Finite Group Databasebeta

← C2×#21449501 #29848666

Subgroups — C2×#21449501 #29848666

Order 15616.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2C22×#14519733C211yesmaximal, characteristic
3#21449501C2116yesmaximal, direct product factor
4C2×#16839703C211yesmaximal, characteristic, complemented
5C2×#16839696C211yesmaximal, characteristic, complemented
6C2×#16839693C211yesmaximal, characteristic, complemented
7C2×#16839682C211yesmaximal, characteristic, complemented
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839648C211yesmaximal, characteristic, complemented
11C2×#16839644C211yesmaximal, characteristic, complemented
12C2×#16839635C211yesmaximal, characteristic
13C2×#16839634C211yesmaximal, characteristic
14C2×#16839623C211yesmaximal, characteristic
15C22×#14519684C211yesmaximal, characteristic
16C2×C61×#380C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754—28no—
21C2×#14519754C2218yes—
22C2×#14519733—28no—
23C2×#14519733C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839703C2218yescomplemented
38#16839696C2218yescomplemented
39#16839693C2218yescomplemented
40#16839682C2218yescomplemented
41#16839666C2218yescomplemented
42#16839657C2218yescomplemented
43#16839648C2218yescomplemented
44#16839644C2218yescomplemented
45#16839635C2218yes—
46#16839634C2218yes—
47#16839623C2218yes—
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2218yes—
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×#380C2218yes—
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C22×Dic122—24no—
70C22×Dic122—24no—
71C22×Dic122—42no—
72C22×Dic122C2314yes—
73C23×Dic61—24no—
74C23×Dic61—24no—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61—42no—
78C23×Dic61Q818yescomplemented
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2314yes—
88C23×Dic61C2311yescharacteristic
89#14519754—232no—
90#14519733—232no—
91C2×C4⋊Dic61—24no—
92C2×C4⋊Dic61C2314yes—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—42no—
100C2×#11758196—42no—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×C22⋊Dic61—24no—
110C2×C22⋊Dic61D418yes—
111C2×C22⋊Dic61C2314yes—
112C2×C22⋊Dic61C2314yes—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
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×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2314yes—
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61—42no—
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61—24no—
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×C61C2×D414yes—
155C24×C61C2×Q814yes—
156C24×C61#4114yes—
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—28no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—28no—
178C22×C4×C61—44no—
179C22×C4×C61—416no—
180C22×C4×C61#4114yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×Dic61—232no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—28no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—28no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—28no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—28no—
211C22×Dic61—44no—
212C22×Dic61—416no—
213C22×Dic61C2×D414yes—
214C22×Dic61C2×D414yes—
215C22×Dic61C2×Q814yes—
216C22×Dic61C2×Q814yes—
217C22×Dic61C2×Q8116yescomplemented
218C22×Dic61#4114yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×Dic122—28no—
228C2×Dic122—28no—
229C2×Dic122—44no—
230C2×Dic122—416no—
231C4⋊C4×C61—28no—
232C4⋊C4×C61—44no—
233C22⋊C4×C61—28no—
234C22⋊C4×C61—28no—
235C22⋊Dic61—28no—
236C22⋊Dic61C2×D4116yes—
237C4⋊Dic61—28no—
238#11758196—28no—
239#11758196—28no—
240#11758196—28no—
241#11758196—28no—
242#11758196—28no—
243#11758196—28no—
244#11758196—44no—
245#11758196—44no—
246C4×Dic61—28no—
247C4×Dic61—28no—
248C23×C61—28no—
249C23×C61—28no—
250C23×C61—28no—
251C23×C61—28no—
252C23×C61—28no—
253C23×C61—28no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61C22⋊Q8116yes—
259C23×C61C22×D414yes—
260C23×C61C22×D412yes—
261C23×C61C22×Q814yes—
262C23×C61C22×Q812yes—
263C23×C61C2×#4114yes—
264C23×C61C2×#4112yes—
265C23×C61C2×#4112yes—
266C23×C61C2×#4112yes—
267C23×C61H(5,𝔽2)12yes—
268C23×C612−1+412yes—
269C23×C61C2511yescharacteristic
270C2×C4×C61—28no—
271C2×C4×C61—22no—
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—22no—
288C2×C4×C61—416no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61—44no—
292C2×C4×C61—44no—
293C2×C4×C61—44no—
294C2×C4×C61C2×#4114yes—
295C2×Dic61—28no—
296C2×Dic61—28no—
297C2×Dic61—232no—
298C2×Dic61—28no—
299C2×Dic61—28no—
300C2×Dic61—28no—
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—22no—
319C2×Dic61—22no—
320C2×Dic61—416no—
321C2×Dic61—44no—
322C2×Dic61—44no—
323C2×Dic61—44no—
324C2×Dic61C22×D414yes—
325C2×Dic61C22×D414yes—
326C2×Dic61C22×Q814yes—
327C2×Dic61C22×Q814yes—
328C2×Dic61C2×#4114yes—
329Dic122—416no—
330C2×#2438—611nomaximal, Sylow
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—232no—
334C22×C61—24no—
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61C2×C22⋊Q818yes—
339C22×C61C2×C22⋊Q814yes—
340C22×C61#53314yes—
341C22×C61#54414yes—
342C22×C61#54614yes—
343C22×C61#54714yes—
344C22×C61#55114yes—
345C22×C61#55214yes—
346C22×C61C23×D411yescharacteristic
347C22×C61C23×Q811yescharacteristic
348C22×C61C22×#4111yescharacteristic
349C22×C61C22×#4111yescharacteristic
350C22×C61C22×#4111yescharacteristic
351C22×C61C2×H(5,𝔽2)11yescharacteristic
352C22×C61C2×2−1+411yescharacteristic
353C4×C61—24no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—42no—
359Dic61—24no—
360Dic61—24no—
361Dic61—24no—
362Dic61—24no—
363Dic61—24no—
364Dic61—42no—
365Dic61—42no—
366Dic61—42no—
367C22×C22⋊Q8—611no—
368C22×#117—611no—
369#2438—6116no—
370C2×#400—611no—
371C2×#398—611no—
372C2×#398—611no—
373C2×#395—611no—
374C2×#391—611no—
375C2×#389—611no—
376C2×#387—611no—
377C2×#387—611no—
378C2×#385—611no—
379C2×#385—611no—
380C2×#381—611no—
381C2×#380D6111yescharacteristic
382C22×#95—611no—
383C2×C61—28no—
384C2×C61#243818yescomplemented
385C2×C61C22×C22⋊Q811yescharacteristic
386C2×C61C2×#53311yescharacteristic
387C2×C61C2×#54411yescharacteristic
388C2×C61C2×#54611yescharacteristic
389C2×C61C2×#54711yescharacteristic
390C2×C61C2×#55111yescharacteristic
391C2×C61C2×#55211yescharacteristic
392C23×Q8—611no—
393C24×C4—611no—
394C24×C4—611no—
395C24×C4C2×D6111yescharacteristic
396C2×C22⋊Q8—618no—
397C2×C22⋊Q8—1228no—
398C2×#117—618no—
399C2×#117—1228no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4C2×D6111yescharacteristic
410C22×C4⋊C4C2×D6111yescharacteristic
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4C2×D6111yescharacteristic
414C22×C22⋊C4C2×D6111yescharacteristic
415C22×C42—611no—
416C22×C42—611no—
417#400—618no—
418#398—618no—
419#398—618no—
420#395—618no—
421#391—618no—
422#389—618no—
423#387—618no—
424#387—618no—
425#385—618no—
426#385—618no—
427#381—618no—
428#380C2×D6118yes—
429C2×#95—611no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—618no—
438C2×#95—611no—
439C2×#95—611no—
440C2×#95—611no—
441C2×#95—611no—
442C2×#95C2×D6111yescharacteristic
443C2×#95C2×D6111yescharacteristic
444C61C2×#243811yescharacteristic, complemented, Sylow
445C25C22×D6111yescharacteristic
446C22×Q8—614no—
447C22×Q8—1224no—
448C22×Q8—1224no—
449C22×Q8—2442no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—42no—
453C23×C4—618no—
454C23×C4—614no—
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×C4—614no—
464C23×C4—1224no—
465C23×C4—1224no—
466C23×C4—1224no—
467C23×C4—1224no—
468C23×C4—2442no—
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6114yes—
475C23×C4C22×D6111yescharacteristic
476C22⋊Q8—12232no—
477#117—12232no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—614no—
489C2×C4⋊C4—1224no—
490C2×C4⋊C4—1224no—
491C2×C4⋊C4—1224no—
492C2×C4⋊C4—1224no—
493C2×C4⋊C4—1224no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—2442no—
497C2×C4⋊C4—2442no—
498C2×C4⋊C4C22×D6114yes—
499C2×C4⋊C4C22×D6114yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—618no—
503C2×C22⋊C4—614no—
504C2×C22⋊C4—614no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4C22×D6114yes—
507C2×C22⋊C4C22×D6114yes—
508C2×C42—614no—
509C2×C42—614no—
510C2×C42—1224no—
511C2×C42—1224no—
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#95—614no—
523#95—614no—
524#95C22×D6114yes—
525#95C22×D6114yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24#1175822214yes—
531C24D4×D6114yes—
532C24Q8×D6114yes—
533C24C23×D6112yes—
534C24C23×D6111yescharacteristic
535C2×Q8—1228no—
536C2×Q8—1228no—
537C2×Q8—2444no—
538C2×Q8—24416no—
539C22×C4—22no—
540C22×C4—22no—
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—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—614no—
561C22×C4—614no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—6116no—
565C22×C4—614no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—1228no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1228no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1228no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—12232no—
588C22×C4—1222no—
589C22×C4—1228no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—2444no—
599C22×C4—24416no—
600C22×C4#1175822414yes—
601C22×C4C23×D6112yes—
602C22×C4C23×D6112yes—
603C22×C4C23×D6112yes—
604C22×C4C23×D6112yes—
605C22×C4C23×D6112yes—
606C22×C4C23×D6112yes—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—1228no—
610C4⋊C4—1228no—
611C4⋊C4—1228no—
612C4⋊C4—1228no—
613C4⋊C4—1228no—
614C4⋊C4—1228no—
615C4⋊C4—1228no—
616C4⋊C4—2444no—
617C4⋊C4—2444no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—6116no—
621C22⋊C4—1228no—
622C42—1228no—
623C42—1228no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23#14519755116yes—
635C23C2×D4×D6114yes—
636C23C2×D4×D6112yes—
637C23C2×Q8×D6114yes—
638C23C2×Q8×D6112yes—
639C23#41×D6112yes—
640C23C2×#1175822412yes—
641C23C2×#1175822214yes—
642C23C2×#1175822212yes—
643C23#1451982212yes—
644C23#1451982412yes—
645C23C24×D6111yescharacteristic
646Q8—24416no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
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—22no—
664C2×C4—22no—
665C2×C4—416no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—614no—
672C2×C4—614no—
673C2×C4—614no—
674C2×C4—614no—
675C2×C4—614no—
676C2×C4—12232no—
677C2×C4—1228no—
678C2×C4—1228no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1228no—
690C2×C4—1228no—
691C2×C4—1228no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—24416no—
702C2×C4—2444no—
703C2×C4—2444no—
704C2×C4—2444no—
705C2×C4C2×#1175822414yes—
706C22—24no—
707C22—232no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—24no—
713C22C2×#1451975518yes—
714C22C2×#1451975514yes—
715C22#1684031414yes—
716C22#1684039114yes—
717C22#1684040114yes—
718C22#1684041214yes—
719C22#1684043814yes—
720C22#1684044514yes—
721C22C22×D4×D6111yescharacteristic
722C22C22×Q8×D6111yescharacteristic
723C22C2×#41×D6111yescharacteristic
724C22C22×#1175822411yescharacteristic
725C22C22×#1175822211yescharacteristic
726C22C2×#1451982211yescharacteristic
727C22C2×#1451982411yescharacteristic
728C4—24no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—1224no—
735C4—1224no—
736C4—1224no—
737C4—1224no—
738C4—1224no—
739C4—2442no—
740C4—2442no—
741C4—2442no—
742C2—28no—
743C2#2144950118yesdirect product factor
744C2C22×#1451975511yescharacteristic
745C2C2×#1684031411yescharacteristic
746C2C2×#1684039111yescharacteristic
747C2C2×#1684040111yescharacteristic
748C2C2×#1684041211yescharacteristic
749C2C2×#1684043811yescharacteristic
750C2C2×#1684044511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#380C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#380D61
hypocenterC61C2×#2438
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #21449501C2direct (N × H)
4. C2×#16839703C2semidirect
5. C2×#16839696C2semidirect
6. C2×#16839693C2semidirect
7. C2×#16839682C2semidirect
8. C2×#16839666C2semidirect
9. C2×#16839657C2semidirect
10. C2×#16839648C2semidirect
11. C2×#16839644C2semidirect
37. #16839703C22semidirect
38. #16839696C22semidirect
39. #16839693C22semidirect
40. #16839682C22semidirect
41. #16839666C22semidirect
42. #16839657C22semidirect
43. #16839648C22semidirect
44. #16839644C22semidirect
78. C23×Dic61Q8semidirect
217. C22×Dic61C2×Q8semidirect
384. C2×C61#2438semidirect
444. C61C2×#2438semidirect
743. C2#21449501direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×#145197332
#214495012
C2×#168397032
C2×#168396962
C2×#168396932
C2×#168396822
C2×#168396662
C2×#168396572
C2×#168396482
C2×#168396442
C2×#168396352
C2×#168396342
C2×#168396232
C22×#145196842
C2×C61×#3802
C2×#243861