Subgroups — C₂²×#6129 #11719640

Order 832.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
3	C₂³×Dic₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×#6129	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁴×C₁₃	C₂²	1	2	yes	—
8	C₂³×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₁₃	C₂²	1	12	yes	complemented
10	C₂²×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
12	C₂²×Dic₁₃	C₂²	1	2	yes	—
13	C₂²×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₃	C₂²	1	24	yes	complemented
15	#6129	C₂²	1	64	yes	direct product factor
16	C₂×C₄×D₁₃	C₂²	1	12	yes	complemented
17	C₂×Dic₂₆	C₂²	1	12	yes	complemented
18	C₂³×C₁₃	—	2	8	no	—
19	C₂³×C₁₃	C₂³	1	12	yes	—
20	C₂³×C₁₃	C₂³	1	1	yes	characteristic
21	C₂²×D₁₃	—	2	4	no	—
22	C₂²×D₁₃	C₂³	1	6	yes	—
23	D₄×C₁₃	C₂³	1	16	yes	complemented
24	C₂×C₄×C₁₃	C₂³	1	6	yes	—
25	C₂²⋊D₁₃	C₂³	1	32	yes	complemented
26	C₂×Dic₁₃	C₂³	1	12	yes	—
27	C₂×Dic₁₃	C₂³	1	6	yes	—
28	C₂×Dic₁₃	C₂³	1	32	yes	complemented
29	C₄×D₁₃	C₂³	1	16	yes	complemented
30	Dic₂₆	C₂³	1	16	yes	complemented
31	C₂²×#41	—	13	1	no	maximal, Sylow
32	C₂²×C₁₃	—	2	24	no	—
33	C₂²×C₁₃	#41	1	4	yes	complemented
34	C₂²×C₁₃	C₂⁴	1	8	yes	—
35	C₂²×C₁₃	C₂⁴	1	3	yes	—
36	C₂×D₁₃	—	2	12	no	—
37	C₂×D₁₃	C₂⁴	1	4	yes	—
38	C₄×C₁₃	C₂⁴	1	4	yes	—
39	Dic₁₃	C₂⁴	1	8	yes	—
40	Dic₁₃	C₂⁴	1	4	yes	—
41	C₂×#41	—	13	24	no	—
42	C₂²×Q₈	—	13	1	no	—
43	C₂²×D₄	—	13	2	no	—
44	C₂²×D₄	D₁₃	1	1	yes	characteristic, complemented
45	C₂³×C₄	—	13	2	no	—
46	C₂³×C₄	—	13	1	no	—
47	C₂×C₁₃	—	2	8	no	—
48	C₂×C₁₃	C₂×#41	1	6	yes	complemented
49	C₂×C₁₃	C₂⁵	1	1	yes	characteristic
50	D₁₃	—	2	4	no	—
51	C₂⁴	—	13	1	no	—
52	C₂⁴	C₂×D₁₃	1	2	yes	—
53	#41	—	13	64	no	—
54	C₂×Q₈	—	13	12	no	—
55	C₂×D₄	—	13	24	no	—
56	C₂×D₄	C₂×D₁₃	1	12	yes	complemented
57	C₂²×C₄	—	13	24	no	—
58	C₂²×C₄	—	13	1	no	—
59	C₂²×C₄	—	13	2	no	—
60	C₂²×C₄	—	13	12	no	—
61	C₂²×C₄	C₂×D₁₃	1	1	yes	characteristic
62	C₁₃	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	2	8	no	—
64	C₂³	—	13	6	no	—
65	C₂³	—	26	4	no	—
66	C₂³	C₂²×D₁₃	1	12	yes	—
67	C₂³	C₂²×D₁₃	1	1	yes	characteristic
68	Q₈	—	13	16	no	—
69	D₄	—	13	32	no	—
70	D₄	C₂²×D₁₃	1	16	yes	complemented
71	C₂×C₄	—	13	6	no	—
72	C₂×C₄	—	13	12	no	—
73	C₂×C₄	—	13	32	no	—
74	C₂×C₄	—	13	16	no	—
75	C₂×C₄	C₂²×D₁₃	1	6	yes	—
76	C₂²	—	2	24	no	—
77	C₂²	—	13	4	no	—
78	C₂²	—	26	12	no	—
79	C₂²	#6129	1	4	yes	direct product factor
80	C₂²	C₂³×D₁₃	1	8	yes	—
81	C₂²	C₂³×D₁₃	1	3	yes	—
82	C₄	—	13	4	no	—
83	C₄	—	13	8	no	—
84	C₄	C₂³×D₁₃	1	4	yes	—
85	C₂	—	2	8	no	—
86	C₂	—	26	4	no	—
87	C₂	C₂×#6129	1	6	yes	direct product factor
88	C₂	C₂⁴×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁵
Frattini	C₂	C₂⁴×D₁₃
Fitting	C₂²×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂³
hypercenter	C₂²×D₄	D₁₃
hypocenter	C₁₃	C₂²×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×C₁₃	C₂	semidirect
2. C₂²×C₂²⋊D₁₃	C₂	semidirect
3. C₂³×Dic₁₃	C₂	semidirect
4. C₂×#6129	C₂	direct (N × H)
5. C₂²×C₄×D₁₃	C₂	semidirect
6. C₂²×Dic₂₆	C₂	semidirect
9. C₂×D₄×C₁₃	C₂²	semidirect
11. C₂×C₂²⋊D₁₃	C₂²	semidirect
14. C₂²×Dic₁₃	C₂²	semidirect
15. #6129	C₂²	direct (N × H)
16. C₂×C₄×D₁₃	C₂²	semidirect
17. C₂×Dic₂₆	C₂²	semidirect
23. D₄×C₁₃	C₂³	semidirect
25. C₂²⋊D₁₃	C₂³	semidirect
28. C₂×Dic₁₃	C₂³	semidirect
29. C₄×D₁₃	C₂³	semidirect
30. Dic₂₆	C₂³	semidirect
33. C₂²×C₁₃	#41	semidirect
44. C₂²×D₄	D₁₃	semidirect
48. C₂×C₁₃	C₂×#41	semidirect
56. C₂×D₄	C₂×D₁₃	semidirect
62. C₁₃	C₂²×#41	semidirect
70. D₄	C₂²×D₁₃	semidirect
79. C₂²	#6129	direct (N × H)
87. C₂	C₂×#6129	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×D₄×C₁₃	2
C₂²×C₂²⋊D₁₃	2
C₂³×Dic₁₃	2
C₂×#6129	2
C₂²×C₄×D₁₃	2
C₂²×Dic₂₆	2
C₂²×#41	13

Subgroups — C22×#6129 #11719640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6129 #11719640