Subgroups — C₂×#21445434 #29667704

Order 15616.

1342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840139	C₂	1	6	yes	maximal, complemented
2	#21445434	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₈²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄₈₈	—	2	12	no	—
5	C₂×#14519774	C₂²	1	4	yes	—
6	#16840139	—	2	12	no	—
7	#16840139	C₂²	1	24	yes	complemented
8	C₂×C₄×C₈×C₆₁	C₂²	1	3	yes	—
9	C₈²×C₆₁	C₂²	1	4	yes	complemented
10	C₂²×D₂₄₄	—	2	12	no	—
11	C₂×D₄₈₈	—	2	48	no	—
12	C₂×D₄₈₈	—	4	48	no	—
13	#14519774	—	2	12	no	—
14	#14519774	C₂³	1	8	yes	—
15	C₂²×C₈×C₆₁	D₄	1	6	yes	—
16	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
17	C₄×C₈×C₆₁	D₄	1	6	yes	—
18	C₄×C₈×C₆₁	C₂³	1	6	yes	—
19	C₂³×D₆₁	—	4	4	no	—
20	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
21	C₂×D₂₄₄	—	2	24	no	—
22	C₂×D₂₄₄	—	4	48	no	—
23	C₂×D₂₄₄	—	4	12	no	—
24	C₂×C₈×C₆₁	D₈	1	24	yes	complemented
25	C₂×C₈×C₆₁	C₂×D₄	1	12	yes	—
26	C₄²×C₆₁	C₂×D₄	1	3	yes	—
27	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
28	D₄₈₈	—	4	96	no	—
29	C₂³×C₆₁	#127	1	1	yes	characteristic
30	C₂²×D₆₁	—	4	8	no	—
31	C₂²×D₆₁	—	8	24	no	—
32	C₂×C₄×C₆₁	#127	1	3	yes	—
33	C₂×C₄×C₆₁	C₂×D₈	1	12	yes	—
34	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
35	D₂₄₄	—	4	48	no	—
36	D₂₄₄	—	8	24	no	—
37	C₈×C₆₁	C₂×D₈	1	24	yes	complemented
38	C₂×#1712	—	61	1	no	maximal, Sylow
39	C₂²×C₆₁	#493	1	6	yes	—
40	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
41	C₂×D₆₁	—	8	24	no	—
42	C₂×D₆₁	—	16	16	no	—
43	C₄×C₆₁	#493	1	6	yes	—
44	C₄×C₆₁	C₂²×D₈	1	6	yes	—
45	C₂×#493	—	61	6	no	—
46	#1712	—	61	8	no	—
47	C₂×C₈²	D₆₁	1	1	yes	characteristic, complemented
48	C₂×C₆₁	#1712	1	4	yes	complemented
49	C₂×C₆₁	C₂×#493	1	3	yes	—
50	D₆₁	—	16	8	no	—
51	C₂²×D₈	—	122	12	no	—
52	C₂×#127	—	61	4	no	—
53	#493	—	61	24	no	—
54	#493	—	122	12	no	—
55	C₂×C₄×C₈	C₂×D₆₁	1	3	yes	—
56	C₈²	C₂×D₆₁	1	4	yes	complemented
57	C₆₁	C₂×#1712	1	1	yes	characteristic, complemented, Sylow
58	C₂²×D₄	—	122	12	no	—
59	C₂×D₈	—	122	48	no	—
60	C₂×D₈	—	244	48	no	—
61	C₂²×C₈	D₂₄₄	1	6	yes	—
62	#127	—	61	8	no	—
63	#127	—	122	12	no	—
64	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
65	C₄×C₈	D₂₄₄	1	6	yes	—
66	C₄×C₈	C₂²×D₆₁	1	6	yes	—
67	C₂⁴	—	244	4	no	—
68	C₂×D₄	—	122	24	no	—
69	C₂×D₄	—	244	12	no	—
70	C₂×D₄	—	244	48	no	—
71	C₂²×C₄	C₂×D₂₄₄	1	3	yes	—
72	D₈	—	244	96	no	—
73	C₂×C₈	D₄₈₈	1	24	yes	complemented
74	C₂×C₈	C₂×D₂₄₄	1	12	yes	—
75	C₄²	C₂×D₂₄₄	1	3	yes	—
76	C₄²	C₂³×D₆₁	1	1	yes	characteristic
77	C₂³	—	488	24	no	—
78	C₂³	—	244	8	no	—
79	C₂³	#14519774	1	1	yes	characteristic
80	D₄	—	488	24	no	—
81	D₄	—	244	48	no	—
82	C₂×C₄	#14519774	1	3	yes	—
83	C₂×C₄	C₂×D₄₈₈	1	12	yes	—
84	C₂×C₄	C₂²×D₂₄₄	1	3	yes	—
85	C₈	C₂×D₄₈₈	1	24	yes	complemented
86	C₂²	—	976	16	no	—
87	C₂²	—	488	24	no	—
88	C₂²	#16840139	1	6	yes	—
89	C₂²	C₂×#14519774	1	1	yes	characteristic
90	C₄	#16840139	1	6	yes	—
91	C₄	C₂²×D₄₈₈	1	6	yes	—
92	C₂	—	976	8	no	—
93	C₂	#21445434	1	4	yes	direct product factor
94	C₂	C₂×#16840139	1	3	yes	—

	subgroup	G/H
center	C₂³	#14519774
commutator, cosocle	C₄²×C₆₁	C₂⁴
Frattini	C₄²	C₂³×D₆₁
Fitting	C₂×C₈²×C₆₁	C₂
socle	C₂³×C₆₁	#127
hypercenter	C₂×C₈²	D₆₁
hypocenter	C₆₁	C₂×#1712
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
1. C₂×#16840139	C₂	semidirect
2. #21445434	C₂	direct (N × H)
3. C₂×C₈²×C₆₁	C₂	semidirect
7. #16840139	C₂²	semidirect
9. C₈²×C₆₁	C₂²	semidirect
24. C₂×C₈×C₆₁	D₈	semidirect
37. C₈×C₆₁	C₂×D₈	semidirect
47. C₂×C₈²	D₆₁	semidirect
48. C₂×C₆₁	#1712	semidirect
56. C₈²	C₂×D₆₁	semidirect
57. C₆₁	C₂×#1712	semidirect
73. C₂×C₈	D₄₈₈	semidirect
85. C₈	C₂×D₄₈₈	semidirect
93. C₂	#21445434	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16840139	2
#21445434	2
C₂×C₈²×C₆₁	2
C₂×#1712	61

Subgroups — C2×#21445434 #29667704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21445434 #29667704