Subgroups — C₂×#10625015 #13092394

Order 1472.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	2	yes	maximal, complemented
3	#10625015	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₂₃	C₄	1	2	yes	—
5	C₂×D₄×C₂₃	—	2	2	no	—
6	C₂×D₄×C₂₃	—	2	2	no	—
7	C₂×D₄×C₂₃	C₄	1	2	yes	—
8	C₂×D₄×C₂₃	C₂²	1	2	yes	—
9	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	#67267	—	2	2	no	—
11	#67267	C₂²	1	4	yes	complemented
12	C₂×C₂₃⋊C₈	—	2	2	no	—
13	C₂³×C₂₃	—	2	2	no	—
14	C₂³×C₂₃	—	2	2	no	—
15	C₂³×C₂₃	—	4	4	no	—
16	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₂₃	C₂×C₄	1	4	yes	—
18	D₄×C₂₃	—	2	4	no	—
19	D₄×C₂₃	—	2	4	no	—
20	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	D₄	1	2	yes	—
22	C₂×C₄×C₂₃	D₄	1	2	yes	—
23	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
24	C₂₃⋊C₈	—	2	4	no	—
25	C₂²×C₂₃	—	2	2	no	—
26	C₂²×C₂₃	—	2	4	no	—
27	C₂²×C₂₃	—	4	4	no	—
28	C₂²×C₂₃	—	4	4	no	—
29	C₂²×C₂₃	—	4	4	no	—
30	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
34	C₄×C₂₃	C₂×D₄	1	2	yes	—
35	C₂×#100	—	23	1	no	maximal, Sylow
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	—	4	4	no	—
39	C₂×C₂₃	#100	1	2	yes	complemented
40	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×D₄	D₂₃	1	1	yes	characteristic
42	C₂×M₁₆	—	23	2	no	—
43	#100	—	23	4	no	—
44	C₂₃	C₂×#100	1	1	yes	characteristic, complemented, Sylow
45	C₂⁴	Dic₂₃	1	2	yes	—
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	—	2	2	no	—
48	C₂×D₄	Dic₂₃	1	2	yes	—
49	C₂×D₄	C₂×D₂₃	1	2	yes	—
50	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
51	M₁₆	—	23	4	no	—
52	M₁₆	—	46	2	no	—
53	C₂×C₈	—	46	2	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	—	4	4	no	—
57	C₂³	C₂×Dic₂₃	1	1	yes	characteristic
58	C₂³	C₂×Dic₂₃	1	4	yes	—
59	D₄	—	2	4	no	—
60	D₄	—	2	4	no	—
61	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
63	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
64	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
65	C₈	—	46	4	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	4	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	—	4	4	no	—
71	C₂²	C₂²⋊Dic₂₃	1	1	yes	characteristic
72	C₂²	C₂²⋊Dic₂₃	1	1	yes	characteristic
73	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
74	C₄	C₂²⋊Dic₂₃	1	2	yes	—
75	C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	4	4	no	—
79	C₂	#10625015	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊Dic₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting, prime radical	C₂²×D₄×C₂₃	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×D₄	D₂₃
hypocenter	C₂₃	C₂×#100
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#67267	C₂	semidirect
3. #10625015	C₂	direct (N × H)
11. #67267	C₂²	semidirect
39. C₂×C₂₃	#100	semidirect
44. C₂₃	C₂×#100	semidirect
79. C₂	#10625015	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×C₂₃	2
C₂×#67267	2
#10625015	2
C₂×#100	23

Subgroups — C2×#10625015 #13092394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625015 #13092394