Subgroups — #14581065

Order 2624.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050164	C₂	1	3	yes	maximal
2	#13050155	C₂	1	6	yes	maximal
3	Q₈×Dic₄₁	C₂	1	2	yes	maximal
4	C₄×Dic₈₂	C₂	1	3	yes	maximal
5	C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₈₂	C₂²	1	3	yes	—
8	C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
9	C₄²×C₄₁	C₂²	1	3	yes	—
10	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₁	C₂²	1	6	yes	—
12	C₄⋊Dic₄₁	C₂²	1	6	yes	—
13	#10620279	C₂²	1	6	yes	—
14	C₄×Dic₄₁	C₂²	1	6	yes	—
15	Q₈×C₄₁	Q₈	1	4	yes	complemented
16	C₂×C₄×C₄₁	C₂³	1	3	yes	—
17	C₂×C₄×C₄₁	C₂³	1	3	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	C₂³	1	2	yes	—
20	C₂×Dic₄₁	C₂³	1	6	yes	—
21	Dic₈₂	—	2	6	no	—
22	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₄₁	—	2	3	no	—
24	C₄×C₄₁	C₂×Q₈	1	6	yes	—
25	C₄×C₄₁	#41	1	2	yes	—
26	Dic₄₁	—	2	6	no	—
27	Dic₄₁	—	2	2	no	—
28	C₂×C₄₁	C₂²×Q₈	1	1	yes	characteristic
29	C₂×C₄₁	C₂×#41	1	1	yes	characteristic
30	C₂×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
31	#557	—	41	1	no	maximal, Sylow
32	C₄₁	#557	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	41	3	no	—
34	#125	—	41	6	no	—
35	C₄×Q₈	—	41	2	no	—
36	C₄×Q₈	—	41	3	no	—
37	C₄×Q₈	D₄₁	1	1	yes	characteristic
38	C₂×Q₈	—	41	3	no	—
39	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
40	C₄⋊C₄	—	41	1	no	—
41	C₄⋊C₄	—	41	6	no	—
42	C₄⋊C₄	—	41	6	no	—
43	C₄⋊C₄	—	41	6	no	—
44	C₄⋊C₄	C₂×D₄₁	1	3	yes	—
45	C₄²	—	41	6	no	—
46	C₄²	C₂×D₄₁	1	3	yes	—
47	Q₈	—	82	6	no	—
48	Q₈	Dic₈₂	1	4	yes	complemented
49	C₂×C₄	—	41	2	no	—
50	C₂×C₄	—	41	6	no	—
51	C₂×C₄	C₂²×D₄₁	1	3	yes	—
52	C₂×C₄	C₂²×D₄₁	1	3	yes	—
53	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
54	C₂²	C₂³×D₄₁	1	1	yes	characteristic
55	C₄	—	2	3	no	—
56	C₄	—	82	6	no	—
57	C₄	—	82	2	no	—
58	C₄	C₂×Dic₈₂	1	6	yes	—
59	C₄	#10620310	1	2	yes	—
60	C₂	C₂²×Dic₈₂	1	1	yes	characteristic
61	C₂	C₂×#10620310	1	1	yes	characteristic
62	C₂	#13050211	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₁
commutator, socle, prime radical, cosocle	C₂²×C₄₁	C₂⁴
Fitting	C₄×Q₈×C₄₁	C₂
hypercenter	C₄×Q₈	D₄₁
hypocenter	C₄₁	#557
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
15. Q₈×C₄₁	Q₈	semidirect
32. C₄₁	#557	semidirect
48. Q₈	Dic₈₂	semidirect

Maximal subgroups

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

subgroup	index
#13050164	2
#13050155	2
Q₈×Dic₄₁	2
C₄×Dic₈₂	2
C₄×Q₈×C₄₁	2
#557	41