Subgroups — #14580362

Order 2624.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620277	C₂	1	1	yes	maximal, characteristic
2	#13050123	C₂	1	1	yes	maximal, characteristic
3	#13050093	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₁	—	2	2	no	—
7	C₂×C₈×C₄₁	C₂²	1	2	yes	—
8	C₂²⋊Dic₄₁	C₄	1	2	yes	—
9	C₄⋊Dic₄₁	C₄	1	2	yes	—
10	C₄×Dic₄₁	C₂²	1	2	yes	—
11	#10620277	—	2	2	no	—
12	C₂×#66491	C₂²	1	2	yes	—
13	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	D₄	1	2	yes	—
16	C₂×C₄×C₄₁	Q₈	1	2	yes	—
17	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₁	C₂×C₄	1	4	yes	—
19	C₈×C₄₁	—	2	2	no	—
20	#66491	—	2	2	no	—
21	C₂²×C₄₁	—	2	2	no	—
22	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
23	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
25	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
26	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
27	Dic₄₁	—	2	4	no	—
28	C₂×C₄₁	—	2	2	no	—
29	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄₁	#131	1	2	yes	—
31	#424	—	41	1	no	maximal, Sylow
32	C₄₁	#424	1	1	yes	characteristic, complemented, Sylow
33	C₂×M₁₆	—	41	1	no	—
34	C₂²×C₈	D₄₁	1	1	yes	characteristic
35	#117	—	41	1	no	—
36	C₄⋊C₈	—	41	4	no	—
37	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
38	M₁₆	—	82	2	no	—
39	C₂×C₈	—	2	2	no	—
40	C₂×C₈	—	41	2	no	—
41	C₂×C₈	C₂×D₄₁	1	2	yes	—
42	C₄⋊C₄	—	41	2	no	—
43	C₂²⋊C₄	—	41	2	no	—
44	C₄²	—	41	2	no	—
45	C₂³	C₄×D₄₁	1	1	yes	characteristic
46	C₂×C₄	—	41	4	no	—
47	C₂×C₄	Dic₈₂	1	2	yes	—
48	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
50	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	82	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	#10620279	1	2	yes	—
55	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
56	C₄	—	82	4	no	—
57	C₄	#10620279	1	2	yes	—
58	C₄	C₂×Dic₈₂	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×#10620279	1	1	yes	characteristic
62	C₂	#13050170	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₂²×C₈×C₄₁	C₂
prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂²×C₈	D₄₁
hypocenter	C₄₁	#424
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #13050093	C₂	semidirect
32. C₄₁	#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620277	2
#13050123	2
#13050093	2
C₂²×C₈×C₄₁	2
#424	41