Finite Group Databasebeta

← #30612721

Subgroups — #30612721

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462713C211yesmaximal, characteristic, complemented
2#21462708C211yesmaximal, characteristic
3#21461449C211yesmaximal, characteristic, complemented
4#21461448C211yesmaximal, characteristic, complemented
5#21461429C211yesmaximal, characteristic, complemented
6#21461428C211yesmaximal, characteristic, complemented
7#21461410C211yesmaximal, characteristic, complemented
8SD16⋊#92420C211yesmaximal, characteristic, complemented
9#21461402C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461162C211yesmaximal, characteristic, complemented
13#21461139C211yesmaximal, characteristic
14#21461037C211yesmaximal, characteristic, complemented
15#21455849C211yesmaximal, characteristic
16#16840811—21no—
17#16840811—21no—
18#16840811C2211yescharacteristic
19#16840811C2211yescharacteristic
20Q8×#92420C2211yescharacteristic
21Q8×#92420C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840797C2211yescharacteristic
24#16840793—21no—
25#16840793—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840784C2211yescharacteristic
29#16840781—21no—
30#16840781C2211yescharacteristic
31#16840780—21no—
32#16840780C2211yescharacteristic
33#16840735—21no—
34#16840735—21no—
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840310C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840079C411yescharacteristic
55#16840079C411yescharacteristic
56#16840048C411yescharacteristic
57#16840047C411yescharacteristic
58#16839959C411yescharacteristic
59#16839899C411yescharacteristic
60#16839899C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839853C2211yescharacteristic
63SD16×Dic61C2211yescharacteristic
64SD16×Dic61C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#460C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C22×#92420—21no—
71C22×#92420—21no—
72#14519844—21no—
73#14519844—21no—
74#14519844D411yescharacteristic
75#14519844D411yescharacteristic
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834D411yescharacteristic
85#14519834D411yescharacteristic
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90#14519832—21no—
91#14519832—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×Q8×D61C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105#14519777C2×C411yescharacteristic
106#14519764—21no—
107#14519748—21no—
108#14519748C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111C4×Dic122—21no—
112C4×Dic122C2×C411yescharacteristic
113#14519742—21no—
114#14519742C2311yescharacteristic
115D4×Dic61—21no—
116D4×Dic61C2311yescharacteristic
117D4×Dic61C2311yescharacteristic
118C4⋊C4×D61—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C42×D61—21no—
121C42×D61C2311yescharacteristic
122#14519709C2×C411yescharacteristic
123#14519709C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139#127×C61C2×C411yescharacteristic
140C4×Q8×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153Q8×D61—22no—
154Q8×D61—22no—
155#11758224—81no—
156#11758224—81no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C22×C411yescharacteristic
165#11758217—81no—
166#11758217—81no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—81no—
174C2×#92420—81no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179#11758213—42no—
180SD16×C61—22no—
181SD16×C61—22no—
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C22×C411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61C22×C411yescharacteristic
186C42×C61—21no—
187C42×C61C22×C411yescharacteristic
188C22⋊Dic61—21no—
189C22⋊Dic61—21no—
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192#11758200—22no—
193#11758200—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61#4111yescharacteristic
207C4×Dic61C2411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C23×C61—21no—
211C23×C61—21no—
212C22×D61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61#13112yes—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—81no—
220D4×C61—81no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C23×C411yescharacteristic
226C22⋊D61—81no—
227C22⋊D61—81no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C2×#4111yescharacteristic
239C4×D61—24no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—41no—
245C4×D61—81no—
246Dic122—24no—
247Dic122—21no—
248Dic122—81no—
249Dic122#13112yes—
250#92420—22no—
251#92420—21no—
252#92420—21no—
253#92420—21no—
254#92420—21no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258#92420—41no—
259#92420—41no—
260C8×C61—21no—
261C8×C61—21no—
262#92418—21no—
263#92418—21no—
264#17923—611nomaximal, Sylow
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×C4×D411yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61C2×#13111yescharacteristic
280C4×C61C2×#13111yescharacteristic
281Dic61—21no—
282Dic61—22no—
283Dic61—21no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61#57711yescharacteristic
288Dic61#57711yescharacteristic
289#3103—611no—
290#2982—611no—
291#2981—611no—
292#1588—611no—
293#1588—611no—
294#1583—611no—
295#1583—611no—
296SD16⋊C8—611no—
297SD16⋊C8—611no—
298C8×SD16—611no—
299C8×SD16—611no—
300#1572—611no—
301#1491—611no—
302#1484—611no—
303#1453—611no—
304C2×C61—81no—
305C2×C61—81no—
306C2×C61#292911yescharacteristic
307C2×C61#294911yescharacteristic
308C2×C61#295611yescharacteristic
309D61—41no—
310#532—611no—
311C2×C4×Q8—611no—
312#481—611no—
313#481—611no—
314#475—611no—
315#475—611no—
316#460—611no—
317#460#692311yescharacteristic
318#448—611no—
319#448—611no—
320C8×Q8—611no—
321C8×Q8—611no—
322C8×Q8—611no—
323C8×Q8—611no—
324C8×Q8—1221no—
325C8×Q8—1221no—
326C4×SD16—611no—
327C4×SD16—611no—
328C4×SD16—611no—
329C4×SD16—611no—
330#436—611no—
331#436—611no—
332#435—1221no—
333#435—1221no—
334C8×D4—611no—
335C8×D4—611no—
336#432—611no—
337#431—611no—
338#431—611no—
339#431—611no—
340#431—1221no—
341#431—1221no—
342#408—1221no—
343#408—1221no—
344C4×M16—611no—
345#335—611no—
346#335—611no—
347#334—611no—
348#334—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356D4⋊C8—611no—
357#322—611no—
358#322—611no—
359#322—611no—
360C82—611no—
361C61#1792311yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—611no—
364C2×SD16—611no—
365C2×SD16—611no—
366C2×SD16C2×#692311yescharacteristic
367C2×SD16C2×#692311yescharacteristic
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C22×C8—1221no—
372C22×C8—1221no—
373C4⋊Q8—611no—
374#127C2×#692311yescharacteristic
375#124—1221no—
376#121—611no—
377#121—611no—
378#121—1221no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8C2×#692311yescharacteristic
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—1221no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C42—611no—
391C2×C42—1221no—
392#106—611no—
393#106—611no—
394#106—611no—
395#106—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8C2×#692311yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#102—611no—
413#102—611no—
414#102C2×#692311yescharacteristic
415#102C2×#692311yescharacteristic
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—1221no—
427#97—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8—1221no—
439#41—4881no—
440#41—4881no—
441C2×Q8—611no—
442C2×Q8—1221no—
443C2×Q8—1222no—
444C2×Q8—1222no—
445C2×Q8—1221no—
446C2×Q8C22×#692311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4C22×#692311yescharacteristic
452C2×D4C22×#692311yescharacteristic
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460SD16—22no—
461SD16—22no—
462SD16—1222no—
463SD16—1222no—
464M16—4881no—
465M16—4881no—
466M16—2442no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—4881no—
480C2×C8—4881no—
481C2×C8C22×#692311yescharacteristic
482C2×C8C22×#692311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—611no—
485C4⋊C4—611no—
486C4⋊C4—611no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4C22×#692311yescharacteristic
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C42—21no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42C22×#692311yescharacteristic
505C23—21no—
506C23—21no—
507C23—611no—
508Q8—21no—
509Q8—612no—
510Q8—1224no—
511Q8—1221no—
512Q8—4881no—
513Q8#1451986412yes—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—81no—
519D4—81no—
520D4—4881no—
521D4—4881no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1224no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—4881no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4D4×#692311yescharacteristic
543C2×C4D4×#692311yescharacteristic
544C2×C4C23×#692311yescharacteristic
545C8—21no—
546C8—21no—
547C8—1221no—
548C8—1221no—
549C8—1221no—
550C8—1221no—
551C8—1222no—
552C8—1221no—
553C8—1221no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—1221no—
566C22—1221no—
567C22—1221no—
568C22C2×D4×#692311yescharacteristic
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—611no—
574C4—611no—
575C4—1221no—
576C4—1222no—
577C4—1221no—
578C4—2441no—
579C4—2441no—
580C4—2441no—
581C4C2×#1451986411yescharacteristic
582C4D61⋊#13111yescharacteristic
583C2—81no—
584C2—81no—
585C2—2441no—
586C2#2146253311yescharacteristic
587C2#2146257911yescharacteristic
588C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#16840310C22
cosocleC4×Dic61C24
hypercenter#460#6923
hypocenterC61#17923
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #21462713C2semidirect
3. #21461449C2semidirect
4. #21461448C2semidirect
5. #21461429C2semidirect
6. #21461428C2semidirect
7. #21461410C2semidirect
8. SD16⋊#92420C2semidirect
9. #21461402C2semidirect
10. SD16×#92420C2semidirect
11. #21461391C2semidirect
12. #21461162C2semidirect
14. #21461037C2semidirect
361. C61#17923semidirect

Maximal subgroups

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

subgroupindex
#214627132
#214627082
#214614492
#214614482
#214614292
#214614282
#214614102
SD16⋊#924202
#214614022
SD16×#924202
#214613912
#214611622
#214611392
#214610372
#214558492
#1792361