Finite Group Databasebeta

← #30606332

Subgroups — #30606332

Order 15616.

752 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840749C211yesmaximal, characteristic
2#21462405C211yesmaximal, characteristic
3#21460918C214yesmaximal, complemented
4C2×#16839734C211yesmaximal, characteristic
5C2×D61⋊M16C411yescharacteristic, complemented
6C2×D61⋊M16C411yescharacteristic, complemented
7C22×#11758217—21no—
8#16840749—21no—
9#16840749—21no—
10#16840749C412yescomplemented
11#16840749C2212yes—
12C2×#14519838C412yescomplemented
13C2×#14519837—21no—
14#16840736—21no—
15#16840736—21no—
16#16840736C412yescomplemented
17#16840736C2212yes—
18#16840732—21no—
19#16840732—21no—
20C22×#11758224C2211yescharacteristic
21C2×#14519733—21no—
22#16839734—21no—
23#16839734—21no—
24#16839734C412yes—
25#16839734C2212yes—
26C2×#14519692C411yescharacteristic
27C2×#14519691—21no—
28C2×#99×C61C411yescharacteristic
29C2×#11758213—21no—
30C2×#11758213C2×C412yescomplemented
31D61⋊M16—41no—
32D61⋊M16—41no—
33D61⋊M16—41no—
34D61⋊M16—41no—
35C2×#11758217—21no—
36C2×#11758217—21no—
37C2×#11758217—22no—
38C2×#11758217—22no—
39C2×#11758217—22no—
40C2×#11758217—41no—
41C2×#11758217—41no—
42C2×#11758217—41no—
43C2×D61⋊C8—21no—
44C2×D61⋊C8C2×C412yescomplemented
45C22×#92420—41no—
46#14519838—22no—
47#14519838C2×C414yescomplemented
48#14519837—22no—
49#14519837—22no—
50C22⋊#92420—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53C22⋊#92420—22no—
54C2×#11758224—41no—
55C2×#11758224—41no—
56C2×#11758224—41no—
57C2×#11758224—41no—
58C2×#11758224C2×C411yescharacteristic
59C2×#11758224C2×C411yescharacteristic
60C2×#11758224C2×C411yescharacteristic
61C2×#11758224D411yescharacteristic
62C2×#11758224D411yescharacteristic
63C2×#11758224D411yescharacteristic
64C2×#11758224Q811yescharacteristic
65C2×#11758224C2311yescharacteristic
66C22×Dic122C2×C411yescharacteristic
67C22×C22⋊D61D411yescharacteristic
68C22×C22⋊D61Q811yescharacteristic
69C23×Dic61D411yescharacteristic
70C23×Dic61D411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72#14519733—22no—
73#14519733—22no—
74#14519733—41no—
75#14519733—41no—
76C2×#11758196—41no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—41no—
79#14519692—21no—
80#14519692C2×C412yes—
81#14519691—22no—
82#14519691—22no—
83C22×D4×C61C2×C411yescharacteristic
84C2×C22⋊C4×C61—21no—
85#99×C61—21no—
86#99×C61C2×C412yes—
87C24×C61C22⋊C411yescharacteristic
88C24×C61C4⋊C411yescharacteristic
89C23×D61C4⋊C411yescharacteristic
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61C4211yescharacteristic
93C2×D4×C61C22⋊C411yescharacteristic
94C2×D4×C61C4⋊C411yescharacteristic
95C2×D4×C61C22×C411yescharacteristic
96C22×C4×C61—41no—
97C22×C4×C61C4211yescharacteristic
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61C22⋊C411yescharacteristic
103C2×C22⋊D61C22⋊C411yescharacteristic
104C2×C22⋊D61C4⋊C411yescharacteristic
105C2×C22⋊D61C4⋊C411yescharacteristic
106C2×C22⋊D61C4⋊C411yescharacteristic
107C2×C22⋊D61C4⋊C411yescharacteristic
108C2×C22⋊D61C2×D411yescharacteristic
109C2×C22⋊D61C2×Q811yescharacteristic
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—41no—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C4⋊C411yescharacteristic
126C22×Dic61C4⋊C411yescharacteristic
127C22×Dic61C4⋊C411yescharacteristic
128C22×Dic61C2×D411yescharacteristic
129C22×Dic61C2×D411yescharacteristic
130#11758224—41no—
131#11758224—41no—
132#11758224—41no—
133#11758224—41no—
134#11758224—41no—
135#11758224—41no—
136#11758224—41no—
137#11758224—41no—
138#11758224—41no—
139#11758224—41no—
140#11758224—41no—
141#11758224—41no—
142#11758224—41no—
143#11758224—41no—
144#11758224—41no—
145#11758224—41no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61C4211yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C4⋊C411yescharacteristic
153C2×C4×D61C22×C411yescharacteristic
154C2×Dic122—41no—
155C2×Dic122—41no—
156C2×Dic122C4211yescharacteristic
157C2×Dic122C22⋊C411yescharacteristic
158C2×Dic122C4⋊C411yescharacteristic
159C2×Dic122C22×C411yescharacteristic
160#11758217—24no—
161#11758217—42no—
162#11758217—42no—
163#11758217—42no—
164#11758217—41no—
165#11758217—41no—
166#11758217—41no—
167#11758217—41no—
168C2×#92420—22no—
169C2×#92420—22no—
170C2×#92420—42no—
171C2×#92420—42no—
172C2×#92420—42no—
173#11758213—42no—
174#11758213—42no—
175D61⋊C8—42no—
176D61⋊C8—42no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—41no—
179C22⋊Dic61—22no—
180C22⋊Dic61—41no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—42no—
184C4×Dic61—42no—
185C23×C61—21no—
186C23×C61—21no—
187C23×C61—21no—
188C23×C61—21no—
189C23×C61—81no—
190C23×C61—81no—
191C23×C61#9511yescharacteristic
192C23×C61#9511yescharacteristic
193C23×C61#9511yescharacteristic
194C23×C61C2×C22⋊C411yescharacteristic
195C23×C61C2×C4⋊C411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—81no—
199C22×D61#9511yescharacteristic
200C22×D61C2×C4⋊C411yescharacteristic
201D4×C61—41no—
202D4×C61—41no—
203D4×C61—41no—
204D4×C61—41no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—42no—
208C2×C4×C61—82no—
209C2×C4×C61#9511yescharacteristic
210C2×C4×C61C2×C4211yescharacteristic
211C22⋊D61—41no—
212C22⋊D61—41no—
213C22⋊D61—41no—
214C22⋊D61—41no—
215C22⋊D61—41no—
216C22⋊D61—41no—
217C22⋊D61—41no—
218C22⋊D61—41no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—42no—
240C2×Dic61—82no—
241C2×Dic61#9511yescharacteristic
242C2×Dic61#9511yescharacteristic
243C2×Dic61#9511yescharacteristic
244C2×Dic61#9911yescharacteristic
245C2×Dic61#9911yescharacteristic
246C2×Dic61#9911yescharacteristic
247C2×Dic61#9911yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C4⋊C411yescharacteristic
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—21no—
259Dic122—41no—
260Dic122—41no—
261Dic122—41no—
262Dic122—41no—
263#92420—44no—
264#92420—42no—
265#92420—42no—
266#12589—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61#34211yescharacteristic
281C22×C61#34211yescharacteristic
282C22×C61C2×#9511yescharacteristic
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—81no—
288C2×D61—81no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—82no—
292Dic61—21no—
293Dic61—21no—
294Dic61—21no—
295Dic61—21no—
296Dic61—82no—
297Dic61#34211yescharacteristic
298Dic61#34211yescharacteristic
299Dic61C2×#9911yescharacteristic
300Dic61C2×#9911yescharacteristic
301C2×#413—611no—
302C2×#410—611no—
303#2879—611no—
304#1395—614no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—41no—
309C2×C61—41no—
310C2×C61—41no—
311C2×C61—41no—
312C2×C61C2×#34211yescharacteristic
313D61—41no—
314D61—41no—
315C22×#41—611no—
316C22×M16—611no—
317C22×M16—611no—
318C22×M16—1221no—
319C2×#117—1221no—
320#413—612no—
321#413—612no—
322#413—1221no—
323#413—1221no—
324C2×#101—612no—
325C2×#100—1221no—
326#410—612no—
327#410—612no—
328#410—1221no—
329#410—1221no—
330C2×#99—611no—
331C2×#99—1221no—
332C2×#99#692311yescharacteristic
333#408—612no—
334#408—612no—
335#408—1221no—
336#408—1221no—
337#407—1221no—
338#407—1221no—
339C61#1258911yescharacteristic, complemented, Sylow
340C2×#41—611no—
341C2×#41—611no—
342C2×#41—611no—
343C2×#41—611no—
344C2×#41—611no—
345C2×#41—611no—
346C2×#41—611no—
347C2×#41—611no—
348C2×#41—2441no—
349C2×#41—2441no—
350C2×#41—2441no—
351C2×#41—2441no—
352C22×Q8—611no—
353C22×D4—611no—
354C22×D4—611no—
355C22×D4C2×#692311yescharacteristic
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—611no—
359C2×M16—612no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C2×M16—1222no—
364C2×M16—1222no—
365C2×M16—1222no—
366C2×M16—2441no—
367C2×M16—2441no—
368C2×M16—2441no—
369C2×M16—2441no—
370C2×M16—2441no—
371C2×M16—2441no—
372C2×M16—2441no—
373C22×C8—612no—
374C22×C8—1221no—
375C22×C8—2441no—
376#117—1222no—
377#117—1222no—
378#117—2441no—
379#117—2441no—
380C2×C4⋊C4—2441no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1221no—
383C2×C42—2441no—
384#101—614no—
385#101—1222no—
386#100—1222no—
387#100—1222no—
388#99—21no—
389#99—612no—
390#99—1222no—
391#99—1222no—
392#99—1221no—
393#99C2×#692312yes—
394C22⋊C8—1222no—
395C22⋊C8—1222no—
396C22⋊C8—1222no—
397C22⋊C8—1222no—
398C24—611no—
399C24C4⋊#692311yescharacteristic
400C24C22⋊#692311yescharacteristic
401#41—2441no—
402#41—2441no—
403#41—2441no—
404#41—2441no—
405#41—2441no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409#41—2441no—
410#41—2441no—
411#41—2441no—
412#41—2441no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417C2×Q8—611no—
418C2×Q8—611no—
419C2×Q8—611no—
420C2×Q8—611no—
421C2×Q8—2441no—
422C2×Q8—2441no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—611no—
426C2×D4—611no—
427C2×D4—611no—
428C2×D4—611no—
429C2×D4—611no—
430C2×D4—611no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4C4×#692311yescharacteristic
438C2×D4C4⋊#692311yescharacteristic
439C2×D4C22⋊#692311yescharacteristic
440C2×D4C22×#692311yescharacteristic
441C22×C4—41no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
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—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—2441no—
470C22×C4C4×#692311yescharacteristic
471M16—1224no—
472M16—2441no—
473M16—2441no—
474M16—2441no—
475M16—2441no—
476M16—2442no—
477M16—2442no—
478M16—2442no—
479M16—2442no—
480M16—2442no—
481C2×C8—1222no—
482C2×C8—1222no—
483C2×C8—2442no—
484C2×C8—2442no—
485C2×C8—2442no—
486C2×C8—2442no—
487C2×C8—2442no—
488C4⋊C4—2442no—
489C4⋊C4—2442no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—1222no—
493C22⋊C4—2441no—
494C42—2442no—
495C42—2442no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—81no—
501C23—81no—
502C23—611no—
503C23—611no—
504C23—1221no—
505C23—1221no—
506C23—4881no—
507C23(C2×#6923)⋊C411yescharacteristic
508C23(C2×#6923)⋊C411yescharacteristic
509C23(C2×#6923)⋊C411yescharacteristic
510C23C2×C22⋊#692311yescharacteristic
511C23C2×C4⋊#692311yescharacteristic
512Q8—2441no—
513Q8—2441no—
514Q8—2441no—
515Q8—2441no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—2441no—
521D4—2441no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—611no—
533C2×C4—611no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—4882no—
571C2×C4—2442no—
572C2×C4(C2×#6923)⋊C411yescharacteristic
573C2×C4C2×C4×#692311yescharacteristic
574C8—2442no—
575C8—2442no—
576C8—2444no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—1221no—
591C22—1221no—
592C22—4881no—
593C22—4881no—
594C22—2441no—
595C22—2441no—
596C22#1684063911yescharacteristic
597C22#1684063911yescharacteristic
598C22C2×(C2×#6923)⋊C411yescharacteristic
599C4—21no—
600C4—21no—
601C4—82no—
602C4—611no—
603C4—611no—
604C4—611no—
605C4—611no—
606C4—1221no—
607C4—1221no—
608C4—1221no—
609C4—1221no—
610C4—4882no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—41no—
615C2—41no—
616C2—41no—
617C2—41no—
618C2—2441no—
619C2—2441no—
620C2C2×#1684063911yescharacteristic
subgroupG/H
centerC2C2×#16840639
commutatorC2×C4×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC2×#99×C61C4
socleC2×C61C2×#342
prime radicalC22×#11758224C22
cosocleC2×#11758224C23
hypercenterC2×#99#6923
hypocenterC61#12589
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #21460918C2semidirect
5. C2×D61⋊M16C4semidirect
6. C2×D61⋊M16C4semidirect
10. #16840749C4semidirect
12. C2×#14519838C4semidirect
16. #16840736C4semidirect
30. C2×#11758213C2×C4semidirect
44. C2×D61⋊C8C2×C4semidirect
47. #14519838C2×C4semidirect
339. C61#12589semidirect

Maximal subgroups

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

subgroupindex
C2×#168407492
#214624052
#214609182
C2×#168397342
#1258961