Finite Group Databasebeta

← #30611536

Subgroups — #30611536

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2D61⋊#432C211yesmaximal, characteristic, complemented
3#21461305C214yesmaximal, complemented
4#21461301C212yesmaximal, complemented
5#21461300C212yesmaximal, complemented
6#21461271C214yesmaximal, complemented
7C2×#16840299C211yesmaximal, characteristic
8#16840785—21no—
9#16840785C2212yescomplemented
10#16840784C2212yescomplemented
11#16840783—21no—
12#16840782C2212yes—
13#16840782C2212yes—
14#16840780—21no—
15#16840779—21no—
16#16840767—21no—
17D61⋊(C4⋊C8)—21no—
18#16840733—21no—
19D61⋊(C22⋊C8)—21no—
20C4×#11758213C2212yescomplemented
21#16840721C2212yescomplemented
22#16840619C2218yescomplemented
23#16840618C2218yescomplemented
24#16840299—21no—
25#16840299—21no—
26#16840299—21no—
27#16840299—21no—
28#16840299C412yes—
29#16840299C412yes—
30#16840299C2212yes—
31#16840299C2212yes—
32C2×#14519772—21no—
33C2×#14519768C2211yescharacteristic
34C2×#14519766C2211yescharacteristic
35C2×#14519762—21no—
36C2×#14519753C411yescharacteristic
37C2×#14519752C411yescharacteristic
38C2×C4×D244—21no—
39C2×C4×D244C411yescharacteristic
40C2×#14519734—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×D61⋊C8—22no—
45#14519844—22no—
46#14519844—22no—
47#14519844—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50#14519834—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832C2314yes—
55#14519832C2314yes—
56C4×#92420—22no—
57C22×D244—21no—
58C22×D244C2×C411yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63#14519772—22no—
64#14519772—22no—
65#14519772—22no—
66#14519772—22no—
67#14519768—21no—
68#14519768—21no—
69#14519768C2×C412yes—
70#14519768C2312yes—
71#14519766—21no—
72#14519766—21no—
73#14519766C2×C412yes—
74#14519766C2312yes—
75#14519762—22no—
76#14519762—22no—
77#14519762—22no—
78#14519762—22no—
79#14519753—21no—
80#14519753—21no—
81#14519753C2×C412yes—
82#14519753C2×C412yes—
83#14519752—21no—
84#14519752—21no—
85#14519752C2×C412yes—
86#14519752C2×C412yes—
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—21no—
92C4×D244—21no—
93C4×D244C2×C412yes—
94C4×D244C2×C412yes—
95#14519734—22no—
96#14519734—22no—
97#14519734—22no—
98#14519734—22no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119C22×Q8×C61C2×C411yescharacteristic
120C4×Q8×C61—21no—
121C4×Q8×C61—21no—
122C4×Q8×C61C2×C412yes—
123C4×Q8×C61C2×C412yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C42×C61—21no—
127C2×C42×C61C2×C411yescharacteristic
128C23×D61—21no—
129C23×D61C22⋊C411yescharacteristic
130C2×Q8×C61—21no—
131C2×Q8×C61—42no—
132C2×Q8×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C2×D244—22no—
143C2×D244—22no—
144C2×D244—21no—
145C2×D244—42no—
146C2×D244—44no—
147C2×D244C22×C412yes—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—44no—
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×#92420—24no—
167C2×#92420—24no—
168#11758213—44no—
169D61⋊C8—44no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C412yes—
174C42×C61—22no—
175C42×C61—22no—
176C42×C61C22⋊C411yescharacteristic
177C42×C61C22⋊C411yescharacteristic
178C42×C61C22×C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198—22no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C22×C411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2411yescharacteristic
210C23×C61C2×C22⋊C411yescharacteristic
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61C2×C22⋊C411yescharacteristic
219C22×D61C2×C22⋊C411yescharacteristic
220Q8×C61—42no—
221Q8×C61—42no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—41no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—42no—
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C2×C22⋊C411yescharacteristic
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C22×D411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246D244—42no—
247D244—42no—
248D244—44no—
249D244—44no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—44no—
263C4×D61—44no—
264#92420—44no—
265#92420—44no—
266#17659—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61#41312yes—
270C22×C61C22×C22⋊C411yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—44no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—84no—
281C2×D61#42112yes—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61#42112yes—
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—21no—
295Dic61—21no—
296Dic61—42no—
297C2×#529—611no—
298#2920—611no—
299C2×#432—611no—
300#1535—614no—
301#1534—612no—
302#1533—612no—
303#1524—614no—
304C2×C61—22no—
305C2×C61C2×#41311yescharacteristic
306C2×C61C2×#42111yescharacteristic
307C2×C61C2×#42111yescharacteristic
308D61—22no—
309D61—41no—
310D61—82no—
311#529—612no—
312#529—612no—
313#529—612no—
314#529—612no—
315#529—1221no—
316#529—1221no—
317#529—1221no—
318#529—1221no—
319C2×#126—1221no—
320C2×#125—611no—
321C2×#124—611no—
322C2×#123—1221no—
323C2×C22⋊Q8—611no—
324C2×#121—611no—
325C2×C4×Q8#692311yescharacteristic
326C2×C4×D4—611no—
327C2×C4×D4—1221no—
328C2×#117—1221no—
329C22×C42—611no—
330#432—612no—
331#432—612no—
332#432—612no—
333#432—612no—
334#432—1221no—
335#432—1221no—
336#431—1221no—
337#431—1221no—
338#423—1221no—
339C2×C4⋊C8—1221no—
340#407—1221no—
341C2×C22⋊C8—1221no—
342C4×M16—612no—
343C2×#97—612no—
344#330—618no—
345#329—618no—
346C61#1765911yescharacteristic, complemented, Sylow
347C22×Q8C2×#692311yescharacteristic
348C22×D4—611no—
349C22×D4—1221no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—1221no—
354C2×M16—1222no—
355C22×C8—1222no—
356#126—1222no—
357#126—1222no—
358#126—1222no—
359#126—1222no—
360#125—612no—
361#125—612no—
362#125—1221no—
363#125—1221no—
364#124—612no—
365#124—612no—
366#124—1221no—
367#124—1221no—
368#123—1222no—
369#123—1222no—
370#123—1222no—
371#123—1222no—
372C22⋊Q8—612no—
373C22⋊Q8—612no—
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376#121—612no—
377#121—612no—
378#121—1221no—
379#121—1221no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C2×#692312yes—
383C4×Q8C2×#692312yes—
384C4×D4—612no—
385C4×D4—612no—
386C4×D4—1222no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1221no—
391C4×D4—1221no—
392#117—1222no—
393#117—1222no—
394#117—1222no—
395#117—1222no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C2×#692311yescharacteristic
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C42—21no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42C2×#692311yescharacteristic
420C4⋊C8—1222no—
421C4⋊C8—1222no—
422C4⋊C8—1222no—
423C4⋊C8—1222no—
424C22⋊C8—1222no—
425C22⋊C8—1222no—
426C22⋊C8—1222no—
427C22⋊C8—1222no—
428#97—614no—
429#97—614no—
430#97—1222no—
431C4×C8—1222no—
432C24—611no—
433C24—1221no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8C22×#692312yes—
437C2×D4—612no—
438C2×D4—1222no—
439C2×D4—1222no—
440C2×D4—1221no—
441C2×D4—2442no—
442C2×D4—2444no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2444no—
466C22×C4—2442no—
467C22×C4C22⋊#692311yescharacteristic
468C22×C4C22⋊#692311yescharacteristic
469C22×C4C22×#692311yescharacteristic
470M16—2444no—
471C2×C8—1224no—
472C2×C8—1224no—
473C2×C8—2444no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—612no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4C22×#692312yes—
486C22⋊C4—1222no—
487C22⋊C4—1222no—
488C22⋊C4—1222no—
489C22⋊C4—1222no—
490C22⋊C4—1222no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C42—22no—
497C42—22no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42C22⋊#692311yescharacteristic
511C42C22⋊#692311yescharacteristic
512C42C22×#692311yescharacteristic
513C42C22×#692311yescharacteristic
514C23—611no—
515C23—611no—
516C23—1222no—
517C23—1222no—
518C23—1222no—
519C23—2441no—
520C23—2442no—
521C23—2442no—
522C23—2442no—
523C23C2×C22⋊#692311yescharacteristic
524Q8—42no—
525Q8—42no—
526D4—2442no—
527D4—2442no—
528D4—2444no—
529D4—2444no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2444no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2442no—
561C2×C4—2444no—
562C2×C4C2×C22⋊#692311yescharacteristic
563C2×C4C2×C22⋊#692311yescharacteristic
564C2×C4C2×C22⋊#692311yescharacteristic
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4C2×C22⋊#692311yescharacteristic
567C2×C4C23×#692311yescharacteristic
568C8—2444no—
569C8—2444no—
570C22—21no—
571C22—21no—
572C22—612no—
573C22—1221no—
574C22—1221no—
575C22—1221no—
576C22—1221no—
577C22—1221no—
578C22—4884no—
579C22—2444no—
580C22—2442no—
581C22—2442no—
582C22—2442no—
583C22#1684074812yes—
584C22C22×C22⋊#692311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—42no—
591C4—42no—
592C4—1221no—
593C4—1221no—
594C4—1221no—
595C4—1221no—
596C4—1221no—
597C4—1221no—
598C4—2442no—
599C4#1684076112yes—
600C2—22no—
601C2—1222no—
602C2—4882no—
603C2—2441no—
604C2C2×#1684074811yescharacteristic
605C2D61⋊#42111yescharacteristic
606C2C2×#1684076111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17659
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. D61⋊#432C2semidirect
3. #21461305C2semidirect
4. #21461301C2semidirect
5. #21461300C2semidirect
6. #21461271C2semidirect
9. #16840785C22semidirect
10. #16840784C22semidirect
20. C4×#11758213C22semidirect
21. #16840721C22semidirect
22. #16840619C22semidirect
23. #16840618C22semidirect
346. C61#17659semidirect

Maximal subgroups

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

subgroupindex
#214624982
D61⋊#4322
#214613052
#214613012
#214613002
#214612712
C2×#168402992
#1765961