Finite Group Databasebeta

← C2×#21449844 #29847992

Subgroups — C2×#21449844 #29847992

Order 15616.

2854 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519756C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3#21449844C2116yesmaximal, direct product factor
4C2×#16839685C211yesmaximal, characteristic
5C2×#16839683C211yesmaximal, characteristic, complemented
6C2×#16839682C211yesmaximal, characteristic, complemented
7C2×#16839674C211yesmaximal, characteristic
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839656C211yesmaximal, characteristic
11C2×#16839656C211yesmaximal, characteristic
12C2×#16839648C211yesmaximal, characteristic, complemented
13C2×#16839647C211yesmaximal, characteristic, complemented
14C2×#16839644C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic61C211yesmaximal, characteristic
16C2×C61×#385C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C2×#14519756—28no—
20C2×#14519756C2218yes—
21C2×#14519742—28no—
22C2×#14519742C2218yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839685C2218yes—
40#16839683C2218yescomplemented
41#16839682C2218yescomplemented
42#16839674C2218yes—
43#16839666C2218yescomplemented
44#16839657C2218yescomplemented
45#16839656C2218yes—
46#16839656C2218yes—
47#16839648C2218yescomplemented
48#16839647C2218yescomplemented
49#16839644C2218yescomplemented
50C4×C22⋊Dic61C2218yes—
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C61×#385C2218yes—
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C22×Dic122—24no—
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122—24no—
74C22×Dic122—42no—
75C22×Dic122C2314yes—
76C22×Dic122C2314yes—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85#14519756—232no—
86#14519742—232no—
87C2×C4⋊Dic61—24no—
88C2×C4⋊Dic61—24no—
89C2×C4⋊Dic61C2314yes—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—42no—
95C2×#11758196—42no—
96C2×#11758196D418yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×C22⋊Dic61—24no—
104C2×C22⋊Dic61—24no—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61Q818yescomplemented
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—24no—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—42no—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129C25×C61C2311yescharacteristic
130C23×C4×C61—24no—
131C23×C4×C61—24no—
132C23×C4×C61—42no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2314yes—
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61—24no—
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61—42no—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61C2×Q814yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—28no—
175C22×C4×C61—28no—
176C22×C4×C61—44no—
177C22×C4×C61—416no—
178C22×C4×C61C2×D414yes—
179C22×C4×C61#4114yes—
180C22×C4×C61#4114yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61C2×D414yes—
207C22×Dic61C2×D414yes—
208C22×Dic61C2×Q814yes—
209C22×Dic61C2×Q814yes—
210C22×Dic61#4114yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C2×Dic122—232no—
220C2×Dic122—28no—
221C2×Dic122—28no—
222C2×Dic122—28no—
223C2×Dic122—28no—
224C2×Dic122—28no—
225C2×Dic122—44no—
226C2×Dic122—416no—
227C4⋊C4×C61—28no—
228C4⋊C4×C61—28no—
229C22⋊C4×C61—28no—
230C22⋊C4×C61—44no—
231C22⋊Dic61—28no—
232C22⋊Dic61—28no—
233C22⋊Dic61—28no—
234C22⋊Dic61C2×Q8116yescomplemented
235C4⋊Dic61—28no—
236C4⋊Dic61—28no—
237#11758196—28no—
238#11758196—28no—
239#11758196—28no—
240#11758196—44no—
241#11758196—44no—
242#11758196C2×D4116yes—
243C4×Dic61—28no—
244C4×Dic61—28no—
245C4×Dic61—28no—
246C4×Dic61—44no—
247C23×C61—28no—
248C23×C61—28no—
249C23×C61—28no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—44no—
257C23×C61—44no—
258C23×C61—44no—
259C23×C61—44no—
260C23×C61C22×D412yes—
261C23×C61C22×Q814yes—
262C23×C61C22×Q812yes—
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C23×C61C2×#4112yes—
266C23×C61H(5,𝔽2)12yes—
267C23×C612−1+412yes—
268C23×C61C2511yescharacteristic
269C2×C4×C61—28no—
270C2×C4×C61—28no—
271C2×C4×C61—28no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—416no—
288C2×C4×C61—44no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61C22×D414yes—
292C2×C4×C61C2×#4114yes—
293C2×C4×C61C2×#4114yes—
294C2×Dic61—28no—
295C2×Dic61—28no—
296C2×Dic61—28no—
297C2×Dic61—28no—
298C2×Dic61—28no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—44no—
319C2×Dic61—44no—
320C2×Dic61—44no—
321C2×Dic61C22×D414yes—
322C2×Dic61C22×D414yes—
323C2×Dic61C22×Q814yes—
324C2×Dic61C22×Q814yes—
325C2×Dic61C2×#4114yes—
326Dic122—232no—
327Dic122—416no—
328C2×#2465—611nomaximal, Sylow
329C22×C61—24no—
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—416no—
337C22×C61#52514yes—
338C22×C61#53314yes—
339C22×C61#54214yes—
340C22×C61#54614yes—
341C22×C61D4×Q814yes—
342C22×C61#55414yes—
343C22×C61#55614yes—
344C22×C61C23×D411yescharacteristic
345C22×C61C23×Q811yescharacteristic
346C22×C61C22×#4111yescharacteristic
347C22×C61C22×#4111yescharacteristic
348C22×C61C22×#4111yescharacteristic
349C22×C61C2×H(5,𝔽2)11yescharacteristic
350C22×C61C2×2−1+411yescharacteristic
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357Dic61—24no—
358Dic61—24no—
359Dic61—24no—
360Dic61—24no—
361Dic61—24no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C22×C22⋊Q8—611no—
366C22×C4×Q8—611no—
367#2465—6116no—
368C2×#396—611no—
369C2×#395—611no—
370C2×#395—611no—
371C2×#393—611no—
372C2×#391—611no—
373C2×#389—611no—
374C2×#388—611no—
375C2×#388—611no—
376C2×#387—611no—
377C2×#387—611no—
378C2×#387—611no—
379C2×#385D6111yescharacteristic
380C2×C4×C22⋊C4—611no—
381C2×C61—44no—
382C2×C61#246518yescomplemented
383C2×C61C2×#52511yescharacteristic
384C2×C61C2×#53311yescharacteristic
385C2×C61C2×#54211yescharacteristic
386C2×C61C2×#54611yescharacteristic
387C2×C61C2×D4×Q811yescharacteristic
388C2×C61C2×#55411yescharacteristic
389C2×C61C2×#55611yescharacteristic
390C23×Q8—611no—
391C23×Q8—611no—
392C24×C4C2×D6111yescharacteristic
393C2×C22⋊Q8—618no—
394C2×C22⋊Q8—1228no—
395C2×C4×Q8—618no—
396C2×C4×Q8—1228no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4C2×D6111yescharacteristic
406C22×C4⋊C4C2×D6111yescharacteristic
407C22×C22⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4C2×D6111yescharacteristic
412C22×C22⋊C4C2×D6111yescharacteristic
413C22×C42—611no—
414C22×C42—611no—
415C22×C42—611no—
416C22×C42—611no—
417#396—618no—
418#395—618no—
419#395—618no—
420#393—618no—
421#391—618no—
422#389—618no—
423#388—618no—
424#388—618no—
425#387—618no—
426#387—618no—
427#387—618no—
428#385C2×D6118yes—
429C4×C22⋊C4—618no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95—611no—
439C2×#95—611no—
440C2×#95C2×D6111yescharacteristic
441C2×#95C2×D6111yescharacteristic
442C61C2×#246511yescharacteristic, complemented, Sylow
443C25C22×D6111yescharacteristic
444C22×Q8—614no—
445C22×Q8—614no—
446C22×Q8—1224no—
447C22×Q8—1224no—
448C22×Q8—1224no—
449C22×Q8—1224no—
450C22×Q8—1224no—
451C22×Q8—2442no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—42no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6114yes—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C22⋊Q8—12232no—
471C4×Q8—12232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—618no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1224no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—2442no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4C22×D6114yes—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—618no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4C22×D6114yes—
503C2×C22⋊C4C22×D6114yes—
504C2×C42—614no—
505C2×C42—614no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—1224no—
509C2×C42—1224no—
510C2×C42—1224no—
511C2×C42—2442no—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—614no—
522#95C22×D6114yes—
523#95C22×D6114yes—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24Q8×D6114yes—
531C24C23×D6112yes—
532C24C23×D6111yescharacteristic
533C2×Q8—1228no—
534C2×Q8—1228no—
535C2×Q8—1228no—
536C2×Q8—12232no—
537C2×Q8—1228no—
538C2×Q8—1228no—
539C2×Q8—2444no—
540C2×Q8—24416no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—614no—
561C22×C4—614no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—614no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4#1175822214yes—
593C22×C4D4×D6114yes—
594C22×C4#1175822414yes—
595C22×C4C23×D6112yes—
596C22×C4C23×D6112yes—
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—6116no—
604C4⋊C4—1228no—
605C4⋊C4—1228no—
606C4⋊C4—1228no—
607C4⋊C4—1228no—
608C4⋊C4—1228no—
609C4⋊C4—2444no—
610C4⋊C4—2444no—
611C22⋊C4—28no—
612C22⋊C4—44no—
613C22⋊C4—6116no—
614C22⋊C4—1228no—
615C22⋊C4—1228no—
616C22⋊C4—1228no—
617C42—1228no—
618C42—1228no—
619C42—1228no—
620C42—2444no—
621C23—28no—
622C23—28no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C2×D4×D6112yes—
635C23C2×Q8×D6114yes—
636C23C2×Q8×D6112yes—
637C23#41×D6112yes—
638C23C2×#1175822412yes—
639C23C2×#1175822212yes—
640C23#1451982212yes—
641C23#1451982412yes—
642C23C24×D6111yescharacteristic
643Q8—12232no—
644Q8—24416no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—614no—
668C2×C4—614no—
669C2×C4—614no—
670C2×C4—614no—
671C2×C4—614no—
672C2×C4—1228no—
673C2×C4—1228no—
674C2×C4—1228no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1228no—
686C2×C4—1228no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4—2444no—
699C2×C4C2×D4×D6114yes—
700C2×C4C2×#1175822414yes—
701C2×C4C2×#1175822214yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—416no—
708C22—42no—
709C22—42no—
710C22#1684027114yes—
711C22#1684031414yes—
712C22#1684038014yes—
713C22#1684039914yes—
714C22#1684042514yes—
715C22#1684046714yes—
716C22#1684048214yes—
717C22C22×D4×D6111yescharacteristic
718C22C22×Q8×D6111yescharacteristic
719C22C2×#41×D6111yescharacteristic
720C22C22×#1175822411yescharacteristic
721C22C22×#1175822211yescharacteristic
722C22C2×#1451982211yescharacteristic
723C22C2×#1451982411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1224no—
731C4—1224no—
732C4—1224no—
733C4—1224no—
734C4—1224no—
735C4—2442no—
736C4—2442no—
737C4—2442no—
738C2—44no—
739C2#2144984418yesdirect product factor
740C2C2×#1684027111yescharacteristic
741C2C2×#1684031411yescharacteristic
742C2C2×#1684038011yescharacteristic
743C2C2×#1684039911yescharacteristic
744C2C2×#1684042511yescharacteristic
745C2C2×#1684046711yescharacteristic
746C2C2×#1684048211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61C2×#2465
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
3. #21449844C2direct (N × H)
5. C2×#16839683C2semidirect
6. C2×#16839682C2semidirect
8. C2×#16839666C2semidirect
9. C2×#16839657C2semidirect
12. C2×#16839648C2semidirect
13. C2×#16839647C2semidirect
14. C2×#16839644C2semidirect
22. C2×#14519742C22semidirect
40. #16839683C22semidirect
41. #16839682C22semidirect
43. #16839666C22semidirect
44. #16839657C22semidirect
47. #16839648C22semidirect
48. #16839647C22semidirect
49. #16839644C22semidirect
106. C2×C22⋊Dic61Q8semidirect
234. C22⋊Dic61C2×Q8semidirect
382. C2×C61#2465semidirect
442. C61C2×#2465semidirect
739. C2#21449844direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197562
C22×#145197422
#214498442
C2×#168396852
C2×#168396832
C2×#168396822
C2×#168396742
C2×#168396662
C2×#168396572
C2×#168396562
C2×#168396482
C2×#168396472
C2×#168396442
C2×C4×C22⋊Dic612
C2×C61×#3852
C2×#246561