Subgroups — #14581232

Order 2624.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050238	C₂	1	2	yes	maximal, complemented
2	C₂×#10620277	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₁	C₄	1	1	yes	characteristic
4	#10620277	—	2	2	no	—
5	C₂×#66491	C₄	1	1	yes	characteristic
6	C₂×#66491	C₂²	1	1	yes	characteristic
7	#10620270	—	2	2	no	—
8	C₂³×C₄₁	C₈	1	1	yes	characteristic
9	C₂×C₄×C₄₁	—	2	1	no	—
10	C₂×C₄×C₄₁	—	2	1	no	—
11	C₂×C₄×C₄₁	C₈	1	1	yes	characteristic
12	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
13	#66491	—	2	1	no	—
14	#66491	D₄	1	2	yes	—
15	C₂²×C₄₁	—	2	1	no	—
16	C₂²×C₄₁	—	4	1	no	—
17	C₂²×C₄₁	C₂×C₈	1	1	yes	characteristic
18	C₄×C₄₁	—	2	1	no	—
19	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₄₁	M₁₆	1	1	yes	characteristic
21	C₂×C₄₁	—	2	1	no	—
22	C₂×C₄₁	—	4	1	no	—
23	C₂×C₄₁	C₂²⋊C₈	1	1	yes	characteristic
24	#349	—	41	1	no	maximal, Sylow
25	C₄₁	#349	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	41	1	no	—
27	M₃₂	—	41	2	no	—
28	C₂²×C₄	#4223	1	1	yes	characteristic
29	M₁₆	—	82	2	no	—
30	C₂×C₈	—	41	1	no	—
31	C₂×C₈	—	41	1	no	—
32	C₁₆	—	82	2	no	—
33	C₂³	#66493	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	#66493	1	1	yes	characteristic
37	C₂×C₄	C₂×#4223	1	1	yes	characteristic
38	C₈	—	41	2	no	—
39	C₈	—	82	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#66493	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	#10620301	1	1	yes	characteristic
45	C₄	C₂²⋊#4223	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#66493	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#4223
commutator	C₂²×C₄₁	C₂×C₈
Frattini	C₂×C₄	C₂×#4223
Fitting	C₂²×C₄×C₄₁	C₄
socle	C₂×C₄₁	C₂²⋊C₈
prime radical	C₂³×C₄₁	C₈
cosocle	C₂×#66491	C₂²
hypercenter	C₂²×C₄	#4223
hypocenter	C₄₁	#349
LCS	G ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #13050238	C₂	semidirect
25. C₄₁	#349	semidirect

Maximal subgroups

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

subgroup	index
#13050238	2
C₂×#10620277	2
#349	41