D4semidirect
311. C2×C4×D3#41semidirect
372. C4⋊Q8D12semidirect
788. C3#59034semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#57282
C3×#23652
#824992
#824572
#766222
#766182
#762092
#760032
#753252
#751522
#738072
#737872
#737712
C4×#8952
#590343