Subgroups — C₂×#10625075 #13093199

Order 1472.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67288	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625075	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#67263	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₂₃	—	2	2	no	—
9	#67288	—	2	4	no	—
10	#67288	C₂²	1	8	yes	complemented
11	C₂×D₉₂	C₂²	1	2	yes	—
12	C₂×C₄×D₂₃	—	2	2	no	—
13	C₂×Dic₄₆	C₂²	1	2	yes	—
14	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₂²	1	4	yes	complemented
17	Dic₉₂	C₂²	1	4	yes	complemented
18	D₁₈₄	C₂²	1	4	yes	complemented
19	#67263	C₂²	1	8	yes	complemented
20	C₂³×C₂₃	D₄	1	1	yes	characteristic
21	C₂²×D₂₃	—	2	2	no	—
22	C₂×C₄×C₂₃	D₄	1	2	yes	—
23	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂³	1	2	yes	—
26	C₂²⋊D₂₃	—	2	8	no	—
27	C₂×Dic₂₃	—	2	2	no	—
28	D₉₂	—	2	2	no	—
29	D₉₂	C₂³	1	4	yes	—
30	C₄×D₂₃	—	2	8	no	—
31	Dic₄₆	—	2	2	no	—
32	Dic₄₆	C₂³	1	4	yes	—
33	C₈×C₂₃	C₂³	1	2	yes	—
34	C₈×C₂₃	C₂³	1	2	yes	—
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	C₂×D₄	1	2	yes	—
37	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
38	C₂×D₂₃	—	2	4	no	—
39	C₂×D₂₃	—	4	4	no	—
40	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
41	C₄×C₂₃	C₂×D₄	1	2	yes	—
42	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
43	Dic₂₃	—	2	4	no	—
44	C₂×#135	—	23	1	no	maximal, Sylow
45	C₂×C₂₃	—	2	2	no	—
46	C₂×C₂₃	#135	1	2	yes	complemented
47	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
48	D₂₃	—	4	4	no	—
49	C₂×#41	—	23	2	no	—
50	#135	—	23	8	no	—
51	C₂×Q₁₆	—	23	1	no	—
52	C₂×SD₁₆	—	23	2	no	—
53	C₂×D₈	—	23	1	no	—
54	C₂²×C₈	D₂₃	1	1	yes	characteristic, complemented
55	C₂₃	C₂×#135	1	1	yes	characteristic, complemented, Sylow
56	#41	—	23	8	no	—
57	#41	—	46	4	no	—
58	C₂×Q₈	—	23	2	no	—
59	C₂×D₄	—	23	2	no	—
60	C₂×D₄	—	46	2	no	—
61	C₂²×C₄	—	46	2	no	—
62	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
63	Q₁₆	—	23	4	no	—
64	SD₁₆	—	23	8	no	—
65	D₈	—	23	4	no	—
66	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
67	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
68	C₂×C₈	C₂×D₂₃	1	4	yes	complemented
69	C₂³	—	46	2	no	—
70	C₂³	D₉₂	1	1	yes	characteristic
71	Q₈	—	23	4	no	—
72	Q₈	—	46	2	no	—
73	D₄	—	23	4	no	—
74	D₄	—	46	8	no	—
75	D₄	—	46	2	no	—
76	C₂×C₄	—	46	2	no	—
77	C₂×C₄	—	46	8	no	—
78	C₂×C₄	D₉₂	1	2	yes	—
79	C₂×C₄	D₉₂	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₂₃	1	2	yes	—
82	C₈	C₂²×D₂₃	1	2	yes	—
83	C₈	C₂²×D₂₃	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	46	4	no	—
86	C₂²	—	92	4	no	—
87	C₂²	C₂×D₉₂	1	2	yes	—
88	C₂²	C₂×D₉₂	1	1	yes	characteristic
89	C₄	—	46	4	no	—
90	C₄	C₂×D₉₂	1	2	yes	—
91	C₄	C₂×D₉₂	1	1	yes	characteristic
92	C₄	C₂³×D₂₃	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	92	4	no	—
95	C₂	#10625075	1	2	yes	direct product factor
96	C₂	C₂²×D₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator, cosocle	C₄×C₂₃	C₂⁴
Frattini	C₄	C₂³×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	C₂×#135
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#67288	C₂	semidirect
2. C₂²×C₈×C₂₃	C₂	semidirect
3. C₂×Dic₉₂	C₂	semidirect
4. #10625075	C₂	direct (N × H)
5. C₂×D₁₈₄	C₂	semidirect
6. C₂×#67263	C₂	semidirect
10. #67288	C₂²	semidirect
16. C₂×C₈×C₂₃	C₂²	semidirect
17. Dic₉₂	C₂²	semidirect
18. D₁₈₄	C₂²	semidirect
19. #67263	C₂²	semidirect
46. C₂×C₂₃	#135	semidirect
54. C₂²×C₈	D₂₃	semidirect
55. C₂₃	C₂×#135	semidirect
68. C₂×C₈	C₂×D₂₃	semidirect
95. C₂	#10625075	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×#67288	2
C₂²×C₈×C₂₃	2
C₂×Dic₉₂	2
#10625075	2
C₂×D₁₈₄	2
C₂×#67263	2
C₂×#135	23

Subgroups — C2×#10625075 #13093199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625075 #13093199