Finite Group Databasebeta

← #30610955

Subgroups — #30610955

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461212C212yesmaximal, complemented
4#21461209C212yesmaximal, complemented
5#21461207C212yesmaximal, complemented
6#21461205C212yesmaximal, complemented
7#21461192C212yesmaximal, complemented
8#21461190C212yesmaximal, complemented
9#21459112C211yesmaximal, characteristic
10C22×C4×#6923—21no—
11#16840785C2212yes—
12#16840784—21no—
13#16840781C2212yes—
14#16840780—21no—
15#16840765—21no—
16#16840734C2212yes—
17C4×#11758217—21no—
18#16840698—21no—
19#16840698—21no—
20#16840698C2212yes—
21#16840698C2212yes—
22C2×(C2×#6923)⋊C4—21no—
23C2×(C2×#6923)⋊C4C2212yes—
24#16840616C2214yes—
25#16840615C2214yes—
26#16840614C2214yes—
27#16840613C2214yes—
28#16840316C411yescharacteristic, complemented
29#16840316C2211yescharacteristic
30#16840315C411yescharacteristic, complemented
31#16840309C411yescharacteristic, complemented
32#16840309C2211yescharacteristic
33#16840308C411yescharacteristic, complemented
34#16840299C411yescharacteristic, complemented
35#16840299C2211yescharacteristic
36#16840294C411yescharacteristic, complemented
37#16840294C2211yescharacteristic
38#16840292—21no—
39#16840292—21no—
40#16840290—21no—
41#16840290—21no—
42#16840274C2211yescharacteristic
43#16840271—21no—
44#16840271—21no—
45#16840269C2211yescharacteristic
46C4×#11758222—21no—
47C4×#11758222—21no—
48C4×#11758222C411yescharacteristic, complemented
49C2×C42×D61C2211yescharacteristic
50C4×#41×C61C411yescharacteristic, complemented
51C23×#6923—22no—
52C2×#11758217—22no—
53C2×C4×#6923—28no—
54C2×C4×#6923—22no—
55C2×C4×#6923—22no—
56#14519844—22no—
57C4⋊#92420—22no—
58#14519834—22no—
59#14519834C2314yes—
60#14519832—22no—
61C4×#92420—22no—
62(C2×#6923)⋊C4—22no—
63(C2×#6923)⋊C4—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4C2314yes—
66C2×#11758222—21no—
67C2×#11758222—21no—
68C2×#11758222C2×C411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72#14519776C2×C411yescharacteristic, complemented
73#14519776C2×C411yescharacteristic, complemented
74#14519775C2×C411yescharacteristic, complemented
75#14519773C2×C411yescharacteristic, complemented
76#14519772—21no—
77#14519772—21no—
78#14519770—21no—
79#14519770—21no—
80#14519768C2×C411yescharacteristic, complemented
81#14519768C2×C411yescharacteristic, complemented
82#14519767—21no—
83#14519767—21no—
84#14519766C2×C411yescharacteristic, complemented
85#14519764C2×C411yescharacteristic, complemented
86#14519763—21no—
87#14519763—21no—
88#14519762—21no—
89#14519762—21no—
90#14519761—21no—
91#14519759—21no—
92#14519759—21no—
93#14519758—21no—
94#14519757C2×C411yescharacteristic
95#14519757C2311yescharacteristic
96#14519755—21no—
97#14519755—21no—
98#14519754—21no—
99#14519754—21no—
100#14519753C2×C411yescharacteristic
101#14519753C2311yescharacteristic
102#14519752C2×C411yescharacteristic
103#14519752C2311yescharacteristic
104#14519750—21no—
105#14519750—21no—
106#14519749—21no—
107#14519749—21no—
108#14519748C2×C411yescharacteristic
109#14519748C2311yescharacteristic
110#14519747—21no—
111#14519745—21no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122—21no—
115C4×Dic122—21no—
116C4×Dic122C2×C411yescharacteristic, complemented
117C4×Dic122C2×C411yescharacteristic, complemented
118C4×D244—21no—
119C4×D244—21no—
120C4×D244—21no—
121C4×D244—21no—
122C4×D244C2×C411yescharacteristic, complemented
123C4×D244C2×C411yescharacteristic, complemented
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134#14519736—21no—
135#14519736—21no—
136#14519736C2×C411yescharacteristic
137#14519734—21no—
138#14519734—21no—
139#14519734—21no—
140#14519734—21no—
141#14519734—21no—
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C42×D61—21no—
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61C2311yescharacteristic
153C42×D61C2311yescharacteristic
154C2×#41×C61C2×C411yescharacteristic
155C4×Q8×C61C2×C411yescharacteristic, complemented
156C4×Q8×C61C2×C411yescharacteristic, complemented
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61C2×C411yescharacteristic, complemented
160C4×D4×C61C2×C411yescharacteristic, complemented
161#117×C61—21no—
162#117×C61C2×C411yescharacteristic
163C2×C42×C61—21no—
164C2×C42×C61C2×C411yescharacteristic
165C23×D61C2×D411yescharacteristic
166C22×#6923—28no—
167C22×#6923—24no—
168C22×#6923—44no—
169C22×#6923—44no—
170#41×C61—42no—
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C22⋊C411yescharacteristic
178C22×C4×C61C22⋊C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188#11758222—44no—
189#11758222—42no—
190#11758222—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244C22×C411yescharacteristic
194C2×C4×D61—24no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
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×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215#11758217—44no—
216C2×#92420—24no—
217C4×#6923—28no—
218C4×#6923—28no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C22⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61C22⋊C411yescharacteristic
230C42×C61C22⋊C411yescharacteristic
231C42×C61C22×C411yescharacteristic
232C42×C61C22×C411yescharacteristic
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235C22⋊Dic61—21no—
236C22⋊Dic61—21no—
237C22⋊Dic61—21no—
238#11758198—21no—
239#11758198—21no—
240#11758198—21no—
241#11758198—21no—
242#11758198—21no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C411yescharacteristic
253C4⋊Dic61C22×C411yescharacteristic
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61C22⋊C411yescharacteristic
268C4×Dic61C22⋊C411yescharacteristic
269C4×Dic61C22⋊C411yescharacteristic
270C4×Dic61C22⋊C411yescharacteristic
271C4×Dic61C22⋊C411yescharacteristic
272C4×Dic61C22⋊C411yescharacteristic
273C4×Dic61C22×C411yescharacteristic
274C4×Dic61C22×C411yescharacteristic
275C4×Dic61C2×D411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278C4×Dic61C2×D411yescharacteristic
279C23×C61—21no—
280C23×C61C2×C22⋊C411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—21no—
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61C22×D411yescharacteristic
287C2×#6923—28no—
288C2×#6923—416no—
289C2×#6923—44no—
290C2×#6923—44no—
291Q8×C61—41no—
292D4×C61—41no—
293D4×C61—42no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C23×C411yescharacteristic
309C22⋊D61—42no—
310C22⋊D61—42no—
311C22⋊D61—42no—
312C22⋊D61—42no—
313C22⋊D61—42no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C22×D411yescharacteristic
326D244—41no—
327D244—42no—
328D244—42no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61#10414yes—
344Dic122—42no—
345Dic122—42no—
346Dic122—41no—
347#92420—44no—
348#17541—611nomaximal, Sylow
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61#41012yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C2×D61—28no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61C2×#10412yes—
365C2×D61#57512yes—
366#6923—48no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61C2×#10412yes—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—21no—
380Dic61—21no—
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61C2×#10412yes—
385#3444—611no—
386#2920—611no—
387C2×#376—611no—
388#1506—612no—
389#1505—612no—
390#1504—612no—
391#1504—612no—
392#1500—612no—
393#1500—612no—
394C2×C61—22no—
395C2×C61—81no—
396C2×C61C2×#41011yescharacteristic
397C2×C61#289611yescharacteristic
398C2×C61C22×#10411yescharacteristic
399D61—22no—
400D61—22no—
401D61—81no—
402#533—611no—
403#533—611no—
404#533—611no—
405#532—611no—
406#532—611no—
407#532—611no—
408#529—611no—
409#529—611no—
410#529—611no—
411#529—611no—
412#529—1221no—
413#529—1221no—
414#529—1221no—
415#529—1221no—
416#525—611no—
417#525—611no—
418#525—1221no—
419#525—1221no—
420C4×#41—611no—
421C4×#41—1221no—
422C4×#41—1221no—
423C4×#41#692311yescharacteristic, complemented
424C22×C42—611no—
425C22×C42—1221no—
426#432—612no—
427#432—1221no—
428#431—612no—
429#431—1221no—
430#423—1221no—
431#407—612no—
432C4×M16—1221no—
433#376—612no—
434#376—612no—
435#376—1221no—
436#376—1221no—
437C2×#95—612no—
438C2×#95—1221no—
439#328—614no—
440#328—614no—
441#327—614no—
442#327—614no—
443C61#1754111yescharacteristic, complemented, Sylow
444C2×#41—611no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41C2×#692311yescharacteristic
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—1222no—
452C2×M16—1222no—
453C4⋊Q8—611no—
454C4⋊Q8—611no—
455C4⋊Q8—611no—
456#127—611no—
457#126—1221no—
458#126—1221no—
459#126—1221no—
460#126—1221no—
461#125—611no—
462#125—611no—
463#125—1221no—
464#125—1221no—
465#124—611no—
466#124—611no—
467#124—1221no—
468#124—1221no—
469#123—1221no—
470#123—1221no—
471#123—1221no—
472#123—1221no—
473#123—1221no—
474#123—1221no—
475C22⋊Q8—611no—
476C22⋊Q8—611no—
477C22⋊Q8—611no—
478C22⋊Q8—611no—
479C22⋊Q8—1221no—
480C22⋊Q8—1221no—
481C22⋊Q8—1221no—
482C22⋊Q8—1221no—
483#121—611no—
484#121—611no—
485#121—611no—
486#121—611no—
487#121—1221no—
488#121—1221no—
489#121—1221no—
490#121—1221no—
491#120—1221no—
492#120—1221no—
493C4×Q8—611no—
494C4×Q8—611no—
495C4×Q8—1221no—
496C4×Q8—1221no—
497C4×Q8—1221no—
498C4×Q8—1221no—
499C4×Q8C2×#692311yescharacteristic, complemented
500C4×Q8C2×#692311yescharacteristic, complemented
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—611no—
504C4×D4—611no—
505C4×D4—1221no—
506C4×D4—1221no—
507C4×D4—1221no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4—1221no—
519C4×D4C2×#692311yescharacteristic, complemented
520C4×D4C2×#692311yescharacteristic, complemented
521#117—21no—
522#117—611no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526#117—1221no—
527#117—1221no—
528#117—1221no—
529#117—1221no—
530#117C2×#692311yescharacteristic
531C2×C42—21no—
532C2×C42—611no—
533C2×C42—611no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—1222no—
544C2×C42—1222no—
545C2×C42—1228no—
546C2×C42—1221no—
547C2×C42C2×#692311yescharacteristic
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C22⋊C8—614no—
551C22⋊C8—1222no—
552#97—1222no—
553C4×C8—1222no—
554#95—614no—
555#95—1222no—
556#95—1222no—
557#95—1222no—
558C24—611no—
559#41—42no—
560#41—2442no—
561#41—2444no—
562#41—2444no—
563C2×Q8—611no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8C22×#692311yescharacteristic
567C2×D4—21no—
568C2×D4—611no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4C22×#692311yescharacteristic
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1228no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4C22⋊#692311yescharacteristic
606C22×C4C22⋊#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608M16—2444no—
609C2×C8—1224no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—611no—
613C4⋊C4—611no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4C22×#692311yescharacteristic
629C4⋊C4C22×#692311yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—1221no—
634C22⋊C4—1221no—
635C22⋊C4—1221no—
636C22⋊C4—1221no—
637C22⋊C4—1221no—
638C22⋊C4—1221no—
639C22⋊C4—1221no—
640C22⋊C4—1221no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—611no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42—611no—
660C42—611no—
661C42—611no—
662C42—611no—
663C42—1228no—
664C42—1228no—
665C42—1221no—
666C42—1221no—
667C42—1221no—
668C42C22⋊#692311yescharacteristic
669C42C22⋊#692311yescharacteristic
670C42C22×#692311yescharacteristic
671C42C22×#692311yescharacteristic
672C23—21no—
673C23—611no—
674C23—611no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23C2×C22⋊#692311yescharacteristic
680Q8—41no—
681Q8—2441no—
682Q8—2442no—
683Q8—2442no—
684D4—41no—
685D4—42no—
686D4—2441no—
687D4—2442no—
688D4—2442no—
689D4—2442no—
690D4—2442no—
691D4—2442no—
692D4—2442no—
693D4—2442no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—611no—
704C2×C4—614no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1228no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4—24416no—
732C2×C4—2444no—
733C2×C4—2442no—
734C2×C4C2×C22⋊#692311yescharacteristic
735C2×C4C2×C22⋊#692311yescharacteristic
736C2×C4C2×C22⋊#692311yescharacteristic
737C2×C4C2×C22⋊#692311yescharacteristic
738C2×C4C2×C22⋊#692311yescharacteristic
739C2×C4C23×#692311yescharacteristic
740C8—2444no—
741C22—21no—
742C22—21no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—612no—
747C22—612no—
748C22—1228no—
749C22—1221no—
750C22—1221no—
751C22—1221no—
752C22—1221no—
753C22—2441no—
754C22—2441no—
755C22—2441no—
756C22#1684074112yes—
757C22C22×C22⋊#692311yescharacteristic
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—612no—
767C4—1221no—
768C4—1221no—
769C4—1221no—
770C4—1221no—
771C4—1221no—
772C4—2448no—
773C4—2441no—
774C4—2441no—
775C4—2441no—
776C4D61⋊#10412yes—
777C2—22no—
778C2—81no—
779C2—1222no—
780C2—1222no—
781C2—4881no—
782C2C2×#1684074111yescharacteristic
783C2#2146243911yescharacteristic
784C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61#17541
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #21462497C2semidirect
2. C2×#16840698C2semidirect
3. #21461212C2semidirect
4. #21461209C2semidirect
5. #21461207C2semidirect
6. #21461205C2semidirect
7. #21461192C2semidirect
8. #21461190C2semidirect
28. #16840316C4semidirect
30. #16840315C4semidirect
31. #16840309C4semidirect
33. #16840308C4semidirect
34. #16840299C4semidirect
36. #16840294C4semidirect
48. C4×#11758222C4semidirect
50. C4×#41×C61C4semidirect
72. #14519776C2×C4semidirect
73. #14519776C2×C4semidirect
74. #14519775C2×C4semidirect
75. #14519773C2×C4semidirect
80. #14519768C2×C4semidirect
81. #14519768C2×C4semidirect
84. #14519766C2×C4semidirect
85. #14519764C2×C4semidirect
116. C4×Dic122C2×C4semidirect
117. C4×Dic122C2×C4semidirect
122. C4×D244C2×C4semidirect
123. C4×D244C2×C4semidirect
155. C4×Q8×C61C2×C4semidirect
156. C4×Q8×C61C2×C4semidirect
159. C4×D4×C61C2×C4semidirect
160. C4×D4×C61C2×C4semidirect
423. C4×#41#6923semidirect
443. C61#17541semidirect
499. C4×Q8C2×#6923semidirect
500. C4×Q8C2×#6923semidirect
519. C4×D4C2×#6923semidirect
520. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624972
C2×#168406982
#214612122
#214612092
#214612072
#214612052
#214611922
#214611902
#214591122
#1754161