Finite Group Databasebeta

← #30620802

Subgroups — #30620802

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462329C211yesmaximal, characteristic
2#21462327C211yesmaximal, characteristic
3#21461925C211yesmaximal, characteristic, complemented
4#21461922C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461882C211yesmaximal, characteristic, complemented
7#21461881C211yesmaximal, characteristic, complemented
8#21461880C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic
10#21461723C211yesmaximal, characteristic
11#21461697C211yesmaximal, characteristic
12#21461634C211yesmaximal, characteristic, complemented
13#107×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic
15#428×D61C211yesmaximal, characteristic
16C2×#14519856—21no—
17C2×#14519846C2211yescharacteristic
18C2×#14519845C2211yescharacteristic
19D61⋊(C22⋊C8)C2211yescharacteristic
20C2×#14519831C2211yescharacteristic
21C2×C8×#6923C2211yescharacteristic
22#16840713C2211yescharacteristic
23#16840713C2211yescharacteristic
24#16840713C2211yescharacteristic
25#16840713C2211yescharacteristic
26#16840712—21no—
27#16840712—21no—
28#16840711—21no—
29#16840711—21no—
30#16840706—21no—
31#16840705—21no—
32#16840704C2211yescharacteristic
33#16840704C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4×C22⋊#6923C2211yescharacteristic
39#16840698—21no—
40#16840636C2211yescharacteristic
41#16840636C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×M16×D61C2211yescharacteristic
53#117×D61C2211yescharacteristic
54C2×C4⋊C4×D61C2211yescharacteristic
55#16839805C411yescharacteristic, complemented
56#16839804C411yescharacteristic, complemented
57#16839803C411yescharacteristic, complemented
58#16839803C411yescharacteristic, complemented
59#16839802C411yescharacteristic, complemented
60#16839801C411yescharacteristic, complemented
61#16839801C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#107×D61C2211yescharacteristic
64#106×D61C2211yescharacteristic
65#106×D61C2211yescharacteristic
66C61×#428C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69#14519856—44no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923C2311yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C22⋊#6923—21no—
79C2×C22⋊#6923—21no—
80C2×C22⋊#6923D411yescharacteristic
81C2×C22⋊#6923D411yescharacteristic
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923C2311yescharacteristic
87C2×C4×#6923C2311yescharacteristic
88#14519846—22no—
89#14519845—22no—
90#14519834—21no—
91C22⋊#92420—21no—
92#14519831—22no—
93C8×#6923—22no—
94(C2×#6923)⋊C4—21no—
95(C2×#6923)⋊C4—21no—
96(C2×#6923)⋊C4—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4D411yescharacteristic
105(C2×#6923)⋊C4D411yescharacteristic
106C22×C4×D61—21no—
107C22×C4×D61C2311yescharacteristic
108C2×#11758194C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110C2×#11758189C2×C411yescharacteristic
111M16×D61—22no—
112M16×D61—22no—
113C2×C8×D61C2311yescharacteristic
114C2×C8×D61C2311yescharacteristic
115#14519736C2×C411yescharacteristic
116#14519735C2×C411yescharacteristic
117#14519735C2×C411yescharacteristic
118#14519734—21no—
119#14519733—21no—
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×#11758196—21no—
122C4⋊C4×D61—21no—
123C4⋊C4×D61—21no—
124C4⋊C4×D61C2×C411yescharacteristic
125C4⋊C4×D61C2×C411yescharacteristic
126C4⋊C4×D61C2311yescharacteristic
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C22⋊C4×D61—21no—
131C42×D61—21no—
132#14519711C2×C411yescharacteristic
133#14519711C2×C411yescharacteristic
134#14519710C2×C411yescharacteristic
135#14519710C2×C411yescharacteristic
136#14519710C2×C411yescharacteristic
137#14519710C2×C411yescharacteristic
138#14519709C2×C411yescharacteristic
139#14519709C2×C411yescharacteristic
140#14519708C2×C411yescharacteristic
141#14519708C2×C411yescharacteristic
142#14519708C2×C411yescharacteristic
143#14519708C2×C411yescharacteristic
144C2×M16×C61C2×C411yescharacteristic
145#117×C61C2×C411yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147#107×C61C2×C411yescharacteristic
148#107×C61C2×C411yescharacteristic
149#106×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic
151C23×D61C2×D411yescharacteristic
152C22×#6923—21no—
153C22×#6923—21no—
154C22×#6923—21no—
155C22×#6923—21no—
156C22×#6923C2×D411yescharacteristic
157C22×#6923C2×D411yescharacteristic
158C22×#6923C2×D411yescharacteristic
159C22×#6923C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61C22×C411yescharacteristic
162C22×Dic61—21no—
163C22×Dic61#4111yescharacteristic
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61#4111yescharacteristic
179C2×C4×D61C2411yescharacteristic
180C22⋊#6923—22no—
181C22⋊#6923—41no—
182C22⋊#6923—42no—
183C22⋊#6923—81no—
184C2×#92420—21no—
185C2×#92420—21no—
186C4⋊#6923—21no—
187C4⋊#6923—21no—
188C4⋊#6923—21no—
189C4⋊#6923—21no—
190C4⋊#6923—21no—
191C4⋊#6923—21no—
192C4⋊#6923—21no—
193C4⋊#6923—21no—
194C4⋊#6923—42no—
195C4⋊#6923—42no—
196C4⋊#6923—81no—
197C4⋊#6923—81no—
198C4×#6923—21no—
199C4×#6923—21no—
200C4×#6923—21no—
201C4×#6923—21no—
202C4×#6923—42no—
203C4×#6923—42no—
204C4×#6923—42no—
205C4×#6923—42no—
206D61⋊C8—21no—
207D61⋊C8—21no—
208D61⋊C8—21no—
209D61⋊C8—21no—
210M16×C61—22no—
211C2×C8×C61C22×C411yescharacteristic
212C2×C8×C61C22×C411yescharacteristic
213C4⋊C4×C61—21no—
214C4⋊C4×C61C22×C411yescharacteristic
215C4⋊C4×C61C22×C411yescharacteristic
216C4⋊C4×C61C22×C411yescharacteristic
217C4⋊C4×C61C22×C411yescharacteristic
218C22⋊C4×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—21no—
221#11758198—21no—
222#11758198—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61C22×C411yescharacteristic
225C4⋊Dic61C22×C411yescharacteristic
226C4⋊Dic61C22×C411yescharacteristic
227C4⋊Dic61C22×C411yescharacteristic
228#11758196—21no—
229#11758196—21no—
230#11758196—21no—
231#11758196—21no—
232#11758196—21no—
233#11758196—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237#11758194—22no—
238C2×#92418C22×C411yescharacteristic
239C2×#92418C22×C411yescharacteristic
240#11758189—22no—
241#11758189—22no—
242C8×D61—21no—
243C8×D61—21no—
244C8×D61#4112yes—
245C8×D61#4112yes—
246C23×C61C4×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61C4×D411yescharacteristic
254C22×D61C22×D411yescharacteristic
255C2×#6923—21no—
256C2×#6923—21no—
257C2×#6923—21no—
258C2×#6923—21no—
259C2×#6923—21no—
260C2×#6923—21no—
261C2×#6923—21no—
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—41no—
267C2×#6923—41no—
268C2×#6923—41no—
269C2×#6923—41no—
270C2×#6923—41no—
271C2×#6923—41no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923AGL(1,ℤ/8)12yes—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—42no—
286C2×C4×C61C4×D411yescharacteristic
287C2×C4×C61C23×C411yescharacteristic
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—42no—
295C2×Dic61C4×D411yescharacteristic
296C2×Dic61C2×#4111yescharacteristic
297C4×D61—21no—
298C4×D61—21no—
299C4×D61—21no—
300C4×D61—21no—
301C4×D61—21no—
302C4×D61—21no—
303C4×D61—42no—
304C4×D61—42no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61C2×#4111yescharacteristic
314C4×D61C2×#4111yescharacteristic
315C4×D612−1+411yescharacteristic
316C4×D612−1+411yescharacteristic
317#92420—41no—
318#92420—41no—
319C8×C61—21no—
320C8×C61#11712yescomplemented
321#92418—21no—
322#92418#11712yescomplemented
323#22624—611nomaximal, Sylow
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61C2×C4×D411yescharacteristic
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—21no—
331C2×D61—41no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61#54711yescharacteristic
336C2×D61#54711yescharacteristic
337C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
338C2×D61#57511yescharacteristic
339C2×D61#57711yescharacteristic
340C2×D61#57811yescharacteristic
341#6923—22no—
342#6923—41no—
343#6923—41no—
344#6923—41no—
345#6923—81no—
346#6923—81no—
347#6923—81no—
348#6923—81no—
349C4×C61—21no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61C2×#11711yescharacteristic
355C4×C61#51911yescharacteristic
356Dic61—21no—
357Dic61—41no—
358Dic61—41no—
359Dic61—41no—
360Dic61—41no—
361Dic61#55211yescharacteristic
362Dic61#55211yescharacteristic
363C2×#428—611no—
364#2346—611no—
365#2344—611no—
366#1944—611no—
367#1941—611no—
368#1921—611no—
369#1920—611no—
370#1919—611no—
371#1918—611no—
372#1825—611no—
373#1824—611no—
374#1809—611no—
375#1776—611no—
376C4×#107—611no—
377#1753—611no—
378C2×C61—41no—
379C2×C61#234411yescharacteristic
380C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
381C2×C61#294711yescharacteristic
382D61—41no—
383D61#334311yescharacteristic
384D61#334811yescharacteristic
385D61#335211yescharacteristic
386D61#335411yescharacteristic
387C22×M16—611no—
388C2×#117—611no—
389C2×#117—1221no—
390C22×C4⋊C4—611no—
391#428—611no—
392#428—611no—
393#428—611no—
394#428—611no—
395#428—611no—
396#428—611no—
397#428—611no—
398#428#692311yescharacteristic, complemented
399C2×#107—611no—
400C2×#107—611no—
401C2×#107—611no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#106—611no—
405C2×C22⋊C8—611no—
406C2×#97—611no—
407C2×C4×C8—611no—
408#389—611no—
409#389—611no—
410#389—611no—
411#389—611no—
412#388—1221no—
413#388—1221no—
414#387—1221no—
415#387—1221no—
416#382—1221no—
417#381—1221no—
418#380—611no—
419#380—611no—
420C4×C4⋊C4—611no—
421C4×C4⋊C4—611no—
422C4×C4⋊C4—611no—
423C4×C4⋊C4—611no—
424C4×C22⋊C4—611no—
425#376—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336—611no—
437#336—611no—
438C61#2262411yescharacteristic, complemented, Sylow
439C23×C4—611no—
440C23×C4—1221no—
441C2×M16—611no—
442C2×M16—611no—
443C2×M16—611no—
444C2×M16—1222no—
445C2×M16—1222no—
446C2×M16C2×#692311yescharacteristic
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451#117—611no—
452#117—611no—
453#117—611no—
454#117—1221no—
455#117—1221no—
456#117—2444no—
457#117C2×#692311yescharacteristic
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C2×#692311yescharacteristic
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—1221no—
485C2×C42—1221no—
486C2×C42—1221no—
487C2×C42—1221no—
488C2×C42—1221no—
489#107—611no—
490#107—611no—
491#107—611no—
492#107—611no—
493#107—611no—
494#107—611no—
495#107—1222no—
496#107C2×#692311yescharacteristic
497#107C2×#692311yescharacteristic
498#106—611no—
499#106—611no—
500#106—611no—
501#106—611no—
502#106—611no—
503#106—611no—
504#106—1222no—
505#106C2×#692311yescharacteristic
506#106C2×#692311yescharacteristic
507C22⋊C8—1221no—
508C22⋊C8—1221no—
509#97—1222no—
510C4×C8—1222no—
511#95—611no—
512#95—611no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523C24—611no—
524C22×C4—21no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—2442no—
550C22×C4—2442no—
551C22×C4C22×#692311yescharacteristic
552M16—22no—
553M16—1222no—
554M16—1222no—
555M16—1222no—
556C2×C8—611no—
557C2×C8—612no—
558C2×C8—612no—
559C2×C8—611no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8C22×#692311yescharacteristic
569C2×C8C22×#692311yescharacteristic
570C4⋊C4—21no—
571C4⋊C4—611no—
572C4⋊C4—611no—
573C4⋊C4—611no—
574C4⋊C4—611no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—4881no—
591C4⋊C4—4881no—
592C4⋊C4—2442no—
593C4⋊C4—2442no—
594C4⋊C4C22×#692311yescharacteristic
595C4⋊C4C22×#692311yescharacteristic
596C4⋊C4C22×#692311yescharacteristic
597C4⋊C4C22×#692311yescharacteristic
598C22⋊C4—21no—
599C22⋊C4—1221no—
600C22⋊C4—1221no—
601C22⋊C4—1222no—
602C22⋊C4—1221no—
603C22⋊C4—4881no—
604C22⋊C4—2441no—
605C22⋊C4—2442no—
606C42—21no—
607C42—1221no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—2442no—
615C42—2442no—
616C42—2442no—
617C42—2442no—
618C23—611no—
619C23—611no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23D4×#692311yescharacteristic
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—42no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—612no—
640C2×C4—611no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2442no—
687C2×C4D4×#692311yescharacteristic
688C2×C4C23×#692311yescharacteristic
689C8—21no—
690C8—612no—
691C8—1221no—
692C8—2441no—
693C8—2441no—
694C8#1451985612yescomplemented
695C22—21no—
696C22—21no—
697C22—21no—
698C22—611no—
699C22—611no—
700C22—611no—
701C22—611no—
702C22—611no—
703C22—611no—
704C22—1221no—
705C22—1221no—
706C22—1221no—
707C22—2441no—
708C22—2441no—
709C22—2441no—
710C22—2441no—
711C22C2×D4×#692311yescharacteristic
712C4—21no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—611no—
718C4—611no—
719C4—1222no—
720C4—1221no—
721C4—4881no—
722C4—4881no—
723C4—4881no—
724C4—4881no—
725C4—2441no—
726C4—2441no—
727C4—2441no—
728C4—2441no—
729C4—2441no—
730C4—2441no—
731C4—2441no—
732C4C2×#1451985611yescharacteristic
733C4#1684083011yescharacteristic
734C2—41no—
735C2—611no—
736C2—611no—
737C2—611no—
738C2—611no—
739C2—2441no—
740C2#2146232711yescharacteristic
741C2AGL(1,ℤ/8)×#692311yescharacteristic
742C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#428C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#428#6923
hypocenterC61#22624
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #21461925C2semidirect
4. #21461922C2semidirect
5. #21461883C2semidirect
6. #21461882C2semidirect
7. #21461881C2semidirect
8. #21461880C2semidirect
12. #21461634C2semidirect
13. #107×#6923C2semidirect
55. #16839805C4semidirect
56. #16839804C4semidirect
57. #16839803C4semidirect
58. #16839803C4semidirect
59. #16839802C4semidirect
60. #16839801C4semidirect
61. #16839801C4semidirect
66. C61×#428C4semidirect
320. C8×C61#117semidirect
322. #92418#117semidirect
398. #428#6923semidirect
438. C61#22624semidirect
694. C8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214623292
#214623272
#214619252
#214619222
#214618832
#214618822
#214618812
#214618802
#214617242
#214617232
#214616972
#214616342
#107×#69232
#214615592
#428×D612
#2262461