Subgroups — #14581385

Order 2624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050231	C₂	1	2	yes	maximal
2	C₄⋊#66493	C₂	1	1	yes	maximal, characteristic
3	C₄×#66493	C₂	1	1	yes	maximal, characteristic
4	C₄×#66493	C₂	1	2	yes	maximal
5	#13050129	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₂	C₄	1	1	yes	characteristic
7	C₂×#66493	C₂²	1	2	yes	—
8	C₂×#66493	C₂²	1	1	yes	characteristic
9	C₂×#66493	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
11	#10620279	C₄	1	2	yes	—
12	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
13	C₄×Dic₄₁	C₂²	1	2	yes	—
14	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
19	Dic₈₂	C₈	1	4	yes	complemented
20	#66493	—	2	2	no	—
21	#66493	—	2	1	no	—
22	#66493	Q₈	1	2	yes	complemented
23	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₄₁	—	2	2	no	—
25	C₄×C₄₁	C₂×C₈	1	2	yes	—
26	Dic₄₁	—	2	1	no	—
27	Dic₄₁	C₂×C₈	1	4	yes	—
28	Dic₄₁	C₂×Q₈	1	1	yes	characteristic
29	Dic₄₁	#41	1	1	yes	characteristic
30	C₂×C₄₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₄₁	#131	1	1	yes	characteristic
33	C₈×Q₈	—	41	1	no	maximal, Sylow
34	C₄₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₄×Q₈	—	41	1	no	—
36	C₄⋊C₈	—	41	1	no	—
37	C₄⋊C₈	—	41	2	no	—
38	C₄×C₈	—	41	2	no	—
39	C₄×C₈	—	41	1	no	—
40	C₂×Q₈	—	41	1	no	—
41	C₂×C₈	—	41	1	no	—
42	C₂×C₈	—	41	2	no	—
43	C₂×C₈	—	41	1	no	—
44	C₄⋊C₄	—	41	2	no	—
45	C₄⋊C₄	#4223	1	1	yes	characteristic
46	C₄²	—	41	2	no	—
47	C₄²	—	41	1	no	—
48	Q₈	—	41	4	no	—
49	C₂×C₄	—	41	1	no	—
50	C₂×C₄	—	41	2	no	—
51	C₂×C₄	—	41	1	no	—
52	C₂×C₄	C₂×#4223	1	2	yes	—
53	C₂×C₄	C₂×#4223	1	1	yes	characteristic
54	C₈	—	41	2	no	—
55	C₈	—	82	2	no	—
56	C₈	—	82	1	no	—
57	C₂²	C₂²×#4223	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	41	1	no	—
60	C₄	—	41	1	no	—
61	C₄	—	41	4	no	—
62	C₄	—	82	1	no	—
63	C₄	#10620296	1	2	yes	—
64	C₂	Q₈×#4223	1	1	yes	characteristic
65	C₂	C₂×#10620296	1	1	yes	characteristic
66	C₂	#13050251	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#4223
commutator	C₂×C₄₁	C₂²×C₈
Fitting	C₄⋊C₄×C₄₁	C₄
socle, prime radical	C₂²×C₄₁	C₂²×C₄
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₄⋊C₄	#4223
hypocenter	C₄₁	C₈×Q₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
19. Dic₈₂	C₈	semidirect
22. #66493	Q₈	semidirect
34. C₄₁	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
#13050231	2
C₄⋊#66493	2
C₄×#66493	2
#13050129	2
C₈×Q₈	41