Subgroups — C₂×#13050129 #14580800

Order 2624.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₂	C₂	1	1	yes	maximal, characteristic
2	#13050129	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10620279	C₂	1	2	yes	maximal
4	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₄₁	C₂	1	2	yes	maximal
6	C₂×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₄₁	C₂²	1	2	yes	—
8	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₁	C₂²	1	2	yes	—
11	C₂²×Dic₄₁	C₂²	1	1	yes	characteristic
12	C₂×Dic₈₂	C₄	1	8	yes	complemented
13	C₂×Dic₈₂	C₂²	1	4	yes	—
14	C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
15	#10620279	C₂²	1	8	yes	—
16	C₄×Dic₄₁	C₂²	1	4	yes	—
17	C₄×Dic₄₁	C₂²	1	8	yes	—
18	C₂³×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₁	—	2	4	no	—
20	C₂×C₄×C₄₁	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₄₁	C₂³	1	4	yes	—
22	C₂×C₄×C₄₁	C₂³	1	2	yes	—
23	C₂×Dic₄₁	—	2	2	no	—
24	C₂×Dic₄₁	C₂×C₄	1	8	yes	—
25	C₂×Dic₄₁	Q₈	1	4	yes	complemented
26	C₂×Dic₄₁	C₂³	1	2	yes	—
27	C₂×Dic₄₁	C₂³	1	4	yes	—
28	C₂×Dic₄₁	C₂³	1	2	yes	—
29	Dic₈₂	C₂×C₄	1	16	yes	complemented
30	C₂²×C₄₁	C₂²×C₄	1	2	yes	—
31	C₂²×C₄₁	C₂×Q₈	1	2	yes	—
32	C₂²×C₄₁	#41	1	2	yes	—
33	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
34	C₄×C₄₁	—	2	4	no	—
35	C₄×C₄₁	C₂²×C₄	1	4	yes	—
36	Dic₄₁	—	2	2	no	—
37	Dic₄₁	C₂²×C₄	1	8	yes	—
38	Dic₄₁	C₂×Q₈	1	4	yes	complemented
39	C₂×C₄₁	C₄×Q₈	1	4	yes	complemented
40	C₂×C₄₁	C₂³×C₄	1	1	yes	characteristic
41	C₂×C₄₁	C₂²×Q₈	1	1	yes	characteristic
42	C₂×C₄₁	C₂×#41	1	1	yes	characteristic
43	C₂×C₄×Q₈	—	41	1	no	maximal, Sylow
44	C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂²×Q₈	—	41	1	no	—
46	C₄×Q₈	—	41	8	no	—
47	C₂×C₄⋊C₄	—	41	2	no	—
48	C₂×C₄⋊C₄	D₄₁	1	1	yes	characteristic
49	C₂×C₄²	—	41	2	no	—
50	C₂×C₄²	—	41	1	no	—
51	C₂×Q₈	—	41	8	no	—
52	C₂×Q₈	—	41	4	no	—
53	C₂²×C₄	—	41	1	no	—
54	C₂²×C₄	—	41	2	no	—
55	C₂²×C₄	—	41	1	no	—
56	C₂²×C₄	C₂×D₄₁	1	2	yes	—
57	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
58	C₄⋊C₄	—	41	8	no	—
59	C₄⋊C₄	C₂×D₄₁	1	4	yes	—
60	C₄²	—	41	8	no	—
61	C₄²	—	41	4	no	—
62	C₂³	C₂²×D₄₁	1	1	yes	characteristic
63	Q₈	—	41	16	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	41	8	no	—
66	C₂×C₄	—	41	4	no	—
67	C₂×C₄	—	41	2	no	—
68	C₂×C₄	—	41	4	no	—
69	C₂×C₄	—	41	2	no	—
70	C₂×C₄	—	82	2	no	—
71	C₂×C₄	C₄×D₄₁	1	4	yes	—
72	C₂×C₄	C₂²×D₄₁	1	4	yes	—
73	C₂×C₄	C₂²×D₄₁	1	2	yes	—
74	C₂²	C₂×C₄×D₄₁	1	2	yes	—
75	C₂²	#10620308	1	2	yes	—
76	C₂²	Q₈×D₄₁	1	2	yes	—
77	C₂²	C₂³×D₄₁	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	41	8	no	—
80	C₄	—	41	4	no	—
81	C₄	—	82	2	no	—
82	C₄	C₂×C₄×D₄₁	1	4	yes	—
83	C₂	#13050129	1	4	yes	direct product factor
84	C₂	C₂²×C₄×D₄₁	1	1	yes	characteristic
85	C₂	C₂×Q₈×D₄₁	1	1	yes	characteristic
86	C₂	C₂×#10620308	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₄₁
commutator	C₂×C₄₁	C₂³×C₄
Frattini	C₂²	C₂³×D₄₁
Fitting	C₂×C₄⋊C₄×C₄₁	C₂
socle, prime radical	C₂³×C₄₁	C₂³
cosocle	C₂²×C₄₁	C₂⁴
hypercenter	C₂×C₄⋊C₄	D₄₁
hypocenter	C₄₁	C₂×C₄×Q₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #13050129	C₂	direct (N × H)
12. C₂×Dic₈₂	C₄	semidirect
25. C₂×Dic₄₁	Q₈	semidirect
29. Dic₈₂	C₂×C₄	semidirect
38. Dic₄₁	C₂×Q₈	semidirect
39. C₂×C₄₁	C₄×Q₈	semidirect
44. C₄₁	C₂×C₄×Q₈	semidirect
83. C₂	#13050129	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×Dic₈₂	2
#13050129	2
C₂×#10620279	2
C₂×C₄×Dic₄₁	2
C₂×C₄⋊C₄×C₄₁	2
C₂×C₄×Q₈	41

Subgroups — C2×#13050129 #14580800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050129 #14580800