Finite Group Databasebeta

← C2×#21449639 #29847762

Subgroups — C2×#21449639 #29847762

Order 15616.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2#21449639C2116yesmaximal, direct product factor
3C2×#16839700C211yesmaximal, characteristic, complemented
4C2×#16839695C211yesmaximal, characteristic, complemented
5C2×#16839684C211yesmaximal, characteristic, complemented
6C2×#16839673C211yesmaximal, characteristic, complemented
7C2×#16839669C211yesmaximal, characteristic, complemented
8C2×#16839643C211yesmaximal, characteristic, complemented
9C2×#16839641C211yesmaximal, characteristic
10C2×#16839639C211yesmaximal, characteristic
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839634C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839619C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737—28no—
22C2×#14519737C2218yes—
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839700C2218yescomplemented
36#16839695C2218yescomplemented
37#16839684C2218yescomplemented
38#16839673C2218yescomplemented
39#16839669C2218yescomplemented
40#16839643C2218yescomplemented
41#16839641C2218yes—
42#16839639C2218yes—
43#16839637C2218yescomplemented
44#16839634C2218yescomplemented
45#16839633C2218yescomplemented
46#16839619C2218yescomplemented
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2218yescomplemented
60C23×Q8×C61C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C2×C22⋊Q8×C61—28no—
63C2×C22⋊Q8×C61C2218yescomplemented
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×C22⋊D61—24no—
71C22×C22⋊D61—24no—
72C22×C22⋊D61Q818yescomplemented
73C22×C22⋊D61C2314yes—
74C23×Dic61—24no—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61—42no—
78C23×Dic61—42no—
79C23×Dic61—42no—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2314yes—
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2314yes—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—42no—
92C22×C4×D61C2314yes—
93#14519737—232no—
94C2×C4⋊Dic61—42no—
95C2×C4⋊Dic61—42no—
96C2×C4⋊Dic61C2314yes—
97C2×C4⋊Dic61C2314yes—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196—42no—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×C22⋊Dic61—24no—
105C2×C22⋊Dic61C2314yes—
106C2×#11758198—24no—
107C2×#11758198—24no—
108C2×#11758198—42no—
109C2×#11758198—42no—
110C2×#11758198—42no—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×C4×Dic61—24no—
117C2×C4×Dic61C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130C25×C61C2311yescharacteristic
131C22×Q8×C61—24no—
132C22×Q8×C61—24no—
133C22×Q8×C61—42no—
134C22×Q8×C61C2314yes—
135C23×C4×C61—24no—
136C23×C4×C61—24no—
137C23×C4×C61—42no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2314yes—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C22⋊Q8×C61—232no—
146C2×C4⋊C4×C61—24no—
147C2×C4⋊C4×C61—24no—
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61C2314yes—
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2314yes—
152C2×C22⋊C4×C61—24no—
153C2×C22⋊C4×C61D418yes—
154C2×C22⋊C4×C61C2314yes—
155C2×C22⋊C4×C61C2314yes—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61C2×D414yes—
161C24×C61C2×Q814yes—
162C24×C61#4114yes—
163C24×C61C2412yes—
164C24×C61C2411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61C2×Q814yes—
172C23×D61C2412yes—
173C2×Q8×C61—28no—
174C2×Q8×C61—28no—
175C2×Q8×C61—44no—
176C2×Q8×C61—416no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—28no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—28no—
194C22×C4×C61—44no—
195C22×C4×C61—416no—
196C22×C4×C61C2×D414yes—
197C22×C4×C61C2×D414yes—
198C22×C4×C61#4114yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2412yes—
205C2×C22⋊D61—232no—
206C2×C22⋊D61—28no—
207C2×C22⋊D61—28no—
208C2×C22⋊D61C2×Q8116yescomplemented
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—28no—
215C22×Dic61—28no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—28no—
231C22×Dic61—44no—
232C22×Dic61—44no—
233C22×Dic61—44no—
234C22×Dic61—416no—
235C22×Dic61—416no—
236C22×Dic61C2×Q814yes—
237C22×Dic61#4114yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C2×C4×D61—28no—
246C2×C4×D61—28no—
247C2×C4×D61—44no—
248C2×C4×D61—416no—
249C4⋊C4×C61—28no—
250C4⋊C4×C61—28no—
251C4⋊C4×C61—28no—
252C22⋊C4×C61—28no—
253C22⋊C4×C61C2×D4116yes—
254C22⋊Dic61—28no—
255#11758198—28no—
256#11758198—28no—
257#11758198—44no—
258#11758198—44no—
259#11758198—44no—
260C4⋊Dic61—44no—
261C4⋊Dic61—44no—
262#11758196—28no—
263#11758196—28no—
264#11758196—44no—
265C4×Dic61—28no—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—28no—
271C23×C61—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61C22⋊Q8116yes—
277C23×C61C22×D414yes—
278C23×C61C22×D412yes—
279C23×C61C22×Q814yes—
280C23×C61C22×Q812yes—
281C23×C61C2×#4114yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C61H(5,𝔽2)12yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C22×Q814yes—
302Q8×C61—416no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—416no—
322C2×C4×C61—44no—
323C2×C4×C61—44no—
324C2×C4×C61—44no—
325C2×C4×C61C22×D414yes—
326C2×C4×C61C22×D414yes—
327C2×C4×C61C2×#4114yes—
328C22⋊D61—232no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—416no—
351C2×Dic61—416no—
352C2×Dic61—44no—
353C2×Dic61—44no—
354C2×Dic61—44no—
355C2×Dic61—44no—
356C2×Dic61—44no—
357C2×Dic61C22×Q814yes—
358C2×Dic61C2×#4114yes—
359C4×D61—416no—
360C2×#2450—611nomaximal, Sylow
361C22×C61—24no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61—24no—
367C22×C61—232no—
368C22×C61C2×C22⋊Q818yes—
369C22×C61C2×C22⋊Q814yes—
370C22×C61#52914yes—
371C22×C61#53814yes—
372C22×C61#54614yes—
373C22×C61#54614yes—
374C22×C61#55414yes—
375C22×C61#55414yes—
376C22×C61C23×D411yescharacteristic
377C22×C61C23×Q811yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C22×C61C2×H(5,𝔽2)11yescharacteristic
382C22×C61C2×H(5,𝔽2)11yescharacteristic
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—416no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397Dic61—24no—
398Dic61—24no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C22×C22⋊Q8D6111yescharacteristic, complemented
405C22×C4×D4—611no—
406#2450—6116no—
407C2×#400—611no—
408C2×#398—611no—
409C2×#396—611no—
410C2×#393—611no—
411C2×#391—611no—
412C2×#387—611no—
413C2×#386—611no—
414C2×#386—611no—
415C2×#385—611no—
416C2×#385—611no—
417C2×#385—611no—
418C2×#380—611no—
419C22×#95—611no—
420C2×C61—28no—
421C2×C61#245018yescomplemented
422C2×C61C22×C22⋊Q811yescharacteristic
423C2×C61C2×#52911yescharacteristic
424C2×C61C2×#53811yescharacteristic
425C2×C61C2×#54611yescharacteristic
426C2×C61C2×#54611yescharacteristic
427C2×C61C2×#55411yescharacteristic
428C2×C61C2×#55411yescharacteristic
429D61—44no—
430C23×Q8C2×D6111yescharacteristic
431C23×D4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C24×C4—611no—
435C24×C4C2×D6111yescharacteristic
436C2×C22⋊Q8—28no—
437C2×C22⋊Q8C2×D6118yescomplemented
438C2×C4×D4—618no—
439C2×C4×D4—1228no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4C2×D6111yescharacteristic
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4C2×D6111yescharacteristic
455C22×C22⋊C4C2×D6111yescharacteristic
456C22×C42—611no—
457#400—618no—
458#398—618no—
459#396—618no—
460#393—618no—
461#391—618no—
462#387—618no—
463#386—618no—
464#386—618no—
465#385—618no—
466#385—618no—
467#385—618no—
468#380—618no—
469C2×#95—611no—
470C2×#95—611no—
471C2×#95—611no—
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—618no—
479C2×#95—611no—
480C2×#95—611no—
481C2×#95—611no—
482C61C2×#245011yescharacteristic, complemented, Sylow
483C25—611no—
484C25C22×D6111yescharacteristic
485C22×Q8—24no—
486C22×Q8—24no—
487C22×Q8—42no—
488C22×Q8C22×D6114yes—
489C22×D4—618no—
490C22×D4—614no—
491C22×D4—1224no—
492C22×D4—1224no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—42no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—614no—
504C23×C4—614no—
505C23×C4—614no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—1224no—
511C23×C4—2442no—
512C23×C4—2442no—
513C23×C4—2442no—
514C23×C4—2442no—
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6114yes—
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C22⋊Q8—232no—
523C4×D4—12232no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—2442no—
535C2×C4⋊C4—2442no—
536C2×C4⋊C4—2442no—
537C2×C4⋊C4C22×D6114yes—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—1224no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—2442no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4C22⋊D6118yes—
554C2×C22⋊C4C22×D6114yes—
555C2×C22⋊C4C22×D6114yes—
556C2×C42—614no—
557C2×C42—1224no—
558#95—614no—
559#95—614no—
560#95—614no—
561#95—614no—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—614no—
575C24—612no—
576C24—1222no—
577C24—1222no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24Q8×D6114yes—
583C24#1175822614yes—
584C24C2×C22⋊D6114yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—28no—
588C2×Q8—28no—
589C2×Q8—44no—
590C2×Q8—416no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—1228no—
594C2×D4—12232no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—28no—
612C22×C4—44no—
613C22×C4—416no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1228no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1228no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1228no—
647C22×C4—2444no—
648C22×C4—24416no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—24416no—
653C22×C4—24416no—
654C22×C4#1175822414yes—
655C22×C4C2×C22⋊D6114yes—
656C22×C4C2×C22⋊D6114yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6112yes—
662C22×C4C23×D6112yes—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—2444no—
669C4⋊C4—2444no—
670C4⋊C4—2444no—
671C22⋊C4—28no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—2444no—
676C22⋊C4—2444no—
677C22⋊C4—2444no—
678C22⋊C4C2×C22⋊D61116yes—
679C42—1228no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—614no—
691C23—1228no—
692C23—1228no—
693C23—1228no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—2444no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23#14519753116yes—
705C23C22×C22⋊D6114yes—
706C23C22×C22⋊D6112yes—
707C23C2×Q8×D6114yes—
708C23C2×Q8×D6112yes—
709C23#41×D6112yes—
710C23C2×#1175822412yes—
711C23C2×#1175822614yes—
712C23C2×#1175822612yes—
713C23#1451982212yes—
714C23#1451982312yes—
715C23C24×D6111yescharacteristic
716Q8—416no—
717D4—12232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—1228no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1228no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—24416no—
764C2×C4—24416no—
765C2×C4—24416no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4C22×C22⋊D6114yes—
772C2×C4C22×C22⋊D6114yes—
773C2×C4C2×#1175822414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—232no—
780C22—24no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—24416no—
788C22—2442no—
789C22C2×#1451975318yes—
790C22C2×#1451975314yes—
791C22#1684029814yes—
792C22#1684035214yes—
793C22#1684040014yes—
794C22#1684040614yes—
795C22#1684046614yes—
796C22#1684047014yes—
797C22C23×C22⋊D6111yescharacteristic
798C22C22×Q8×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C22×#1175822411yescharacteristic
801C22C22×#1175822611yescharacteristic
802C22C2×#1451982211yescharacteristic
803C22C2×#1451982311yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—1224no—
811C4—1224no—
812C4—2442no—
813C4—2442no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—28no—
818C2—2444no—
819C2#2144963918yesdirect product factor
820C2C22×#1451975311yescharacteristic
821C2C2×#1684029811yescharacteristic
822C2C2×#1684035211yescharacteristic
823C2C2×#1684040011yescharacteristic
824C2C2×#1684040611yescharacteristic
825C2C2×#1684046611yescharacteristic
826C2C2×#1684047011yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×C22⋊Q8×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22×C22⋊Q8D61
hypocenterC61C2×#2450
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21449639C2direct (N × H)
3. C2×#16839700C2semidirect
4. C2×#16839695C2semidirect
5. C2×#16839684C2semidirect
6. C2×#16839673C2semidirect
7. C2×#16839669C2semidirect
8. C2×#16839643C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839634C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839619C2semidirect
15. C22×#14519684C2semidirect
16. C22×C22⋊Q8×C61C2semidirect
35. #16839700C22semidirect
36. #16839695C22semidirect
37. #16839684C22semidirect
38. #16839673C22semidirect
39. #16839669C22semidirect
40. #16839643C22semidirect
43. #16839637C22semidirect
44. #16839634C22semidirect
45. #16839633C22semidirect
46. #16839619C22semidirect
59. C2×#14519684C22semidirect
63. C2×C22⋊Q8×C61C22semidirect
72. C22×C22⋊D61Q8semidirect
208. C2×C22⋊D61C2×Q8semidirect
404. C22×C22⋊Q8D61semidirect
421. C2×C61#2450semidirect
437. C2×C22⋊Q8C2×D61semidirect
482. C61C2×#2450semidirect
819. C2#21449639direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
#214496392
C2×#168397002
C2×#168396952
C2×#168396842
C2×#168396732
C2×#168396692
C2×#168396432
C2×#168396412
C2×#168396392
C2×#168396372
C2×#168396342
C2×#168396332
C2×#168396192
C22×#145196842
C22×C22⋊Q8×C612
C2×#245061