Subgroups — #14581186

Order 2624.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#66493	C₂	1	1	yes	maximal, characteristic
2	C₄×#66493	C₂	1	1	yes	maximal, characteristic
3	#13050129	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₂	C₄	1	1	yes	characteristic
5	C₂×#66493	—	2	1	no	—
6	C₂×#66493	—	2	1	no	—
7	C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
8	#10620279	—	2	1	no	—
9	C₄×Dic₄₁	—	2	1	no	—
10	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₁	—	2	1	no	—
12	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₄₁	—	2	1	no	—
14	C₂×Dic₄₁	D₄	1	1	yes	characteristic
15	C₂×Dic₄₁	D₄	1	1	yes	characteristic
16	Dic₈₂	—	2	1	no	—
17	Dic₈₂	C₈	1	2	yes	complemented
18	#66493	—	2	2	no	—
19	#66493	—	4	1	no	—
20	C₂²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₁	—	4	1	no	—
22	C₄×C₄₁	C₂×C₈	1	1	yes	characteristic
23	C₄×C₄₁	M₁₆	1	1	yes	characteristic
24	Dic₄₁	—	2	2	no	—
25	Dic₄₁	—	2	1	no	—
26	Dic₄₁	SD₁₆	1	1	yes	characteristic
27	Dic₄₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₄₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₄₁	#103	1	1	yes	characteristic
30	C₂×C₄₁	#104	1	1	yes	characteristic
31	Q₈⋊C₈	—	41	1	no	maximal, Sylow
32	C₄₁	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
33	C₄×Q₈	—	41	1	no	—
34	C₄⋊C₈	—	41	1	no	—
35	C₄×C₈	—	41	1	no	—
36	C₂×Q₈	—	41	1	no	—
37	C₂×C₈	—	82	1	no	—
38	C₂×C₈	—	82	1	no	—
39	C₄⋊C₄	—	82	1	no	—
40	C₄⋊C₄	#4223	1	1	yes	characteristic
41	C₄²	—	41	1	no	—
42	C₄²	—	82	1	no	—
43	Q₈	—	41	2	no	—
44	Q₈	—	82	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	41	1	no	—
47	C₂×C₄	—	41	1	no	—
48	C₂×C₄	—	82	1	no	—
49	C₂×C₄	C₂×#4223	1	1	yes	characteristic
50	C₈	—	82	2	no	—
51	C₈	—	164	1	no	—
52	C₂²	C₂²⋊#4223	1	1	yes	characteristic
53	C₄	—	4	1	no	—
54	C₄	—	41	1	no	—
55	C₄	—	41	1	no	—
56	C₄	—	82	2	no	—
57	C₄	—	82	1	no	—
58	C₄	#10620296	1	1	yes	characteristic
59	C₄	#10620297	1	1	yes	characteristic
60	C₂	#13050221	1	1	yes	characteristic
61	C₂	#13050227	1	1	yes	characteristic
62	C₂	#13050228	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
17. Dic₈₂	C₈	semidirect
32. C₄₁	Q₈⋊C₈	semidirect

Maximal subgroups

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

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