Finite Group Databasebeta

← #29696232

Subgroups — #29696232

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic
2C2×D4×#92418C211yesmaximal, characteristic
3#21446783C211yesmaximal, characteristic, complemented
4#21446776C211yesmaximal, characteristic, complemented
5#21446240C211yesmaximal, characteristic, complemented
6#21446240C211yesmaximal, characteristic, complemented
7#21446131C211yesmaximal, characteristic, complemented
8#21446126C211yesmaximal, characteristic, complemented
9#21445911C211yesmaximal, characteristic, complemented
10#21445903C211yesmaximal, characteristic, complemented
11#21445831C211yesmaximal, characteristic, complemented
12C4×#14519700C211yesmaximal, characteristic, complemented
13#21445535C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16840452—24no—
19#16840452C418yescomplemented
20C2×#14519770—21no—
21C2×#14519769C2211yescharacteristic
22C2×#14519767—21no—
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30D4×#92418—24no—
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C61×#388—21no—
55C61×#387—21no—
56C61×#386—21no—
57C61×#382C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C22×Dic122C2311yescharacteristic
63C23×Dic61—21no—
64C22×#92418—22no—
65C22×#92418—22no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519770—28no—
75#14519769—22no—
76#14519769C2×C414yescomplemented
77#14519767—28no—
78#14519758—28no—
79#14519756—22no—
80#14519756—22no—
81#14519756C2×C414yes—
82#14519756C2×C414yescomplemented
83C4×Dic122—22no—
84C4×Dic122C2×C414yescomplemented
85#14519736—22no—
86#14519736C2×C414yescomplemented
87#14519733—28no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2×C414yes—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C4⋊#92418—22no—
105#14519700—22no—
106#14519700—22no—
107#14519700—41no—
108#14519700—41no—
109C22⋊#92418—22no—
110C22⋊#92418—22no—
111C4×#92418—22no—
112C22×D4×C61D411yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C4×D4×C61C2×C414yes—
117C4×D4×C61D414yes—
118#117×C61—22no—
119#117×C61—41no—
120C2×C4⋊C4×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61C22⋊C414yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—81no—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—24no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122C22×C412yes—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—42no—
191C4⋊C4×C61C22⋊C414yes—
192C4⋊C4×C61#4112yes—
193C22⋊C4×C61—42no—
194C22⋊C4×C61—42no—
195C22⋊C4×C61—81no—
196C22⋊C4×C61C22⋊C414yes—
197C22⋊C4×C61C22⋊C414yes—
198C42×C61—42no—
199C42×C61—81no—
200C42×C61C22×C412yes—
201C42×C61C2×D412yes—
202C22⋊Dic61—24no—
203C22⋊Dic61—24no—
204C22⋊Dic61—24no—
205C4⋊Dic61—24no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C22×C412yes—
210C4⋊Dic61C22×C412yes—
211C4⋊Dic61C22×C412yes—
212#11758196—24no—
213#11758196—24no—
214#11758196—24no—
215#11758196—24no—
216#11758196—24no—
217C4×Dic61—24no—
218C4×Dic61—24no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—44no—
231C2×#92418—44no—
232C2×#92418#4112yes—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C22⋊C412yes—
244C23×C61C2×C22⋊C412yes—
245C23×C61#13512yes—
246C23×C61#13512yes—
247C23×C61C22×D411yescharacteristic
248D4×C61—28no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
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×C61—41no—
277C2×C4×C61—84no—
278C2×C4×C61C2×C22⋊C412yes—
279C2×C4×C61C2×C22⋊C412yes—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C612−1+411yescharacteristic
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
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×Dic61—48no—
301Dic122—22no—
302Dic122—22no—
303Dic122—41no—
304Dic122—41no—
305#92418—22no—
306#92418—41no—
307#92418—41no—
308#92418—41no—
309#22486—611nomaximal, Sylow
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61#41614yes—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61#54611yescharacteristic
326C22×C61#54711yescharacteristic
327C22×C61C2×#13511yescharacteristic
328C22×C61C2×#13511yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57811yescharacteristic
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—42no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61—81no—
339C4×C61C4×#4111yescharacteristic
340C4×C61#52011yescharacteristic
341C4×C61#54611yescharacteristic
342C4×C61#54711yescharacteristic
343Dic61—42no—
344Dic61—42no—
345Dic61—42no—
346Dic61—42no—
347C2×#552—611no—
348C2×C8×D4—611no—
349#2352D6111yescharacteristic
350#1991—611no—
351#1989—611no—
352#1892—611no—
353#1892—611no—
354#1873—611no—
355#1872—611no—
356#1825—611no—
357#1823—611no—
358#1805—611no—
359C4×#103—611no—
360#1735—611no—
361C2×#340—611no—
362C2×C61—24no—
363C2×C61—42no—
364C2×C61#233911yescharacteristic
365C2×C61C2×#41611yescharacteristic
366C2×C61#289811yescharacteristic
367C2×C61#329611yescharacteristic
368C2×C61#330011yescharacteristic
369C2×C61#333611yescharacteristic
370C2×C61#333711yescharacteristic
371C23×C8—611no—
372C23×C8—611no—
373#552—618no—
374#552—1224no—
375C2×#126—1221no—
376C2×#125—611no—
377C2×#125—1221no—
378C2×#123—1221no—
379C2×C22⋊Q8—611no—
380C2×C22⋊Q8—611no—
381C2×C4×Q8—611no—
382C2×C4×D4C2×D6111yescharacteristic
383C2×#117—611no—
384C2×#117—1221no—
385C2×#117C2×D6111yescharacteristic
386C22×C4⋊C4—611no—
387C22×C4⋊C4C2×D6111yescharacteristic
388C8×D4—1224no—
389C2×C4⋊C8—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×C22⋊C8—611no—
395C2×C22⋊C8—611no—
396C2×C4×C8—611no—
397#388—21no—
398#387—21no—
399#386—21no—
400#382C2×D6111yescharacteristic
401#380C2×D6111yescharacteristic
402#380C2×D6111yescharacteristic
403C4×C4⋊C4C2×D6111yescharacteristic
404C4×C22⋊C4—21no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417C61#2248611yescharacteristic, complemented, Sylow
418C22×Q8—611no—
419C22×D4C22⋊D6111yescharacteristic
420C23×C4—21no—
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C23×C4C22×D6111yescharacteristic
424C22×C8—611no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—1222no—
429C22×C8—1222no—
430C22×C8—1222no—
431C22×C8—1222no—
432C22×C8—2441no—
433C22×C8—2441no—
434#126—1228no—
435#125—614no—
436#125—1228no—
437#125—1222no—
438#123—1228no—
439C22⋊Q8—614no—
440C22⋊Q8—614no—
441C22⋊Q8—1222no—
442C22⋊Q8—1222no—
443C4×Q8—614no—
444C4×Q8—1222no—
445C4×D4C4×D6114yes—
446C4×D4D24414yes—
447#117—22no—
448#117—41no—
449#117—614no—
450#117—1222no—
451#117—1228no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—614no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—1222no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4C22⋊D6111yescharacteristic
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4C22⋊D6111yescharacteristic
478C2×C22⋊C4C22⋊D6111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1221no—
482C2×C42—1221no—
483C2×C42C22×D6111yescharacteristic
484C4⋊C8—1222no—
485#103—1222no—
486#103—1222no—
487#103—2441no—
488#103—2441no—
489C22⋊C8—1222no—
490C22⋊C8—1222no—
491C4×C8—1222no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24C2×C22⋊D6111yescharacteristic
498C24C2×C22⋊D6111yescharacteristic
499C2×Q8—612no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4#1175819814yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1224no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4C2×C4×D6112yes—
531C22×C4C2×C4×D6112yes—
532C22×C4C2×D24412yes—
533C22×C4C2×D24412yes—
534C22×C4C2×C22⋊D6111yescharacteristic
535C22×C4C2×C22⋊D6111yescharacteristic
536C22×C4C2×C22⋊D6111yescharacteristic
537C22×C4C2×C22⋊D6111yescharacteristic
538C22×C4C23×D6111yescharacteristic
539C2×C8—612no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—2444no—
552C2×C8—2444no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—612no—
562C4⋊C4—612no—
563C4⋊C4—612no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1224no—
568C4⋊C4—1224no—
569C4⋊C4—1224no—
570C4⋊C4—1224no—
571C4⋊C4—1224no—
572C4⋊C4—1224no—
573C4⋊C4#1175819814yes—
574C4⋊C4#1175822412yes—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—1224no—
579C22⋊C4—1224no—
580C22⋊C4—1224no—
581C22⋊C4#1175819814yes—
582C22⋊C4#1175819814yes—
583C42—42no—
584C42—81no—
585C42—1224no—
586C42—1224no—
587C42C2×C4×D6112yes—
588C42C2×D24412yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23C2×#1175819812yes—
600C23C2×#1175819812yes—
601C23#1451979712yes—
602C23#1451979712yes—
603C23C22×C22⋊D6111yescharacteristic
604Q8—1222no—
605Q8—1222no—
606Q8—2441no—
607Q8—2441no—
608D4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—2448no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4C2×#1175819812yes—
652C2×C4C2×#1175819812yes—
653C2×C4C2×#1175819812yes—
654C2×C4C2×#1175819812yes—
655C2×C4C22×C4×D6111yescharacteristic
656C2×C4C22×D24411yescharacteristic
657C2×C4#41×D6111yescharacteristic
658C2×C4C2×#1175822411yescharacteristic
659C2×C4#1451982211yescharacteristic
660C2×C4#1451982411yescharacteristic
661C8—1222no—
662C8—2441no—
663C8—2441no—
664C8—2441no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22#1683975614yes—
679C22C22×#1175819811yescharacteristic
680C22#1684040611yescharacteristic
681C22#1684041111yescharacteristic
682C22C2×#1451979711yescharacteristic
683C22C2×#1451979711yescharacteristic
684C22#1684057311yescharacteristic
685C22#1684057711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—2442no—
695C4—2442no—
696C4—2442no—
697C4—2442no—
698C4C4×#1175822411yescharacteristic
699C4#1684024111yescharacteristic
700C4#1684040711yescharacteristic
701C4#1684041611yescharacteristic
702C2—24no—
703C2—42no—
704C2#2144864411yescharacteristic
705C2C2×#1683975611yescharacteristic
706C2#2145434911yescharacteristic
707C2#2145765411yescharacteristic
708C2#2145770611yescharacteristic
709C2#2145818111yescharacteristic
710C2#2145819211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenter#2352D61
hypocenterC61#22486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #21446783C2semidirect
4. #21446776C2semidirect
5. #21446240C2semidirect
6. #21446240C2semidirect
7. #21446131C2semidirect
8. #21446126C2semidirect
9. #21445911C2semidirect
10. #21445903C2semidirect
11. #21445831C2semidirect
12. C4×#14519700C2semidirect
13. #21445535C2semidirect
14. C2×#16839524C2semidirect
19. #16840452C4semidirect
76. #14519769C2×C4semidirect
82. #14519756C2×C4semidirect
84. C4×Dic122C2×C4semidirect
86. #14519736C2×C4semidirect
417. C61#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×D4×#924182
#214467832
#214467762
#214462402
#214461312
#214461262
#214459112
#214459032
#214458312
C4×#145197002
#214455352
C2×#168395242
C61×#23522
#2248661