Finite Group Databasebeta

← #30552099

Subgroups — #30552099

Order 15616.

1800 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic, complemented
3#21456995C214yesmaximal, complemented
4#21456985C214yesmaximal, complemented
5#21456980C211yesmaximal, characteristic, complemented
6#21456978C211yesmaximal, characteristic, complemented
7#21456971C211yesmaximal, characteristic, complemented
8#21456964C211yesmaximal, characteristic, complemented
9#21456951C211yesmaximal, characteristic, complemented
10#21456943C211yesmaximal, characteristic, complemented
11#21456936C211yesmaximal, characteristic, complemented
12#21456330C211yesmaximal, characteristic, complemented
13#21456328C211yesmaximal, characteristic, complemented
14#21456138C211yesmaximal, characteristic, complemented
15#21456138C211yesmaximal, characteristic, complemented
16#21455731C214yesmaximal, complemented
17#21455604C214yesmaximal, complemented
18#431×D61C211yesmaximal, characteristic, complemented
19C61×#3228C211yesmaximal, characteristic, complemented
20#16840319C2211yescharacteristic
21#16840319C2211yescharacteristic
22#16840318C2212yes—
23#16840317C2211yescharacteristic
24#16840317C2211yescharacteristic
25#16840317C2211yescharacteristic
26#16840317C2211yescharacteristic
27#16840316—21no—
28#16840316—21no—
29#16840315C2212yes—
30#16840314—21no—
31#16840314—21no—
32#16840310C2211yescharacteristic
33#16840310C2211yescharacteristic
34C4⋊Q8×D61C2211yescharacteristic
35C4⋊Q8×D61C2211yescharacteristic
36#16840294—21no—
37#16840294C2212yes—
38#16840293—21no—
39#16840293C2212yes—
40#16840291—21no—
41#16840291—21no—
42#125×D61C2212yes—
43#16840272—21no—
44#16840272C2212yes—
45#16840269—21no—
46C22⋊Q8×D61—21no—
47C22⋊Q8×D61—21no—
48#41×Dic61—21no—
49C4×#11758224—21no—
50C4×#11758224C2212yes—
51C4×Q8×D61—21no—
52C4×Q8×D61—21no—
53#117×D61C2212yes—
54C2×C42×D61C2211yescharacteristic
55#16840167C2211yescharacteristic, complemented
56#16840165C2211yescharacteristic, complemented
57#16840165C2211yescharacteristic, complemented
58#16840163C2214yescomplemented
59#16840162C2214yescomplemented
60#16840160C2211yescharacteristic, complemented
61#16840158C2211yescharacteristic, complemented
62#16840158C2211yescharacteristic, complemented
63#16840115C2214yescomplemented
64#16840115C2214yescomplemented
65#16840114C2211yescharacteristic, complemented
66#16840114C2211yescharacteristic, complemented
67#16840113C2211yescharacteristic, complemented
68#16840113C2211yescharacteristic, complemented
69#16840108C2211yescharacteristic, complemented
70#16840108C2211yescharacteristic, complemented
71#16840104C2214yes—
72#16840103C2214yes—
73#16840099C2214yes—
74#16840094C2214yes—
75#16840083C2214yes—
76#16840079C2214yes—
77#16840074C2214yes—
78#16840070C2214yescomplemented
79#16840066C2214yescomplemented
80#16840062C2214yescomplemented
81#16840056C2214yescomplemented
82#16840050C2214yescomplemented
83#16840046C2214yescomplemented
84#16840040C2214yescomplemented
85#16839815C2211yescharacteristic
86#16839814C2212yes—
87#16839813C2211yescharacteristic
88#16839813C2211yescharacteristic
89#16839812C2212yes—
90#16839799C2214yes—
91#16839797C2214yes—
92C4⋊C8×D61C2212yes—
93#16839755C2214yes—
94#16839755C2214yes—
95C22⋊C8×D61C2212yes—
96C4×C8×D61C2211yescharacteristic
97C4×C8×D61C2211yescharacteristic
98C61×#533C2211yescharacteristic
99C61×#532C2211yescharacteristic
100C61×#500C2211yescharacteristic, complemented
101C61×#498C2211yescharacteristic, complemented
102C61×#486C2211yescharacteristic, complemented
103C61×#486C2211yescharacteristic, complemented
104C61×#482C2214yes—
105C61×#478C2214yescomplemented
106C61×#431C2211yescharacteristic
107C2×#11758224—21no—
108C2×#11758224C2312yes—
109C2×Q8×D61—21no—
110C2×Q8×D61—21no—
111C22×C4×D61D411yescharacteristic
112C22×C4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C2×C8×D61C2312yes—
115C2×C8×D61C2312yes—
116#14519777C2311yescharacteristic
117#14519777C2311yescharacteristic
118#14519777C2311yescharacteristic
119#14519777C2311yescharacteristic
120#14519776—21no—
121#14519776—21no—
122#14519776C2312yes—
123#14519776C2312yes—
124#14519775—21no—
125#14519775—21no—
126#14519770—22no—
127#14519770—22no—
128#14519769—21no—
129#14519769C2312yes—
130#14519768—21no—
131#14519768C2312yes—
132#14519768C2312yes—
133#14519768C2312yes—
134#14519767—22no—
135#14519767—22no—
136#14519764—21no—
137#14519764C2312yes—
138#14519759—22no—
139#14519759—22no—
140#14519758—22no—
141#14519757—21no—
142#14519757—21no—
143#14519757—21no—
144#14519757C2312yes—
145#14519756—21no—
146#14519756—21no—
147#14519756—21no—
148#14519756C2312yes—
149#14519755—22no—
150#14519755—22no—
151#14519754—22no—
152#14519754—22no—
153#14519753—21no—
154#14519753—21no—
155#14519753—21no—
156#14519753—21no—
157#14519748—21no—
158#14519748—21no—
159#14519748—21no—
160#14519748C2312yes—
161#14519745—22no—
162Q8×Dic61—21no—
163Q8×Dic61—21no—
164Q8×Dic61—21no—
165Q8×Dic61—21no—
166C4×Dic122—21no—
167C4×Dic122—21no—
168C4×Dic122—21no—
169C4×Dic122—22no—
170C4×Dic122—22no—
171C4×Dic122C2312yes—
172#14519742—21no—
173#14519742—21no—
174#14519742—22no—
175#14519742—22no—
176#14519742—21no—
177#14519742C2312yes—
178D4×Dic61—22no—
179D4×Dic61—22no—
180D4×Dic61—21no—
181D4×Dic61—21no—
182D4×Dic61—21no—
183D4×Dic61C2312yes—
184C4×C22⋊D61—22no—
185C4×C22⋊D61—22no—
186#14519737—22no—
187#14519737—22no—
188#14519736—21no—
189#14519736—22no—
190#14519736C2312yes—
191#14519735—21no—
192#14519735C2312yes—
193#14519735C2312yes—
194#14519735C2312yes—
195#14519734—22no—
196#14519733—22no—
197#14519733—22no—
198#14519733—22no—
199C4⋊C4×D61—22no—
200C4⋊C4×D61—22no—
201C4⋊C4×D61—21no—
202C4⋊C4×D61—21no—
203C4⋊C4×D61C2312yes—
204C4⋊C4×D61C2312yes—
205C22⋊C4×D61—22no—
206C2×C4×Dic61—22no—
207C2×C4×Dic61D411yescharacteristic
208C2×C4×Dic61D411yescharacteristic
209C2×C4×Dic61C2311yescharacteristic
210C42×D61—22no—
211C42×D61D411yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61C2311yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219#14519711C2314yes—
220#14519710C2314yes—
221#14519710C2314yes—
222#14519709C2314yes—
223#14519708C2314yes—
224#14519708C2314yes—
225C4⋊#92418C2312yes—
226#14519706C2312yes—
227#14519706C2312yes—
228#14519702C2314yes—
229#14519702C2314yes—
230#14519700C2314yes—
231#14519700C2314yes—
232#14519698C2314yes—
233#14519698C2314yes—
234C22⋊#92418C2312yes—
235#14519689C2312yes—
236#14519689C2312yes—
237C4×#92418C2311yescharacteristic
238C4×#92418C2311yescharacteristic
239C8×Dic61C2312yes—
240C8×Dic61C2312yes—
241C2×#41×C61—21no—
242C4⋊Q8×C61C2311yescharacteristic
243C4⋊Q8×C61C2311yescharacteristic
244C4⋊Q8×C61C2311yescharacteristic
245#127×C61C2311yescharacteristic
246#125×C61C2312yes—
247#124×C61—21no—
248C22⋊Q8×C61—21no—
249C22⋊Q8×C61—21no—
250#121×C61—21no—
251#121×C61C2312yes—
252C4×Q8×C61—21no—
253C4×Q8×C61—21no—
254C4×D4×C61—21no—
255C4×D4×C61C2312yes—
256#117×C61C2312yes—
257C2×C42×C61C2311yescharacteristic
258#107×C61C2314yes—
259#106×C61C2314yes—
260C4⋊C8×C61C2312yes—
261#102×C61C2314yes—
262#102×C61C2314yes—
263C22⋊C8×C61C2312yes—
264C4×C8×C61C2311yescharacteristic
265C4×C8×C61C2311yescharacteristic
266C23×D61C2×D411yescharacteristic
267#41×C61—44no—
268C2×Q8×C61—21no—
269C2×Q8×C61—21no—
270C2×Q8×C61—21no—
271C2×D4×C61—22no—
272C2×D4×C61—21no—
273C2×D4×C61—21no—
274C2×D4×C61C2412yes—
275C22×C4×C61—22no—
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2411yescharacteristic
279C2×C22⋊D61—22no—
280C2×C22⋊D61—22no—
281C22×Dic61—22no—
282C22×Dic61—22no—
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D411yescharacteristic
286Q8×D61—44no—
287Q8×D61—44no—
288#11758224—28no—
289#11758224—44no—
290C2×C4×D61—24no—
291C2×C4×D61—24no—
292C2×C4×D61—22no—
293C2×C4×D61—22no—
294C2×C4×D61—42no—
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61C2×D411yescharacteristic
299C2×C4×D61C2×D411yescharacteristic
300C2×C4×D61C2×D411yescharacteristic
301C2×C4×D61C2×D411yescharacteristic
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
304C2×C4×D61C2×D411yescharacteristic
305C2×C4×D61C2411yescharacteristic
306C2×C4×D61C2411yescharacteristic
307C2×Dic122—21no—
308C2×Dic122—21no—
309C2×Dic122—21no—
310C2×Dic122—22no—
311C2×Dic122—22no—
312C2×Dic122C2412yes—
313C2×C8×C61C2412yes—
314C2×C8×C61C2412yes—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—22no—
317C4⋊C4×C61—22no—
318C4⋊C4×C61—21no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61C2412yes—
321C4⋊C4×C61C2412yes—
322C4⋊C4×C61C2412yes—
323C22⋊C4×C61—22no—
324C22⋊C4×C61—22no—
325C22⋊C4×C61—22no—
326C42×C61—22no—
327C42×C61C2×D411yescharacteristic
328C42×C61C2×D411yescharacteristic
329C42×C61C2411yescharacteristic
330C42×C61C2411yescharacteristic
331C22⋊Dic61—22no—
332C22⋊Dic61—22no—
333C22⋊Dic61—22no—
334C22⋊Dic61—22no—
335C22⋊Dic61—22no—
336C22⋊Dic61—22no—
337#11758198—22no—
338#11758198—22no—
339#11758198—22no—
340#11758198—22no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4⋊Dic61—21no—
346C4⋊Dic61—22no—
347C4⋊Dic61—22no—
348C4⋊Dic61—22no—
349C4⋊Dic61—22no—
350C4⋊Dic61C2412yes—
351C4⋊Dic61C2412yes—
352C4⋊Dic61C2412yes—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360#11758196—22no—
361#11758196—22no—
362#11758196—22no—
363#11758196—22no—
364#11758196—22no—
365C4×Dic61—22no—
366C4×Dic61—22no—
367C4×Dic61—22no—
368C4×Dic61—22no—
369C4×Dic61—22no—
370C4×Dic61—22no—
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C4×Dic61C2411yescharacteristic
382C4×Dic61C2411yescharacteristic
383C2×#92418C2412yes—
384C2×#92418C2412yes—
385C8×D61—24no—
386C8×D61—24no—
387C23×C61—22no—
388C23×C61C22×D411yescharacteristic
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—41no—
392C22×D61C22×D411yescharacteristic
393C22×D61C22×D411yescharacteristic
394Q8×C61—42no—
395Q8×C61—42no—
396Q8×C61—42no—
397D4×C61—24no—
398D4×C61—44no—
399D4×C61—42no—
400D4×C61—42no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—44no—
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61C22×D411yescharacteristic
413C2×C4×C61C2511yescharacteristic
414C22⋊D61—44no—
415C22⋊D61—44no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—41no—
423C2×Dic61—44no—
424C2×Dic61—44no—
425C2×Dic61C22×D411yescharacteristic
426C2×Dic61C22×D411yescharacteristic
427C2×Dic61C22×D411yescharacteristic
428C2×Dic61C22×D411yescharacteristic
429C2×Dic61C22×D411yescharacteristic
430C2×Dic61C22×D411yescharacteristic
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—22no—
439C4×D61—41no—
440C4×D61—41no—
441C4×D61—44no—
442C4×D61—44no—
443C4×D61#13514yes—
444C4×D612−1+414yes—
445Dic122—24no—
446Dic122—44no—
447Dic122—42no—
448Dic122—42no—
449Dic122—42no—
450Dic122—44no—
451C8×C61—22no—
452C8×C61—22no—
453#92418—22no—
454#92418—22no—
455#60846—611nomaximal, Sylow
456C22×C61—21no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—42no—
460C22×C61—42no—
461C22×C61—42no—
462C22×C61C23×D411yescharacteristic
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—44no—
468C2×D61#53612yes—
469C2×D61C2×#13512yes—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—42no—
474C4×C61—42no—
475C4×C61—42no—
476C4×C61C2×#13512yes—
477C4×C61#57512yes—
478C4×C61C2×2−1+412yes—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—21no—
483Dic61—42no—
484Dic61—42no—
485Dic61—42no—
486Dic61—42no—
487Dic61#53612yes—
488Dic61C2×#13512yes—
489#3444—611no—
490C2×#533—611no—
491#3233—614no—
492#3232—614no—
493#3231—611no—
494#3231—611no—
495#3230—611no—
496#3229—611no—
497#3228—611no—
498#3228D6111yescharacteristic, complemented
499#3227—611no—
500#3226—611no—
501#3160—611no—
502#3160—611no—
503#3131—611no—
504#3131—611no—
505#3091—614no—
506#3076—614no—
507C2×#431—611no—
508C2×C61—41no—
509C2×C61—82no—
510C2×C61C2×#53611yescharacteristic
511C2×C61C22×#13511yescharacteristic
512C2×C61C2×#57511yescharacteristic
513D61—22no—
514D61—22no—
515#533—611no—
516#533—611no—
517#533—611no—
518#533—612no—
519#533—612no—
520#533—611no—
521#533—611no—
522#533—611no—
523#533—1221no—
524#533—1221no—
525#533—1221no—
526#533—1221no—
527#533C2×D6111yescharacteristic
528#532—611no—
529#532—611no—
530#532C2×D6111yescharacteristic
531C2×C4⋊Q8—611no—
532C2×C4⋊Q8—611no—
533#529—612no—
534#529—612no—
535#529—1221no—
536#529—1221no—
537#529—1221no—
538#529—1221no—
539C2×#125—612no—
540#525—612no—
541#525—1221no—
542#525—1221no—
543C2×C22⋊Q8—1221no—
544C2×C22⋊Q8—1221no—
545C4×#41—612no—
546C4×#41—1221no—
547C4×#41—1221no—
548C2×C4×Q8—1221no—
549C2×C4×Q8—1221no—
550C2×#117—612no—
551C22×C42—611no—
552#500—611no—
553#500—611no—
554#500—611no—
555#500C2×D6111yescharacteristic, complemented
556#499—614no—
557#499—614no—
558#498—611no—
559#498—611no—
560#498—611no—
561#498C2×D6111yescharacteristic, complemented
562#488—614no—
563#488—614no—
564#487—611no—
565#487—611no—
566#487—611no—
567#487—611no—
568#486—611no—
569#486—611no—
570#486C2×D6111yescharacteristic, complemented
571#486C2×D6111yescharacteristic, complemented
572#485—614no—
573#485—614no—
574#484—614no—
575#483—614no—
576#482—614no—
577#482C2×D6114yes—
578#481—614no—
579#480—614no—
580#479—614no—
581#479—614no—
582#478—614no—
583#478C2×D6114yescomplemented
584#477—614no—
585#476—614no—
586#475—614no—
587#474—614no—
588#431—611no—
589#431—612no—
590#431—612no—
591#431—611no—
592#431—611no—
593#431C2×D6111yescharacteristic
594#427—614no—
595#427—614no—
596C2×C4⋊C8—612no—
597#416—614no—
598#416—614no—
599C2×C22⋊C8—612no—
600C2×C4×C8—611no—
601C2×C4×C8—611no—
602C61#6084611yescharacteristic, complemented, Sylow
603C2×#41—21no—
604C2×#41—612no—
605C2×#41—1221no—
606C22×Q8—1221no—
607C22×Q8—1221no—
608C23×C4—611no—
609C23×C4—611no—
610C23×C4—611no—
611C22×C8—612no—
612C22×C8—612no—
613C4⋊Q8—612no—
614C4⋊Q8—612no—
615C4⋊Q8—611no—
616C4⋊Q8—611no—
617C4⋊Q8—611no—
618C4⋊Q8—611no—
619C4⋊Q8—1221no—
620C4⋊Q8—1221no—
621C4⋊Q8—1221no—
622C4⋊Q8—1221no—
623C4⋊Q8C22×D6111yescharacteristic
624C4⋊Q8C22×D6111yescharacteristic
625C4⋊Q8C22×D6111yescharacteristic
626#127C22×D6111yescharacteristic
627#126—1222no—
628#126—1222no—
629#125—612no—
630#125—612no—
631#125—612no—
632#125—612no—
633#125—1222no—
634#125—1222no—
635#125—1221no—
636#125—1221no—
637#125C22×D6112yes—
638#124—21no—
639#124—612no—
640#124—1221no—
641#123—1222no—
642#123—1222no—
643#123—1222no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—612no—
647C22⋊Q8—612no—
648C22⋊Q8—1222no—
649C22⋊Q8—1222no—
650C22⋊Q8—1222no—
651C22⋊Q8—1222no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8—1221no—
662#121—21no—
663#121—612no—
664#121—1221no—
665#121—1221no—
666#121—1221no—
667#121C22×D6112yes—
668#120—1222no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8—612no—
672C4×Q8—612no—
673C4×Q8—1222no—
674C4×Q8—1222no—
675C4×Q8—1222no—
676C4×Q8—1222no—
677C4×Q8—1221no—
678C4×Q8—1221no—
679C4×Q8—1221no—
680C4×Q8—1221no—
681C4×Q8—1221no—
682C4×Q8—1221no—
683C4×Q8—1221no—
684C4×Q8—1221no—
685C4×Q8—1221no—
686C4×Q8—1221no—
687C4×D4—21no—
688C4×D4—612no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C4×D4—1222no—
693C4×D4—1222no—
694C4×D4—1222no—
695C4×D4—1222no—
696C4×D4—1222no—
697C4×D4—1222no—
698C4×D4C22×D6112yes—
699#117—612no—
700#117—612no—
701#117—612no—
702#117—612no—
703#117—1222no—
704#117—1222no—
705#117—1222no—
706#117—1222no—
707#117—1222no—
708#117—1221no—
709#117—1221no—
710#117C22×D6112yes—
711C2×C4⋊C4—612no—
712C2×C4⋊C4—612no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C22⋊C4—1222no—
718C2×C42—611no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—611no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42C22×D6111yescharacteristic
732#107—614no—
733#107—614no—
734#107—614no—
735#107C22×D6114yes—
736#106—614no—
737#106—614no—
738#106—614no—
739#106C22×D6114yes—
740C4⋊C8—612no—
741C4⋊C8—612no—
742C4⋊C8—612no—
743C4⋊C8C22×D6112yes—
744#103—614no—
745#103—614no—
746#103—614no—
747#103—614no—
748#102—614no—
749#102—614no—
750#102C22×D6114yes—
751#102C22×D6114yes—
752C22⋊C8—612no—
753C22⋊C8—612no—
754C22⋊C8—612no—
755C22⋊C8C22×D6112yes—
756C4×C8—612no—
757C4×C8—612no—
758C4×C8—611no—
759C4×C8—611no—
760C4×C8C22×D6111yescharacteristic
761C4×C8C22×D6111yescharacteristic
762C24—611no—
763#41—44no—
764#41—1228no—
765#41—2444no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—612no—
770C2×Q8—1222no—
771C2×Q8—1222no—
772C2×Q8—1221no—
773C2×Q8—1221no—
774C2×Q8—1221no—
775C2×Q8—2444no—
776C2×Q8—2444no—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—1222no—
781C2×D4—1222no—
782C2×D4C23×D6112yes—
783C22×C4—22no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—1224no—
800C22×C4—1224no—
801C22×C4—1222no—
802C22×C4—1222no—
803C22×C4—1222no—
804C22×C4—1222no—
805C22×C4—2442no—
806C22×C4D4×D6111yescharacteristic
807C22×C4D4×D6111yescharacteristic
808C22×C4C23×D6111yescharacteristic
809C2×C8—612no—
810C2×C8—612no—
811C2×C8—1224no—
812C2×C8—1224no—
813C2×C8C23×D6112yes—
814C2×C8C23×D6112yes—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—612no—
821C4⋊C4—612no—
822C4⋊C4—612no—
823C4⋊C4—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—1222no—
828C4⋊C4—1222no—
829C4⋊C4—1222no—
830C4⋊C4—1222no—
831C4⋊C4—1222no—
832C4⋊C4—1222no—
833C4⋊C4—1222no—
834C4⋊C4—1222no—
835C4⋊C4—1222no—
836C4⋊C4—1222no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1222no—
840C4⋊C4—1222no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4C23×D6112yes—
845C4⋊C4C23×D6112yes—
846C4⋊C4C23×D6112yes—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—1222no—
851C22⋊C4—1222no—
852C22⋊C4—1222no—
853C22⋊C4—1222no—
854C22⋊C4—1222no—
855C22⋊C4—1222no—
856C22⋊C4—1222no—
857C22⋊C4—1222no—
858C22⋊C4—1222no—
859C22⋊C4—1222no—
860C42—22no—
861C42—611no—
862C42—611no—
863C42—611no—
864C42—611no—
865C42—611no—
866C42—611no—
867C42—611no—
868C42—611no—
869C42—611no—
870C42—611no—
871C42—611no—
872C42—611no—
873C42—1222no—
874C42—1222no—
875C42—1222no—
876C42—1222no—
877C42—1222no—
878C42—1222no—
879C42D4×D6111yescharacteristic
880C42D4×D6111yescharacteristic
881C42C23×D6111yescharacteristic
882C42C23×D6111yescharacteristic
883C23—22no—
884C23—611no—
885C23—611no—
886C23—1222no—
887C23—1222no—
888C23—2441no—
889C23C2×D4×D6111yescharacteristic
890Q8—42no—
891Q8—42no—
892Q8—42no—
893Q8—1224no—
894Q8—2444no—
895Q8—2444no—
896Q8—2442no—
897Q8—2442no—
898Q8—2442no—
899D4—24no—
900D4—44no—
901D4—42no—
902D4—42no—
903D4—2444no—
904D4—2444no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—44no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—614no—
915C2×C4—614no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—611no—
919C2×C4—611no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2444no—
937C2×C4—2444no—
938C2×C4—2444no—
939C2×C4—2444no—
940C2×C4—2441no—
941C2×C4C2×D4×D6111yescharacteristic
942C2×C4C2×D4×D6111yescharacteristic
943C2×C4C2×D4×D6111yescharacteristic
944C2×C4C2×D4×D6111yescharacteristic
945C2×C4C2×D4×D6111yescharacteristic
946C2×C4C24×D6111yescharacteristic
947C8—22no—
948C8—22no—
949C8—1222no—
950C8—1222no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—612no—
958C22—612no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—2444no—
964C22C22×D4×D6111yescharacteristic
965C4—21no—
966C4—21no—
967C4—21no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—612no—
972C4—612no—
973C4—1221no—
974C4—1221no—
975C4—1221no—
976C4—1221no—
977C4—2442no—
978C4—2442no—
979C4—2442no—
980C4—2442no—
981C4#135×D6112yes—
982C4#1684055812yes—
983C42−1+4×D6112yes—
984C2—41no—
985C2—82no—
986C2—1222no—
987C2—1222no—
988C2#536×D6111yescharacteristic
989C2C2×#135×D6111yescharacteristic
990C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3228C2
socleC22×C61C23×D4
prime radical#21459114C2
hypercenter#3228D61
hypocenterC61#60846
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
2. #533×D61C2semidirect
3. #21456995C2semidirect
4. #21456985C2semidirect
5. #21456980C2semidirect
6. #21456978C2semidirect
7. #21456971C2semidirect
8. #21456964C2semidirect
9. #21456951C2semidirect
10. #21456943C2semidirect
11. #21456936C2semidirect
12. #21456330C2semidirect
13. #21456328C2semidirect
14. #21456138C2semidirect
15. #21456138C2semidirect
16. #21455731C2semidirect
17. #21455604C2semidirect
18. #431×D61C2semidirect
19. C61×#3228C2semidirect
55. #16840167C22semidirect
56. #16840165C22semidirect
57. #16840165C22semidirect
58. #16840163C22semidirect
59. #16840162C22semidirect
60. #16840160C22semidirect
61. #16840158C22semidirect
62. #16840158C22semidirect
63. #16840115C22semidirect
64. #16840115C22semidirect
65. #16840114C22semidirect
66. #16840114C22semidirect
67. #16840113C22semidirect
68. #16840113C22semidirect
69. #16840108C22semidirect
70. #16840108C22semidirect
78. #16840070C22semidirect
79. #16840066C22semidirect
80. #16840062C22semidirect
81. #16840056C22semidirect
82. #16840050C22semidirect
83. #16840046C22semidirect
84. #16840040C22semidirect
100. C61×#500C22semidirect
101. C61×#498C22semidirect
102. C61×#486C22semidirect
103. C61×#486C22semidirect
105. C61×#478C22semidirect
498. #3228D61semidirect
555. #500C2×D61semidirect
561. #498C2×D61semidirect
570. #486C2×D61semidirect
571. #486C2×D61semidirect
583. #478C2×D61semidirect
602. C61#60846semidirect

Maximal subgroups

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

subgroupindex
#214591142
#533×D612
#214569952
#214569852
#214569802
#214569782
#214569712
#214569642
#214569512
#214569432
#214569362
#214563302
#214563282
#214561382
#214557312
#214556042
#431×D612
C61×#32282
#6084661