Finite Group Databasebeta

← #29679529

Subgroups — #29679529

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840238C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic
4C2×#103×D61C211yesmaximal, characteristic
5#21448444C211yesmaximal, characteristic
6#21445833C211yesmaximal, characteristic, complemented
7#21445832C211yesmaximal, characteristic, complemented
8#21445831C211yesmaximal, characteristic, complemented
9#21445825C211yesmaximal, characteristic, complemented
10#21445824C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445822C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic
14#21445534C211yesmaximal, characteristic
15C61×#1805C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840238—24no—
20#16840238C418yescomplemented
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×Dic122—21no—
23C2×C4×Dic122C2211yescharacteristic
24C2×#14519742—21no—
25C2×#14519742C2211yescharacteristic
26C2×#14519735—21no—
27C2×#14519735C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519734—21no—
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839787—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36#16839769—24no—
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44#16839659—21no—
45#16839659—21no—
46#16839636—21no—
47#16839636—21no—
48#16839632C2211yescharacteristic
49#16839631C2211yescharacteristic
50#16839627C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#382C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61C2×C414yes—
70C2×Q8×D61D414yes—
71C2×Q8×D61Q814yes—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83Q8×Dic61—22no—
84Q8×Dic61C2×C414yescomplemented
85C4×Dic122—22no—
86C4×Dic122—28no—
87C4×Dic122C2×C414yescomplemented
88#14519742—28no—
89#14519742—22no—
90#14519742C2×C414yescomplemented
91#14519735—22no—
92#14519735—28no—
93#14519735—22no—
94#14519735—22no—
95#14519735C2×C414yes—
96#14519734—28no—
97#14519734C2×C414yes—
98#14519734D414yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196D411yescharacteristic
111C2×#11758196D411yescharacteristic
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×#11758198D411yescharacteristic
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124C4⋊#92418—22no—
125#14519706—22no—
126#14519706—22no—
127#14519702—22no—
128#14519702—22no—
129#14519701—22no—
130#14519701—22no—
131#14519700—22no—
132#14519700—22no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61C2×C414yescomplemented
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—22no—
147#103×C61—22no—
148#103×C61—22no—
149#95×C61—21no—
150#95×C61—21no—
151C23×D61C2×D411yescharacteristic
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C22×C412yes—
156C2×Q8×C61C2×D412yes—
157C2×Q8×C61C2×Q812yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172Q8×D61—28no—
173Q8×D61—28no—
174Q8×D61—28no—
175Q8×D61C4⋊C4116yescomplemented
176C2×C4×D61—24no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—42no—
180C2×C4×D61—81no—
181C2×C4×D61—81no—
182C2×C4×D61C22×C412yes—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×D412yes—
185C2×C4×D61C2×Q812yes—
186C2×C4×D61#4112yes—
187C2×C4×D61#4112yes—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—24no—
192C2×Dic122—24no—
193C2×Dic122—24no—
194C2×Dic122C22×C412yes—
195C2×Dic122C2×D412yes—
196C2×Dic122C2×Q812yes—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C22×C412yes—
210C42×C61—24no—
211C42×C61C22×C412yes—
212C42×C61C2×D412yes—
213#11758198—24no—
214#11758198—42no—
215#11758198C22⋊C414yes—
216#11758198C22⋊C414yes—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—81no—
224C4⋊Dic61—81no—
225C4⋊Dic61C22×C412yes—
226#11758196—24no—
227#11758196—24no—
228#11758196—42no—
229#11758196—81no—
230#11758196—81no—
231#11758196C22⋊C414yes—
232#11758196C22⋊C414yes—
233C4×Dic61—24no—
234C4×Dic61—24no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61—42no—
238C4×Dic61C22×C412yes—
239C4×Dic61C2×D412yes—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246#11758189—44no—
247C8×D61—44no—
248C23×C61C22×D411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61C2×C22⋊C412yes—
254C22×D61#12112yes—
255C22×D61C22⋊Q812yes—
256Q8×C61—22no—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61C2×C4⋊C414yes—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61C2×C22⋊C412yes—
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C23×C411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C22×Q811yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61C2×C22⋊C412yes—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61#12112yes—
304C2×Dic61C22⋊Q812yes—
305C4×D61—216no—
306C4×D61—84no—
307C4×D61C2×C4⋊C414yes—
308C4×D61#11714yes—
309C4×D61#12114yes—
310C4×D61C22⋊Q814yes—
311Dic122—22no—
312Dic122—22no—
313Dic122—22no—
314Dic122—216no—
315Dic122C2×C4⋊C414yes—
316C8×C61—41no—
317C8×C61—41no—
318#92418—41no—
319#92418—41no—
320#20651—611nomaximal, Sylow
321C22×C61C22×C22⋊C411yescharacteristic
322C22×C61C2×#12111yescharacteristic
323C22×C61C2×C22⋊Q811yescharacteristic
324C22×C61#57711yescharacteristic
325C22×C61#57711yescharacteristic
326C22×C61#57811yescharacteristic
327C22×C61#57811yescharacteristic
328C2×D61—22no—
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61#38014yes—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—24no—
338C4×C61—42no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61C22×C4⋊C411yescharacteristic
342C4×C61C2×#11711yescharacteristic
343C4×C61C2×#12111yescharacteristic
344C4×C61C2×C22⋊Q811yescharacteristic
345Dic61—22no—
346Dic61—22no—
347Dic61—24no—
348Dic61—42no—
349Dic61—81no—
350Dic61—81no—
351Dic61#38014yes—
352C2×#519—611no—
353C2×#424—611no—
354C2×#419—611no—
355C22×#103—611no—
356#2317—611no—
357#1805—611no—
358#1805—611no—
359#1805—611no—
360#1805D6111yescharacteristic, complemented
361#1803—611no—
362#1803—611no—
363#1803—611no—
364#1803—611no—
365#1736—611no—
366#1735—611no—
367C2×C61C2×#38011yescharacteristic
368C2×C61#289811yescharacteristic
369C2×C61#289811yescharacteristic
370C2×C61#304311yescharacteristic
371C2×C61#304411yescharacteristic
372C2×C61#308211yescharacteristic
373C2×C61#308211yescharacteristic
374D61—24no—
375C23×Q8—611no—
376C22×M16—611no—
377C23×C8—611no—
378#519—618no—
379#519—1224no—
380C2×C4×Q8—611no—
381C2×C4×Q8—611no—
382C2×C4×Q8—611no—
383C2×C4×Q8—1221no—
384C2×C4×Q8—1221no—
385C2×C4×Q8C2×D6111yescharacteristic
386C2×#117—611no—
387C2×#117—611no—
388C2×#117—611no—
389C2×#117—1221no—
390C2×#117—1221no—
391C22×C4⋊C4—611no—
392#424—1224no—
393C2×C4⋊C8—611no—
394C2×C4⋊C8—611no—
395C2×C4⋊C8—611no—
396C2×C4⋊C8C2×D6111yescharacteristic
397#419—1224no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—1224no—
405C2×#103C2×D6111yescharacteristic
406C2×#103C2×D6111yescharacteristic
407#389—1221no—
408#389—1221no—
409#385—1221no—
410#385—1221no—
411#384—611no—
412#384—611no—
413#382—611no—
414#382C2×D6111yescharacteristic
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2065111yescharacteristic, complemented, Sylow
424C22×Q8—614no—
425C22×Q8—614no—
426C22×Q8—614no—
427C22×Q8—611no—
428C22×Q8—1221no—
429C22×Q8—1222no—
430C22×Q8—1222no—
431C22×Q8—1222no—
432C22×Q8C22×D6111yescharacteristic
433C23×C4—611no—
434C23×C4—1221no—
435C23×C4—1221no—
436C2×M16—1222no—
437C2×M16—1222no—
438C2×M16—1222no—
439C22×C8—611no—
440C22×C8—611no—
441C22×C8—1222no—
442C22×C8—1222no—
443C22×C8—1222no—
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C4×Q8—22no—
447C4×Q8—614no—
448C4×Q8—614no—
449C4×Q8—614no—
450C4×Q8—1228no—
451C4×Q8—1222no—
452C4×Q8—1222no—
453C4×Q8—1228no—
454C4×Q8—1222no—
455C4×Q8C4×D6114yescomplemented
456#117—614no—
457#117—614no—
458#117—614no—
459#117—1228no—
460#117—1228no—
461#117—1222no—
462#117—1222no—
463#117—1222no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1222no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C42—21no—
488C2×C42—611no—
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494C2×C42C22×D6111yescharacteristic
495C4⋊C8—22no—
496C4⋊C8—1222no—
497C4⋊C8—1222no—
498C4⋊C8—1222no—
499#103—22no—
500#103—22no—
501#103—1222no—
502#103—1222no—
503#103—1222no—
504#103—1222no—
505#103—1222no—
506#103—1222no—
507#95—21no—
508#95—21no—
509#95—1221no—
510#95—1221no—
511C24—611no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—6116no—
516C2×Q8—612no—
517C2×Q8—612no—
518C2×Q8—612no—
519C2×Q8—1224no—
520C2×Q8—1224no—
521C2×Q8—1224no—
522C2×Q8—1228no—
523C2×Q8—1228no—
524C2×Q8—1228no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8C2×C4×D6112yes—
529C2×Q8D4×D6112yes—
530C2×Q8Q8×D6112yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—611no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—1224no—
545C22×C4—1224no—
546C22×C4—1224no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—4881no—
552C22×C4—4881no—
553C22×C4—2442no—
554C22×C4D4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556C22×C4C23×D6111yescharacteristic
557M16—2444no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—2444no—
571C4⋊C4—21no—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—614no—
578C4⋊C4—614no—
579C4⋊C4—612no—
580C4⋊C4—1224no—
581C4⋊C4—1224no—
582C4⋊C4—1221no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—4881no—
589C4⋊C4—4881no—
590C4⋊C4—4881no—
591C4⋊C4—4881no—
592C4⋊C4—2442no—
593C4⋊C4C2×C4×D6112yes—
594C22⋊C4—614no—
595C22⋊C4—614no—
596C22⋊C4—1224no—
597C22⋊C4—2442no—
598C42—24no—
599C42—612no—
600C42—612no—
601C42—1224no—
602C42—1224no—
603C42—1224no—
604C42—1224no—
605C42—2442no—
606C42C2×C4×D6112yes—
607C42D4×D6112yes—
608C23—612no—
609C23—612no—
610C23—612no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23C2×D4×D6111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—614no—
620Q8—12216no—
621Q8—1222no—
622Q8—1222no—
623Q8—1222no—
624Q8C4⋊C4×D6114yes—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—614no—
645C2×C4—614no—
646C2×C4—614no—
647C2×C4—614no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—12216no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1222no—
659C2×C4—4884no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4C22⋊C4×D6112yes—
669C2×C4C22⋊C4×D6112yes—
670C2×C4C22×C4×D6111yescharacteristic
671C2×C4C2×D4×D6111yescharacteristic
672C2×C4C2×D4×D6111yescharacteristic
673C2×C4C2×Q8×D6111yescharacteristic
674C2×C4#41×D6111yescharacteristic
675C2×C4#41×D6111yescharacteristic
676C8—41no—
677C8—41no—
678C8—2441no—
679C8—2441no—
680C22—614no—
681C22—1222no—
682C22—1222no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—1222no—
687C22C2×C22⋊C4×D6111yescharacteristic
688C22#121×D6111yescharacteristic
689C22C22⋊Q8×D6111yescharacteristic
690C22#1684056911yescharacteristic
691C22#1684057111yescharacteristic
692C22#1684057611yescharacteristic
693C22#1684057811yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—614no—
701C4—1222no—
702C4—1222no—
703C4—1224no—
704C4—4881no—
705C4—4881no—
706C4—2442no—
707C4C2×C4⋊C4×D6111yescharacteristic
708C4#117×D6111yescharacteristic
709C4#121×D6111yescharacteristic
710C4C22⋊Q8×D6111yescharacteristic
711C2—1224no—
712C2#380×D6111yescharacteristic
713C2#2145434811yescharacteristic
714C2#2145435111yescharacteristic
715C2#2145533811yescharacteristic
716C2#2145534711yescharacteristic
717C2#2145565811yescharacteristic
718C2#2145566011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1805C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1805D61
hypocenterC61#20651
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
6. #21445833C2semidirect
7. #21445832C2semidirect
8. #21445831C2semidirect
9. #21445825C2semidirect
10. #21445824C2semidirect
11. #21445823C2semidirect
12. #21445822C2semidirect
15. C61×#1805C2semidirect
20. #16840238C4semidirect
84. Q8×Dic61C2×C4semidirect
87. C4×Dic122C2×C4semidirect
90. #14519742C2×C4semidirect
139. C4×Q8×C61C2×C4semidirect
175. Q8×D61C4⋊C4semidirect
360. #1805D61semidirect
423. C61#20651semidirect
455. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402382
C2×#168397872
C2×#168397692
C2×#103×D612
#214484442
#214458332
#214458322
#214458312
#214458252
#214458242
#214458232
#214458222
#214455372
#214455342
C61×#18052
#2065161