Finite Group Databasebeta

← #29646450

Subgroups — #29646450

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3#21454447C211yesmaximal, characteristic, complemented
4#21444260C214yesmaximal, complemented
5#21444245C211yesmaximal, characteristic, complemented
6#21444244C211yesmaximal, characteristic, complemented
7#21444243C211yesmaximal, characteristic, complemented
8#21444208C214yesmaximal, complemented
9C61×#1486C211yesmaximal, characteristic, complemented
10C22×D4×D61C411yescharacteristic
11C23×C4×D61—21no—
12C2×C4×D244C2211yescharacteristic
13C2×D4×Dic61C411yescharacteristic
14C2×#14519739C411yescharacteristic
15C2×C4×C22⋊D61—21no—
16C2×#14519737—21no—
17C4×D4×D61—21no—
18C4×D4×D61—21no—
19C4×D4×D61—21no—
20C4×D4×D61—21no—
21C4×D4×D61C412yes—
22C4×D4×D61C412yes—
23C4×D4×D61C2212yes—
24C4×D4×D61C2212yes—
25C2×C4⋊C4×D61C411yescharacteristic
26C2×C22⋊C4×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818—21no—
30#16839818C2212yescomplemented
31#16839816—21no—
32#16839815C2211yescharacteristic, complemented
33#16839814—21no—
34#16839814C2212yescomplemented
35#16839813C2212yescomplemented
36#16839786C2211yescharacteristic, complemented
37#16839784—21no—
38#16839725—21no—
39#16839724—21no—
40M16×Dic61—21no—
41C4×#11758189C2212yescomplemented
42#16839491C2214yescomplemented
43D4⋊#92418C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic, complemented
47C61×#423C2211yescharacteristic, complemented
48C61×D4⋊C8C2214yescomplemented
49C24×D61—21no—
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61—21no—
52C2×D4×D61—28no—
53C2×D4×D61—21no—
54C2×D4×D61—21no—
55C2×D4×D61C2×C412yes—
56C2×D4×D61C2×C412yes—
57C23×Dic61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—44no—
66C22×C4×D61—44no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C2×#11758194—21no—
71C2×#11758189—22no—
72C4×D244—21no—
73C4×D244—21no—
74C4×D244C2×C412yes—
75C4×D244C2312yes—
76D4×Dic61—21no—
77D4×Dic61—21no—
78D4×Dic61C2×C412yes—
79D4×Dic61C2×C412yes—
80#14519739—21no—
81#14519739—21no—
82#14519739C2×C412yes—
83#14519739C2×C412yes—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61C2×C412yes—
97C4⋊C4×D61C2×C412yes—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C22⋊C4×D61—22no—
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C4⋊#92418—21no—
117C4⋊#92418—21no—
118C4⋊#92418C2312yescomplemented
119#14519706—22no—
120C22⋊#92418—21no—
121#14519689—22no—
122#14519689—22no—
123#14519689—22no—
124#14519687—22no—
125#14519687—22no—
126C4×#92418C2312yescomplemented
127C8×Dic61—22no—
128C22×D4×C61C2×C411yescharacteristic
129C23×C4×C61—21no—
130C2×M16×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133C4×D4×C61C2×C412yes—
134C4×D4×C61C2312yes—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2312yescomplemented
141C22⋊C8×C61—21no—
142C4×C8×C61C2312yescomplemented
143C24×C61—21no—
144C23×D61—28no—
145C23×D61—21no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—44no—
149C23×D61—44no—
150C23×D61C22⋊C411yescharacteristic
151C2×D4×C61—24no—
152C2×D4×C61—21no—
153C2×D4×C61C22×C412yes—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C2×C22⋊D61—28no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—44no—
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172D4×D61—28no—
173D4×D61—28no—
174D4×D61—24no—
175D4×D61—24no—
176D4×D61—24no—
177D4×D61M1618yescomplemented
178C2×D244—21no—
179C2×D244—24no—
180C2×D244C22×C412yes—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—24no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—42no—
191C2×C4×D61—44no—
192C2×C4×D61—44no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
195C2×C4×D61—48no—
196C2×C4×D61—48no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213M16×C61—42no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C22×C412yes—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C42×C61C22×C411yescharacteristic
221C42×C61C2×D411yescharacteristic
222C42×C61C2×D411yescharacteristic
223C42×C61C2411yescharacteristic
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230C4⋊Dic61—21no—
231C4⋊Dic61C22×C412yes—
232#11758196—22no—
233#11758196—22no—
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22⋊C411yescharacteristic
236C4×Dic61C22⋊C411yescharacteristic
237C4×Dic61C22⋊C411yescharacteristic
238C4×Dic61C22⋊C411yescharacteristic
239C4×Dic61C22⋊C411yescharacteristic
240C4×Dic61C22×C411yescharacteristic
241C4×Dic61C22×C411yescharacteristic
242C4×Dic61C2×D411yescharacteristic
243C4×Dic61C2×D411yescharacteristic
244C4×Dic61C2×D411yescharacteristic
245C4×Dic61C2×D411yescharacteristic
246#11758194—42no—
247C2×#92418—22no—
248C2×#92418—22no—
249#11758189—44no—
250C23×C61—24no—
251C23×C61—22no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61C2×C22⋊C411yescharacteristic
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—28no—
260C22×D61—22no—
261C22×D61—28no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61—432no—
265C22×D61—44no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—44no—
269C22×D61C2×C22⋊C411yescharacteristic
270C22×D61C2×C22⋊C411yescharacteristic
271D4×C61—24no—
272D4×C61—22no—
273D4×C61C2×M1614yes—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—41no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—44no—
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×C4×C61C2×C22⋊C411yescharacteristic
283C2×C4×C61C2×C22⋊C411yescharacteristic
284C2×C4×C61AGL(1,ℤ/8)12yes—
285C2×C4×C61AGL(1,ℤ/8)12yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C22⋊D61—28no—
290C22⋊D61—28no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—41no—
295C2×Dic61—44no—
296C2×Dic61—44no—
297C2×Dic61—42no—
298C2×Dic61C2×C22⋊C411yescharacteristic
299C2×Dic61C2×C22⋊C411yescharacteristic
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304D244—24no—
305D244—22no—
306D244C2×M1614yes—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—21no—
314C4×D61—21no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—44no—
321C4×D61—44no—
322C4×D61—44no—
323C4×D61—44no—
324C4×D61—42no—
325C4×D61—42no—
326C4×D61—44no—
327C4×D61C2×M1614yes—
328C8×C61—42no—
329C8×C61—42no—
330#92418—42no—
331#92418—42no—
332#17448—611nomaximal, Sylow
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—24no—
336C22×C61—48no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61#41812yes—
340C22×C61C22×C22⋊C411yescharacteristic
341C2×D61—28no—
342C2×D61—21no—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—21no—
346C2×D61—24no—
347C2×D61—416no—
348C2×D61—416no—
349C2×D61—48no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61#40712yes—
353C2×D61#42112yes—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—42no—
358C4×C61#41812yes—
359C4×C61C22×M1612yes—
360C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
362Dic61—21no—
363Dic61—21no—
364Dic61—21no—
365Dic61—21no—
366Dic61—21no—
367Dic61—42no—
368Dic61#40712yes—
369C22×C4×D4—611no—
370#2920—611no—
371#2920—611no—
372#1490—614no—
373#1486—611no—
374#1486—611no—
375#1486—611no—
376#1486D6111yescharacteristic, complemented
377#1478—614no—
378C2×C61—22no—
379C2×C61—44no—
380C2×C61C2×#40711yescharacteristic
381C2×C61C2×#41811yescharacteristic
382C2×C61C2×#42111yescharacteristic
383D61—22no—
384D61—22no—
385D61—44no—
386C23×D4—611no—
387C24×C4—1221no—
388C2×C4×D4—611no—
389C2×C4×D4—612no—
390C2×C4×D4—612no—
391C2×C4×D4—612no—
392C2×C4×D4—612no—
393C2×C4×D4—611no—
394C2×C4×D4—611no—
395C2×C4×D4—1221no—
396C2×C4×D4—1221no—
397C2×C4×D4—1221no—
398C2×C4×D4—1221no—
399C2×C4×D4—1221no—
400C2×C4×D4—1221no—
401C2×C4×D4C2×D6111yescharacteristic
402C22×C4⋊C4—611no—
403C22×C22⋊C4—1221no—
404C22×C42—611no—
405#432—612no—
406#432—1221no—
407#432—1221no—
408#432—1221no—
409#431—611no—
410#431—612no—
411#431—612no—
412#431—1221no—
413#431C2×D6111yescharacteristic, complemented
414#423—611no—
415#423—1221no—
416#423C2×D6111yescharacteristic, complemented
417#407—1221no—
418#407—1221no—
419C4×M16—612no—
420C4×M16—1221no—
421D4⋊C8—614no—
422D4⋊C8—614no—
423D4⋊C8—614no—
424D4⋊C8C2×D6114yescomplemented
425C61#1744811yescharacteristic, complemented, Sylow
426C25—1221no—
427C22×D4—612no—
428C22×D4—612no—
429C22×D4—611no—
430C22×D4—1221no—
431C22×D4—1221no—
432C22×D4—1221no—
433C22×D4—1228no—
434C22×D4C4×D6111yescharacteristic
435C23×C4—21no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—1221no—
440C23×C4—1222no—
441C23×C4—1222no—
442C23×C4—1222no—
443C23×C4—1222no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C23×C4—2444no—
448C23×C4—2444no—
449C2×M16—21no—
450C2×M16—1222no—
451C2×M16—1221no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—612no—
455C4×D4—612no—
456C4×D4—612no—
457C4×D4—612no—
458C4×D4—612no—
459C4×D4—612no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1221no—
465C4×D4—1221no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1221no—
471C4×D4—1221no—
472C4×D4—1221no—
473C4×D4—1221no—
474C4×D4C4×D6112yes—
475C4×D4C22×D6112yes—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C4×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1222no—
485C2×C22⋊C4—1222no—
486C2×C22⋊C4—1222no—
487C2×C22⋊C4—1222no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42C22×D6111yescharacteristic
503C4⋊C8—21no—
504C4⋊C8—21no—
505C4⋊C8—612no—
506C4⋊C8—1222no—
507C4⋊C8—1221no—
508C4⋊C8—1221no—
509C4⋊C8C22×D6112yescomplemented
510C22⋊C8—21no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—1222no—
514C22⋊C8—1221no—
515#97—1222no—
516#97—1222no—
517C4×C8—612no—
518C4×C8—1222no—
519C4×C8C22×D6112yescomplemented
520C24—21no—
521C24—611no—
522C24—1222no—
523C24—1222no—
524C24—1228no—
525C24—1221no—
526C24—2444no—
527C24—2444no—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—618no—
531C2×D4—612no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—1224no—
537C2×D4—1228no—
538C2×D4—1228no—
539C2×D4—1228no—
540C2×D4—1224no—
541C2×D4—1221no—
542C2×D4C2×C4×D6112yes—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—1224no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—2442no—
576C22×C4—2444no—
577C22×C4—2448no—
578C22×C4—2448no—
579C22×C4—2444no—
580C22×C4—2444no—
581C22×C4—2444no—
582C22×C4—2444no—
583C22×C4—2444no—
584C22×C4—2444no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4D4×D6111yescharacteristic
590M16—42no—
591M16—2444no—
592M16—2442no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—1222no—
596C2×C8—1222no—
597C4⋊C4—21no—
598C4⋊C4—612no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1221no—
602C4⋊C4C2×C4×D6112yes—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C42—611no—
612C42—611no—
613C42—611no—
614C42—611no—
615C42—611no—
616C42—611no—
617C42—611no—
618C42—611no—
619C42—611no—
620C42—611no—
621C42—611no—
622C42—611no—
623C42C2×C4×D6111yescharacteristic
624C42D4×D6111yescharacteristic
625C42D4×D6111yescharacteristic
626C42C23×D6111yescharacteristic
627C23—24no—
628C23—22no—
629C23—42no—
630C23—42no—
631C23—611no—
632C23—611no—
633C23—1222no—
634C23—1222no—
635C23—1228no—
636C23—1224no—
637C23—1228no—
638C23—1222no—
639C23—1222no—
640C23—2442no—
641C23—2444no—
642C23—2444no—
643C23—2444no—
644C23—24432no—
645C23—2444no—
646C23—2442no—
647C23C22⋊C4×D6111yescharacteristic
648D4—24no—
649D4—22no—
650D4—614no—
651D4—1224no—
652D4—1228no—
653D4—1228no—
654D4—1222no—
655D4M16×D6114yes—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—44no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—611no—
664C2×C4—614no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—611no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2444no—
687C2×C4—2444no—
688C2×C4—2444no—
689C2×C4—2444no—
690C2×C4—2441no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2442no—
694C2×C4—2444no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22⋊C4×D6111yescharacteristic
698C2×C4C22⋊C4×D6111yescharacteristic
699C2×C4C22⋊C4×D6111yescharacteristic
700C2×C4#1451980112yes—
701C2×C4#1451980412yes—
702C2×C4C22×C4×D6111yescharacteristic
703C2×C4C2×D4×D6111yescharacteristic
704C2×C4C2×D4×D6111yescharacteristic
705C8—42no—
706C8—42no—
707C8—2442no—
708C8—2442no—
709C22—21no—
710C22—21no—
711C22—24no—
712C22—48no—
713C22—42no—
714C22—42no—
715C22—612no—
716C22—612no—
717C22—1228no—
718C22—1221no—
719C22—1221no—
720C22—1221no—
721C22—1221no—
722C22—1224no—
723C22—2448no—
724C22—24416no—
725C22—24416no—
726C22—2442no—
727C22—2442no—
728C22#1683976512yes—
729C22C2×C22⋊C4×D6111yescharacteristic
730C4—21no—
731C4—21no—
732C4—21no—
733C4—42no—
734C4—612no—
735C4—1221no—
736C4—1221no—
737C4—1221no—
738C4—1221no—
739C4—1221no—
740C4—2442no—
741C4#1683976512yes—
742C4C2×M16×D6112yes—
743C4C2×#1451980111yescharacteristic
744C4C2×#1451980411yescharacteristic
745C2—22no—
746C2—44no—
747C2—1222no—
748C2—1222no—
749C2—2444no—
750C2#407×D6111yescharacteristic
751C2C2×#1683976511yescharacteristic
752C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1486C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC42×C61C24
hypercenter#1486D61
hypocenterC61#17448
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. #21454447C2semidirect
4. #21444260C2semidirect
5. #21444245C2semidirect
6. #21444244C2semidirect
7. #21444243C2semidirect
8. #21444208C2semidirect
9. C61×#1486C2semidirect
30. #16839818C22semidirect
32. #16839815C22semidirect
34. #16839814C22semidirect
35. #16839813C22semidirect
36. #16839786C22semidirect
41. C4×#11758189C22semidirect
42. #16839491C22semidirect
43. D4⋊#92418C22semidirect
44. #16839489C22semidirect
46. C61×#431C22semidirect
47. C61×#423C22semidirect
48. C61×D4⋊C8C22semidirect
118. C4⋊#92418C23semidirect
126. C4×#92418C23semidirect
140. C4⋊C8×C61C23semidirect
142. C4×C8×C61C23semidirect
177. D4×D61M16semidirect
376. #1486D61semidirect
413. #431C2×D61semidirect
416. #423C2×D61semidirect
424. D4⋊C8C2×D61semidirect
425. C61#17448semidirect
509. C4⋊C8C22×D61semidirect
519. C4×C8C22×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
#214544512
#214544472
#214442602
#214442452
#214442442
#214442432
#214442082
C61×#14862
#1744861