Subgroups — C₂×#13092138 #15671672

Order 2944.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃⋊C₈	C₂	1	2	yes	maximal
2	#13092138	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₄	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₂₃⋊C₈	C₄	1	4	yes	—
7	C₄×C₈×C₂₃	C₄	1	2	yes	—
8	C₄×C₈×C₂₃	C₂²	1	2	yes	—
9	C₄×C₂₃⋊C₈	C₄	1	4	yes	—
10	C₄×C₂₃⋊C₈	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₈	1	8	yes	complemented
14	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
15	C₄²×C₂₃	C₂×C₄	1	2	yes	—
16	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×C₂₃⋊C₈	—	2	8	no	—
19	C₂×C₂₃⋊C₈	C₂×C₄	1	8	yes	—
20	C₂³×C₂₃	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₂₃	C₄²	1	2	yes	—
23	C₂×C₄×C₂₃	C₂×C₈	1	4	yes	—
24	C₂×C₄×C₂₃	M₁₆	1	8	yes	—
25	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
26	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₂₃	C₂×C₈	1	8	yes	complemented
28	C₂₃⋊C₈	—	2	8	no	—
29	C₂×#322	—	23	1	no	maximal, Sylow
30	C₂²×C₂₃	C₄×C₈	1	2	yes	—
31	C₂²×C₂₃	#97	1	4	yes	—
32	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
33	C₄×C₂₃	C₄×C₈	1	2	yes	—
34	C₄×C₂₃	#97	1	4	yes	—
35	C₄×C₂₃	C₂²×C₈	1	2	yes	—
36	C₄×C₂₃	C₂×M₁₆	1	4	yes	—
37	C₂×C₄×C₈	—	23	2	no	—
38	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
39	#322	—	23	4	no	—
40	C₂×C₂₃	#322	1	4	yes	complemented
41	C₂×C₂₃	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₂₃	C₂×#97	1	2	yes	—
43	C₂²×C₈	—	23	4	no	—
44	C₂²×C₈	Dic₂₃	1	2	yes	—
45	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
46	C₄×C₈	—	23	4	no	—
47	C₄×C₈	—	23	4	no	—
48	C₄×C₈	Dic₂₃	1	2	yes	—
49	C₄×C₈	C₂×D₂₃	1	2	yes	—
50	C₂₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	C₄×D₂₃	1	2	yes	—
52	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
53	C₂×C₈	—	23	8	no	—
54	C₂×C₈	—	46	8	no	—
55	C₂×C₈	C₂₃⋊C₈	1	8	yes	complemented
56	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
57	C₄²	C₄×D₂₃	1	2	yes	—
58	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
59	C₄²	C₂²×D₂₃	1	1	yes	characteristic
60	C₂³	C₄×Dic₂₃	1	1	yes	characteristic
61	C₂×C₄	#67262	1	8	yes	—
62	C₂×C₄	C₂×C₂₃⋊C₈	1	4	yes	—
63	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
64	C₂×C₄	C₄×Dic₂₃	1	2	yes	—
65	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
66	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
67	C₈	—	46	8	no	—
68	C₈	C₂×C₂₃⋊C₈	1	8	yes	complemented
69	C₂²	C₄×C₂₃⋊C₈	1	2	yes	—
70	C₂²	#10624997	1	4	yes	—
71	C₂²	C₂×C₄×Dic₂₃	1	1	yes	characteristic
72	C₄	C₄×C₂₃⋊C₈	1	2	yes	—
73	C₄	#10624997	1	4	yes	—
74	C₄	C₂×#67262	1	4	yes	—
75	C₄	C₂²×C₂₃⋊C₈	1	2	yes	—
76	C₂	#13092138	1	4	yes	direct product factor
77	C₂	C₂×C₄×C₂₃⋊C₈	1	1	yes	characteristic
78	C₂	C₂×#10624997	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₄²
cosocle	C₄²×C₂₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	C₂×#322
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13092138	C₂	direct (N × H)
13. C₂×C₈×C₂₃	C₈	semidirect
27. C₈×C₂₃	C₂×C₈	semidirect
40. C₂×C₂₃	#322	semidirect
50. C₂₃	C₂×#322	semidirect
55. C₂×C₈	C₂₃⋊C₈	semidirect
68. C₈	C₂×C₂₃⋊C₈	semidirect
76. C₂	#13092138	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×C₄×C₂₃⋊C₈	2
#13092138	2
C₂×C₄×C₈×C₂₃	2
C₂×#322	23

Subgroups — C2×#13092138 #15671672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092138 #15671672