Finite Group Databasebeta

← #30610264

Subgroups — #30610264

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462509C212yesmaximal, complemented
2#21461101C212yesmaximal, complemented
3#21461088C212yesmaximal, complemented
4#21461087C212yesmaximal, complemented
5#21461080C211yesmaximal, characteristic, complemented
6#21461072C211yesmaximal, characteristic, complemented
7#21461065C211yesmaximal, characteristic, complemented
8#21461060C211yesmaximal, characteristic, complemented
9#21461052C211yesmaximal, characteristic, complemented
10D61⋊#323C211yesmaximal, characteristic, complemented
11C2×#16840437C211yesmaximal, characteristic
12#16840787—22no—
13#16840787—22no—
14#16840782C2212yescomplemented
15#16840782C2212yescomplemented
16#16840778C2212yescomplemented
17#16840778C2212yescomplemented
18#16840769—22no—
19#16840733C2212yes—
20D61⋊(C22⋊C8)C2212yes—
21#16840727—22no—
22#16840608C2212yescomplemented
23#16840608C2212yescomplemented
24#16840606C2211yescharacteristic
25#16840606C2211yescharacteristic
26#16840606C2211yescharacteristic
27#16840606C2211yescharacteristic
28#16840606C2212yescomplemented
29#16840606C2212yescomplemented
30#16840605C2212yes—
31#16840605C2212yes—
32#16840437—22no—
33#16840437—22no—
34#16840437—22no—
35#16840437—22no—
36C2×#14519770C2211yescharacteristic
37C2×#14519763C2211yescharacteristic
38C2×#14519762C411yescharacteristic
39C2×#14519762C2211yescharacteristic
40C2×#14519759C411yescharacteristic
41C2×#14519757C411yescharacteristic
42C2×#14519755C411yescharacteristic
43C2×#14519747C411yescharacteristic
44C2×C4×D244C411yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519735C2211yescharacteristic
47C2×#14519734C2211yescharacteristic
48C2×C22⋊C4×D61C411yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×#126×C61C411yescharacteristic
51C2×#11758213—22no—
52C2×D61⋊C8—22no—
53#14519844—22no—
54#14519844—22no—
55C4⋊#92420—22no—
56C4⋊#92420—22no—
57#14519834—22no—
58#14519834—22no—
59C22⋊#92420C2312yes—
60C22⋊#92420C2312yes—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67C24×D61C2×C411yescharacteristic
68C22×Dic122C2×C411yescharacteristic
69C22×D244C2×C411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519770—22no—
78#14519770—22no—
79#14519763—22no—
80#14519763—22no—
81#14519762—22no—
82#14519762—22no—
83#14519762—22no—
84#14519762—22no—
85#14519759—22no—
86#14519759—22no—
87#14519757—22no—
88#14519757—22no—
89#14519755—22no—
90#14519755—22no—
91#14519747—22no—
92#14519747—22no—
93C4×D244—21no—
94C4×D244—21no—
95C4×D244—21no—
96C4×D244—21no—
97#14519739—22no—
98#14519739—22no—
99#14519735D412yes—
100#14519735D412yes—
101#14519735D412yes—
102#14519735D412yes—
103#14519734—22no—
104#14519734—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2311yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2311yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2311yescharacteristic
120C2×#11758198C2311yescharacteristic
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C22⋊C4×D61—21no—
124C22⋊C4×D61—21no—
125C22⋊C4×D61—21no—
126C22⋊C4×D61—21no—
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129#126×C61—22no—
130#126×C61—22no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—22no—
142C23×D61—41no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—81no—
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C2411yescharacteristic
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—41no—
166C2×D244—42no—
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—42no—
177C2×C4×D61—41no—
178C2×C4×D61—81no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C4×D61C2×D412yes—
182C2×C4×D61C2×D412yes—
183C2×Dic122—22no—
184C2×Dic122—81no—
185C2×#92420—22no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—22no—
189#11758213—44no—
190D61⋊C8—44no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61C22⋊C412yes—
194C4⋊C4×C61C22⋊C412yes—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61—22no—
199C42×C61—21no—
200C42×C61—21no—
201C22⋊Dic61—21no—
202C22⋊Dic61—21no—
203C22⋊Dic61—22no—
204#11758198—21no—
205#11758198—21no—
206#11758198—22no—
207#11758198—21no—
208#11758198—21no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198C22⋊C411yescharacteristic
214#11758198C22⋊C411yescharacteristic
215#11758198C22⋊C411yescharacteristic
216#11758198C22⋊C411yescharacteristic
217#11758198C22⋊C412yes—
218#11758198C22⋊C412yes—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61C22⋊C412yes—
222C4⋊Dic61C22⋊C412yes—
223#11758196—22no—
224#11758196—22no—
225#11758196—22no—
226C4×Dic61C2×D412yes—
227C4×Dic61C2×D412yes—
228C4×Dic61C2×D412yes—
229C4×Dic61C2×D412yes—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61C23×C411yescharacteristic
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—22no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—41no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—42no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—81no—
254C22×D61—81no—
255C22×D61—84no—
256C22×D61—84no—
257C22×D61C2×C22⋊C411yescharacteristic
258C22×D61C2×C22⋊C411yescharacteristic
259C22×D61#13112yes—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61C2×C22⋊C412yes—
272C2×C4×C61C2×C22⋊C411yescharacteristic
273C2×C4×C61C2×C22⋊C411yescharacteristic
274C2×C4×C61C2×C22⋊C412yes—
275C22⋊D61—82no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C22×D412yes—
288D244—44no—
289D244—42no—
290D244—42no—
291C4×D61—24no—
292C4×D61—42no—
293C4×D61—42no—
294C4×D61—42no—
295C4×D61—81no—
296C4×D61—81no—
297C4×D61—81no—
298C4×D61—81no—
299C4×D61—81no—
300C4×D61—81no—
301Dic122—82no—
302#92420—42no—
303#92420—42no—
304#92420—42no—
305#92420—42no—
306#17412—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61C22×C22⋊C411yescharacteristic
315C22×C61C2×#13111yescharacteristic
316C22×C61#56811yescharacteristic
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—22no—
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—42no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—42no—
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—84no—
333C2×D61—84no—
334C2×D61—81no—
335C2×D61—81no—
336C2×D61#41012yes—
337C4×C61—21no—
338C4×C61—21no—
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—41no—
344Dic61—22no—
345Dic61—22no—
346Dic61—21no—
347Dic61—21no—
348Dic61—41no—
349Dic61—41no—
350C2×#551—611no—
351#2924—612no—
352#1473—612no—
353#1469—612no—
354#1468—612no—
355#1466—611no—
356#1464—611no—
357#1462—611no—
358#1460—611no—
359#1458—611no—
360C2×#323—611no—
361C2×C61—21no—
362C2×C61—21no—
363C2×C61—81no—
364C2×C61#288011yescharacteristic
365C2×C61C2×#41011yescharacteristic
366C2×C61#288811yescharacteristic
367D61—22no—
368D61—41no—
369D61—42no—
370D61—81no—
371#551—1222no—
372#551—1222no—
373#551—1222no—
374#551—1222no—
375C2×#126—611no—
376C2×#126#692311yescharacteristic
377C2×#124—611no—
378C2×#123—611no—
379C2×#123—611no—
380C2×#123—611no—
381C2×C22⋊Q8—611no—
382C2×C22⋊Q8—611no—
383C2×#120—611no—
384C2×C4×D4—611no—
385C2×C4×D4—611no—
386C2×#117—611no—
387C2×#117—611no—
388C22×C22⋊C4—611no—
389C22×C22⋊C4—611no—
390#433—1222no—
391#433—1222no—
392#432—612no—
393#432—612no—
394#431—612no—
395#431—612no—
396#424—1222no—
397#407—612no—
398C2×C22⋊C8—612no—
399#405—1222no—
400#324—612no—
401#324—612no—
402#323—612no—
403#323—612no—
404#323—611no—
405#323—611no—
406#323—611no—
407#323—611no—
408#323—612no—
409#323—612no—
410C61#1741211yescharacteristic, complemented, Sylow
411C25—611no—
412C22×Q8—611no—
413C22×D4—611no—
414C22×D4—611no—
415C22×D4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C2×M16—1222no—
422C22×C8—1222no—
423#126—22no—
424#126—22no—
425#126—1222no—
426#126—1222no—
427#124—1222no—
428#124—1222no—
429#123—1222no—
430#123—1222no—
431#123—1222no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435C22⋊Q8—1222no—
436C22⋊Q8—1222no—
437C22⋊Q8—1222no—
438C22⋊Q8—1222no—
439#120—1222no—
440#120—1222no—
441C4×D4—1221no—
442C4×D4—1221no—
443C4×D4—1221no—
444C4×D4—1221no—
445C4×D4—1222no—
446C4×D4—1222no—
447#117—612no—
448#117—612no—
449#117—612no—
450#117—612no—
451#117—1222no—
452#117—1222no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4C2×#692311yescharacteristic
459C2×C4⋊C4C2×#692311yescharacteristic
460C2×C4⋊C4C2×#692311yescharacteristic
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4—611no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4C2×#692311yescharacteristic
479C2×C22⋊C4C2×#692311yescharacteristic
480C2×C22⋊C4C2×#692311yescharacteristic
481C2×C42—611no—
482C2×C42—611no—
483C2×C42C2×#692311yescharacteristic
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C4⋊C8—1222no—
487C4⋊C8—1222no—
488C22⋊C8—612no—
489C22⋊C8—612no—
490C22⋊C8—612no—
491C22⋊C8—612no—
492C22⋊C8—1222no—
493C22⋊C8—1222no—
494#97—1222no—
495#97—1222no—
496C4×C8—1222no—
497C4×C8—1222no—
498C24—611no—
499C24—611no—
500C24—611no—
501C24—1222no—
502C24—1221no—
503C24—1221no—
504C24—4881no—
505C24—2441no—
506C24—2442no—
507C24C22×#692311yescharacteristic
508C2×Q8—1222no—
509C2×Q8—4881no—
510C2×D4—1221no—
511C2×D4—1221no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—4881no—
516C2×D4—2441no—
517C2×D4—2442no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1222no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—4881no—
535C22×C4—4881no—
536C22×C4—4881no—
537C22×C4—2441no—
538C22×C4—2442no—
539C22×C4C22×#692311yescharacteristic
540C22×C4C22×#692311yescharacteristic
541C22×C4C22×#692311yescharacteristic
542C22×C4C22×#692311yescharacteristic
543C22×C4C22×#692311yescharacteristic
544C22×C4C22×#692311yescharacteristic
545M16—2444no—
546C2×C8—1222no—
547C2×C8—1222no—
548C2×C8—1222no—
549C2×C8—1222no—
550C2×C8—2444no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—612no—
554C4⋊C4—612no—
555C4⋊C4—1222no—
556C4⋊C4—1222no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1222no—
560C4⋊C4C22⋊#692312yes—
561C4⋊C4C22⋊#692312yes—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—611no—
567C22⋊C4—611no—
568C22⋊C4—611no—
569C22⋊C4—611no—
570C22⋊C4—612no—
571C22⋊C4—612no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1221no—
576C22⋊C4—1221no—
577C22⋊C4—1221no—
578C22⋊C4—1221no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1221no—
582C22⋊C4—1221no—
583C22⋊C4—1222no—
584C42—21no—
585C42—21no—
586C42—612no—
587C42—612no—
588C42—612no—
589C42—612no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—611no—
596C23—611no—
597C23—612no—
598C23—1222no—
599C23—1221no—
600C23—1221no—
601C23—1221no—
602C23—1221no—
603C23—1221no—
604C23—1221no—
605C23—1221no—
606C23—4881no—
607C23—4881no—
608C23—4884no—
609C23—4884no—
610C23—2441no—
611C23—2441no—
612C23—2441no—
613C23—2441no—
614C23—2441no—
615C23—2442no—
616C23—2442no—
617C23—2442no—
618C23—2442no—
619C23C23×#692311yescharacteristic
620Q8—4882no—
621D4—4882no—
622D4—2444no—
623D4—2442no—
624D4—2442no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—1224no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—4881no—
646C2×C4—4881no—
647C2×C4—4881no—
648C2×C4—4881no—
649C2×C4—4881no—
650C2×C4—4881no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4C2×C22⋊#692311yescharacteristic
659C2×C4C2×C22⋊#692311yescharacteristic
660C2×C4C2×C22⋊#692312yes—
661C2×C4C2×C22⋊#692312yes—
662C8—2442no—
663C8—2442no—
664C8—2442no—
665C8—2442no—
666C22—21no—
667C22—21no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—81no—
672C22—81no—
673C22—612no—
674C22—1221no—
675C22—1221no—
676C22—1222no—
677C22—1221no—
678C22—1221no—
679C22—1221no—
680C22—4881no—
681C22—4881no—
682C22—4884no—
683C22—4884no—
684C22—2442no—
685C22—2442no—
686C22—2442no—
687C22—2442no—
688C22—2441no—
689C22—2441no—
690C22—2441no—
691C22—2441no—
692C22—2441no—
693C22C22×C22⋊#692311yescharacteristic
694C22D61⋊#13111yescharacteristic
695C22#1684084111yescharacteristic
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—1222no—
704C4—1221no—
705C4—1221no—
706C4—1222no—
707C4—2441no—
708C4—2441no—
709C2—21no—
710C2—21no—
711C2—81no—
712C2—1222no—
713C2—4881no—
714C2—2441no—
715C2—2442no—
716C2#2146240911yescharacteristic
717C2D61⋊#41011yescharacteristic
718C2#2146243011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#126×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C4
cosocleC22×Dic61C24
hypercenterC2×#126#6923
hypocenterC61#17412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #21462509C2semidirect
2. #21461101C2semidirect
3. #21461088C2semidirect
4. #21461087C2semidirect
5. #21461080C2semidirect
6. #21461072C2semidirect
7. #21461065C2semidirect
8. #21461060C2semidirect
9. #21461052C2semidirect
10. D61⋊#323C2semidirect
14. #16840782C22semidirect
15. #16840782C22semidirect
16. #16840778C22semidirect
17. #16840778C22semidirect
22. #16840608C22semidirect
23. #16840608C22semidirect
28. #16840606C22semidirect
29. #16840606C22semidirect
410. C61#17412semidirect

Maximal subgroups

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

subgroupindex
#214625092
#214611012
#214610882
#214610872
#214610802
#214610722
#214610652
#214610602
#214610522
D61⋊#3232
C2×#168404372
#1741261