Subgroups — C₂×#13050212 #14581170

Order 2624.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050212	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10620310	C₂	1	4	yes	maximal, complemented
3	C₂×#10620306	C₂	1	6	yes	maximal, complemented
4	C₂×Q₈×D₄₁	C₂	1	4	yes	maximal, complemented
5	C₂²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₁	C₂²	1	4	yes	—
7	C₂×Q₈×C₄₁	C₂²	1	8	yes	complemented
8	C₂²×C₄×C₄₁	C₂²	1	3	yes	—
9	C₂×C₂²⋊D₄₁	C₂²	1	4	yes	—
10	#10620310	C₂²	1	32	yes	complemented
11	Q₈×D₄₁	C₂²	1	32	yes	complemented
12	#10620306	C₂²	1	48	yes	complemented
13	C₂×D₁₆₄	C₂²	1	6	yes	—
14	C₂×C₄×D₄₁	C₂²	1	12	yes	—
15	C₂×Dic₈₂	C₂²	1	6	yes	—
16	C₂³×C₄₁	C₂³	1	1	yes	characteristic
17	C₂²×D₄₁	C₂³	1	4	yes	—
18	Q₈×C₄₁	C₂³	1	16	yes	—
19	C₂×C₄×C₄₁	C₂³	1	6	yes	—
20	C₂×C₄×C₄₁	C₂³	1	12	yes	—
21	C₂²⋊D₄₁	C₂³	1	16	yes	—
22	C₂×Dic₄₁	C₂³	1	4	yes	—
23	D₁₆₄	C₂³	1	24	yes	—
24	C₄×D₄₁	C₂³	1	48	yes	—
25	Dic₈₂	C₂³	1	24	yes	—
26	C₂²×C₄₁	—	2	2	no	—
27	C₂²×C₄₁	C₂⁴	1	2	yes	—
28	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
29	C₂×D₄₁	—	2	8	no	—
30	C₂×D₄₁	C₂⁴	1	8	yes	—
31	C₄×C₄₁	C₂⁴	1	12	yes	—
32	Dic₄₁	C₂⁴	1	8	yes	—
33	C₂×C₄₁	—	2	2	no	—
34	C₂×C₄₁	2₋¹⁺⁴	1	2	yes	complemented
35	C₂×C₄₁	C₂⁵	1	1	yes	characteristic
36	D₄₁	—	2	8	no	—
37	C₂×2₋¹⁺⁴	—	41	1	no	maximal, Sylow
38	C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
39	2₋¹⁺⁴	—	41	16	no	—
40	C₂×#41	—	41	4	no	—
41	C₂×#41	—	41	6	no	—
42	C₂²×Q₈	—	41	4	no	—
43	C₂²×Q₈	D₄₁	1	1	yes	characteristic, complemented
44	#41	—	41	32	no	—
45	#41	—	41	48	no	—
46	C₂×Q₈	—	41	32	no	—
47	C₂×Q₈	—	41	6	no	—
48	C₂×Q₈	C₂×D₄₁	1	4	yes	—
49	C₂×Q₈	C₂×D₄₁	1	8	yes	complemented
50	C₂×D₄	—	41	4	no	—
51	C₂×D₄	—	41	6	no	—
52	C₂²×C₄	—	41	12	no	—
53	C₂²×C₄	C₂×D₄₁	1	3	yes	—
54	C₂³	—	41	4	no	—
55	C₂³	C₂²×D₄₁	1	1	yes	characteristic
56	Q₈	—	41	24	no	—
57	Q₈	C₂²×D₄₁	1	16	yes	—
58	D₄	—	41	16	no	—
59	D₄	—	41	24	no	—
60	C₂×C₄	—	41	4	no	—
61	C₂×C₄	—	41	48	no	—
62	C₂×C₄	C₂²×D₄₁	1	12	yes	—
63	C₂×C₄	C₂²×D₄₁	1	6	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	—	41	8	no	—
66	C₂²	—	82	8	no	—
67	C₂²	C₂³×D₄₁	1	2	yes	—
68	C₂²	C₂³×D₄₁	1	1	yes	characteristic
69	C₄	—	41	8	no	—
70	C₄	C₂³×D₄₁	1	12	yes	—
71	C₂	—	2	2	no	—
72	C₂	—	82	8	no	—
73	C₂	#13050212	1	2	yes	direct product factor
74	C₂	C₂⁴×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₄₁
commutator, cosocle	C₂×C₄₁	C₂⁵
Frattini	C₂	C₂⁴×D₄₁
Fitting	C₂²×Q₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂⁴
hypercenter	C₂²×Q₈	D₄₁
hypocenter	C₄₁	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. #13050212	C₂	direct (N × H)
2. C₂×#10620310	C₂	semidirect
3. C₂×#10620306	C₂	semidirect
4. C₂×Q₈×D₄₁	C₂	semidirect
5. C₂²×Q₈×C₄₁	C₂	semidirect
7. C₂×Q₈×C₄₁	C₂²	semidirect
10. #10620310	C₂²	semidirect
11. Q₈×D₄₁	C₂²	semidirect
12. #10620306	C₂²	semidirect
34. C₂×C₄₁	2₋¹⁺⁴	semidirect
38. C₄₁	C₂×2₋¹⁺⁴	semidirect
43. C₂²×Q₈	D₄₁	semidirect
49. C₂×Q₈	C₂×D₄₁	semidirect
73. C₂	#13050212	direct (N × H)

Maximal subgroups

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

subgroup	index
#13050212	2
C₂×#10620310	2
C₂×#10620306	2
C₂×Q₈×D₄₁	2
C₂²×Q₈×C₄₁	2
C₂×2₋¹⁺⁴	41

Subgroups — C2×#13050212 #14581170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050212 #14581170