Subgroups — C₂×#10625118 #13092935

Order 1472.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₉₂	C₂	1	1	yes	maximal, characteristic
3	#10625118	C₂	1	8	yes	maximal, direct product factor
4	C₂×(C₂×D₂₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₂₃	C₂²	1	2	yes	—
7	C₂×Q₈×C₂₃	—	2	4	no	—
8	C₂×Q₈×C₂₃	C₂²	1	4	yes	complemented
9	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₂₃	C₂²	1	2	yes	—
12	C₂×D₉₂	—	2	4	no	—
13	C₂×D₉₂	C₂²	1	4	yes	—
14	(C₂×D₂₃)⋊C₄	C₂²	1	16	yes	complemented
15	C₄×Dic₂₃	C₂²	1	4	yes	complemented
16	C₂³×C₂₃	C₂³	1	1	yes	characteristic
17	C₂²×D₂₃	—	2	4	no	—
18	C₂²×D₂₃	—	2	8	no	—
19	C₂²×D₂₃	C₂³	1	4	yes	—
20	Q₈×C₂₃	—	2	8	no	—
21	C₂×C₄×C₂₃	—	2	4	no	—
22	C₂×C₄×C₂₃	D₄	1	4	yes	—
23	C₂×C₄×C₂₃	C₂³	1	4	yes	—
24	C₂×C₄×C₂₃	C₂³	1	2	yes	—
25	C₂×Dic₂₃	—	2	4	no	—
26	C₂×Dic₂₃	C₂³	1	4	yes	—
27	D₉₂	—	2	8	no	—
28	C₂²×C₂₃	C₂×D₄	1	2	yes	—
29	C₂²×C₂₃	#41	1	4	yes	—
30	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
31	C₂×D₂₃	—	2	4	no	—
32	C₂×D₂₃	—	2	8	no	—
33	C₂×D₂₃	—	4	8	no	—
34	C₄×C₂₃	—	2	4	no	—
35	C₄×C₂₃	C₂×D₄	1	4	yes	—
36	Dic₂₃	—	2	4	no	—
37	C₂×#124	—	23	1	no	maximal, Sylow
38	C₂×C₂₃	#124	1	4	yes	complemented
39	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₂₃	C₂×#41	1	2	yes	—
41	D₂₃	—	4	4	no	—
42	C₂²×Q₈	D₂₃	1	1	yes	characteristic, complemented
43	C₂²×D₄	—	23	1	no	—
44	#124	—	23	8	no	—
45	C₂×C₂²⋊C₄	—	23	4	no	—
46	C₂×C₄²	—	23	1	no	—
47	C₂₃	C₂×#124	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	—	23	2	no	—
49	C₂×Q₈	—	2	4	no	—
50	C₂×Q₈	C₂×D₂₃	1	4	yes	complemented
51	C₂×D₄	—	23	4	no	—
52	C₂×D₄	—	46	4	no	—
53	C₂²×C₄	—	23	2	no	—
54	C₂²×C₄	C₂×D₂₃	1	2	yes	—
55	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
56	C₂²⋊C₄	—	23	16	no	—
57	C₄²	—	23	4	no	—
58	C₂³	—	23	4	no	—
59	C₂³	—	46	8	no	—
60	C₂³	—	46	4	no	—
61	C₂³	C₂²×D₂₃	1	1	yes	characteristic
62	Q₈	—	2	8	no	—
63	D₄	—	46	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	23	4	no	—
66	C₂×C₄	—	46	4	no	—
67	C₂×C₄	C₂²⋊D₂₃	1	4	yes	—
68	C₂×C₄	C₂²×D₂₃	1	4	yes	—
69	C₂×C₄	C₂²×D₂₃	1	2	yes	—
70	C₂²	—	46	8	no	—
71	C₂²	—	46	4	no	—
72	C₂²	—	92	8	no	—
73	C₂²	#67292	1	4	yes	—
74	C₂²	C₂×C₂²⋊D₂₃	1	2	yes	—
75	C₂²	C₂³×D₂₃	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	46	4	no	—
78	C₄	C₂×C₂²⋊D₂₃	1	4	yes	—
79	C₂	—	92	4	no	—
80	C₂	#10625118	1	4	yes	direct product factor
81	C₂	C₂×#67292	1	2	yes	—
82	C₂	C₂²×C₂²⋊D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂²×Q₈×C₂₃	C₂
socle	C₂³×C₂₃	C₂³
prime radical	C₂²×D₉₂	C₂
hypercenter	C₂²×Q₈	D₂₃
hypocenter	C₂₃	C₂×#124
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₂₃	C₂	semidirect
3. #10625118	C₂	direct (N × H)
4. C₂×(C₂×D₂₃)⋊C₄	C₂	semidirect
5. C₂×C₄×Dic₂₃	C₂	semidirect
8. C₂×Q₈×C₂₃	C₂²	semidirect
14. (C₂×D₂₃)⋊C₄	C₂²	semidirect
15. C₄×Dic₂₃	C₂²	semidirect
38. C₂×C₂₃	#124	semidirect
42. C₂²×Q₈	D₂₃	semidirect
47. C₂₃	C₂×#124	semidirect
50. C₂×Q₈	C₂×D₂₃	semidirect
80. C₂	#10625118	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×Q₈×C₂₃	2
C₂²×D₉₂	2
#10625118	2
C₂×(C₂×D₂₃)⋊C₄	2
C₂×C₄×Dic₂₃	2
C₂×#124	23

Subgroups — C2×#10625118 #13092935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625118 #13092935