Finite Group Databasebeta

← #30614508

Subgroups — #30614508

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic
2C2×SD16×#6923C211yesmaximal, characteristic
3#21462259C211yesmaximal, characteristic, complemented
4#21462258C211yesmaximal, characteristic
5#21461634C211yesmaximal, characteristic, complemented
6#21461633C211yesmaximal, characteristic, complemented
7#107×#6923C211yesmaximal, characteristic, complemented
8#21461592C211yesmaximal, characteristic, complemented
9#21461590C211yesmaximal, characteristic
10#103×#6923C211yesmaximal, characteristic, complemented
11C4×#14519840C211yesmaximal, characteristic, complemented
12#102×#6923C211yesmaximal, characteristic
13C4×#14519839C211yesmaximal, characteristic
14#21461477C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801C418yescomplemented
21SD16×#6923C418yescomplemented
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519831C2211yescharacteristic
29C2×#14519831C2211yescharacteristic
30C4×D61⋊C8C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33C4⋊C4×#6923—21no—
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4×C4⋊#6923—21no—
40C4×C4⋊#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42C22⋊C4×#6923—21no—
43C22⋊C4×#6923—21no—
44C4×C22⋊#6923—21no—
45#16840698—21no—
46#16840698C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C4×Q8×D61C2211yescharacteristic
56C4×D4×D61C2211yescharacteristic
57#16839865C411yescharacteristic, complemented
58#16839864C411yescharacteristic, complemented
59#16839863C411yescharacteristic, complemented
60#16839862C411yescharacteristic, complemented
61#16839861C411yescharacteristic, complemented
62#16839860C411yescharacteristic, complemented
63#16839859C411yescharacteristic, complemented
64#107×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#97×D61C2211yescharacteristic
68C61×#440C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923C2×C414yescomplemented
76Q8×#6923C2×C414yescomplemented
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923C2×C414yes—
80D4×#6923C2×C414yes—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846C2×C414yescomplemented
100#14519845C2×C414yescomplemented
101#14519840C2×C414yescomplemented
102#14519840C2×C414yescomplemented
103#14519839C2×C414yes—
104#14519839C2×C414yes—
105#14519831—22no—
106#14519831C2×C414yescomplemented
107C4×#92420—21no—
108C4×#92420—21no—
109C8×#6923—22no—
110C8×#6923C2×C414yescomplemented
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61C2311yescharacteristic
123C22×C4×D61—21no—
124C2×#11758190C2×C411yescharacteristic
125C2×#11758200C2×C411yescharacteristic
126C2×#11758201C2×C411yescharacteristic
127SD16×D61C2×C414yes—
128SD16×D61C2×C414yes—
129C2×C8×D61C2311yescharacteristic
130C2×C8×D61C2311yescharacteristic
131Q8×Dic61C2×C411yescharacteristic, complemented
132C4×Dic122—21no—
133C4×Dic122C2×C411yescharacteristic, complemented
134#14519742—21no—
135#14519742C2×C411yescharacteristic, complemented
136C4×D244C2×C411yescharacteristic
137D4×Dic61C2×C411yescharacteristic
138#14519739C2×C411yescharacteristic
139C4×C22⋊D61—21no—
140#14519737—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144C22⋊C4×D61—21no—
145C42×D61—21no—
146C42×D61C2311yescharacteristic
147#14519711C2×C411yescharacteristic, complemented
148#14519710C2×C411yescharacteristic, complemented
149#14519710C2×C411yescharacteristic, complemented
150#14519702C2×C411yescharacteristic, complemented
151#14519701C2×C411yescharacteristic, complemented
152#14519700C2×C411yescharacteristic, complemented
153#14519699C2×C411yescharacteristic
154#14519698C2×C411yescharacteristic
155#14519697C2×C411yescharacteristic
156#14519688C2×C411yescharacteristic, complemented
157#14519687C2×C411yescharacteristic, complemented
158#14519687C2×C411yescharacteristic, complemented
159C2×SD16×C61C2×C411yescharacteristic
160C4×Q8×C61C2×C411yescharacteristic, complemented
161C4×D4×C61C2×C411yescharacteristic
162#107×C61C2×C411yescharacteristic, complemented
163#103×C61C2×C411yescharacteristic, complemented
164#102×C61C2×C411yescharacteristic
165#97×C61C2×C411yescharacteristic, complemented
166C23×D61—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—24no—
172C22×#6923—24no—
173C22×#6923—81no—
174C22×#6923—81no—
175C22×#6923—81no—
176C22×#6923—81no—
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C2×C22⋊D61—21no—
185C22×Dic61—21no—
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61C22×C412yes—
189Q8×D61C22×C412yes—
190D4×D61—21no—
191D4×D61—21no—
192D4×D61C22×C412yes—
193D4×D61C22×C412yes—
194C2×D244C22×C411yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2411yescharacteristic
205C2×Dic122—21no—
206C2×Dic122C22×C411yescharacteristic
207C22⋊#6923—24no—
208C22⋊#6923—24no—
209C2×#92420—21no—
210C2×#92420—21no—
211C4⋊#6923—24no—
212C4⋊#6923—24no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923C22×C412yes—
218C4⋊#6923C22×C412yes—
219C4⋊#6923C22×C412yes—
220C4⋊#6923C22×C412yes—
221C4×#6923—24no—
222C4×#6923—24no—
223C4×#6923—81no—
224C4×#6923—81no—
225C4×#6923—81no—
226C4×#6923—81no—
227C4×#6923—81no—
228C4×#6923—81no—
229C4×#6923C22×C412yes—
230C4×#6923C22×C412yes—
231C4×#6923#4112yes—
232C4×#6923#4112yes—
233D61⋊C8—21no—
234D61⋊C8—21no—
235D61⋊C8C22×C412yes—
236D61⋊C8C22×C412yes—
237SD16×C61C4214yescomplemented
238C2×C8×C61C22×C411yescharacteristic
239C2×C8×C61C22×C411yescharacteristic
240C4⋊C4×C61—21no—
241C4⋊C4×C61C22×C411yescharacteristic
242C4⋊C4×C61C22×C411yescharacteristic
243C22⋊C4×C61—21no—
244C42×C61—21no—
245C42×C61C22×C411yescharacteristic
246C22⋊Dic61—21no—
247#11758201C4214yescomplemented
248#11758200C4214yescomplemented
249#11758198—21no—
250#11758198—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C411yescharacteristic
253C4⋊Dic61C22×C411yescharacteristic
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61C22×C411yescharacteristic
262C4×Dic61#4111yescharacteristic
263C4×Dic61#4111yescharacteristic
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758190C4214yescomplemented
267C8×D61—21no—
268C8×D61—21no—
269C8×D61C22×C412yes—
270C8×D61C22×C412yes—
271C23×C61—21no—
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61C22×D411yescharacteristic
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—22no—
289C2×#6923—22no—
290C2×#6923—22no—
291C2×#6923—22no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—84no—
301C2×#6923—84no—
302C2×#6923C4×D412yes—
303C2×#6923C4×D412yes—
304C2×#6923C4×D412yes—
305C2×#6923C4×D412yes—
306Q8×C61—21no—
307Q8×C61C2×C4212yes—
308D4×C61—21no—
309D4×C61C2×C4212yes—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—81no—
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C22⋊D61—22no—
318C22⋊D61—22no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—81no—
323C2×Dic61C4×D411yescharacteristic
324C2×Dic61C4×D411yescharacteristic
325C2×Dic61C2×#4111yescharacteristic
326D244—21no—
327D244C2×C4212yes—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—81no—
339C4×D61—81no—
340C4×D61C23×C411yescharacteristic
341C4×D61C23×C411yescharacteristic
342C4×D61C2×#4111yescharacteristic
343C4×D61C2×#4111yescharacteristic
344Dic122—21no—
345Dic122—22no—
346Dic122—22no—
347Dic122C2×C4212yes—
348#92420—22no—
349#92420—22no—
350C8×C61—21no—
351C8×C61C2×C4212yes—
352#92418—21no—
353#92418C2×C4212yes—
354#20504—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×C4×D411yescharacteristic
359C2×D61—22no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61C2×C4×D411yescharacteristic
367C2×D61C2×C4×D411yescharacteristic
368C2×D61#57611yescharacteristic
369C2×D61#57711yescharacteristic
370C2×D61#57711yescharacteristic
371C2×D61#57811yescharacteristic
372#6923—22no—
373#6923—22no—
374#6923—22no—
375#6923—22no—
376#6923—42no—
377#6923—42no—
378#6923—42no—
379#6923—42no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—22no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61C22×C4211yescharacteristic
386C4×C61C4×#4111yescharacteristic
387Dic61—21no—
388Dic61—21no—
389Dic61—22no—
390Dic61—41no—
391Dic61—41no—
392Dic61C4×#4111yescharacteristic
393Dic61C4×#4111yescharacteristic
394C2×#440—611no—
395C2×#440—611no—
396C2×C4×SD16—611no—
397#2276—611no—
398#2275—611no—
399#1776—611no—
400#1776—611no—
401C4×#107—611no—
402#1763—611no—
403#1762—611no—
404C4×#103—611no—
405C4×#103—611no—
406C4×#102—611no—
407C4×#102—611no—
408#1726—611no—
409C2×C61—42no—
410C2×C61C42×D411yescharacteristic
411C2×C61#294611yescharacteristic
412C2×C61#294711yescharacteristic
413D61—42no—
414D61#294611yescharacteristic
415D61#294711yescharacteristic
416D61#294911yescharacteristic
417D61#295111yescharacteristic
418C22×SD16—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×Q8—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425#440—618no—
426#440—611no—
427#440—611no—
428#440—611no—
429#440—611no—
430#440—611no—
431#440—611no—
432#440—611no—
433#440#692311yescharacteristic, complemented
434C4×SD16—618no—
435C2×#107—611no—
436C2×#107—611no—
437C2×#106—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#97—611no—
445C2×#97—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448C2×C4×C8—611no—
449C2×C4×C8—611no—
450C4×C4⋊C4—611no—
451C4×C4⋊C4—611no—
452C4×C4⋊C4—611no—
453C4×C4⋊C4—611no—
454C4×C4⋊C4—611no—
455C4×C4⋊C4—611no—
456C4×C4⋊C4—1221no—
457C4×C4⋊C4—1221no—
458C4×C4⋊C4—1221no—
459C4×C22⋊C4—1221no—
460C4×C22⋊C4—1221no—
461C4×C22⋊C4—1221no—
462#376—611no—
463#376—1221no—
464C2×#95—1221no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#340—611no—
471C61#2050411yescharacteristic, complemented, Sylow
472C22×Q8—611no—
473C22×D4—611no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C2×SD16—611no—
478C2×SD16—611no—
479C2×SD16—614no—
480C2×SD16—614no—
481C2×SD16—611no—
482C2×SD16C2×#692311yescharacteristic
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C4×Q8—614no—
488C4×Q8—614no—
489C4×Q8—611no—
490C4×Q8—611no—
491C4×Q8—611no—
492C4×Q8—1221no—
493C4×Q8—1221no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×Q8C2×#692311yescharacteristic, complemented
497C4×D4—614no—
498C4×D4—614no—
499C4×D4—611no—
500C4×D4—611no—
501C4×D4—611no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4C2×#692311yescharacteristic
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531#107—614no—
532#107—611no—
533#107—611no—
534#107—611no—
535#107C2×#692311yescharacteristic, complemented
536#106—614no—
537#103—614no—
538#103—614no—
539#103—611no—
540#103—611no—
541#103—611no—
542#103C2×#692311yescharacteristic, complemented
543#102—614no—
544#102—614no—
545#102—611no—
546#102—611no—
547#102—611no—
548#102C2×#692311yescharacteristic
549#97—614no—
550#97—611no—
551#97—611no—
552#97—611no—
553#97—1222no—
554#97C2×#692311yescharacteristic, complemented
555C4×C8—614no—
556C4×C8—1222no—
557C4×C8—1221no—
558C4×C8—1221no—
559#95—611no—
560#95—611no—
561#95—611no—
562#95—611no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—1221no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—611no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8C22×#692311yescharacteristic
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—611no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4C22×#692311yescharacteristic
584C22×C4—21no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1224no—
598C22×C4—1224no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—4881no—
605C22×C4—4881no—
606C22×C4—4881no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—4881no—
610SD16—614no—
611SD16—614no—
612SD16—614no—
613SD16C4×#692314yescomplemented
614C2×C8—611no—
615C2×C8—612no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—612no—
619C2×C8—611no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8C22×#692311yescharacteristic
627C2×C8C22×#692311yescharacteristic
628C4⋊C4—21no—
629C4⋊C4—612no—
630C4⋊C4—612no—
631C4⋊C4—612no—
632C4⋊C4—612no—
633C4⋊C4—611no—
634C4⋊C4—611no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1221no—
646C4⋊C4C22×#692311yescharacteristic
647C4⋊C4C22×#692311yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1221no—
654C42—21no—
655C42—612no—
656C42—612no—
657C42—612no—
658C42—612no—
659C42—611no—
660C42—611no—
661C42—611no—
662C42—1221no—
663C42—1221no—
664C42—1224no—
665C42—1224no—
666C42—1221no—
667C42—4881no—
668C42—4881no—
669C42—4881no—
670C42—4881no—
671C42—4881no—
672C42—4881no—
673C42C22×#692311yescharacteristic
674C23—21no—
675C23—611no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683Q8—21no—
684Q8—612no—
685Q8—1222no—
686Q8—1222no—
687Q8—1221no—
688Q8C2×C4×#692312yes—
689D4—21no—
690D4—612no—
691D4—1222no—
692D4—1222no—
693D4—1221no—
694D4C2×C4×#692312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—81no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—4881no—
732C2×C4—4881no—
733C2×C4—4881no—
734C2×C4—4884no—
735C2×C4—4884no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4D4×#692311yescharacteristic
749C2×C4D4×#692311yescharacteristic
750C2×C4C23×#692311yescharacteristic
751C8—21no—
752C8—612no—
753C8—1222no—
754C8—1222no—
755C8—1221no—
756C8C2×C4×#692312yes—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—611no—
761C22—611no—
762C22—611no—
763C22—611no—
764C22—611no—
765C22—611no—
766C22—1222no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22—2441no—
772C22—2441no—
773C22C2×D4×#692311yescharacteristic
774C4—21no—
775C4—21no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—611no—
780C4—611no—
781C4—1222no—
782C4—1222no—
783C4—1222no—
784C4—1222no—
785C4—1221no—
786C4—1221no—
787C4—1222no—
788C4—2442no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4—2441no—
793C4—2441no—
794C4C22×C4×#692311yescharacteristic
795C4#41×#692311yescharacteristic
796C2—42no—
797C2—611no—
798C2—611no—
799C2—611no—
800C2—611no—
801C2—2442no—
802C2C4×D4×#692311yescharacteristic
803C2#2146257611yescharacteristic
804C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#440#6923
hypocenterC61#20504
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #21462259C2semidirect
5. #21461634C2semidirect
6. #21461633C2semidirect
7. #107×#6923C2semidirect
8. #21461592C2semidirect
10. #103×#6923C2semidirect
11. C4×#14519840C2semidirect
14. #21461477C2semidirect
20. #16840801C4semidirect
21. SD16×#6923C4semidirect
57. #16839865C4semidirect
58. #16839864C4semidirect
59. #16839863C4semidirect
60. #16839862C4semidirect
61. #16839861C4semidirect
62. #16839860C4semidirect
63. #16839859C4semidirect
68. C61×#440C4semidirect
75. Q8×#6923C2×C4semidirect
76. Q8×#6923C2×C4semidirect
99. #14519846C2×C4semidirect
100. #14519845C2×C4semidirect
101. #14519840C2×C4semidirect
102. #14519840C2×C4semidirect
106. #14519831C2×C4semidirect
110. C8×#6923C2×C4semidirect
131. Q8×Dic61C2×C4semidirect
133. C4×Dic122C2×C4semidirect
135. #14519742C2×C4semidirect
147. #14519711C2×C4semidirect
148. #14519710C2×C4semidirect
149. #14519710C2×C4semidirect
150. #14519702C2×C4semidirect
151. #14519701C2×C4semidirect
152. #14519700C2×C4semidirect
156. #14519688C2×C4semidirect
157. #14519687C2×C4semidirect
158. #14519687C2×C4semidirect
160. C4×Q8×C61C2×C4semidirect
162. #107×C61C2×C4semidirect
163. #103×C61C2×C4semidirect
165. #97×C61C2×C4semidirect
237. SD16×C61C42semidirect
247. #11758201C42semidirect
248. #11758200C42semidirect
266. #11758190C42semidirect
433. #440#6923semidirect
471. C61#20504semidirect
496. C4×Q8C2×#6923semidirect
535. #107C2×#6923semidirect
542. #103C2×#6923semidirect
554. #97C2×#6923semidirect
613. SD16C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×SD16×#69232
#214622592
#214622582
#214616342
#214616332
#107×#69232
#214615922
#214615902
#103×#69232
C4×#145198402
#102×#69232
C4×#145198392
#214614772
#440×D612
#2050461