Finite Group Databasebeta

← C2×#21449647 #29847770

Subgroups — C2×#21449647 #29847770

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×#14519756C211yesmaximal, characteristic, complemented
2C22×D4×Dic61C211yesmaximal, characteristic
3#21449647C2116yesmaximal, direct product factor
4C2×#16839704C211yesmaximal, characteristic, complemented
5C2×#16839694C211yesmaximal, characteristic, complemented
6C2×#16839685C211yesmaximal, characteristic, complemented
7C2×#16839674C211yesmaximal, characteristic, complemented
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839642C211yesmaximal, characteristic
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839637C211yesmaximal, characteristic, complemented
13C2×#16839634C211yesmaximal, characteristic, complemented
14C2×#16839620C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic, complemented
16C2×C61×#386C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C24×Dic61C2211yescharacteristic
21C2×#14519756—28no—
22C2×#14519756C2218yescomplemented
23C2×D4×Dic61—28no—
24C2×D4×Dic61C2218yes—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839704C2218yescomplemented
40#16839694C2218yescomplemented
41#16839685C2218yescomplemented
42#16839674C2218yescomplemented
43#16839666C2218yescomplemented
44#16839645C2218yescomplemented
45#16839642C2218yes—
46#16839637C2218yescomplemented
47#16839637C2218yescomplemented
48#16839634C2218yescomplemented
49#16839620C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2218yescomplemented
61C23×D4×C61C2211yescharacteristic
62C24×C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C61×#386C2218yes—
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—24no—
78C23×Dic61—42no—
79C23×Dic61—42no—
80C23×Dic61—42no—
81C23×Dic61—42no—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2314yes—
88C23×Dic61C2314yes—
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2314yes—
93#14519756—232no—
94D4×Dic61—232no—
95C2×C4⋊Dic61—24no—
96C2×C4⋊Dic61—24no—
97C2×C4⋊Dic61—24no—
98C2×C4⋊Dic61—42no—
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2314yes—
101C2×C4⋊Dic61C2314yes—
102C2×C4⋊Dic61C2314yes—
103C2×#11758196—24no—
104C2×#11758196—24no—
105C2×#11758196—42no—
106C2×#11758196—42no—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×C22⋊Dic61—24no—
112C2×C22⋊Dic61—24no—
113C2×C22⋊Dic61—42no—
114C2×C22⋊Dic61—42no—
115C2×C22⋊Dic61D418yes—
116C2×C22⋊Dic61C2314yes—
117C2×C22⋊Dic61C2314yes—
118C2×C22⋊Dic61C2314yes—
119C2×C22⋊Dic61C2314yes—
120C2×C22⋊Dic61C2314yes—
121C2×C4×Dic61—24no—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133C25×C61C2311yescharacteristic
134C25×C61C2311yescharacteristic
135C22×D4×C61—24no—
136C22×D4×C61—24no—
137C22×D4×C61Q818yescomplemented
138C22×D4×C61C2314yes—
139C23×C4×C61—24no—
140C23×C4×C61—24no—
141C23×C4×C61—42no—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2314yes—
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61—24no—
150C2×C22⋊C4×C61—42no—
151C2×C22⋊C4×C61C2314yes—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154#95×C61C2314yes—
155#95×C61C2314yes—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61C2×D414yes—
167C24×C61C2×Q814yes—
168C24×C61C2×Q814yes—
169C24×C61#4114yes—
170C24×C61C2412yes—
171C24×C61C2412yes—
172C24×C61C2411yescharacteristic
173C2×D4×C61—232no—
174C2×D4×C61—28no—
175C2×D4×C61—28no—
176C2×D4×C61C2×Q8116yescomplemented
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—28no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—28no—
192C22×C4×C61—44no—
193C22×C4×C61—416no—
194C22×C4×C61C2×Q814yes—
195C22×C4×C61#4114yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—28no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—28no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
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—28no—
225C22×Dic61—28no—
226C22×Dic61—28no—
227C22×Dic61—44no—
228C22×Dic61—44no—
229C22×Dic61—44no—
230C22×Dic61—44no—
231C22×Dic61—416no—
232C22×Dic61—416no—
233C22×Dic61—416no—
234C22×Dic61C2×D414yes—
235C22×Dic61C2×D414yes—
236C22×Dic61#4114yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C2×Dic122—28no—
246C2×Dic122—28no—
247C2×Dic122—44no—
248C2×Dic122—416no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61—28no—
251C22⋊C4×C61—44no—
252C22⋊Dic61—28no—
253C22⋊Dic61—28no—
254C22⋊Dic61—44no—
255C22⋊Dic61—44no—
256C22⋊Dic61C2×D4116yes—
257C4⋊Dic61—28no—
258C4⋊Dic61—28no—
259C4⋊Dic61—28no—
260C4⋊Dic61—44no—
261#11758196—28no—
262#11758196—28no—
263#11758196—44no—
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×C61—28no—
277C23×C61—28no—
278C23×C61—28no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—44no—
286C23×C61—44no—
287C23×C61—44no—
288C23×C61—44no—
289C23×C61C22⋊Q8116yes—
290C23×C61C22×D414yes—
291C23×C61C22×D412yes—
292C23×C61C22×Q814yes—
293C23×C61C22×Q814yes—
294C23×C61C22×Q812yes—
295C23×C61C2×#4114yes—
296C23×C61C2×#4112yes—
297C23×C61C2×#4112yes—
298C23×C61C2×#4112yes—
299C23×C61H(5,𝔽2)12yes—
300C23×C61H(5,𝔽2)12yes—
301C23×C61C2511yescharacteristic
302D4×C61—232no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—22no—
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—416no—
319C2×C4×C61—44no—
320C2×C4×C61—44no—
321C2×C4×C61—44no—
322C2×C4×C61C22×Q814yes—
323C2×C4×C61C2×#4114yes—
324C2×Dic61—28no—
325C2×Dic61—28no—
326C2×Dic61—28no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
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—416no—
349C2×Dic61—416no—
350C2×Dic61—416no—
351C2×Dic61—44no—
352C2×Dic61—44no—
353C2×Dic61—44no—
354C2×Dic61—44no—
355C2×Dic61—44no—
356C2×Dic61C22×D414yes—
357C2×Dic61C22×D414yes—
358C2×Dic61C2×#4114yes—
359Dic122—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×C61—24no—
369C22×C61—24no—
370C22×C61—24no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—416no—
376C22×C61C2×C22⋊Q818yes—
377C22×C61C2×C22⋊Q814yes—
378C22×C61#52914yes—
379C22×C61#53814yes—
380C22×C61#54614yes—
381C22×C61#54614yes—
382C22×C61#55414yes—
383C22×C61#55414yes—
384C22×C61C23×D411yescharacteristic
385C22×C61C23×Q811yescharacteristic
386C22×C61C22×#4111yescharacteristic
387C22×C61C22×#4111yescharacteristic
388C22×C61C22×#4111yescharacteristic
389C22×C61C2×H(5,𝔽2)11yescharacteristic
390C22×C61C2×H(5,𝔽2)11yescharacteristic
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—42no—
396Dic61—24no—
397Dic61—24no—
398Dic61—24no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C22×C22⋊Q8—611no—
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×#386D6111yescharacteristic
415C2×#385—611no—
416C2×#385—611no—
417C2×#385—611no—
418C2×#380—611no—
419C22×#95—611no—
420C2×C61—28no—
421C2×C61—44no—
422C2×C61#245018yescomplemented
423C2×C61C22×C22⋊Q811yescharacteristic
424C2×C61C2×#52911yescharacteristic
425C2×C61C2×#53811yescharacteristic
426C2×C61C2×#54611yescharacteristic
427C2×C61C2×#54611yescharacteristic
428C2×C61C2×#55411yescharacteristic
429C2×C61C2×#55411yescharacteristic
430C23×Q8—611no—
431C23×D4C2×D6111yescharacteristic
432C24×C4—611no—
433C24×C4—611no—
434C24×C4—611no—
435C24×C4C2×D6111yescharacteristic
436C2×C22⋊Q8—618no—
437C2×C22⋊Q8—1228no—
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⋊C4—611no—
446C22×C4⋊C4—611no—
447C22×C4⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4C2×D6111yescharacteristic
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#386C2×D6118yes—
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—618no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95—611no—
480C2×#95C2×D6111yescharacteristic
481C2×#95C2×D6111yescharacteristic
482C61C2×#245011yescharacteristic, complemented, Sylow
483C25C22×D6111yescharacteristic
484C25C22×D6111yescharacteristic
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×Q8—2442no—
489C22×D4—24no—
490C22×D4—24no—
491C22×D4Dic12218yescomplemented
492C22×D4C22×D6114yes—
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—611no—
504C23×C4—614no—
505C23×C4—614no—
506C23×C4—614no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—1224no—
511C23×C4—1224no—
512C23×C4—2442no—
513C23×C4—2442no—
514C23×C4—2442no—
515C23×C4—2442no—
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519C23×C4C22×D6114yes—
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C22⋊Q8—12232no—
523C4×D4—12232no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
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—1224no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4—1224no—
537C2×C4⋊C4—2442no—
538C2×C4⋊C4—2442no—
539C2×C4⋊C4—2442no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—618no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4C22×D6114yes—
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#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24C2×Dic12214yes—
581C24C2×Dic12214yes—
582C24D4×D6114yes—
583C24#1175822414yes—
584C24C23×D6112yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—1228no—
588C2×Q8—1228no—
589C2×Q8—2444no—
590C2×Q8—24416no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—232no—
594C2×D4C2×Dic122116yescomplemented
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
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—1228no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1228no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1228no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4—24416no—
654C22×C4—24416no—
655C22×C4—24416no—
656C22×C4C2×Dic12214yes—
657C22×C4#1175822414yes—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6112yes—
662C22×C4C23×D6112yes—
663C4⋊C4—1228no—
664C4⋊C4—1228no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—2444no—
669C4⋊C4—2444no—
670C4⋊C4—2444no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—44no—
674C22⋊C4—6116no—
675C22⋊C4—1228no—
676C22⋊C4—1228no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C42—1228no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23#14519754116yes—
704C23C2×D4×D6114yes—
705C23C2×D4×D6112yes—
706C23C22×Dic12214yes—
707C23C22×Dic12214yes—
708C23C22×Dic12212yes—
709C23#41×D6112yes—
710C23C2×#1175822414yes—
711C23C2×#1175822412yes—
712C23C2×#1175822412yes—
713C23#1451982212yes—
714C23#1451982312yes—
715C23C24×D6111yescharacteristic
716Q8—24416no—
717D4—232no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1228no—
747C2×C4—1228no—
748C2×C4—1228no—
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—1222no—
764C2×C4—24416no—
765C2×C4—24416no—
766C2×C4—24416no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4—2444no—
772C2×C4C22×Dic12214yes—
773C2×C4C2×#1175822414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—232no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—416no—
788C22—42no—
789C22C2×#1451975418yes—
790C22C2×#1451975414yes—
791C22#1684029314yes—
792C22#1684034914yes—
793C22#1684039914yes—
794C22#1684040414yes—
795C22#1684046914yes—
796C22#1684047114yes—
797C22C22×D4×D6111yescharacteristic
798C22C23×Dic12211yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C22×#1175822411yescharacteristic
801C22C22×#1175822411yescharacteristic
802C22C2×#1451982211yescharacteristic
803C22C2×#1451982311yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—1224no—
810C4—1224no—
811C4—1224no—
812C4—2442no—
813C4—2442no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—28no—
818C2—44no—
819C2#2144964718yesdirect product factor
820C2C22×#1451975411yescharacteristic
821C2C2×#1684029311yescharacteristic
822C2C2×#1684034911yescharacteristic
823C2C2×#1684039911yescharacteristic
824C2C2×#1684040411yescharacteristic
825C2C2×#1684046911yescharacteristic
826C2C2×#1684047111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#386C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#386D61
hypocenterC61C2×#2450
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#14519756C2semidirect
3. #21449647C2direct (N × H)
4. C2×#16839704C2semidirect
5. C2×#16839694C2semidirect
6. C2×#16839685C2semidirect
7. C2×#16839674C2semidirect
8. C2×#16839666C2semidirect
9. C2×#16839645C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839637C2semidirect
13. C2×#16839634C2semidirect
14. C2×#16839620C2semidirect
15. C22×#14519684C2semidirect
22. C2×#14519756C22semidirect
39. #16839704C22semidirect
40. #16839694C22semidirect
41. #16839685C22semidirect
42. #16839674C22semidirect
43. #16839666C22semidirect
44. #16839645C22semidirect
46. #16839637C22semidirect
47. #16839637C22semidirect
48. #16839634C22semidirect
49. #16839620C22semidirect
60. C2×#14519684C22semidirect
137. C22×D4×C61Q8semidirect
176. C2×D4×C61C2×Q8semidirect
422. C2×C61#2450semidirect
482. C61C2×#2450semidirect
491. C22×D4Dic122semidirect
594. C2×D4C2×Dic122semidirect
819. C2#21449647direct (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×D4×Dic612
#214496472
C2×#168397042
C2×#168396942
C2×#168396852
C2×#168396742
C2×#168396662
C2×#168396452
C2×#168396422
C2×#168396372
C2×#168396342
C2×#168396202
C22×#145196842
C2×C61×#3862
C2×#245061