Finite Group Databasebeta

← #10700702

Subgroups — #10700702

Order 768.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic
2C2×C3×#417C211yesmaximal, characteristic
3C22×#837C211yesmaximal, characteristic
4C2×#4554C211yesmaximal, characteristic, complemented
5C2×#4555C211yesmaximal, characteristic, complemented
6#71563C211yesmaximal, characteristic, complemented
7#71558C211yesmaximal, characteristic, complemented
8#10781—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12#5827—22no—
13#5827—22no—
14#5827—22no—
15#5827C414yescomplemented
16C2×Q8×Dic3—21no—
17C2×D4×Dic3—21no—
18C2×D4×Dic3—22no—
19C2×#926—21no—
20C2×#926C2211yescharacteristic
21C22×C4⋊Dic3—21no—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C3×#417—22no—
26C3×#417C414yescomplemented
27C2×C3×#103—21no—
28C2×C3×#102—21no—
29C2×#837—22no—
30C2×#837—22no—
31C2×#837C414yescomplemented
32C2×C3⋊#95—22no—
33#4555—22no—
34#4554—22no—
35#4529—21no—
36#4529—21no—
37C2×#520—31no—
38C22×#104—31no—
39C2×#417D311yescharacteristic
40C2×#343—31no—
41#1736—31no—
42C2×#339—31no—
43C4⋊#95—31no—
44C2×C3×#41—21no—
45C2×C3×#41—21no—
46C2×C3×#41—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41C2×C412yes—
51C2×C3×#41C2×C412yes—
52C2×C3×#41C2×C412yes—
53C2×C3×#41D412yes—
54C2×C3×#41D412yes—
55C2×C3×#41Q812yes—
56C22×C3×Q8D411yescharacteristic
57C22×C3×D4—21no—
58C22×C3×D4D411yescharacteristic
59C23×C3×C4—21no—
60C23×C3×C4—21no—
61C23×C3×C4C2311yescharacteristic
62C23×Dic3—21no—
63C23×Dic3—22no—
64C23×Dic3D412yes—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16C2×C412yescomplemented
71C22×C3×C8—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4C2×C412yescomplemented
78C2×#217—22no—
79C2×#217—21no—
80Q8×Dic3—24no—
81Q8×Dic3—24no—
82D4×Dic3—28no—
83D4×Dic3—24no—
84D4×Dic3—24no—
85D4×Dic3—28no—
86#926—24no—
87#926—21no—
88#926—21no—
89#926—24no—
90#926C2×C412yes—
91#926D412yes—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—24no—
94C2×C4⋊Dic3—21no—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—21no—
98C2×C4⋊Dic3—24no—
99C2×C4⋊Dic3C2×C412yes—
100C2×C4⋊Dic3D412yes—
101C2×C4⋊Dic3D411yescharacteristic
102C2×C4⋊Dic3D411yescharacteristic
103C2×C4×Dic3—22no—
104C2×C4×Dic3—21no—
105C2×C4×Dic3—21no—
106C2×C4×Dic3—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3—21no—
109C2×C4×Dic3—21no—
110C2×C4×Dic3C2×C412yescomplemented
111C2×#208—21no—
112C2×#208—21no—
113C2×#208—21no—
114C2×#208—21no—
115C2×#208—21no—
116C2×#208C2×C412yescomplemented
117C22×C3⋊C8—21no—
118C3×#103—24no—
119C3×#102—24no—
120#837—28no—
121C3⋊#95—44no—
122C22×#41C2×D311yescharacteristic
123C22×M16—31no—
124C22×M16C2×D311yescharacteristic
125#520—34no—
126#520—62no—
127#520—62no—
128#520—62no—
129C2×C4×Q8—61no—
130C2×C4×D4—62no—
131C2×C4×D4—61no—
132C2×#117—31no—
133C2×#117—61no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4—61no—
136C22×C4⋊C4C2×D311yescharacteristic
137C22×C42—31no—
138C2×#104—34no—
139C2×#104—62no—
140C2×#104—62no—
141#417—22no—
142#417Dic314yescomplemented
143C2×#103—21no—
144C2×#102—21no—
145C2×#95—62no—
146#343—62no—
147#340—61no—
148#340—61no—
149#339—62no—
150C24×C3—21no—
151C24×C3C2×D411yescharacteristic
152C3×#41—22no—
153C3×#41—22no—
154C3×#41—22no—
155C3×#41—22no—
156C3×#41—22no—
157C3×#41—22no—
158C3×#41—22no—
159C3×#41—22no—
160C3×#41—22no—
161C3×#41—22no—
162C3×#41—22no—
163C3×#41—22no—
164C3×#41C4214yes—
165C3×#41C22⋊C414yes—
166C3×#41C4⋊C414yes—
167C3×#41C4⋊C414yes—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8C22⋊C412yes—
172C2×C3×Q8C22⋊C412yes—
173C2×C3×Q8C4⋊C412yes—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4C22⋊C412yes—
184C2×C3×D4C22⋊C412yes—
185C2×C3×D4C4⋊C412yes—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—42no—
195C22×C3×C4—42no—
196C22×C3×C4—41no—
197C22×C3×C4—41no—
198C22×C3×C4C22×C411yescharacteristic
199C22×C3×C4C22×C411yescharacteristic
200C22×C3×C4C22×C411yescharacteristic
201C22×C3×C4C2×D411yescharacteristic
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×Q811yescharacteristic
208C22×C3×C4#4111yescharacteristic
209C22×C3×C4#4111yescharacteristic
210C22×C3×C4#4111yescharacteristic
211C22×C3×C4#4111yescharacteristic
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—28no—
219C22×Dic3—22no—
220C22×Dic3—41no—
221C22×Dic3—41no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3—42no—
225C22×Dic3—42no—
226C22×Dic3—82no—
227C22×Dic3—82no—
228C22×Dic3C22⋊C414yes—
229C3×M16—22no—
230C3×M16—22no—
231C3×M16—41no—
232C3×M16—41no—
233C2×C3×C8—22no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240#217—28no—
241#217—22no—
242#217—22no—
243C4⋊Dic3—28no—
244C4⋊Dic3—22no—
245C4⋊Dic3—22no—
246C4⋊Dic3—22no—
247C4⋊Dic3—21no—
248C4⋊Dic3—22no—
249C4⋊Dic3—21no—
250C4⋊Dic3C22⋊C412yes—
251C4⋊Dic3C22⋊C412yes—
252C4×Dic3—28no—
253C4×Dic3—22no—
254C4×Dic3—22no—
255C4×Dic3—22no—
256C4×Dic3—22no—
257C4×Dic3—41no—
258C4×Dic3—41no—
259#208—22no—
260#208—22no—
261#208—41no—
262#208—41no—
263C2×C3⋊C8—22no—
264C2×C3⋊C8—41no—
265C2×C3⋊C8—41no—
266C2×#41—21no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41Dic612yes—
273C2×#41C4×D312yes—
274C2×#41C4×D312yes—
275C2×#41D1212yes—
276C2×#41C2×Dic312yes—
277C2×#41#6712yes—
278C22×Q8#6711yescharacteristic
279C22×D4—21no—
280C22×D4#6711yescharacteristic
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—32no—
284C23×C4—61no—
285C23×C4—62no—
286C23×C4C22×D311yescharacteristic
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—32no—
293C2×M16—61no—
294C2×M16—61no—
295C2×M16—61no—
296C2×M16—61no—
297C2×M16—61no—
298C2×M16C2×Dic312yescomplemented
299C22×C8—21no—
300C22×C8—61no—
301C4×Q8—64no—
302C4×Q8—64no—
303C4×D4—68no—
304C4×D4—68no—
305C4×D4—64no—
306C4×D4—64no—
307#117—32no—
308#117—32no—
309#117—64no—
310#117—64no—
311#117—61no—
312#117—61no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—64no—
323C2×C4⋊C4—62no—
324C2×C4⋊C4—64no—
325C2×C4⋊C4—61no—
326C2×C4⋊C4—61no—
327C2×C4⋊C4—61no—
328C2×C4⋊C4—61no—
329C2×C4⋊C4C2×Dic312yescomplemented
330C2×C22⋊C4—62no—
331C2×C22⋊C4—61no—
332C2×C42—32no—
333C2×C42—62no—
334C2×C42—61no—
335C2×C42—61no—
336C2×C42—61no—
337C2×C42—61no—
338C2×C42—61no—
339C2×C42—61no—
340#104—68no—
341#103—24no—
342#102—24no—
343#95—124no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3C2×C22⋊C411yescharacteristic
356C23×C3C4×D411yescharacteristic
357C23×C3C4×D411yescharacteristic
358C23×C3#12011yescharacteristic
359C23×C3#12011yescharacteristic
360C23×C3#12111yescharacteristic
361C23×C3C22⋊Q811yescharacteristic
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8#9514yescomplemented
366C3×D4—24no—
367C3×D4—24no—
368C3×D4—24no—
369C3×D4—24no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4#9514yescomplemented
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—44no—
382C2×C3×C4—42no—
383C2×C3×C4—82no—
384C2×C3×C4—81no—
385C2×C3×C4—81no—
386C2×C3×C4C2×C4211yescharacteristic
387C2×C3×C4C2×C22⋊C411yescharacteristic
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4C2×C22⋊C411yescharacteristic
390C2×C3×C4C2×C22⋊C411yescharacteristic
391C2×C3×C4C2×C4⋊C411yescharacteristic
392C2×C3×C4C2×C4⋊C411yescharacteristic
393C2×C3×C4C2×C4⋊C411yescharacteristic
394C2×C3×C4#11711yescharacteristic
395C2×C3×C4#11711yescharacteristic
396C2×C3×C4C4×D411yescharacteristic
397C2×C3×C4C4×D411yescharacteristic
398C2×C3×C4C4×D411yescharacteristic
399C2×C3×C4C4×D411yescharacteristic
400C2×C3×C4C4×D411yescharacteristic
401C2×C3×C4C4×D411yescharacteristic
402C2×C3×C4#12011yescharacteristic
403C2×C3×C4#12011yescharacteristic
404C2×C3×C4#12111yescharacteristic
405C2×C3×C4#12111yescharacteristic
406C2×C3×C4#12111yescharacteristic
407C2×C3×C4C22⋊Q811yescharacteristic
408C2×C3×C4C22⋊Q811yescharacteristic
409C2×C3×C4C22⋊Q811yescharacteristic
410C2×C3×C4#12311yescharacteristic
411C2×C3×C4#12311yescharacteristic
412C2×C3×C4#12311yescharacteristic
413C2×C3×C4#12311yescharacteristic
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—24no—
417C2×Dic3—22no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—44no—
431C2×Dic3—82no—
432C2×Dic3—88no—
433C3×C8—42no—
434C3⋊C8—42no—
435C24—21no—
436C24D3×D411yescharacteristic
437#41—22no—
438#41—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41—22no—
449#41C4×Dic314yes—
450#41Dic3⋊C414yes—
451#41C4⋊Dic314yes—
452#41(C2×D3)⋊C414yes—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8Dic3⋊C412yes—
457C2×Q8(C2×D3)⋊C412yes—
458C2×Q8#21712yes—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4Dic3⋊C412yes—
469C2×D4(C2×D3)⋊C412yes—
470C2×D4#21712yes—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—34no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—68no—
491C22×C4—62no—
492C22×C4—121no—
493C22×C4—121no—
494C22×C4—121no—
495C22×C4—121no—
496C22×C4—122no—
497C22×C4—122no—
498C22×C4—242no—
499C22×C4—242no—
500C22×C4C2×Dic611yescharacteristic
501C22×C4C2×C4×D311yescharacteristic
502C22×C4C2×C4×D311yescharacteristic
503C22×C4C2×D1211yescharacteristic
504C22×C4D3×D411yescharacteristic
505C22×C4D3×D411yescharacteristic
506C22×C4D3×D411yescharacteristic
507C22×C4#23711yescharacteristic
508C22×C4#23711yescharacteristic
509C22×C4#23711yescharacteristic
510C22×C4#23711yescharacteristic
511C22×C4C22×Dic311yescharacteristic
512C22×C4C2×#6711yescharacteristic
513C22×C4C2×#6711yescharacteristic
514M16—22no—
515M16—22no—
516M16—41no—
517M16—41no—
518M16—62no—
519M16—62no—
520M16—121no—
521M16—121no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—62no—
526C2×C8—121no—
527C2×C8—121no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—32no—
531C4⋊C4—32no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—68no—
535C4⋊C4—62no—
536C4⋊C4—61no—
537C4⋊C4—62no—
538C4⋊C4—61no—
539C4⋊C4—62no—
540C4⋊C4—62no—
541C22⋊C4—68no—
542C22⋊C4—62no—
543C22⋊C4—62no—
544C42—68no—
545C42—62no—
546C42—62no—
547C42—62no—
548C42—62no—
549C42—121no—
550C42—121no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—24no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3C4×C22⋊C411yescharacteristic
571C22×C3#37911yescharacteristic
572C22×C3#38011yescharacteristic
573C22×C3#38511yescharacteristic
574C22×C3#38511yescharacteristic
575C22×C3#38611yescharacteristic
576C22×C3#38611yescharacteristic
577C22×C3#45311yescharacteristic
578C22×C3#45411yescharacteristic
579C22×C3#45511yescharacteristic
580C22×C3#45611yescharacteristic
581C3×C4—24no—
582C3×C4—82no—
583C3×C4C2×#9511yescharacteristic
584C3×C4C4×C22⋊C411yescharacteristic
585C3×C4#38011yescharacteristic
586C3×C4#38111yescharacteristic
587C3×C4#38511yescharacteristic
588C3×C4#38511yescharacteristic
589C3×C4#38611yescharacteristic
590C3×C4#38611yescharacteristic
591Dic3—44no—
592Dic3—44no—
593Dic3—42no—
594Dic3—42no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23#87811yescharacteristic
607C23D3×C22⋊C411yescharacteristic
608C23#67⋊C411yescharacteristic
609C23#88211yescharacteristic
610C23D4×Dic311yescharacteristic
611C23#93711yescharacteristic
612C23#93911yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8C3⋊#9514yescomplemented
617D4—24no—
618D4—24no—
619D4—24no—
620D4—24no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4C3⋊#9514yescomplemented
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—44no—
633C2×C4—42no—
634C2×C4—64no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—64no—
638C2×C4—82no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—122no—
642C2×C4—122no—
643C2×C4—122no—
644C2×C4—122no—
645C2×C4—122no—
646C2×C4—122no—
647C2×C4—121no—
648C2×C4—121no—
649C2×C4—122no—
650C2×C4—121no—
651C2×C4—121no—
652C2×C4—122no—
653C2×C4—124no—
654C2×C4—242no—
655C2×C4—248no—
656C2×C4#87711yescharacteristic
657C2×C4#87711yescharacteristic
658C2×C4#87811yescharacteristic
659C2×C4#87811yescharacteristic
660C2×C4#87811yescharacteristic
661C2×C4D3×C22⋊C411yescharacteristic
662C2×C4#67⋊C411yescharacteristic
663C2×C4#67⋊C411yescharacteristic
664C2×C4#67⋊C411yescharacteristic
665C2×C4#88211yescharacteristic
666C2×C4#88611yescharacteristic
667C2×C4#88611yescharacteristic
668C2×C4C2×C4×Dic311yescharacteristic
669C2×C4C2×Dic3⋊C411yescharacteristic
670C2×C4C2×Dic3⋊C411yescharacteristic
671C2×C4C2×C4⋊Dic311yescharacteristic
672C2×C4C2×(C2×D3)⋊C411yescharacteristic
673C2×C4C2×(C2×D3)⋊C411yescharacteristic
674C2×C4D4×Dic311yescharacteristic
675C2×C4D4×Dic311yescharacteristic
676C2×C4D4×Dic311yescharacteristic
677C2×C4#93511yescharacteristic
678C2×C4#93511yescharacteristic
679C2×C4#93711yescharacteristic
680C2×C4#93911yescharacteristic
681C2×C4#93911yescharacteristic
682C2×C4#93911yescharacteristic
683C2×C4C2×#21711yescharacteristic
684C8—42no—
685C8—122no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—44no—
691C2×C3C22⋊#9511yescharacteristic
692C2×C3#179211yescharacteristic
693C2×C3#179311yescharacteristic
694C2×C3#185911yescharacteristic
695C2×C3#186011yescharacteristic
696C2×C3#188211yescharacteristic
697C2×C3#188311yescharacteristic
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22Dic3×C22⋊C411yescharacteristic
718C22#494211yescharacteristic
719C22#494611yescharacteristic
720C22#495011yescharacteristic
721C22#495511yescharacteristic
722C22#495811yescharacteristic
723C22#519811yescharacteristic
724C22#520111yescharacteristic
725C22#520211yescharacteristic
726C22#520511yescharacteristic
727C22#522011yescharacteristic
728C4—24no—
729C4—82no—
730C4—124no—
731C4—124no—
732C4—122no—
733C4—122no—
734C4Dic3×C22⋊C411yescharacteristic
735C4#494211yescharacteristic
736C4#494311yescharacteristic
737C4#494611yescharacteristic
738C4#495011yescharacteristic
739C4#495811yescharacteristic
740C4C2×C3⋊#9511yescharacteristic
741C4#522011yescharacteristic
742C3#1078111yescharacteristic, complemented, Sylow
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—44no—
748C2#7029711yescharacteristic
749C2#7029811yescharacteristic
750C2#7030511yescharacteristic
751C2#7030811yescharacteristic
752C2#7154411yescharacteristic
753C2#7208811yescharacteristic
754C2#7210011yescharacteristic
subgroupG/H
centerC23#937
commutatorC2×C3×C4C2×C42
FrattiniC23×C4C22×D3
FittingC2×C3×#417C2
socleC23×C3#120
prime radicalC22×C3×#41C22
cosocleC23×C3×C4C23
hypercenterC2×#417D3
hypocenterC3#10781
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
4. C2×#4554C2semidirect
5. C2×#4555C2semidirect
6. #71563C2semidirect
7. #71558C2semidirect
15. #5827C4semidirect
26. C3×#417C4semidirect
31. C2×#837C4semidirect
70. C2×C3×M16C2×C4semidirect
77. C2×C3×C4⋊C4C2×C4semidirect
110. C2×C4×Dic3C2×C4semidirect
116. C2×#208C2×C4semidirect
142. #417Dic3semidirect
298. C2×M16C2×Dic3semidirect
329. C2×C4⋊C4C2×Dic3semidirect
365. C3×Q8#95semidirect
373. C3×D4#95semidirect
616. Q8C3⋊#95semidirect
624. D4C3⋊#95semidirect
742. C3#10781semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4172
C22×#8372
C2×#45542
C2×#45552
#715632
#715582
#107813