Subgroups — C₂×#13050153 #14580854

Order 2624.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₆₄	C₂	1	1	yes	maximal, characteristic
2	#13050153	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10620281	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄₁	C₂²	1	2	yes	—
7	C₂×Q₈×C₄₁	—	2	4	no	—
8	C₂×Q₈×C₄₁	C₂²	1	4	yes	complemented
9	C₂²×C₄×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×Dic₄₁	C₂²	1	2	yes	—
12	C₂×D₁₆₄	—	2	4	no	—
13	C₂×D₁₆₄	C₂²	1	4	yes	—
14	#10620281	C₂²	1	16	yes	complemented
15	C₄×Dic₄₁	C₂²	1	4	yes	complemented
16	C₂³×C₄₁	C₂³	1	1	yes	characteristic
17	C₂²×D₄₁	—	2	4	no	—
18	C₂²×D₄₁	—	2	8	no	—
19	C₂²×D₄₁	C₂³	1	4	yes	—
20	Q₈×C₄₁	—	2	8	no	—
21	C₂×C₄×C₄₁	—	2	4	no	—
22	C₂×C₄×C₄₁	D₄	1	4	yes	—
23	C₂×C₄×C₄₁	C₂³	1	4	yes	—
24	C₂×C₄×C₄₁	C₂³	1	2	yes	—
25	C₂×Dic₄₁	—	2	4	no	—
26	C₂×Dic₄₁	C₂³	1	4	yes	—
27	D₁₆₄	—	2	8	no	—
28	C₂²×C₄₁	C₂×D₄	1	2	yes	—
29	C₂²×C₄₁	#41	1	4	yes	—
30	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
31	C₂×D₄₁	—	2	4	no	—
32	C₂×D₄₁	—	2	8	no	—
33	C₂×D₄₁	—	4	8	no	—
34	C₄×C₄₁	—	2	4	no	—
35	C₄×C₄₁	C₂×D₄	1	4	yes	—
36	Dic₄₁	—	2	4	no	—
37	C₂×C₄₁	#124	1	4	yes	complemented
38	C₂×C₄₁	C₂²×D₄	1	1	yes	characteristic
39	C₂×C₄₁	C₂×#41	1	2	yes	—
40	D₄₁	—	4	4	no	—
41	C₂×#124	—	41	1	no	maximal, Sylow
42	C₄₁	C₂×#124	1	1	yes	characteristic, complemented, Sylow
43	C₂²×Q₈	D₄₁	1	1	yes	characteristic, complemented
44	C₂²×D₄	—	41	1	no	—
45	#124	—	41	8	no	—
46	C₂×C₂²⋊C₄	—	41	4	no	—
47	C₂×C₄²	—	41	1	no	—
48	C₂⁴	—	41	2	no	—
49	C₂×Q₈	—	2	4	no	—
50	C₂×Q₈	C₂×D₄₁	1	4	yes	complemented
51	C₂×D₄	—	41	4	no	—
52	C₂×D₄	—	82	4	no	—
53	C₂²×C₄	—	41	2	no	—
54	C₂²×C₄	C₂×D₄₁	1	2	yes	—
55	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
56	C₂²⋊C₄	—	41	16	no	—
57	C₄²	—	41	4	no	—
58	C₂³	—	41	4	no	—
59	C₂³	—	82	8	no	—
60	C₂³	—	82	4	no	—
61	C₂³	C₂²×D₄₁	1	1	yes	characteristic
62	Q₈	—	2	8	no	—
63	D₄	—	82	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	41	4	no	—
66	C₂×C₄	—	82	4	no	—
67	C₂×C₄	C₂²⋊D₄₁	1	4	yes	—
68	C₂×C₄	C₂²×D₄₁	1	4	yes	—
69	C₂×C₄	C₂²×D₄₁	1	2	yes	—
70	C₂²	—	82	4	no	—
71	C₂²	—	82	8	no	—
72	C₂²	—	164	8	no	—
73	C₂²	#10620310	1	4	yes	—
74	C₂²	C₂×C₂²⋊D₄₁	1	2	yes	—
75	C₂²	C₂³×D₄₁	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	82	4	no	—
78	C₄	C₂×C₂²⋊D₄₁	1	4	yes	—
79	C₂	—	164	4	no	—
80	C₂	#13050153	1	4	yes	direct product factor
81	C₂	C₂²×C₂²⋊D₄₁	1	1	yes	characteristic
82	C₂	C₂×#10620310	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₄₁
commutator, cosocle	C₂²×C₄₁	C₂⁴
Frattini	C₂²	C₂³×D₄₁
Fitting	C₂²×Q₈×C₄₁	C₂
socle	C₂³×C₄₁	C₂³
prime radical	C₂²×D₁₆₄	C₂
hypercenter	C₂²×Q₈	D₄₁
hypocenter	C₄₁	C₂×#124
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #13050153	C₂	direct (N × H)
3. C₂×#10620281	C₂	semidirect
4. C₂×C₄×Dic₄₁	C₂	semidirect
5. C₂²×Q₈×C₄₁	C₂	semidirect
8. C₂×Q₈×C₄₁	C₂²	semidirect
14. #10620281	C₂²	semidirect
15. C₄×Dic₄₁	C₂²	semidirect
37. C₂×C₄₁	#124	semidirect
42. C₄₁	C₂×#124	semidirect
43. C₂²×Q₈	D₄₁	semidirect
50. C₂×Q₈	C₂×D₄₁	semidirect
80. C₂	#13050153	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×D₁₆₄	2
#13050153	2
C₂×#10620281	2
C₂×C₄×Dic₄₁	2
C₂²×Q₈×C₄₁	2
C₂×#124	41

Subgroups — C2×#13050153 #14580854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050153 #14580854