Finite Group Databasebeta

← #30544694

Subgroups — #30544694

Order 15616.

1914 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459383C211yesmaximal, characteristic
2#21454836C212yesmaximal, complemented
3#21454821C214yesmaximal, complemented
4#21454817C212yesmaximal, complemented
5#21454802C214yesmaximal, complemented
6#21454788C212yesmaximal, complemented
7#21454780C212yesmaximal, complemented
8#21454762C211yesmaximal, characteristic, complemented
9#21454749C211yesmaximal, characteristic, complemented
10#21454554C211yesmaximal, characteristic, complemented
11#21454549C212yesmaximal, complemented
12#21454525C212yesmaximal, complemented
13C2×#16839839C211yesmaximal, characteristic, complemented
14#21454474C212yesmaximal, complemented
15C4×#14519784C211yesmaximal, characteristic, complemented
16#21454235C212yesmaximal, complemented
17C61×#2925C211yesmaximal, characteristic, complemented
18C2×#14519784C2211yescharacteristic
19C2×#14519784C2211yescharacteristic
20C22×#11758189C2212yes—
21C2×M16×D61C2212yes—
22#16840485C411yescharacteristic
23#16840477C411yescharacteristic
24#16840472C411yescharacteristic
25#16840462C412yes—
26#16840453C412yes—
27#16840452C412yes—
28#16840441C414yes—
29#16840417C411yescharacteristic
30#16840408C412yes—
31#16840319C2211yescharacteristic
32#16840296C2212yes—
33#16840290C2214yes—
34#16840269C2212yes—
35C4×#11758222C2212yes—
36C2×C4×D244C2211yescharacteristic
37#117×D61C2212yes—
38#16839891C2214yescomplemented
39#16839889C2212yescomplemented
40#16839889C2212yescomplemented
41#16839889C2212yescomplemented
42#16839886C2212yescomplemented
43#16839886C2212yescomplemented
44#16839886C2212yescomplemented
45#16839839C2211yescharacteristic
46#16839839C2211yescharacteristic
47#16839839C2212yes—
48#16839839C2211yescharacteristic
49#16839839C2212yes—
50#16839839C2211yescharacteristic
51#16839839C2212yes—
52#16839837C2214yescomplemented
53#16839837C2214yescomplemented
54#16839837C2214yescomplemented
55#16839836C2214yescomplemented
56#16839832C2214yes—
57#16839830C2214yescomplemented
58#16839830C2214yescomplemented
59#16839830C2214yescomplemented
60#16839827C2212yes—
61#16839825C2214yescomplemented
62#16839824C2214yescomplemented
63#16839821C2214yescomplemented
64#16839817C2214yescomplemented
65#16839813C2214yescomplemented
66#16839790C2212yes—
67#16839788C2212yes—
68#16839725C2212yes—
69C2×#14519689C2212yes—
70#16839720C2212yes—
71#16839719C2214yescomplemented
72#16839718C2211yescharacteristic
73#16839718C2211yescharacteristic
74#16839718C2212yescomplemented
75#16839718C2212yescomplemented
76#16839717C2212yes—
77#16839716C2214yescomplemented
78C4×#11758194C2211yescharacteristic
79C4×#11758194C2212yescomplemented
80#16839714C2214yescomplemented
81C4×#11758189C2214yescomplemented
82C2×C4×#92418C2211yescharacteristic
83C2×C4×#92418C2212yescomplemented
84C4×#41×C61C2211yescharacteristic
85C61×#433C2214yescomplemented
86C61×#432C2212yescomplemented
87C61×#431C2212yescomplemented
88C61×#423C2211yescharacteristic
89C2×C4⋊C8×C61C2211yescharacteristic
90C61×#408C2212yes—
91C61×#405C2212yes—
92C2×#11758222C2×C412yes—
93C22×D244C2×C411yescharacteristic
94C22×C4×D61C2312yes—
95#14519784—24no—
96#14519784—24no—
97C2×#11758194C2311yescharacteristic
98C2×#11758194C2312yes—
99C2×#11758194C2312yes—
100C2×#11758194C2311yescharacteristic
101C2×#11758189—28no—
102C2×#11758189C2312yes—
103C2×#11758189C2314yes—
104C2×#11758189C2312yes—
105C2×#11758189C2312yes—
106C2×#11758189C2312yes—
107M16×D61—28no—
108C22×#92418C2311yescharacteristic
109C22×#92418C2312yes—
110C22×#92418C2312yes—
111C22×#92418C2311yescharacteristic
112C2×C8×D61C2314yes—
113#14519777C2×C411yescharacteristic
114#14519777C2×C411yescharacteristic
115#14519772C2×C414yes—
116#14519771C2×C414yes—
117#14519770C2×C414yes—
118#14519769C2×C412yes—
119#14519769C2×C412yes—
120#14519767C2×C414yes—
121#14519765C2×C412yes—
122#14519763C2×C414yes—
123#14519762C2×C414yes—
124#14519760C2×C414yes—
125#14519759C2×C414yes—
126#14519758C2×C414yes—
127#14519756C2×C412yes—
128#14519756C2×C412yes—
129#14519756C2×C412yes—
130#14519755C2×C414yes—
131#14519753C2×C412yes—
132#14519753C2×C412yes—
133#14519751C2×C412yes—
134#14519750C2×C414yes—
135#14519748C2×C412yes—
136#14519748C2×C412yes—
137#14519745C2×C414yes—
138C4×Dic122C2×C412yes—
139C4×Dic122C2312yes—
140C4×Dic122C2312yes—
141C4×D244C2×C412yes—
142C4×D244C2×C411yescharacteristic
143C4×D244C2×C412yes—
144C4×D244C2×C411yescharacteristic
145C4×D244C2311yescharacteristic
146C4×D244C2312yes—
147C4×D244C2311yescharacteristic
148C4×C22⋊D61C2×C414yes—
149C4×C22⋊D61C2314yes—
150C4×C22⋊D61C2314yes—
151#14519736C2×C412yes—
152#14519736C2312yes—
153#14519735C2×C412yes—
154#14519735C2×C412yes—
155#14519734C2×C414yes—
156#14519734C2314yes—
157#14519733C2×C414yes—
158C2×C4⋊Dic61C2×C411yescharacteristic
159C4⋊C4×D61C2×C412yes—
160C4⋊C4×D61C2×C412yes—
161C2×#11758198C2×C412yes—
162C22⋊C4×D61C2×C414yes—
163C42×D61C2314yes—
164#14519706C2314yes—
165#14519706C2314yes—
166#14519706C2314yes—
167#14519706C2314yes—
168#14519689C2312yes—
169#14519689C2312yes—
170#14519689C2312yes—
171#14519689C2312yes—
172#14519689C2314yes—
173#14519689C2314yes—
174#14519688C2312yes—
175#14519688C2312yes—
176#14519688C2312yes—
177#14519687C2314yes—
178#14519687C2314yes—
179C4×#92418C2311yescharacteristic
180C4×#92418C2311yescharacteristic
181C4×#92418C2311yescharacteristic
182C4×#92418C2311yescharacteristic
183C4×#92418C2312yes—
184C4×#92418C2312yes—
185C4×#92418C2312yes—
186C8×Dic61C2314yes—
187C8×Dic61C2314yes—
188C2×#41×C61C2311yescharacteristic
189C2×M16×C61C2312yes—
190C22×C8×C61C2312yes—
191C4×Q8×C61C2×C411yescharacteristic
192C4×Q8×C61C2×C411yescharacteristic
193C4×D4×C61C2×C412yes—
194C4×D4×C61C2×C411yescharacteristic
195C4×D4×C61C2×C411yescharacteristic
196C4×D4×C61C2×C412yes—
197#117×C61C2311yescharacteristic
198#117×C61C2312yes—
199C2×C42×C61C2311yescharacteristic
200C2×C42×C61C2312yes—
201C4⋊C8×C61C2312yes—
202C4⋊C8×C61C2311yescharacteristic
203C4⋊C8×C61C2311yescharacteristic
204C4⋊C8×C61C2312yes—
205C4⋊C8×C61C2312yes—
206C22⋊C8×C61C2314yes—
207C22⋊C8×C61C2314yes—
208#97×C61C2314yes—
209C4×C8×C61C2314yes—
210C23×D61C22×C412yes—
211#41×C61—22no—
212#41×C61—22no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61C22×C412yes—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C412yes—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61C22×C414yes—
223C2×C22⋊D61C22×C414yes—
224C22×Dic61C22×C412yes—
225#11758222—44no—
226C2×D244—42no—
227C2×D244C22×C411yescharacteristic
228C2×D244C22×C411yescharacteristic
229C2×D244C22×C412yes—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C22×C412yes—
234C2×C4×D61C22×C414yes—
235C2×C4×D61C22×C414yes—
236C2×C4×D61C2412yes—
237C2×C4×D61C2412yes—
238C2×Dic122C22×C412yes—
239C2×Dic122C22×C412yes—
240M16×C61—24no—
241C2×C8×C61—24no—
242C2×C8×C61C2412yes—
243C2×C8×C61C2414yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61C22×C411yescharacteristic
246C4⋊C4×C61C22×C411yescharacteristic
247C4⋊C4×C61C22×C412yes—
248C4⋊C4×C61C22×C412yes—
249C22⋊C4×C61C22×C412yes—
250C22⋊C4×C61C22×C412yes—
251C22⋊C4×C61C22×C412yes—
252C42×C61C22×C412yes—
253C42×C61C22×C411yescharacteristic
254C42×C61C22×C411yescharacteristic
255C42×C61C22×C412yes—
256C42×C61C2412yes—
257C42×C61C2411yescharacteristic
258C42×C61C2411yescharacteristic
259C22⋊Dic61C22×C414yes—
260C22⋊Dic61C22×C414yes—
261C22⋊Dic61C22×C414yes—
262#11758198C22×C414yes—
263#11758198C22×C414yes—
264#11758198C22×C412yes—
265#11758198C22×C412yes—
266#11758198C22×C412yes—
267#11758198C22×C412yes—
268#11758198C22×C414yes—
269#11758198C22×C414yes—
270C4⋊Dic61C22×C412yes—
271C4⋊Dic61C22×C412yes—
272C4⋊Dic61C22×C411yescharacteristic
273C4⋊Dic61C22×C411yescharacteristic
274C4⋊Dic61C22×C412yes—
275C4⋊Dic61C22×C412yes—
276C4⋊Dic61C22×C412yes—
277#11758196C22×C414yes—
278#11758196C22×C414yes—
279#11758196C22×C414yes—
280#11758196C22×C414yes—
281#11758196C22×C414yes—
282#11758196C22×C414yes—
283C4×Dic61C22×C414yes—
284C4×Dic61C22×C414yes—
285C4×Dic61C2414yes—
286#11758194—22no—
287#11758194—24no—
288#11758194—24no—
289#11758194#4114yescomplemented
290C2×#92418—22no—
291C2×#92418—24no—
292C2×#92418—24no—
293C2×#92418#4114yescomplemented
294C2×#92418C2411yescharacteristic
295C2×#92418C2411yescharacteristic
296C2×#92418C2412yes—
297C2×#92418C2411yescharacteristic
298C2×#92418C2412yes—
299C2×#92418C2411yescharacteristic
300#11758189—28no—
301#11758189—24no—
302#11758189—24no—
303#11758189—24no—
304#11758189—24no—
305C8×D61—28no—
306C23×C61C23×C412yes—
307C23×C61C23×C411yescharacteristic
308C22×D61—24no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61C23×C412yes—
312C22×D61C23×C412yes—
313Q8×C61—22no—
314D4×C61—24no—
315D4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—24no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61C23×C412yes—
323C2×C4×C61C23×C412yes—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C23×C411yescharacteristic
326C2×C4×C61C23×C412yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C23×C411yescharacteristic
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61C2×#4112yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—44no—
334C22⋊D61—44no—
335C2×Dic61—24no—
336C2×Dic61C23×C412yes—
337C2×Dic61C23×C414yes—
338C2×Dic61C23×C414yes—
339C2×Dic61C23×C412yes—
340D244—22no—
341D244—22no—
342D244—42no—
343C4×D61—24no—
344C4×D61—24no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—44no—
350C4×D61—44no—
351Dic122—24no—
352Dic122—42no—
353C8×C61—24no—
354C8×C61—22no—
355C8×C61—22no—
356#92418—21no—
357#92418—21no—
358#92418—22no—
359#92418C2×#4114yes—
360#92418C2×#4112yes—
361#92418C2×#4112yes—
362#60217—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61C4×#4112yes—
369C22×C61C24×C411yescharacteristic
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—84no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—22no—
382C4×C61—21no—
383C4×C61C4×#4112yes—
384C4×C61#56812yes—
385C4×C61C22×#4111yescharacteristic
386C4×C61C22×#4111yescharacteristic
387Dic61—22no—
388Dic61—22no—
389Dic61—24no—
390Dic61—24no—
391#3475—611no—
392#2971—612no—
393#2969—614no—
394#2969—612no—
395#2967—614no—
396#2966—612no—
397#2965—612no—
398#2962—611no—
399#2960—611no—
400D4×M16—611no—
401#2933—612no—
402#2930—612no—
403C2×#436—611no—
404#2925D6111yescharacteristic, complemented
405#2924—612no—
406C4×#131—611no—
407#2873—612no—
408C2×C61—22no—
409C2×C61—42no—
410C2×C61C2×C4×#4111yescharacteristic
411C2×C61C2×#56811yescharacteristic
412C2×C61#357311yescharacteristic
413D61—42no—
414D61—42no—
415C2×#131—611no—
416C2×#131—611no—
417C22×M16—612no—
418C22×M16—612no—
419#556—611no—
420#555—611no—
421#554—611no—
422#553—612no—
423#552—612no—
424#552—612no—
425#551—614no—
426#547—611no—
427#546—612no—
428#533—611no—
429#529—614no—
430#529—612no—
431#525—612no—
432C4×#41—612no—
433C4×#41C2×D6111yescharacteristic
434C2×C4×D4—611no—
435C2×#117—612no—
436#446—612no—
437#446—612no—
438#446—612no—
439#446—614no—
440C8×Q8—612no—
441C8×Q8—612no—
442C8×Q8—612no—
443#436—611no—
444#436—611no—
445#436—612no—
446#436—611no—
447#436—612no—
448#436—611no—
449#436—612no—
450#436—614no—
451#436—614no—
452#436—614no—
453#435—614no—
454#435—614no—
455#435—614no—
456#435—614no—
457#435—614no—
458C8×D4—612no—
459C8×D4—614no—
460#433—614no—
461#433—614no—
462#433C2×D6114yescomplemented
463#432—614no—
464#432C2×D6112yescomplemented
465#431—614no—
466#431C2×D6112yescomplemented
467#424—612no—
468#424—612no—
469#423C2×D6111yescharacteristic
470C2×C4⋊C8C2×D6111yescharacteristic
471#408C2×D6112yes—
472#407—612no—
473C2×C22⋊C8—612no—
474#405—612no—
475#405—612no—
476#405—611no—
477#405—611no—
478#405—612no—
479#405—612no—
480#405—614no—
481#405—614no—
482#405C2×D6112yes—
483C4×M16—611no—
484C4×M16—612no—
485C4×M16—614no—
486C4×M16—614no—
487C2×C4×C8—611no—
488C2×C4×C8—612no—
489C61#6021711yescharacteristic, complemented, Sylow
490C2×#41—612no—
491C2×#41C22×D6111yescharacteristic
492C22×D4—611no—
493C23×C4—612no—
494#131—1224no—
495#131—1224no—
496C2×M16—611no—
497C2×M16—611no—
498C2×M16—612no—
499C2×M16—612no—
500C2×M16—614no—
501C2×M16—612no—
502C2×M16—612no—
503C2×M16—612no—
504C2×M16—612no—
505C2×M16—1228no—
506C2×M16—1228no—
507C2×M16C22×D6112yes—
508C22×C8—611no—
509C22×C8—611no—
510C22×C8—612no—
511C22×C8—612no—
512C22×C8—614no—
513C22×C8C22×D6112yes—
514C4⋊Q8—611no—
515C4⋊Q8—611no—
516#126—614no—
517#126—614no—
518#126—614no—
519#125—614no—
520#125—612no—
521#125—612no—
522#124—614no—
523#124—612no—
524#123—614no—
525#123—614no—
526#123—614no—
527#123—614no—
528C22⋊Q8—612no—
529C22⋊Q8—612no—
530C22⋊Q8—612no—
531C22⋊Q8—612no—
532C22⋊Q8—612no—
533C22⋊Q8—614no—
534#121—612no—
535#121—612no—
536#121—612no—
537#121—614no—
538#120—614no—
539C4×Q8—612no—
540C4×Q8—612no—
541C4×Q8—612no—
542C4×Q8C4×D6111yescharacteristic
543C4×Q8C4×D6111yescharacteristic
544C4×D4—614no—
545C4×D4—614no—
546C4×D4—614no—
547C4×D4—611no—
548C4×D4—612no—
549C4×D4—611no—
550C4×D4—612no—
551C4×D4—611no—
552C4×D4—611no—
553C4×D4—612no—
554C4×D4C4×D6112yes—
555C4×D4C4×D6111yescharacteristic
556C4×D4C4×D6112yes—
557C4×D4C4×D6111yescharacteristic
558#117—612no—
559#117—612no—
560#117—612no—
561#117—612no—
562#117—614no—
563#117—614no—
564#117—614no—
565#117C22×D6111yescharacteristic
566#117C22×D6112yes—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—612no—
570C2×C22⋊C4—612no—
571C2×C22⋊C4—614no—
572C2×C42—614no—
573C2×C42C22×D6111yescharacteristic
574C2×C42C22×D6112yes—
575C4⋊C8—614no—
576C4⋊C8—614no—
577C4⋊C8—614no—
578C4⋊C8—614no—
579C4⋊C8C22×D6111yescharacteristic
580C4⋊C8C22×D6111yescharacteristic
581C4⋊C8C22×D6112yes—
582C4⋊C8C22×D6112yes—
583C4⋊C8C22×D6112yes—
584C22⋊C8—612no—
585C22⋊C8—612no—
586C22⋊C8—612no—
587C22⋊C8—612no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590C22⋊C8C22×D6114yes—
591C22⋊C8C22×D6114yes—
592#97—614no—
593#97—614no—
594#97—612no—
595#97—612no—
596#97—612no—
597#97C22×D6114yes—
598C4×C8—614no—
599C4×C8—614no—
600C4×C8—611no—
601C4×C8—612no—
602C4×C8—612no—
603C4×C8—611no—
604C4×C8—612no—
605C4×C8—611no—
606C4×C8—611no—
607C4×C8C22×D6114yes—
608C24—612no—
609#41—22no—
610#41—22no—
611#41—2444no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8C2×C4×D6111yescharacteristic
615C2×D4—614no—
616C2×D4—614no—
617C2×D4—611no—
618C2×D4—611no—
619C2×D4—612no—
620C2×D4—2442no—
621C2×D4C2×C4×D6112yes—
622C2×D4C2×C4×D6111yescharacteristic
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—614no—
629C22×C4—614no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6112yes—
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4C2×C4×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638M16—24no—
639M16—614no—
640M16—1224no—
641M16—1224no—
642M16—1224no—
643M16—1224no—
644M16—1228no—
645M16—1224no—
646M16—1224no—
647M16—1222no—
648C2×C8—24no—
649C2×C8—614no—
650C2×C8—611no—
651C2×C8—611no—
652C2×C8—612no—
653C2×C8—611no—
654C2×C8—612no—
655C2×C8—611no—
656C2×C8—1228no—
657C2×C8—1224no—
658C2×C8—1224no—
659C2×C8—1222no—
660C2×C8C23×D6112yes—
661C2×C8C23×D6114yes—
662C2×C8C23×D6112yes—
663C4⋊C4—614no—
664C4⋊C4—614no—
665C4⋊C4—611no—
666C4⋊C4—612no—
667C4⋊C4—612no—
668C4⋊C4—611no—
669C4⋊C4—612no—
670C4⋊C4—614no—
671C4⋊C4—614no—
672C4⋊C4—614no—
673C4⋊C4—614no—
674C4⋊C4—612no—
675C4⋊C4—612no—
676C4⋊C4C2×C4×D6111yescharacteristic
677C4⋊C4C2×C4×D6111yescharacteristic
678C4⋊C4C2×C4×D6112yes—
679C4⋊C4C2×C4×D6112yes—
680C22⋊C4—614no—
681C22⋊C4—614no—
682C22⋊C4—614no—
683C22⋊C4—612no—
684C22⋊C4—614no—
685C22⋊C4—614no—
686C22⋊C4—612no—
687C22⋊C4—612no—
688C22⋊C4—612no—
689C22⋊C4—614no—
690C22⋊C4—614no—
691C22⋊C4C2×C4×D6112yes—
692C22⋊C4C2×C4×D6112yes—
693C22⋊C4C2×C4×D6112yes—
694C42—614no—
695C42—614no—
696C42—614no—
697C42C2×C4×D6112yes—
698C42C2×C4×D6111yescharacteristic
699C42C2×C4×D6111yescharacteristic
700C42C2×C4×D6112yes—
701C42C23×D6111yescharacteristic
702C42C23×D6112yes—
703C42C23×D6111yescharacteristic
704C23—612no—
705C23—612no—
706C23—1224no—
707C23—2442no—
708C23—2442no—
709C23C22×C4×D6112yes—
710C23C22×C4×D6111yescharacteristic
711Q8—22no—
712Q8—1224no—
713Q8—2442no—
714D4—24no—
715D4—22no—
716D4—1222no—
717D4—1222no—
718D4—2442no—
719D4—2444no—
720D4—2444no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—612no—
728C2×C4—614no—
729C2×C4—614no—
730C2×C4—612no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4C22×C4×D6112yes—
741C2×C4C22×C4×D6112yes—
742C2×C4C22×C4×D6111yescharacteristic
743C2×C4C22×C4×D6112yes—
744C2×C4C22×C4×D6111yescharacteristic
745C2×C4C22×C4×D6111yescharacteristic
746C2×C4C22×C4×D6111yescharacteristic
747C2×C4C22×C4×D6111yescharacteristic
748C2×C4#41×D6112yes—
749C2×C4#41×D6112yes—
750C2×C4C24×D6111yescharacteristic
751C8—22no—
752C8—22no—
753C8—24no—
754C8—612no—
755C8—612no—
756C8—614no—
757C8—1221no—
758C8—1222no—
759C8—1221no—
760C22—21no—
761C22—21no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—4884no—
772C22#1684023012yes—
773C22C23×C4×D6111yescharacteristic
774C4—22no—
775C4—21no—
776C4—21no—
777C4—22no—
778C4—21no—
779C4—22no—
780C4—1224no—
781C4—1224no—
782C4—1222no—
783C4—1222no—
784C4#1684023012yes—
785C4#1684052712yes—
786C4C2×#41×D6111yescharacteristic
787C4C2×#41×D6111yescharacteristic
788C2—22no—
789C2—42no—
790C2—2442no—
791C2—2442no—
792C2C2×#1684023011yescharacteristic
793C2C2×#1684052711yescharacteristic
794C2#2146053211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2925C2
prime radical#21459383C2
cosocleC2×C4×C61C25
hypercenter#2925D61
hypocenterC61#60217
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #21454836C2semidirect
3. #21454821C2semidirect
4. #21454817C2semidirect
5. #21454802C2semidirect
6. #21454788C2semidirect
7. #21454780C2semidirect
8. #21454762C2semidirect
9. #21454749C2semidirect
10. #21454554C2semidirect
11. #21454549C2semidirect
12. #21454525C2semidirect
13. C2×#16839839C2semidirect
14. #21454474C2semidirect
15. C4×#14519784C2semidirect
16. #21454235C2semidirect
17. C61×#2925C2semidirect
38. #16839891C22semidirect
39. #16839889C22semidirect
40. #16839889C22semidirect
41. #16839889C22semidirect
42. #16839886C22semidirect
43. #16839886C22semidirect
44. #16839886C22semidirect
52. #16839837C22semidirect
53. #16839837C22semidirect
54. #16839837C22semidirect
55. #16839836C22semidirect
57. #16839830C22semidirect
58. #16839830C22semidirect
59. #16839830C22semidirect
61. #16839825C22semidirect
62. #16839824C22semidirect
63. #16839821C22semidirect
64. #16839817C22semidirect
65. #16839813C22semidirect
71. #16839719C22semidirect
74. #16839718C22semidirect
75. #16839718C22semidirect
77. #16839716C22semidirect
79. C4×#11758194C22semidirect
80. #16839714C22semidirect
81. C4×#11758189C22semidirect
83. C2×C4×#92418C22semidirect
85. C61×#433C22semidirect
86. C61×#432C22semidirect
87. C61×#431C22semidirect
289. #11758194#41semidirect
293. C2×#92418#41semidirect
404. #2925D61semidirect
462. #433C2×D61semidirect
464. #432C2×D61semidirect
466. #431C2×D61semidirect
489. C61#60217semidirect

Maximal subgroups

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

subgroupindex
#214593832
#214548362
#214548212
#214548172
#214548022
#214547882
#214547802
#214547622
#214547492
#214545542
#214545492
#214545252
C2×#168398392
#214544742
C4×#145197842
#214542352
C61×#29252
#6021761