Subgroups — #14581306

Order 2624.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620301	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#66493	C₂	1	4	yes	maximal, complemented
3	C₂³×Dic₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₄₁	C₄	1	1	yes	characteristic
5	C₂²×Dic₄₁	—	2	4	no	—
6	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₄	1	2	yes	—
8	C₂²×Dic₄₁	C₂²	1	2	yes	—
9	C₂²×Dic₄₁	C₂²	1	1	yes	characteristic
10	#10620301	—	2	4	no	—
11	C₂×#66493	C₂²	1	4	yes	complemented
12	C₂³×C₄₁	—	2	2	no	—
13	C₂³×C₄₁	—	2	4	no	—
14	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₄₁	—	2	2	no	—
17	C₂×Dic₄₁	—	2	4	no	—
18	C₂×Dic₄₁	—	2	4	no	—
19	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
20	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₄₁	D₄	1	4	yes	—
22	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
23	#66493	—	2	4	no	—
24	C₂²×C₄₁	—	2	8	no	—
25	C₂²×C₄₁	—	2	2	no	—
26	C₂²×C₄₁	—	2	2	no	—
27	C₂²×C₄₁	—	2	2	no	—
28	C₂²×C₄₁	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄₁	M₁₆	1	4	yes	complemented
30	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	Dic₄₁	—	2	2	no	—
32	Dic₄₁	C₂²⋊C₄	1	2	yes	—
33	Dic₄₁	C₂×D₄	1	2	yes	—
34	C₂×C₄₁	—	2	2	no	—
35	C₂×C₄₁	—	2	4	no	—
36	C₂×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄₁	C₂×M₁₆	1	2	yes	—
38	#407	—	41	1	no	maximal, Sylow
39	C₄₁	#407	1	1	yes	characteristic, complemented, Sylow
40	C₂³×C₄	—	41	1	no	—
41	C₂×M₁₆	—	41	2	no	—
42	C₂²⋊C₈	—	41	4	no	—
43	C₂⁴	#4223	1	1	yes	characteristic
44	C₂²×C₄	—	41	1	no	—
45	C₂²×C₄	—	41	2	no	—
46	C₂²×C₄	—	41	2	no	—
47	C₂²×C₄	—	41	1	no	—
48	C₂²×C₄	—	82	4	no	—
49	M₁₆	—	82	4	no	—
50	C₂×C₈	—	41	4	no	—
51	C₂³	—	2	4	no	—
52	C₂³	—	2	2	no	—
53	C₂³	C₂×#4223	1	2	yes	—
54	C₂³	C₂×#4223	1	1	yes	characteristic
55	C₂×C₄	—	41	4	no	—
56	C₂×C₄	—	41	1	no	—
57	C₂×C₄	—	41	1	no	—
58	C₂×C₄	—	41	2	no	—
59	C₂×C₄	—	82	4	no	—
60	C₂×C₄	—	82	4	no	—
61	C₂×C₄	—	82	2	no	—
62	C₈	—	82	4	no	—
63	C₂²	—	2	8	no	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	—	2	2	no	—
67	C₂²	#10620301	1	4	yes	complemented
68	C₂²	C₂²⋊#4223	1	2	yes	—
69	C₂²	C₂²×#4223	1	1	yes	characteristic
70	C₄	—	41	2	no	—
71	C₄	—	41	2	no	—
72	C₄	—	82	2	no	—
73	C₂	—	2	4	no	—
74	C₂	—	2	2	no	—
75	C₂	C₂×C₂²⋊#4223	1	1	yes	characteristic
76	C₂	C₂×#10620301	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#4223
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting, prime radical	C₂⁴×C₄₁	C₄
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₂⁴	#4223
hypocenter	C₄₁	#407
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂×#10620301	C₂	semidirect
2. C₂²⋊#66493	C₂	semidirect
11. C₂×#66493	C₂²	semidirect
29. C₂²×C₄₁	M₁₆	semidirect
39. C₄₁	#407	semidirect
67. C₂²	#10620301	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620301	2
C₂²⋊#66493	2
C₂³×Dic₄₁	2
#407	41