Finite Group Databasebeta

← #30612722

Subgroups — #30612722

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#21462712C211yesmaximal, characteristic, complemented
2#21462709C211yesmaximal, characteristic
3#21461448C211yesmaximal, characteristic, complemented
4#21461446C211yesmaximal, characteristic, complemented
5#21461428C211yesmaximal, characteristic, complemented
6#21461426C211yesmaximal, characteristic, complemented
7#21461409C211yesmaximal, characteristic, complemented
8SD16⋊#92420C211yesmaximal, characteristic, complemented
9#21461403C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461161C211yesmaximal, characteristic, complemented
13#21461138C211yesmaximal, characteristic
14#21461036C211yesmaximal, characteristic, complemented
15#21455845C211yesmaximal, characteristic
16Q8×#92420—21no—
17Q8×#92420—21no—
18Q8×#92420C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20Q8×#92420C2211yescharacteristic
21Q8×#92420C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840794—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840783C2211yescharacteristic
29#16840778—21no—
30#16840778—21no—
31#16840778C2211yescharacteristic
32#16840778C2211yescharacteristic
33#16840736—21no—
34#16840735—21no—
35C4×#11758217C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840307C2211yescharacteristic
53C2×Q8×Dic61C2211yescharacteristic
54#16840081C411yescharacteristic
55#16840078C411yescharacteristic
56#16840045C411yescharacteristic
57#16840045C411yescharacteristic
58#16839960C411yescharacteristic
59#16839960C411yescharacteristic
60#16839901C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#448C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C22×#92420—21no—
72C4⋊#92420—21no—
73C4⋊#92420—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84C22⋊#92420—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420D411yescharacteristic
89C22⋊#92420D411yescharacteristic
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×#11758201C2×C411yescharacteristic
103C2×#11758201C2×C411yescharacteristic
104#14519776C2×C411yescharacteristic
105#14519773C2×C411yescharacteristic
106#14519763—21no—
107#14519751C2×C411yescharacteristic
108#14519749—21no—
109Q8×Dic61—21no—
110Q8×Dic61—21no—
111Q8×Dic61C2×C411yescharacteristic
112Q8×Dic61C2×C411yescharacteristic
113Q8×Dic61C2311yescharacteristic
114Q8×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739C2311yescharacteristic
117#14519737—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519709C2×C411yescharacteristic
123#14519709C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22×Q8×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C2×SD16×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×Q8×C61C22×C411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61#4111yescharacteristic
160#11758224—81no—
161#11758224—81no—
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×Dic122—21no—
165#11758217—42no—
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×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178#11758213—81no—
179D61⋊C8—81no—
180SD16×C61—22no—
181SD16×C61—22no—
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊Dic61—21no—
187#11758201—22no—
188#11758201—22no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61C22×C411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61#4111yescharacteristic
207C4×Dic61C2411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—24no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61#13112yes—
217Q8×C61#13112yes—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—81no—
221C2×C4×C61—24no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C22⋊D61—81no—
230C22⋊D61—81no—
231C22⋊D61—81no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—81no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C4×D411yescharacteristic
243C2×Dic61C22×D411yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245D244—21no—
246D244—21no—
247C4×D61—41no—
248C4×D61—41no—
249Dic122—81no—
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—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×C4×D411yescharacteristic
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—22no—
276C4×C61—22no—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61C2×#13111yescharacteristic
280C4×C61C2×#13111yescharacteristic
281Dic61—21no—
282Dic61—21no—
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—41no—
305C2×C61—81no—
306C2×C61#292911yescharacteristic
307C2×C61#294911yescharacteristic
308C2×C61#295611yescharacteristic
309D61—81no—
310#532—611no—
311C2×C4×Q8—611no—
312#481—611no—
313#481—611no—
314#475—611no—
315#475—611no—
316#460—611no—
317#460—611no—
318#448—611no—
319#448#692311yescharacteristic
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×Q8C2×#692311yescharacteristic
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#127—611no—
375#124—1221no—
376#121—611no—
377#121—1221no—
378#121C2×#692311yescharacteristic
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×Q8—611no—
383C4×Q8—1221no—
384C4×Q8—1221no—
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—611no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408#103—611no—
409#103—611no—
410#103C2×#692311yescharacteristic
411#103C2×#692311yescharacteristic
412#102—611no—
413#102—611no—
414#102—611no—
415#102—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8C2×#692311yescharacteristic
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—22no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—1221no—
445C2×Q8C22×#692311yescharacteristic
446C2×Q8C22×#692311yescharacteristic
447C2×D4—21no—
448C2×D4—611no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4C22×#692311yescharacteristic
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4C22×#692311yescharacteristic
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—611no—
484C4⋊C4—611no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4C22×#692311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C23—21no—
506C23—1221no—
507C23D4×#692311yescharacteristic
508Q8—24no—
509Q8—21no—
510Q8—21no—
511Q8—4881no—
512Q8#1451986412yes—
513Q8#1451986412yes—
514D4—21no—
515D4—21no—
516D4—81no—
517D4—1221no—
518D4—1221no—
519D4—4881no—
520D4—4881no—
521D4—4881no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—4881no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
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—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22C2×D4×#692311yescharacteristic
569C4—22no—
570C4—22no—
571C4—21no—
572C4—41no—
573C4—611no—
574C4—611no—
575C4—1221no—
576C4—1221no—
577C4—1221no—
578C4—2441no—
579C4—2441no—
580C4—2441no—
581C4C2×#1451986411yescharacteristic
582C4C2×#1451986411yescharacteristic
583C2—41no—
584C2—81no—
585C2—4881no—
586C2#2146253411yescharacteristic
587C2#2146257911yescharacteristic
588C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#448C4
socleC22×C61C2×C4×D4
prime radical#16840307C22
cosocleC4×Dic61C24
hypercenter#448#6923
hypocenterC61#17923
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #21462712C2semidirect
3. #21461448C2semidirect
4. #21461446C2semidirect
5. #21461428C2semidirect
6. #21461426C2semidirect
7. #21461409C2semidirect
8. SD16⋊#92420C2semidirect
9. #21461403C2semidirect
10. SD16×#92420C2semidirect
11. #21461390C2semidirect
12. #21461161C2semidirect
14. #21461036C2semidirect
361. C61#17923semidirect

Maximal subgroups

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

subgroupindex
#214627122
#214627092
#214614482
#214614462
#214614282
#214614262
#214614092
SD16⋊#924202
#214614032
SD16×#924202
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