Subgroups — C₂×#13050211 #14581169

Order 2624.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050211	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10620306	C₂	1	3	yes	maximal, complemented
3	C₂×#10620308	C₂	1	6	yes	maximal, complemented
4	C₂²×Dic₈₂	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×D₄₁	C₂	1	2	yes	maximal, complemented
6	C₂×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×C₄₁	C₂²	1	8	yes	complemented
8	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₄₁	C₂²	1	3	yes	—
10	C₂²×C₄×C₄₁	C₂²	1	3	yes	—
11	C₂×C₂²⋊D₄₁	C₂²	1	6	yes	—
12	C₂²×Dic₄₁	C₂²	1	6	yes	—
13	Q₈×D₄₁	C₂²	1	16	yes	complemented
14	#10620308	C₂²	1	48	yes	complemented
15	#10620306	C₂²	1	24	yes	complemented
16	C₂×D₁₆₄	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄₁	C₂²	1	6	yes	—
18	C₂×Dic₈₂	C₂²	1	6	yes	—
19	C₂×Dic₈₂	C₂²	1	3	yes	—
20	C₂×Dic₈₂	C₂²	1	24	yes	complemented
21	C₂³×C₄₁	C₂³	1	3	yes	—
22	C₂²×D₄₁	C₂³	1	2	yes	—
23	Q₈×C₄₁	C₂³	1	4	yes	—
24	D₄×C₄₁	C₂³	1	12	yes	—
25	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₄₁	C₂³	1	3	yes	—
27	C₂×C₄×C₄₁	C₂³	1	12	yes	—
28	C₂²⋊D₄₁	C₂³	1	24	yes	—
29	C₂×Dic₄₁	C₂³	1	6	yes	—
30	C₂×Dic₄₁	C₂³	1	24	yes	—
31	D₁₆₄	C₂³	1	4	yes	—
32	C₄×D₄₁	C₂³	1	24	yes	—
33	Dic₈₂	C₂³	1	12	yes	—
34	Dic₈₂	C₂³	1	24	yes	—
35	C₂²×C₄₁	—	2	6	no	—
36	C₂²×C₄₁	C₂⁴	1	6	yes	—
37	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
38	C₂×D₄₁	—	2	4	no	—
39	C₂×D₄₁	C₂⁴	1	4	yes	—
40	C₄×C₄₁	C₂⁴	1	2	yes	—
41	C₄×C₄₁	C₂⁴	1	6	yes	—
42	Dic₄₁	C₂⁴	1	12	yes	—
43	C₂×C₄₁	—	2	6	no	—
44	C₂×C₄₁	2₋¹⁺⁴	1	2	yes	complemented
45	C₂×C₄₁	C₂⁵	1	1	yes	characteristic
46	D₄₁	—	2	4	no	—
47	C₂×2₋¹⁺⁴	—	41	1	no	maximal, Sylow
48	C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
49	2₋¹⁺⁴	—	41	16	no	—
50	C₂×#41	—	41	6	no	—
51	C₂×#41	—	41	3	no	—
52	C₂×#41	D₄₁	1	1	yes	characteristic, complemented
53	C₂²×Q₈	—	41	2	no	—
54	C₂²×Q₈	—	41	3	no	—
55	#41	—	41	48	no	—
56	#41	—	41	24	no	—
57	#41	C₂×D₄₁	1	8	yes	complemented
58	C₂×Q₈	—	41	16	no	—
59	C₂×Q₈	—	41	6	no	—
60	C₂×Q₈	—	41	3	no	—
61	C₂×Q₈	—	41	24	no	—
62	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
63	C₂×D₄	—	41	6	no	—
64	C₂×D₄	—	41	1	no	—
65	C₂×D₄	C₂×D₄₁	1	3	yes	—
66	C₂²×C₄	—	41	6	no	—
67	C₂²×C₄	—	41	6	no	—
68	C₂²×C₄	C₂×D₄₁	1	3	yes	—
69	C₂³	—	41	2	no	—
70	C₂³	C₂²×D₄₁	1	3	yes	—
71	Q₈	—	41	24	no	—
72	Q₈	—	41	12	no	—
73	Q₈	C₂²×D₄₁	1	4	yes	—
74	D₄	—	41	24	no	—
75	D₄	—	41	4	no	—
76	D₄	C₂²×D₄₁	1	12	yes	—
77	C₂×C₄	—	41	24	no	—
78	C₂×C₄	—	41	6	no	—
79	C₂×C₄	—	41	24	no	—
80	C₂×C₄	C₂²×D₄₁	1	12	yes	—
81	C₂×C₄	C₂²×D₄₁	1	3	yes	—
82	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
83	C₂²	—	2	6	no	—
84	C₂²	—	41	4	no	—
85	C₂²	—	82	4	no	—
86	C₂²	C₂³×D₄₁	1	6	yes	—
87	C₂²	C₂³×D₄₁	1	1	yes	characteristic
88	C₄	—	41	12	no	—
89	C₄	C₂³×D₄₁	1	6	yes	—
90	C₄	C₂³×D₄₁	1	2	yes	—
91	C₂	—	2	6	no	—
92	C₂	—	82	4	no	—
93	C₂	#13050211	1	2	yes	direct product factor
94	C₂	C₂⁴×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₄₁
commutator, cosocle	C₂×C₄₁	C₂⁵
Frattini	C₂	C₂⁴×D₄₁
Fitting	C₂×#41×C₄₁	C₂
socle	C₂²×C₄₁	C₂⁴
hypercenter	C₂×#41	D₄₁
hypocenter	C₄₁	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #13050211	C₂	direct (N × H)
2. C₂×#10620306	C₂	semidirect
3. C₂×#10620308	C₂	semidirect
4. C₂²×Dic₈₂	C₂	semidirect
5. C₂×Q₈×D₄₁	C₂	semidirect
6. C₂×#41×C₄₁	C₂	semidirect
7. #41×C₄₁	C₂²	semidirect
13. Q₈×D₄₁	C₂²	semidirect
14. #10620308	C₂²	semidirect
15. #10620306	C₂²	semidirect
20. C₂×Dic₈₂	C₂²	semidirect
44. C₂×C₄₁	2₋¹⁺⁴	semidirect
48. C₄₁	C₂×2₋¹⁺⁴	semidirect
52. C₂×#41	D₄₁	semidirect
57. #41	C₂×D₄₁	semidirect
93. C₂	#13050211	direct (N × H)

Maximal subgroups

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

subgroup	index
#13050211	2
C₂×#10620306	2
C₂×#10620308	2
C₂²×Dic₈₂	2
C₂×Q₈×D₄₁	2
C₂×#41×C₄₁	2
C₂×2₋¹⁺⁴	41

Subgroups — C2×#13050211 #14581169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050211 #14581169