Subgroups — C₂×#10625003 #13092405

Order 1472.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625003	C₂	1	4	yes	maximal, direct product factor
5	C₂³×D₂₃	—	2	1	no	—
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	—	2	1	no	—
8	C₂×D₉₂	—	2	1	no	—
9	C₂×D₉₂	—	2	2	no	—
10	C₂×D₉₂	C₄	1	4	yes	complemented
11	C₂×D₉₂	C₂²	1	2	yes	—
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	C₂²	1	2	yes	complemented
14	C₄⋊Dic₂₃	—	2	1	no	—
15	C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
16	C₂³×C₂₃	D₄	1	1	yes	characteristic
17	C₂²×D₂₃	—	2	4	no	—
18	C₂²×D₂₃	—	2	2	no	—
19	C₂²×D₂₃	—	4	2	no	—
20	C₂²×D₂₃	—	4	2	no	—
21	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	D₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₃	—	2	2	no	—
26	C₂×Dic₂₃	—	4	2	no	—
27	D₉₂	—	2	4	no	—
28	D₉₂	—	2	2	no	—
29	D₉₂	C₂×C₄	1	4	yes	complemented
30	C₈×C₂₃	—	2	2	no	—
31	C₂²×C₂₃	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₂₃	D₈	1	2	yes	—
33	C₂²×C₂₃	SD₁₆	1	2	yes	—
34	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
35	C₂×D₂₃	—	2	4	no	—
36	C₂×D₂₃	—	4	8	no	—
37	C₂×D₂₃	—	4	2	no	—
38	C₂×D₂₃	—	4	2	no	—
39	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
40	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
42	Dic₂₃	—	4	2	no	—
43	C₂×#102	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	#102	1	4	yes	complemented
45	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
47	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
48	D₂₃	—	4	4	no	—
49	C₂²×D₄	—	23	1	no	—
50	C₂²×C₈	D₂₃	1	1	yes	characteristic, complemented
51	C₂×C₄⋊C₄	—	23	1	no	—
52	#102	—	23	4	no	—
53	C₂₃	C₂×#102	1	1	yes	characteristic, complemented, Sylow
54	C₂⁴	—	46	1	no	—
55	C₂×D₄	—	23	4	no	—
56	C₂×D₄	—	23	2	no	—
57	C₂×D₄	—	46	1	no	—
58	C₂×D₄	—	46	2	no	—
59	C₂²×C₄	—	46	1	no	—
60	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
61	C₂×C₈	—	2	2	no	—
62	C₂×C₈	C₂×D₂₃	1	2	yes	complemented
63	C₄⋊C₄	—	23	2	no	—
64	C₄⋊C₄	—	46	1	no	—
65	C₂³	—	46	4	no	—
66	C₂³	—	46	2	no	—
67	C₂³	—	92	2	no	—
68	C₂³	—	92	2	no	—
69	C₂³	D₉₂	1	1	yes	characteristic
70	D₄	—	23	4	no	—
71	D₄	—	46	4	no	—
72	D₄	—	46	2	no	—
73	C₂×C₄	—	46	2	no	—
74	C₂×C₄	—	92	2	no	—
75	C₂×C₄	C₄×D₂₃	1	2	yes	—
76	C₂×C₄	D₉₂	1	1	yes	characteristic
77	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
78	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₂²	—	46	4	no	—
81	C₂²	—	92	2	no	—
82	C₂²	—	92	2	no	—
83	C₂²	—	92	8	no	—
84	C₂²	#67263	1	2	yes	—
85	C₂²	D₁₈₄	1	2	yes	—
86	C₂²	(C₂×D₂₃)⋊C₄	1	2	yes	—
87	C₂²	C₂×D₉₂	1	1	yes	characteristic
88	C₄	—	92	2	no	—
89	C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
90	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
91	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
92	C₂	—	92	4	no	—
93	C₂	#10625003	1	4	yes	direct product factor
94	C₂	C₂×#67263	1	1	yes	characteristic
95	C₂	C₂×D₁₈₄	1	1	yes	characteristic
96	C₂	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂³×C₂₃	D₄
prime radical	C₂²×D₉₂	C₂
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	C₂×#102
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₂₃	C₂	semidirect
3. C₂×C₄⋊Dic₂₃	C₂	semidirect
4. #10625003	C₂	direct (N × H)
10. C₂×D₉₂	C₄	semidirect
13. C₂×C₈×C₂₃	C₂²	semidirect
15. C₄⋊Dic₂₃	C₂²	semidirect
29. D₉₂	C₂×C₄	semidirect
44. C₂×C₂₃	#102	semidirect
50. C₂²×C₈	D₂₃	semidirect
53. C₂₃	C₂×#102	semidirect
62. C₂×C₈	C₂×D₂₃	semidirect
93. C₂	#10625003	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×D₉₂	2
C₂²×C₈×C₂₃	2
C₂×C₄⋊Dic₂₃	2
#10625003	2
C₂×#102	23

Subgroups — C2×#10625003 #13092405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625003 #13092405