Finite Group Databasebeta

← #11633852

Subgroups — #11633852

Order 768.

2374 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5727C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3C3×#2365C211yesmaximal, characteristic, complemented
4#82500C212yesmaximal, complemented
5Q8×(C2×D3)⋊C4C212yesmaximal, complemented
6#76623C212yesmaximal, complemented
7#76619C212yesmaximal, complemented
8#76016C212yesmaximal, complemented
9#75997C212yesmaximal, complemented
10#75394C214yesmaximal, complemented
11#75329C214yesmaximal, complemented
12#73807C211yesmaximal, characteristic, complemented
13C4×#897C211yesmaximal, characteristic, complemented
14C4×#895C211yesmaximal, characteristic
15#73721C211yesmaximal, characteristic, complemented
16#73714C212yesmaximal, complemented
17#73649C212yesmaximal
18#59036—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2212yes—
22C2×#946C2212yes—
23C2×#946C2212yes—
24C2×Q8×Dic3C2212yes—
25#5728—28no—
26#5727—28no—
27C2×#897C2211yescharacteristic
28C2×#897C2212yes—
29C2×#896C2214yes—
30C2×#895C2211yescharacteristic
31C2×#893C2212yes—
32C2×#892C2212yes—
33C2×#890C2212yes—
34C2×#888C2212yes—
35C2×#887C2212yes—
36C2×C4×D12C2211yescharacteristic
37C2×C4×D12C2212yes—
38C2×C42×D3C2211yescharacteristic
39C2×#869C2211yescharacteristic
40C2×C4×Dic6C2211yescharacteristic
41C3×#391C2212yes—
42C3×#389C2212yes—
43C3×#387C2214yes—
44C3×C4×C4⋊C4C2211yescharacteristic
45C3×C4×C4⋊C4C2211yescharacteristic
46C3×C4×C4⋊C4C2212yes—
47#4994C2214yes—
48#4994C2214yes—
49#4988C2211yescharacteristic
50#4987C2211yescharacteristic
51#4987C2211yescharacteristic
52#4987C2212yes—
53#4987C2214yes—
54#4987C2212yes—
55#4984C2211yescharacteristic
56#4984C2211yescharacteristic
57#4984C2212yes—
58#4984C2212yes—
59#4973C2211yescharacteristic
60#4973C2214yes—
61#4939C2214yes—
62#4939C2212yes—
63C4×(C2×D3)⋊C4C2212yes—
64C4×(C2×D3)⋊C4C2212yes—
65C4×(C2×D3)⋊C4C2214yes—
66#4936C2212yes—
67#4935C2212yes—
68C4×C4⋊Dic3C2212yes—
69#4929C2212yes—
70#4929C2214yes—
71#4928C2214yes—
72#4677C2214yes—
73#4673C2214yes—
74#4673C2214yes—
75#4670C2212yes—
76#4670C2214yes—
77#4668C2212yes—
78#4668C2214yes—
79#4665C2212yes—
80#4665C2214yes—
81#4661C2214yes—
82#4656C2214yes—
83#4656C2214yes—
84#4653C2212yes—
85#4653C2214yes—
86C2×D4×Q8—31no—
87C2×#533—31no—
88#2692—34no—
89#2567—31no—
90#2563—31no—
91#2550—32no—
92#2538—32no—
93#2465—34no—
94#2454—32no—
95#2439—32no—
96#2423—32no—
97#2409—32no—
98#2365D311yescharacteristic, complemented
99#2363—32no—
100Q8×C22⋊C4—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C2×D3×Q8—28no—
105C2×D3×Q8—28no—
106C2×D3×Q8—44no—
107C22×D12C2311yescharacteristic
108C22×D12C2312yes—
109C22×C4×D3C2312yes—
110C22×C4×D3C2311yescharacteristic
111C22×C4×D3C2314yes—
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×Dic6C2314yes—
115C22×Dic6C2311yescharacteristic
116C22×Dic6C2312yes—
117C3×C4⋊Q8D418yescomplemented
118C3×C4×Q8—44no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C42C2312yes—
127C2×C3×C42C2312yes—
128C2×C3×C42C2314yes—
129C2×C3×C42C2311yescharacteristic
130#946—28no—
131#946—28no—
132Q8×Dic3—28no—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2312yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×C4⋊Dic3C2312yes—
145C2×C4⋊Dic3C2314yes—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2312yes—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2314yes—
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2314yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2312yes—
161C2×C4×Dic3C2311yescharacteristic
162#897—24no—
163#897—28no—
164#896—216no—
165#895Q818yescomplemented
166#893—28no—
167#892—28no—
168#890—28no—
169#888—28no—
170#887—28no—
171C4×D12—24no—
172C4×D12—44no—
173C42×D3—24no—
174#869—24no—
175C4×Dic6—24no—
176C3×#95C2312yes—
177C3×#95C2314yes—
178C3×#95C2312yes—
179C3×#95C2314yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C23×Q8—32no—
191D4×Q8—68no—
192#533—68no—
193C2×C4⋊Q8—32no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—31no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—34no—
202C2×#121—31no—
203C2×C4×Q8—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8—31no—
206C2×C4×Q8C2×D312yes—
207C2×C4×D4—32no—
208C2×C4×D4—31no—
209C2×C4×D4—32no—
210C2×#117—32no—
211C22×C42—31no—
212#399—34no—
213#398—34no—
214#396—34no—
215#396—34no—
216#395—34no—
217#395—34no—
218#393—34no—
219#393—34no—
220#391—31no—
221#391—34no—
222#391—32no—
223#391—34no—
224#391C2×D312yes—
225#390—31no—
226#390—32no—
227#390—34no—
228#389—32no—
229#389—32no—
230#389—31no—
231#389—31no—
232#389—34no—
233#389C2×D312yes—
234#388—34no—
235#388—32no—
236#387—34no—
237#387—32no—
238#387C2×D314yes—
239#386—34no—
240#386—32no—
241#385—34no—
242#385—32no—
243#384—32no—
244#382—32no—
245#380—32no—
246#380—32no—
247#380—34no—
248#380—31no—
249#380—31no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4C2×D311yescharacteristic
252C4×C4⋊C4C2×D311yescharacteristic
253C4×C4⋊C4C2×D312yes—
254C4×C22⋊C4—34no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C23×D3C2411yescharacteristic
258C23×D3C2412yes—
259C2×C3×Q8—24no—
260C2×C3×Q8—24no—
261C2×C3×Q8C2×D418yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2414yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×Dic3C2412yes—
271C22×Dic3C2411yescharacteristic
272C22×Dic3C2414yes—
273C22×Dic3C2411yescharacteristic
274C22×Dic3C2412yes—
275C22×Dic3C2411yescharacteristic
276C22×Dic3C2412yes—
277D3×Q8—432no—
278C2×D12—22no—
279C2×D12—22no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12C2×Q814yes—
283C2×D12C2×Q818yescomplemented
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—24no—
289C2×C4×D3—28no—
290C2×C4×D3—22no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—24no—
294C2×C4×D3—28no—
295C2×C4×D3—41no—
296C2×C4×D3—41no—
297C2×C4×D3—44no—
298C2×C4×D3C2×Q814yescomplemented
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—24no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—42no—
305C2×Dic6—42no—
306C2×Dic6—44no—
307C2×Dic6#4114yes—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—44no—
312C3×C4⋊C4C2×D418yes—
313C3×C4⋊C4C2×D418yes—
314C3×C4⋊C4C2×Q814yescomplemented
315C3×C42—24no—
316C3×C42—24no—
317C3×C42—44no—
318C3×C42C2×D414yes—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4—44no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4C2×Q818yescomplemented
330C4⋊Dic3—22no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3—22no—
334C4⋊Dic3—28no—
335C4⋊Dic3—24no—
336C4⋊Dic3—42no—
337C4⋊Dic3—42no—
338C4⋊Dic3—44no—
339C4⋊Dic3—44no—
340Dic3⋊C4—24no—
341Dic3⋊C4—28no—
342Dic3⋊C4—28no—
343C4×Dic3—24no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—28no—
348C22×Q8—31no—
349C22×Q8—34no—
350C22×Q8—32no—
351C22×Q8—68no—
352C22×Q8—68no—
353C22×Q8—124no—
354C22×Q8C22×D312yes—
355C22×D4—31no—
356C22×D4—32no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—32no—
360C23×C4—34no—
361C23×C4—31no—
362C4⋊Q8—68no—
363C4⋊Q8—64no—
364C4⋊Q8D1218yescomplemented
365#125—68no—
366C22⋊Q8—64no—
367C22⋊Q8—68no—
368C22⋊Q8—68no—
369C22⋊Q8—68no—
370C22⋊Q8—616no—
371#121—38no—
372C4×Q8—44no—
373C4×Q8—68no—
374C4×Q8—68no—
375C4×Q8—64no—
376C4×D4—68no—
377C4×D4—64no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D314yes—
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C42—34no—
412C2×C42—32no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—64no—
417C2×C42C22×D312yes—
418C2×C42C22×D312yes—
419C2×C42C22×D314yes—
420C2×C42C22×D311yescharacteristic
421#95—32no—
422#95—32no—
423#95—34no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—32no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95C22×D312yes—
432#95C22×D312yes—
433#95C22×D314yes—
434#95C22×D314yes—
435C23×C3C2511yescharacteristic
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—21no—
439C22×D3—22no—
440C22×D3—21no—
441C22×D3—22no—
442C22×D3—21no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—21no—
448C22×D3C22×Q814yes—
449C22×D3C22×Q812yes—
450C3×Q8—216no—
451C2×C3×C4—24no—
452C2×C3×C4—22no—
453C2×C3×C4—24no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4C22×D418yes—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×Q814yes—
471C2×C3×C4C22×Q812yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4H(5,𝔽2)12yes—
474C2×C3×C42−1+412yes—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—21no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—21no—
494C2×Dic3C22×Q812yes—
495C2×Dic3C2×#4114yes—
496D12—28no—
497D12—48no—
498C4×D3—28no—
499C4×D3—416no—
500C4×D3—44no—
501C4×D3—44no—
502C4×D3—48no—
503Dic6—28no—
504Dic6—416no—
505Dic6—48no—
506C24—32no—
507C24—31no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—34no—
511C2×Q8—68no—
512C2×Q8—62no—
513C2×Q8—64no—
514C2×Q8—68no—
515C2×Q8—62no—
516C2×Q8—124no—
517C2×Q8—122no—
518C2×Q8—122no—
519C2×Q8—1232no—
520C2×Q8C2×D1218yes—
521C2×D4—34no—
522C2×D4—38no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—122no—
526C2×D4—122no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—34no—
533C22×C4—31no—
534C22×C4—32no—
535C22×C4—68no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—68no—
541C22×C4—64no—
542C22×C4—62no—
543C22×C4—64no—
544C22×C4—62no—
545C22×C4—64no—
546C22×C4—124no—
547C22×C4—121no—
548C22×C4—121no—
549C22×C4C23×D312yes—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D314yes—
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—44no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—62no—
564C4⋊C4—64no—
565C4⋊C4—62no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—64no—
569C4⋊C4—68no—
570C4⋊C4—122no—
571C4⋊C4—124no—
572C4⋊C4—122no—
573C4⋊C4—124no—
574C4⋊C4C2×D1218yes—
575C4⋊C4C2×D1218yes—
576C4⋊C4D3×Q814yescomplemented
577C22⋊C4—38no—
578C22⋊C4—64no—
579C22⋊C4—68no—
580C22⋊C4—68no—
581C22⋊C4—64no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—124no—
586C22⋊C4—124no—
587C22⋊C4—122no—
588C42—24no—
589C42—24no—
590C42—44no—
591C42—62no—
592C42—62no—
593C42—62no—
594C42—68no—
595C42—64no—
596C42C2×D1214yes—
597C22×C3C23×D411yescharacteristic
598C22×C3C23×Q811yescharacteristic
599C22×C3C22×#4111yescharacteristic
600C22×C3C2×H(5,𝔽2)11yescharacteristic
601C22×C3C2×2−1+411yescharacteristic
602C22×C3#58511yescharacteristic
603C22×C3#58511yescharacteristic
604C2×D3—22no—
605C2×D3—24no—
606C2×D3—22no—
607C2×D3—24no—
608C2×D3—22no—
609C2×D3—24no—
610C2×D3—42no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—42no—
614C2×D3—41no—
615C2×D3—42no—
616C2×D3—41no—
617C2×D3—42no—
618C3×C4—28no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4#54614yes—
625C3×C4D4×Q814yes—
626Dic3—24no—
627Dic3—22no—
628Dic3—42no—
629Dic3—41no—
630Dic3—44no—
631Dic3—41no—
632Dic3—42no—
633C23—34no—
634C23—32no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—62no—
639C23—61no—
640C23—62no—
641C23—61no—
642C23—62no—
643C23—62no—
644C23—61no—
645C23—62no—
646C23—61no—
647C23C24×D311yescharacteristic
648Q8—216no—
649Q8—68no—
650Q8—1216no—
651Q8—128no—
652D4—68no—
653D4—128no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—32no—
670C2×C4—34no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—68no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—64no—
680C2×C4—62no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—1216no—
692C2×C4—124no—
693C2×C4—128no—
694C2×C4—124no—
695C2×C4C22×D1212yes—
696C2×C4C22×D1218yes—
697C2×C4C22×D1212yes—
698C2×C4C22×D1212yes—
699C2×C4#100412yes—
700C2×C4C2×D3×Q814yes—
701C2×C4C2×D3×Q812yes—
702C2×C4D3×#4112yes—
703C2×C4#101012yes—
704C2×C3C2×#54611yescharacteristic
705C2×C3C2×D4×Q811yescharacteristic
706C2×C3Q8×#4111yescharacteristic
707C2×C3#348711yescharacteristic
708C2×C3#350111yescharacteristic
709C2×C3#351811yescharacteristic
710C2×C3#354711yescharacteristic
711D3—42no—
712D3—44no—
713C22—62no—
714C22—64no—
715C22—64no—
716C22—62no—
717C22—62no—
718C22—64no—
719C22—122no—
720C22—121no—
721C22—121no—
722C22—122no—
723C22—121no—
724C22—122no—
725C22—121no—
726C22—122no—
727C22C23×D1211yescharacteristic
728C22C2×#100411yescharacteristic
729C22C22×D3×Q811yescharacteristic
730C22C2×D3×#4111yescharacteristic
731C22C2×#101011yescharacteristic
732C22#596811yescharacteristic
733C22#596811yescharacteristic
734C4—28no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—64no—
741C4—62no—
742C4—122no—
743C4—121no—
744C4—121no—
745C4—124no—
746C4—122no—
747C4#555414yes—
748C4Q8×D1214yes—
749C3#5903611yescharacteristic, complemented, Sylow
750C2—122no—
751C2—124no—
752C2C2×#555411yescharacteristic
753C2C2×Q8×D1211yescharacteristic
754C2#8587411yescharacteristic
755C2#8670811yescharacteristic
756C2#8676111yescharacteristic
757C2#8698911yescharacteristic
758C2#8701511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2365C2
prime radicalC2×#895C22
hypercenter#2365D3
hypocenterC3#59036
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#5727C2semidirect
2. C2×#5728C2semidirect
3. C3×#2365C2semidirect
4. #82500C2semidirect
5. Q8×(C2×D3)⋊C4C2semidirect
6. #76623C2semidirect
7. #76619C2semidirect
8. #76016C2semidirect
9. #75997C2semidirect
10. #75394C2semidirect
11. #75329C2semidirect
12. #73807C2semidirect
13. C4×#897C2semidirect
15. #73721C2semidirect
16. #73714C2semidirect
98. #2365D3semidirect
117. C3×C4⋊Q8D4semidirect
165. #895Q8semidirect
283. C2×D12C2×Q8semidirect
298. C2×C4×D3C2×Q8semidirect
314. C3×C4⋊C4C2×Q8semidirect
329. (C2×D3)⋊C4C2×Q8semidirect
364. C4⋊Q8D12semidirect
576. C4⋊C4D3×Q8semidirect
749. C3#59036semidirect

Maximal subgroups

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

subgroupindex
C2×#57272
C2×#57282
C3×#23652
#825002
Q8×(C2×D3)⋊C42
#766232
#766192
#760162
#759972
#753942
#753292
#738072
C4×#8972
C4×#8952
#737212
#737142
#736492
#590363