Finite Group Databasebeta

← #30620418

Subgroups — #30620418

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C212yesmaximal, complemented
2#21462010C212yesmaximal, complemented
3#21462010C212yesmaximal, complemented
4#21462008C212yesmaximal, complemented
5#21461681C211yesmaximal, characteristic
6#21461681C211yesmaximal, characteristic
7#21461679C211yesmaximal, characteristic
8#21461566C211yesmaximal, characteristic
9#21461566C211yesmaximal, characteristic
10C4×#14519835C211yesmaximal, characteristic
11C2×#16840466C211yesmaximal, characteristic
12C2×#14519835C2211yescharacteristic
13C2×#14519835C2211yescharacteristic
14C2×#14519835C2211yescharacteristic
15C2×#14519835C2211yescharacteristic
16#16840713—22no—
17#16840711—22no—
18#16840711—22no—
19#16840704C2212yes—
20#16840704C2212yes—
21#16840704C2212yes—
22C4⋊C4×#6923—22no—
23C4×C22⋊#6923C2212yes—
24C4×C22⋊#6923C2212yes—
25C4×C22⋊#6923C2212yes—
26#16840640C2212yes—
27#16840640C2212yes—
28#16840640C2212yes—
29#16840640C2212yes—
30#16840640C2212yes—
31#16840640C2212yes—
32#16840466—22no—
33#16840466—22no—
34#16840466—22no—
35#16840466—22no—
36C2×#14519775C411yescharacteristic, complemented
37C2×#14519767C411yescharacteristic, complemented
38C2×#14519767C411yescharacteristic, complemented
39C2×#14519755C2211yescharacteristic
40C2×#14519755C2211yescharacteristic
41C2×#14519754C411yescharacteristic, complemented
42C2×#14519754C411yescharacteristic, complemented
43C2×#14519753C2211yescharacteristic
44C2×#14519742C411yescharacteristic, complemented
45C2×C4×C22⋊D61C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C22×#11758196C411yescharacteristic, complemented
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C22⋊Q8×C61C411yescharacteristic, complemented
51C2×C4⋊#6923—22no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923C2312yes—
55C2×C22⋊#6923C2312yes—
56C2×C22⋊#6923C2312yes—
57C2×C22⋊#6923C2312yes—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61#14519835—22no—
62#14519835—22no—
63#14519835—22no—
64#14519835Q814yescomplemented
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—22no—
71C22×Dic122C2×C411yescharacteristic
72C22×Dic122C2×C411yescharacteristic
73C22×C22⋊D61C2311yescharacteristic
74C23×Dic61C2×C411yescharacteristic
75C23×Dic61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79#14519775—22no—
80#14519775—22no—
81#14519767—22no—
82#14519767—22no—
83#14519767—22no—
84#14519767—22no—
85#14519755—22no—
86#14519755—22no—
87#14519755—22no—
88#14519755—22no—
89#14519754—22no—
90#14519754—22no—
91#14519754—22no—
92#14519754—22no—
93#14519753—22no—
94#14519753—22no—
95#14519742—21no—
96#14519742—21no—
97#14519742—21no—
98#14519742—21no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101#14519737—22no—
102#14519737—22no—
103#14519737—22no—
104#14519737—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C4⋊C4×D61D412yes—
123C4⋊C4×D61D412yes—
124C4⋊C4×D61D412yes—
125C4⋊C4×D61D412yes—
126C2×C22⋊Dic61C2×C411yescharacteristic
127C2×#11758198C2311yescharacteristic
128C2×#11758198C2311yescharacteristic
129C2×#11758198C2311yescharacteristic
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C2×C4×Dic61C2×C411yescharacteristic
133C22×Q8×C61C2×C411yescharacteristic
134C23×C4×C61C2×C411yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C23×D61C2411yescharacteristic
144C22×#6923—22no—
145C22×#6923—22no—
146C22×#6923—22no—
147C22×#6923—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—81no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—81no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61C2×Q812yes—
162C2×C22⋊D61#4112yes—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—42no—
168C22×Dic61—81no—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C2×C4×D61—42no—
177C2×C4×D61—81no—
178C2×C4×D61—81no—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D412yes—
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×D412yes—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—22no—
188C2×Dic122—42no—
189C2×Dic122—81no—
190C22⋊#6923—22no—
191C22⋊#6923—22no—
192C22⋊#6923—22no—
193C22⋊#6923—22no—
194C22⋊#6923—22no—
195C22⋊#6923—22no—
196C22⋊#6923—22no—
197C22⋊#6923C2×Q814yes—
198C4⋊#6923—44no—
199C4⋊#6923—82no—
200C4⋊#6923—82no—
201C4×#6923—44no—
202C4×#6923—82no—
203C4×#6923—82no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61C22⋊C412yes—
208C4⋊C4×C61C22⋊C412yes—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊Dic61—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61C22⋊C412yes—
217C4⋊Dic61C22⋊C412yes—
218#11758196—21no—
219#11758196—21no—
220#11758196—22no—
221#11758196—22no—
222#11758196—22no—
223#11758196—21no—
224#11758196—21no—
225#11758196—21no—
226#11758196—21no—
227#11758196—22no—
228#11758196—21no—
229#11758196—21no—
230#11758196—22no—
231#11758196C22⋊C411yescharacteristic
232#11758196C22⋊C411yescharacteristic
233#11758196C22⋊C411yescharacteristic
234#11758196C22⋊C411yescharacteristic
235#11758196C22⋊C412yes—
236#11758196C22⋊C412yes—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C4×Q812yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—41no—
250C22×D61—41no—
251C22×D61C22×D412yes—
252C22×D61C22×Q811yescharacteristic
253C22×D61C2×#4111yescharacteristic
254C22×D612−1+412yes—
255C2×#6923—24no—
256C2×#6923—42no—
257C2×#6923—42no—
258C2×#6923—42no—
259C2×#6923—42no—
260C2×#6923—42no—
261C2×#6923—42no—
262C2×#6923—42no—
263C2×#6923—42no—
264C2×#6923—42no—
265C2×#6923—42no—
266C2×#6923—42no—
267Q8×C61—82no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
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—81no—
278C2×C4×C61—81no—
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C2×C22⋊C411yescharacteristic
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C2×C22⋊C412yes—
283C22⋊D61—24no—
284C22⋊D61—24no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—22no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—81no—
299C2×Dic61—81no—
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C412yes—
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C4×Q812yes—
306C4×D61—24no—
307C4×D61—42no—
308C4×D61—42no—
309C4×D61—42no—
310C4×D61—42no—
311C4×D61—42no—
312Dic122—42no—
313Dic122—42no—
314Dic122—82no—
315#22513—611nomaximal, Sylow
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—22no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61C22×C22⋊C411yescharacteristic
324C22×C61C2×C4×Q811yescharacteristic
325C22×C61#51911yescharacteristic
326C2×D61—22no—
327C2×D61—22no—
328C2×D61—41no—
329C2×D61—41no—
330C2×D61—42no—
331C2×D61#54812yes—
332C2×D61D4×Q812yes—
333#6923—44no—
334#6923—82no—
335#6923—82no—
336#6923—82no—
337C4×C61—22no—
338C4×C61—21no—
339C4×C61—21no—
340C4×C61—22no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—41no—
344Dic61—22no—
345Dic61—21no—
346Dic61—22no—
347Dic61—21no—
348Dic61—21no—
349Dic61—41no—
350Dic61—41no—
351Dic61—41no—
352Dic61#41012yes—
353C2×#554—611no—
354#2345—612no—
355#1996—612no—
356#1996—612no—
357#1996—612no—
358#1799—611no—
359#1799—611no—
360#1799—611no—
361C4×#99—611no—
362C4×#99—611no—
363C4×#99—611no—
364C2×C61—21no—
365C2×C61—21no—
366C2×C61—42no—
367C2×C61Q8×C22⋊C411yescharacteristic
368C2×C61C2×#41011yescharacteristic
369C2×C61#288311yescharacteristic
370D61—22no—
371D61—22no—
372#554—1222no—
373#554—1222no—
374#554—1222no—
375#554—1222no—
376C2×C4⋊Q8—611no—
377C2×#125—611no—
378C2×#125—611no—
379C2×C22⋊Q8—611no—
380C2×C22⋊Q8—611no—
381C2×C22⋊Q8—611no—
382C2×C22⋊Q8—611no—
383C2×C22⋊Q8—611no—
384C2×C22⋊Q8#692311yescharacteristic, complemented
385C2×C4×Q8—611no—
386C2×C4×D4—611no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C22×C4⋊C4—611no—
390C22×C4⋊C4—611no—
391C2×#99—611no—
392C2×#99—611no—
393C2×#99—611no—
394C2×#99—611no—
395#389—1222no—
396#387—1222no—
397#387—1222no—
398#380—612no—
399#380—612no—
400#380—612no—
401C4×C4⋊C4—1222no—
402C4×C22⋊C4—612no—
403C4×C22⋊C4—612no—
404C4×C22⋊C4—612no—
405#342—612no—
406#342—612no—
407#342—612no—
408#342—612no—
409#342—612no—
410#342—612no—
411C61#2251311yescharacteristic, complemented, Sylow
412C22×Q8—611no—
413C22×Q8—611no—
414C22×Q8C2×#692311yescharacteristic
415C22×D4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4C2×#692311yescharacteristic
422C4⋊Q8—1222no—
423C4⋊Q8—1222no—
424#125—1222no—
425#125—1222no—
426#125—1222no—
427#125—1222no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—1222no—
431C22⋊Q8—1222no—
432C22⋊Q8—1222no—
433C22⋊Q8—1222no—
434C22⋊Q8—1222no—
435C22⋊Q8—1222no—
436C22⋊Q8—1222no—
437C22⋊Q8—1222no—
438C22⋊Q8—1222no—
439C22⋊Q8—1222no—
440C4×Q8—1221no—
441C4×Q8—1221no—
442C4×Q8—1221no—
443C4×Q8—1221no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1222no—
447C4×D4—1222no—
448C4×D4—1222no—
449C4×D4—1222no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4—612no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—611no—
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—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4C2×#692311yescharacteristic
475C2×C4⋊C4C2×#692311yescharacteristic
476C2×C4⋊C4C2×#692311yescharacteristic
477C2×C22⋊C4—612no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—612no—
483C2×C22⋊C4—612no—
484C2×C22⋊C4—612no—
485C2×C22⋊C4C2×#692311yescharacteristic
486C2×C22⋊C4C2×#692311yescharacteristic
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1222no—
493#99—614no—
494#99—1222no—
495#99—1222no—
496#99—1222no—
497#95—1222no—
498#95—1222no—
499#95—1222no—
500#95—1222no—
501#95—1222no—
502#95—1222no—
503C24—611no—
504C24C22×#692311yescharacteristic
505C2×Q8—22no—
506C2×Q8—81no—
507C2×Q8—1222no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—4881no—
511C2×Q8—2442no—
512C2×D4—612no—
513C2×D4—612no—
514C2×D4—1222no—
515C2×D4—1222no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—81no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—612no—
524C22×C4—612no—
525C22×C4—612no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—4881no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4C22×#692311yescharacteristic
546C22×C4C22×#692311yescharacteristic
547C22×C4C22×#692311yescharacteristic
548C22×C4C22×#692311yescharacteristic
549C22×C4C22×#692311yescharacteristic
550C22×C4C22×#692311yescharacteristic
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—611no—
555C4⋊C4—611no—
556C4⋊C4—611no—
557C4⋊C4—611no—
558C4⋊C4—612no—
559C4⋊C4—612no—
560C4⋊C4—612no—
561C4⋊C4—612no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1222no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1222no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—4882no—
577C4⋊C4—4882no—
578C4⋊C4—2444no—
579C4⋊C4C22⋊#692312yes—
580C4⋊C4C22⋊#692312yes—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—614no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4—1222no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C22⋊C4—1222no—
595C42—1221no—
596C42—1221no—
597C42—1221no—
598C42—1221no—
599C42—1221no—
600C42—1221no—
601C42—4882no—
602C42—4882no—
603C42—2444no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—612no—
609C23—611no—
610C23—611no—
611C23—612no—
612C23—2441no—
613C23—2441no—
614C23Q8×#692312yes—
615C23C23×#692311yescharacteristic
616Q8—82no—
617Q8—4882no—
618Q8—2442no—
619Q8—2442no—
620D4—1224no—
621D4—1224no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—1224no—
640C2×C4—1222no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1224no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—4881no—
648C2×C4—4881no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2442no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4C2×C22⋊#692311yescharacteristic
673C2×C4C2×C22⋊#692311yescharacteristic
674C2×C4C2×C22⋊#692312yes—
675C2×C4C2×C22⋊#692312yes—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—42no—
680C22—42no—
681C22—41no—
682C22—41no—
683C22—612no—
684C22—612no—
685C22—1222no—
686C22—1222no—
687C22—2441no—
688C22—2441no—
689C22—2442no—
690C22C22×C22⋊#692311yescharacteristic
691C22C2×Q8×#692311yescharacteristic
692C22#1684083011yescharacteristic
693C4—22no—
694C4—21no—
695C4—21no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—612no—
701C4—1222no—
702C4—1221no—
703C4—1221no—
704C4—1221no—
705C4—1222no—
706C4—4882no—
707C4—4882no—
708C4—4882no—
709C4—2444no—
710C4—2441no—
711C4—2441no—
712C4—2441no—
713C2—21no—
714C2—21no—
715C2—42no—
716C2—1222no—
717C2—1222no—
718C2Q8×C22⋊#692311yescharacteristic
719C2D61⋊#41011yescharacteristic
720C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22513
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462328C2semidirect
2. #21462010C2semidirect
3. #21462010C2semidirect
4. #21462008C2semidirect
36. C2×#14519775C4semidirect
37. C2×#14519767C4semidirect
38. C2×#14519767C4semidirect
41. C2×#14519754C4semidirect
42. C2×#14519754C4semidirect
44. C2×#14519742C4semidirect
48. C22×#11758196C4semidirect
50. C2×C22⋊Q8×C61C4semidirect
64. #14519835Q8semidirect
384. C2×C22⋊Q8#6923semidirect
411. C61#22513semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214620102
#214620082
#214616812
#214616792
#214615662
C4×#145198352
C2×#168404662
#2251361