Subgroups — C₂×#13050093 #14580356

Order 2624.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050093	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
8	C₂×C₈×C₄₁	—	2	2	no	—
9	C₂×C₈×C₄₁	C₂²	1	2	yes	—
10	C₄×Dic₄₁	C₄	1	2	yes	—
11	C₄×Dic₄₁	C₂²	1	2	yes	—
12	C₂×#66491	—	2	2	no	—
13	C₂×#66491	C₂²	1	2	yes	—
14	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁	D₄	1	2	yes	—
17	C₂×C₄×C₄₁	Q₈	1	2	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	—	2	2	no	—
20	C₂×Dic₄₁	C₈	1	4	yes	complemented
21	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
22	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
23	C₈×C₄₁	—	2	2	no	—
24	#66491	—	2	2	no	—
25	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
26	C₂²×C₄₁	C₂×C₈	1	2	yes	—
27	C₂²×C₄₁	M₁₆	1	2	yes	—
28	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₄₁	—	2	2	no	—
33	Dic₄₁	C₂×C₈	1	4	yes	complemented
34	C₂×C₄₁	C₄⋊C₈	1	4	yes	complemented
35	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₄₁	C₂×M₁₆	1	1	yes	characteristic
38	C₂×C₄⋊C₈	—	41	1	no	maximal, Sylow
39	C₄₁	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	—	41	1	no	—
41	C₂²×C₈	D₄₁	1	1	yes	characteristic
42	C₂×C₄²	—	41	1	no	—
43	C₄⋊C₈	—	41	4	no	—
44	C₂²×C₄	—	41	1	no	—
45	C₂²×C₄	—	41	1	no	—
46	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
47	C₂×C₈	—	2	2	no	—
48	C₂×C₈	—	41	2	no	—
49	C₂×C₈	—	82	2	no	—
50	C₂×C₈	C₂×D₄₁	1	2	yes	—
51	C₄²	—	41	2	no	—
52	C₄²	—	41	2	no	—
53	C₂³	C₄×D₄₁	1	1	yes	characteristic
54	C₂×C₄	—	41	4	no	—
55	C₂×C₄	—	41	2	no	—
56	C₂×C₄	—	41	2	no	—
57	C₂×C₄	—	82	2	no	—
58	C₂×C₄	Dic₈₂	1	2	yes	—
59	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
61	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	82	2	no	—
64	C₂²	C₈×D₄₁	1	2	yes	—
65	C₂²	#10620272	1	2	yes	—
66	C₂²	#10620279	1	2	yes	—
67	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
68	C₄	—	41	4	no	—
69	C₄	—	82	2	no	—
70	C₄	#10620279	1	2	yes	—
71	C₄	C₂×Dic₈₂	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
73	C₂	#13050093	1	4	yes	direct product factor
74	C₂	C₂×#10620279	1	1	yes	characteristic
75	C₂	C₂×C₈×D₄₁	1	1	yes	characteristic
76	C₂	C₂×#10620272	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #13050093	C₂	direct (N × H)
20. C₂×Dic₄₁	C₈	semidirect
33. Dic₄₁	C₂×C₈	semidirect
34. C₂×C₄₁	C₄⋊C₈	semidirect
39. C₄₁	C₂×C₄⋊C₈	semidirect
73. C₂	#13050093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66491	2
C₂×C₄×Dic₄₁	2
#13050093	2
C₂²×C₈×C₄₁	2
C₂×C₄⋊C₈	41

Subgroups — C2×#13050093 #14580356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050093 #14580356