Finite Group Databasebeta

← #11633856

Subgroups — #11633856

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×D4×Dic6C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×#121C211yesmaximal, characteristic
4#82637C212yesmaximal
5#82384C211yesmaximal, characteristic, complemented
6#82376C212yesmaximal, complemented
7#82349C212yesmaximal, complemented
8C4×#924C211yesmaximal, characteristic, complemented
9#76324C212yesmaximal, complemented
10#76062C212yesmaximal, complemented
11#75514C214yesmaximal, complemented
12#74803C214yesmaximal, complemented
13#73898C212yesmaximal, complemented
14#73721C211yesmaximal, characteristic, complemented
15#73651C211yesmaximal, characteristic, complemented
16#73484C212yesmaximal, complemented
17C22⋊C4×Dic6C212yesmaximal, complemented
18#59036—31nomaximal, Sylow
19C23×Dic6C2212yes—
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×D4×Dic3C2212yes—
25C2×#926C2212yes—
26C2×#924C2212yes—
27C2×#924C2212yes—
28C2×#924C2211yescharacteristic
29C2×#924C2212yes—
30D4×Dic6—28no—
31C2×#888C2212yes—
32C2×#878C2214yes—
33#5470—28no—
34C2×#870C2212yes—
35C2×#869C2211yescharacteristic
36C2×#869C2211yescharacteristic
37C2×C4×Dic6C2212yes—
38C2×C4×Dic6C2211yescharacteristic
39C2×C4×Dic6C2212yes—
40C2×C4×Dic6C2212yes—
41C3×#390C2211yescharacteristic
42C3×#389C2211yescharacteristic
43C3×#388C2212yes—
44C3×#386C2212yes—
45C3×#380C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C22⋊C4C2212yes—
48#5221C2212yes—
49#5221C2214yes—
50#5220C2214yes—
51#5212C2212yes—
52#5212C2211yescharacteristic
53#5212C2212yes—
54#5210C2212yes—
55C4×#217C2212yes—
56#4984C2212yes—
57#4984C2212yes—
58#4979C2214yes—
59#4977C2212yes—
60Dic3×C4⋊C4C2212yes—
61#4972C2214yes—
62#4972C2212yes—
63#4951C2214yes—
64#4949C2214yes—
65#4948C2214yes—
66#4948C2214yes—
67#4947C2214yes—
68#4947C2214yes—
69#4946C2214yes—
70#4942C2214yes—
71Dic3×C22⋊C4C2214yes—
72#4935C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74#4933C2212yes—
75C4×Dic3⋊C4C2212yes—
76#4929C2212yes—
77#4929C2211yescharacteristic
78#4929C2212yes—
79#4928C2211yescharacteristic
80#4657C2214yes—
81#4656C2214yes—
82#4654C2214yes—
83#4654C2214yes—
84#4646C2214yes—
85#4646C2214yes—
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#2365—31no—
99#2363—32no—
100Q8×C22⋊C4—32no—
101C4×C22⋊Q8—31no—
102C4×#121D311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2312yes—
105C23×C3×C4C2312yes—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×Dic3C2314yes—
110C22×Dic6—28no—
111C22×Dic6—28no—
112C22×Dic6—44no—
113C22×Dic6C2314yes—
114C22×Dic6C2312yes—
115C22×Dic6C2311yescharacteristic
116C22×Dic6C2312yes—
117C3×#121Q818yescomplemented
118C3×C4×D4—24no—
119C3×C4×D4—44no—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C42—24no—
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2312yes—
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×#217C2312yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2312yes—
141D4×Dic3—28no—
142#926—28no—
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2314yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152#924—28no—
153#924—28no—
154#924—24no—
155#924—28no—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2314yes—
167#888—28no—
168#878—216no—
169#870—28no—
170#869—24no—
171#869D418yescomplemented
172C4×Dic6—28no—
173C4×Dic6—24no—
174C4×Dic6—28no—
175C4×Dic6—44no—
176C3×#95C2312yes—
177C3×#95C2312yes—
178C3×#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C23×Q8—32no—
191D4×Q8—68no—
192#533—68no—
193C2×C4⋊Q8—32no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8—31no—
196C2×#125—32no—
197C2×C22⋊Q8—31no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—34no—
202C2×#121C2×D311yescharacteristic
203C2×C4×Q8—31no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×D4—32no—
208C2×C4×D4C2×D311yescharacteristic
209C2×C4×D4C2×D312yes—
210C2×#117—32no—
211C22×C42C2×D311yescharacteristic
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—32no—
221#391—31no—
222#391—32no—
223#391—34no—
224#391—34no—
225#390—32no—
226#390—34no—
227#390C2×D311yescharacteristic
228#389—32no—
229#389—32no—
230#389—32no—
231#389—34no—
232#389—31no—
233#389C2×D311yescharacteristic
234#388—34no—
235#388C2×D312yes—
236#387—32no—
237#387—34no—
238#387—34no—
239#386—34no—
240#386C2×D312yes—
241#385—32no—
242#385—34no—
243#384—32no—
244#382—32no—
245#380—32no—
246#380—32no—
247#380—31no—
248#380—34no—
249#380C2×D311yescharacteristic
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4C2×D312yes—
257C24×C3C2411yescharacteristic
258C24×C3C2412yes—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4C2×Q814yes—
264C2×C3×D4C2×Q818yescomplemented
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—22no—
271C22×C3×C4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—41no—
275C22×C3×C4—41no—
276C22×C3×C4C2×Q814yescomplemented
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—44no—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2414yes—
292C22×Dic3C2412yes—
293C22×Dic3C2414yes—
294C22×Dic3C2412yes—
295C2×Dic6—22no—
296C2×Dic6—24no—
297C2×Dic6—24no—
298C2×Dic6—22no—
299C2×Dic6—24no—
300C2×Dic6—28no—
301C2×Dic6—28no—
302C2×Dic6—432no—
303C2×Dic6—44no—
304C2×Dic6—42no—
305C2×Dic6—42no—
306C2×Dic6C2×D418yes—
307C2×Dic6#4114yes—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4C2×Q814yescomplemented
312C3×C22⋊C4—24no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4C2×Q818yescomplemented
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—24no—
321C3×C42C2×D414yes—
322#217—28no—
323#217—28no—
324#217—24no—
325#217—44no—
326#217—42no—
327#217—44no—
328C4⋊Dic3—24no—
329C4⋊Dic3—22no—
330C4⋊Dic3—24no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—44no—
334C4⋊Dic3—44no—
335C4⋊Dic3C2×D418yes—
336C4⋊Dic3C2×D418yes—
337Dic3⋊C4—24no—
338Dic3⋊C4—28no—
339Dic3⋊C4—28no—
340Dic3⋊C4—28no—
341Dic3⋊C4—24no—
342Dic3⋊C4—44no—
343Dic3⋊C4—42no—
344C4×Dic3—24no—
345C4×Dic3—24no—
346C4×Dic3—28no—
347C4×Dic3—44no—
348C22×Q8—32no—
349C22×Q8—31no—
350C22×Q8—34no—
351C22×Q8—32no—
352C22×Q8—68no—
353C22×Q8—68no—
354C22×Q8—124no—
355C22×D4C22×D311yescharacteristic
356C22×D4C22×D312yes—
357C23×C4—34no—
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D312yes—
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362C4⋊Q8—38no—
363C4⋊Q8—68no—
364C4⋊Q8—64no—
365#125—68no—
366C22⋊Q8—616no—
367C22⋊Q8—68no—
368C22⋊Q8—68no—
369C22⋊Q8—68no—
370C22⋊Q8—64no—
371#121Dic618yescomplemented
372C4×Q8—68no—
373C4×Q8—68no—
374C4×Q8—64no—
375C4×Q8—124no—
376C4×D4—24no—
377C4×D4—44no—
378C4×D4—68no—
379#117—68no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4C22×D312yes—
407C2×C22⋊C4C22×D312yes—
408C2×C22⋊C4C22×D312yes—
409C2×C22⋊C4C22×D312yes—
410C2×C22⋊C4C22×D312yes—
411C2×C42—24no—
412C2×C42—34no—
413C2×C42—32no—
414C2×C42—32no—
415C2×C42—34no—
416C2×C42C22×D312yes—
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421#95—32no—
422#95—34no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95C22×D312yes—
433#95C22×D312yes—
434#95C22×D312yes—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—22no—
441C23×C3—21no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—22no—
446C23×C3—21no—
447C23×C3C22×Q814yes—
448C23×C3C22×Q812yes—
449C23×C3C2511yescharacteristic
450C3×D4—28no—
451C3×D4—48no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—28no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—44no—
472C2×C3×C4—48no—
473C2×C3×C4—44no—
474C2×C3×C4C22×D412yes—
475C2×C3×C4C22×D412yes—
476C2×C3×C4C22×D412yes—
477C2×C3×C4C22×Q812yes—
478C2×C3×C4C22×Q814yes—
479C2×C3×C4C22×Q812yes—
480C2×C3×C4C2×#4112yes—
481C2×C3×C4H(5,𝔽2)12yes—
482C2×C3×C42−1+412yes—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—416no—
500C2×Dic3C22×D418yes—
501C2×Dic3C2×#4114yes—
502Dic6—28no—
503Dic6—216no—
504Dic6—416no—
505Dic6—48no—
506C24C23×D311yescharacteristic
507C24C23×D312yes—
508C2×Q8—38no—
509C2×Q8—34no—
510C2×Q8—68no—
511C2×Q8—68no—
512C2×Q8—62no—
513C2×Q8—64no—
514C2×Q8—64no—
515C2×Q8—62no—
516C2×Q8—64no—
517C2×Q8—124no—
518C2×Q8—122no—
519C2×Q8—122no—
520C2×Q8—1232no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C2×Dic614yes—
526C2×D4C2×Dic618yescomplemented
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—32no—
537C22×C4—34no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—34no—
541C22×C4—32no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—68no—
545C22×C4—68no—
546C22×C4—124no—
547C22×C4C2×Dic614yescomplemented
548C22×C4C23×D312yes—
549C22×C4C23×D312yes—
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D312yes—
554C22×C4C23×D311yescharacteristic
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—38no—
560C4⋊C4—38no—
561C4⋊C4—42no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—62no—
569C4⋊C4—64no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—124no—
573C4⋊C4—122no—
574C4⋊C4—124no—
575C4⋊C4—124no—
576C4⋊C4C2×Dic614yescomplemented
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—68no—
582C22⋊C4—68no—
583C22⋊C4—64no—
584C22⋊C4—122no—
585C22⋊C4—124no—
586C22⋊C4—124no—
587C22⋊C4C2×Dic618yescomplemented
588C42—22no—
589C42—22no—
590C42—22no—
591C42—24no—
592C42—68no—
593C42—64no—
594C42—64no—
595C42—124no—
596C42D3×D414yes—
597C22×C3—22no—
598C22×C3—24no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—42no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—42no—
611C22×C3C23×D411yescharacteristic
612C22×C3C23×Q811yescharacteristic
613C22×C3C22×#4111yescharacteristic
614C22×C3C2×H(5,𝔽2)11yescharacteristic
615C22×C3C2×2−1+411yescharacteristic
616C22×C3#58511yescharacteristic
617C22×C3#58511yescharacteristic
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4#54614yes—
626C3×C4D4×Q814yes—
627Dic3—24no—
628Dic3—28no—
629Dic3—44no—
630Dic3—42no—
631Dic3—42no—
632Dic3—42no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—22no—
644C23—21no—
645C23C22×Dic614yes—
646C23C22×Dic612yes—
647C23C24×D311yescharacteristic
648Q8—68no—
649Q8—616no—
650Q8—128no—
651Q8—1216no—
652D4—28no—
653D4—48no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—28no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—38no—
674C2×C4—34no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—44no—
678C2×C4—62no—
679C2×C4—64no—
680C2×C4—62no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—1216no—
695C2×C4C22×Dic612yes—
696C2×C4C22×Dic614yes—
697C2×C4C22×Dic612yes—
698C2×C4C2×D3×D412yes—
699C2×C4C2×D3×D412yes—
700C2×C4C2×D3×D412yes—
701C2×C4#100412yes—
702C2×C4D3×#4112yes—
703C2×C4#101012yes—
704C2×C3—42no—
705C2×C3—44no—
706C2×C3C2×#54611yescharacteristic
707C2×C3C2×D4×Q811yescharacteristic
708C2×C3Q8×#4111yescharacteristic
709C2×C3#348711yescharacteristic
710C2×C3#350111yescharacteristic
711C2×C3#351811yescharacteristic
712C2×C3#354711yescharacteristic
713C22—22no—
714C22—24no—
715C22—22no—
716C22—24no—
717C22—22no—
718C22—24no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22C23×Dic611yescharacteristic
728C22C22×D3×D411yescharacteristic
729C22C2×#100411yescharacteristic
730C22C2×D3×#4111yescharacteristic
731C22C2×#101011yescharacteristic
732C22#596411yescharacteristic
733C22#596411yescharacteristic
734C4—24no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—64no—
742C4—68no—
743C4—124no—
744C4—122no—
745C4—122no—
746C4—122no—
747C4D4×Dic614yes—
748C4#561214yes—
749C3#5903611yescharacteristic, complemented, Sylow
750C2—42no—
751C2—44no—
752C2C2×D4×Dic611yescharacteristic
753C2#8576611yescharacteristic
754C2#41×Dic611yescharacteristic
755C2C2×#561211yescharacteristic
756C2#8602311yescharacteristic
757C2#8612711yescharacteristic
758C2#8623011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
prime radicalC2×C3×#121C22
hypercenterC4×#121D3
hypocenterC3#59036
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic6C2semidirect
2. C2×#5470C2semidirect
5. #82384C2semidirect
6. #82376C2semidirect
7. #82349C2semidirect
8. C4×#924C2semidirect
9. #76324C2semidirect
10. #76062C2semidirect
11. #75514C2semidirect
12. #74803C2semidirect
13. #73898C2semidirect
14. #73721C2semidirect
15. #73651C2semidirect
16. #73484C2semidirect
17. C22⋊C4×Dic6C2semidirect
117. C3×#121Q8semidirect
171. #869D4semidirect
264. C2×C3×D4C2×Q8semidirect
276. C22×C3×C4C2×Q8semidirect
311. C3×C4⋊C4C2×Q8semidirect
316. C3×C22⋊C4C2×Q8semidirect
371. #121Dic6semidirect
526. C2×D4C2×Dic6semidirect
547. C22×C4C2×Dic6semidirect
576. C4⋊C4C2×Dic6semidirect
587. C22⋊C4C2×Dic6semidirect
749. C3#59036semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic62
C2×#54702
C3×C4×#1212
#826372
#823842
#823762
#823492
C4×#9242
#763242
#760622
#755142
#748032
#738982
#737212
#736512
#734842
C22⋊C4×Dic62
#590363