Finite Group Databasebeta

← #29648947

Subgroups — #29648947

Order 15616.

1112 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459599C211yesmaximal, characteristic
2#21454946C211yesmaximal, characteristic, complemented
3#21454941C211yesmaximal, characteristic, complemented
4#21444551C211yesmaximal, characteristic, complemented
5#21444544C211yesmaximal, characteristic, complemented
6#21444543C211yesmaximal, characteristic, complemented
7#21444514C211yesmaximal, characteristic, complemented
8#21444511C211yesmaximal, characteristic, complemented
9#21444511C211yesmaximal, characteristic, complemented
10#21444498C211yesmaximal, characteristic, complemented
11#21444498C211yesmaximal, characteristic, complemented
12#21444478C211yesmaximal, characteristic, complemented
13C2×#16839510C211yesmaximal, characteristic, complemented
14#333×D61C211yesmaximal, characteristic, complemented
15C61×#1551C211yesmaximal, characteristic, complemented
16C2×#14519824C412yes—
17D4×Dic122—21no—
18D4×Dic122—21no—
19#16840417—21no—
20#16840417—21no—
21#16840412—21no—
22#16840412—21no—
23#16840412—21no—
24#16840412—21no—
25#16840333C412yes—
26#16840332C412yes—
27#16840332C412yes—
28#16840310C2211yescharacteristic
29#16840310C2211yescharacteristic
30C2×#14519777C2211yescharacteristic
31C4⋊Q8×D61C2211yescharacteristic
32C4⋊Q8×D61C2211yescharacteristic
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839890—21no—
36#16839835—21no—
37#16839833—21no—
38#16839832—21no—
39#16839830—21no—
40C8×C22⋊D61—21no—
41#16839825—21no—
42#16839819C2211yescharacteristic
43#16839818C2211yescharacteristic
44#16839818C2211yescharacteristic
45#16839814C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839784C2211yescharacteristic
48#16839784C2211yescharacteristic
49C2×C4⋊#92418C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51C4⋊C8×D61C2211yescharacteristic
52#16839511C2211yescharacteristic
53#16839511C2211yescharacteristic
54#16839510C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839510C2211yescharacteristic
60#16839510C2211yescharacteristic
61#16839510C2211yescharacteristic
62#16839506C2211yescharacteristic
63#16839506C2211yescharacteristic
64C61×#532C2211yescharacteristic
65C61×#432C2211yescharacteristic
66C2×C4⋊C8×C61C2211yescharacteristic
67C61×#333C2211yescharacteristic
68C61×#333C2211yescharacteristic
69C61×#331C2211yescharacteristic
70C61×#331C2211yescharacteristic
71#14519824—48no—
72C2×#11758222—22no—
73C2×#11758222C2×C411yescharacteristic
74C2×#11758224—22no—
75C2×#11758224—22no—
76C2×#11758224C2×C412yes—
77C2×#11758224C2×C412yes—
78C22×Dic122—22no—
79C22×Dic122C2×C412yes—
80C2×Q8×D61C2×C412yes—
81C2×Q8×D61C2×C412yes—
82C2×#11758189—21no—
83C2×#11758189—21no—
84C22×#92418—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519777—21no—
88#14519777—21no—
89#14519777C2×C412yes—
90#14519777C2311yescharacteristic
91#14519777C2311yescharacteristic
92#14519776—21no—
93#14519776—21no—
94#14519776—21no—
95#14519776—21no—
96#14519775C2×C412yes—
97#14519775C2×C412yes—
98#14519764C2×C412yes—
99#14519764C2×C412yes—
100#14519759—22no—
101#14519759—22no—
102#14519759—22no—
103#14519759—22no—
104#14519758—22no—
105#14519758—22no—
106#14519756—22no—
107#14519756—22no—
108#14519754—22no—
109#14519754—22no—
110#14519754—22no—
111#14519754—22no—
112#14519748—21no—
113#14519748—21no—
114#14519748—21no—
115#14519748—21no—
116C4×Dic122D411yescharacteristic
117C4×Dic122D411yescharacteristic
118C4×D244D411yescharacteristic
119C4×D244D411yescharacteristic
120D4×Dic61—21no—
121D4×Dic61—21no—
122D4×Dic61—21no—
123D4×Dic61—21no—
124C4×C22⋊D61D411yescharacteristic
125C4×C22⋊D61D411yescharacteristic
126C4×C22⋊D61D411yescharacteristic
127C4×C22⋊D61D411yescharacteristic
128#14519736C2×C411yescharacteristic
129#14519734C2×C411yescharacteristic
130#14519734C2×C411yescharacteristic
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61—21no—
137C42×D61C2311yescharacteristic
138C42×D61C2311yescharacteristic
139C4⋊#92418—21no—
140C4⋊#92418C2311yescharacteristic
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143C4⋊#92418C2311yescharacteristic
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147#14519706—21no—
148C22⋊#92418—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689—21no—
152#14519689—21no—
153#14519688—21no—
154#14519687—21no—
155#14519687—21no—
156C8×Dic61—21no—
157C8×Dic61—21no—
158C2×#41×C61C2×C412yes—
159C22×C8×C61—21no—
160C4⋊Q8×C61C2311yescharacteristic
161#127×C61C2311yescharacteristic
162#124×C61C2×C412yes—
163#121×C61—21no—
164#121×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C2×C42×C61C2311yescharacteristic
168C4⋊C8×C61—21no—
169C4⋊C8×C61C2311yescharacteristic
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C4⋊C8×C61C2311yescharacteristic
173C22⋊C8×C61—21no—
174#97×C61—21no—
175#41×C61—44no—
176C2×Q8×C61C22×C412yes—
177C2×D4×C61—22no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61C22×C412yes—
181C22×C4×C61—22no—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61C22⋊C411yescharacteristic
188C2×C22⋊D61C22⋊C411yescharacteristic
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192Q8×D61—44no—
193Q8×D61—44no—
194#11758224—44no—
195#11758224—44no—
196#11758224—48no—
197#11758224—48no—
198#11758222—24no—
199#11758222—48no—
200C2×D244C22⋊C411yescharacteristic
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61C22×C411yescharacteristic
204C2×C4×D61C22×C411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—48no—
213C2×Dic122—44no—
214C2×Dic122C22⋊C411yescharacteristic
215C2×Dic122C22×C412yes—
216C2×Dic122C22×C412yes—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—81no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C42×C61C22×C411yescharacteristic
227C42×C61C2×D411yescharacteristic
228C42×C61C2×D411yescharacteristic
229C42×C61C2411yescharacteristic
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61C22⋊C411yescharacteristic
235C22⋊Dic61C22⋊C411yescharacteristic
236#11758198C22⋊C411yescharacteristic
237#11758198C22⋊C411yescharacteristic
238#11758198C22⋊C411yescharacteristic
239#11758198C22⋊C411yescharacteristic
240C4⋊Dic61—22no—
241C4⋊Dic61—22no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61C22⋊C411yescharacteristic
247C4⋊Dic61C22⋊C411yescharacteristic
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196C22⋊C411yescharacteristic
253#11758196C22⋊C411yescharacteristic
254#11758196C22⋊C411yescharacteristic
255#11758196C22⋊C411yescharacteristic
256C4×Dic61C22×C411yescharacteristic
257C4×Dic61C22×C411yescharacteristic
258C4×Dic61C2×D411yescharacteristic
259C4×Dic61C2×D411yescharacteristic
260C4×Dic61C2×D411yescharacteristic
261C4×Dic61C2×D411yescharacteristic
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—81no—
267#11758189—81no—
268#11758189—81no—
269C8×D61—81no—
270C8×D61—81no—
271C23×C61—22no—
272C23×C61C2×C22⋊C411yescharacteristic
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C2×C22⋊C411yescharacteristic
275Q8×C61—42no—
276D4×C61—42no—
277D4×C61—44no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—44no—
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C22⋊D61—22no—
296C22⋊D61—44no—
297C22⋊D61—44no—
298C22⋊D61#10014yes—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—44no—
302C2×Dic61—44no—
303C2×Dic61—44no—
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C2×C22⋊C411yescharacteristic
308C2×Dic61C2×C22⋊C411yescharacteristic
309C2×Dic61C2×C22⋊C411yescharacteristic
310D244—22no—
311C4×D61—22no—
312C4×D61—21no—
313C4×D61—21no—
314C4×D61—21no—
315C4×D61—21no—
316C4×D61—21no—
317C4×D61—21no—
318C4×D61—21no—
319C4×D61—21no—
320C4×D61—22no—
321C4×D61—44no—
322C4×D61—44no—
323Dic122—22no—
324Dic122—44no—
325Dic122—44no—
326Dic122—44no—
327Dic122—42no—
328Dic122—42no—
329C8×C61—41no—
330C8×C61—41no—
331C8×C61—41no—
332C8×C61—41no—
333#92418—41no—
334#92418—41no—
335#92418—41no—
336#92418—41no—
337#17779—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61C2×#10012yes—
344C22×C61C22×C22⋊C411yescharacteristic
345C2×D61—21no—
346C2×D61—21no—
347C2×D61—21no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61C2×#10012yes—
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—42no—
356C4×C61#57711yescharacteristic
357C4×C61#57711yescharacteristic
358C4×C61#57811yescharacteristic
359C4×C61#57811yescharacteristic
360Dic61—21no—
361Dic61—21no—
362Dic61—21no—
363Dic61—21no—
364Dic61—21no—
365Dic61—42no—
366Dic61—42no—
367Dic61C2×#10012yes—
368#3499—611no—
369#2990—611no—
370#2990—611no—
371#1560—611no—
372#1558—611no—
373#1558—611no—
374#1551—611no—
375#1551—611no—
376#1551—611no—
377#1551D6111yescharacteristic, complemented
378#1548—611no—
379#1548—611no—
380#1543—611no—
381C2×#333—611no—
382C2×#333—611no—
383C2×C61—22no—
384C2×C61—82no—
385C2×C61C22×#10011yescharacteristic
386C2×C61#289811yescharacteristic
387C2×C61#289811yescharacteristic
388D61—22no—
389D61—41no—
390C2×2−1+4—612no—
391D4×Q8—1221no—
392D4×Q8—1221no—
393#547—1221no—
394#547—1221no—
395#547—1221no—
396#547—1221no—
397#547—1221no—
398#547—1221no—
399#536—612no—
400#536—612no—
401#536—612no—
402#532—611no—
403#532—611no—
404#532C2×D6111yescharacteristic
405C2×C4⋊Q8—611no—
406C2×C4⋊Q8—611no—
407C2×C4⋊Q8—611no—
408C4×#41—611no—
409#446—1221no—
410#446—1221no—
411#435—1221no—
412#435—1221no—
413#435—1221no—
414#435—1221no—
415C8×D4—1221no—
416C8×D4—1221no—
417#432—611no—
418#432—611no—
419#432—611no—
420#432C2×D6111yescharacteristic
421#431—611no—
422#431—611no—
423#423—611no—
424#423—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8C2×D6111yescharacteristic
429#333—611no—
430#333—611no—
431#333—611no—
432#333—611no—
433#333—611no—
434#333—611no—
435#333—611no—
436#333—611no—
437#333—611no—
438#333—611no—
439#333C2×D6111yescharacteristic
440#333C2×D6111yescharacteristic
441#331—611no—
442#331—611no—
443#331C2×D6111yescharacteristic
444#331C2×D6111yescharacteristic
445C61#1777911yescharacteristic, complemented, Sylow
4462−1+4—2448no—
447C2×#41—611no—
448C2×#41—612no—
449C2×#41—612no—
450C2×#41—1222no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41C4×D6112yes—
454C22×Q8—612no—
455C22×Q8—612no—
456C22×Q8—612no—
457C22×Q8—1222no—
458C2×M16—1221no—
459C2×M16—1221no—
460C22×C8—21no—
461C22×C8—1221no—
462C22×C8—1221no—
463C22×C8—1221no—
464C4⋊Q8—612no—
465C4⋊Q8—612no—
466C4⋊Q8—612no—
467C4⋊Q8—611no—
468C4⋊Q8—611no—
469C4⋊Q8—1221no—
470C4⋊Q8—1221no—
471C4⋊Q8—1221no—
472C4⋊Q8—1221no—
473C4⋊Q8—1221no—
474C4⋊Q8—1221no—
475C4⋊Q8C22×D6111yescharacteristic
476#127C22×D6111yescharacteristic
477#124—612no—
478#124—612no—
479#124C4×D6112yes—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484#123—1222no—
485#123—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—1222no—
492#121—21no—
493#121—21no—
494#121—1221no—
495#121—1221no—
496#121—1221no—
497#121—1221no—
498C4×Q8—611no—
499C4×Q8—611no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—611no—
503C4×D4—611no—
504C4×D4—611no—
505C4×D4—611no—
506C4×D4—611no—
507C4×D4—611no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512#117—611no—
513#117—611no—
514#117—611no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42C22×D6111yescharacteristic
524C4⋊C8—21no—
525C4⋊C8—611no—
526C4⋊C8—611no—
527C4⋊C8—611no—
528C4⋊C8—611no—
529C4⋊C8—1221no—
530C4⋊C8—1221no—
531C4⋊C8—1221no—
532C4⋊C8—1221no—
533C4⋊C8—1221no—
534C4⋊C8C22×D6111yescharacteristic
535C4⋊C8C22×D6111yescharacteristic
536C4⋊C8C22×D6111yescharacteristic
537C4⋊C8C22×D6111yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—1221no—
540C22⋊C8—1221no—
541C22⋊C8—1221no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544#97—21no—
545#97—1221no—
546#97—1221no—
547#97—1221no—
548C4×C8—1221no—
549C4×C8—1221no—
550#41—44no—
551#41—1224no—
552#41—2448no—
553#41—2444no—
554#41—2444no—
555#41—2448no—
556#41—2448no—
557C2×Q8—611no—
558C2×Q8—612no—
559C2×Q8—612no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—2444no—
564C2×Q8—2448no—
565C2×Q8—2444no—
566C2×Q8—2444no—
567C2×Q8C2×C4×D6112yes—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—611no—
572C2×D4—611no—
573C2×D4—611no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4C2×C4×D6112yes—
577C22×C4—22no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4C2×C4×D6111yescharacteristic
590C22×C4D4×D6111yescharacteristic
591C22×C4D4×D6111yescharacteristic
592M16—4881no—
593M16—4881no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—81no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—4881no—
604C2×C8—4881no—
605C2×C8—4881no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—611no—
609C4⋊C4—611no—
610C4⋊C4—611no—
611C4⋊C4—611no—
612C4⋊C4—611no—
613C4⋊C4—611no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1222no—
623C4⋊C4—1222no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—611no—
627C22⋊C4—611no—
628C22⋊C4—611no—
629C22⋊C4—611no—
630C22⋊C4—611no—
631C22⋊C4—611no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C42—611no—
637C42—611no—
638C42—611no—
639C42—611no—
640C42—611no—
641C42—611no—
642C42C2×C4×D6111yescharacteristic
643C42D4×D6111yescharacteristic
644C42D4×D6111yescharacteristic
645C42C23×D6111yescharacteristic
646C23—22no—
647C23—611no—
648C23—611no—
649C23C22⋊C4×D6111yescharacteristic
650Q8—42no—
651Q8—1222no—
652Q8—2442no—
653Q8—2442no—
654Q8—2444no—
655Q8—2444no—
656Q8—2444no—
657D4—42no—
658D4—44no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—614no—
664D4—1222no—
665D4—1222no—
666D4—2444no—
667D4—2444no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—44no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—611no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—2444no—
694C2×C4—2444no—
695C2×C4—2444no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4C22⋊C4×D6111yescharacteristic
699C2×C4C22⋊C4×D6111yescharacteristic
700C2×C4C22⋊C4×D6111yescharacteristic
701C2×C4C22×C4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×D4×D6111yescharacteristic
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—2441no—
709C8—2441no—
710C8—2441no—
711C8—2441no—
712C22—21no—
713C22—21no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—612no—
718C22—1221no—
719C22—1221no—
720C22—1221no—
721C22—1221no—
722C22—1221no—
723C22#100×D6112yes—
724C22C2×C22⋊C4×D6111yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—42no—
730C4—612no—
731C4—1221no—
732C4—1221no—
733C4—1221no—
734C4—1221no—
735C4—1221no—
736C4—2442no—
737C4—2442no—
738C4#1684056911yescharacteristic
739C4#1684057211yescharacteristic
740C4#1684057611yescharacteristic
741C4#1684057811yescharacteristic
742C2—22no—
743C2—82no—
744C2—1222no—
745C2—2441no—
746C2C2×#100×D6111yescharacteristic
747C2#2145434811yescharacteristic
748C2#2145435011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1551C2
socleC22×C61C22×C22⋊C4
prime radical#21459599C2
cosocleC42×C61C24
hypercenter#1551D61
hypocenterC61#17779
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #21454946C2semidirect
3. #21454941C2semidirect
4. #21444551C2semidirect
5. #21444544C2semidirect
6. #21444543C2semidirect
7. #21444514C2semidirect
8. #21444511C2semidirect
9. #21444511C2semidirect
10. #21444498C2semidirect
11. #21444498C2semidirect
12. #21444478C2semidirect
13. C2×#16839510C2semidirect
14. #333×D61C2semidirect
15. C61×#1551C2semidirect
377. #1551D61semidirect
445. C61#17779semidirect

Maximal subgroups

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

subgroupindex
#214595992
#214549462
#214549412
#214445512
#214445442
#214445432
#214445142
#214445112
#214444982
#214444782
C2×#168395102
#333×D612
C61×#15512
#1777961