Subgroups — C₂×#10625115 #13092959

Order 1472.

290 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
2	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic
3	#10625115	C₂	1	8	yes	maximal, direct product factor
4	C₂×Dic₂₃⋊C₄	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₃	—	2	4	no	—
7	C₂×Q₈×C₂₃	C₂²	1	4	yes	—
8	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
9	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₂₃	C₂²	1	2	yes	—
11	C₂²×Dic₂₃	C₂²	1	2	yes	—
12	C₂×Dic₄₆	—	2	4	no	—
13	C₂×Dic₄₆	C₂²	1	4	yes	—
14	Dic₂₃⋊C₄	C₂²	1	16	yes	—
15	C₄×Dic₂₃	C₂²	1	4	yes	—
16	C₂³×C₂₃	C₂³	1	1	yes	characteristic
17	Q₈×C₂₃	—	2	8	no	—
18	C₂×C₄×C₂₃	—	2	4	no	—
19	C₂×C₄×C₂₃	D₄	1	4	yes	—
20	C₂×C₄×C₂₃	C₂³	1	4	yes	—
21	C₂×C₄×C₂₃	C₂³	1	2	yes	—
22	C₂×Dic₂₃	—	2	4	no	—
23	C₂×Dic₂₃	Q₈	1	8	yes	complemented
24	C₂×Dic₂₃	C₂³	1	4	yes	—
25	C₂×Dic₂₃	C₂³	1	4	yes	—
26	Dic₄₆	—	2	8	no	—
27	C₂²×C₂₃	C₂×D₄	1	2	yes	—
28	C₂²×C₂₃	C₂×Q₈	1	4	yes	—
29	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
30	C₄×C₂₃	—	2	4	no	—
31	C₄×C₂₃	C₂×D₄	1	4	yes	—
32	Dic₂₃	—	2	4	no	—
33	Dic₂₃	C₂×Q₈	1	8	yes	complemented
34	C₂×C₄⋊Q₈	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	C₄⋊Q₈	1	4	yes	complemented
36	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
37	C₂×C₂₃	C₂²×Q₈	1	2	yes	—
38	C₂²×Q₈	—	23	1	no	—
39	C₂²×Q₈	D₂₃	1	1	yes	characteristic
40	C₄⋊Q₈	—	23	8	no	—
41	C₂×C₄⋊C₄	—	23	4	no	—
42	C₂×C₄²	—	23	1	no	—
43	C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	2	4	no	—
45	C₂×Q₈	—	23	4	no	—
46	C₂×Q₈	—	46	4	no	—
47	C₂×Q₈	C₂×D₂₃	1	4	yes	—
48	C₂²×C₄	—	23	2	no	—
49	C₂²×C₄	—	23	2	no	—
50	C₂²×C₄	C₂×D₂₃	1	2	yes	—
51	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
52	C₄⋊C₄	—	23	16	no	—
53	C₄²	—	23	4	no	—
54	C₂³	C₂²×D₂₃	1	1	yes	characteristic
55	Q₈	—	2	8	no	—
56	Q₈	—	46	8	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	—	23	8	no	—
59	C₂×C₄	—	23	4	no	—
60	C₂×C₄	—	23	4	no	—
61	C₂×C₄	—	46	4	no	—
62	C₂×C₄	C₂²⋊D₂₃	1	4	yes	—
63	C₂×C₄	C₂²×D₂₃	1	4	yes	—
64	C₂×C₄	C₂²×D₂₃	1	2	yes	—
65	C₂²	Q₈×D₂₃	1	4	yes	—
66	C₂²	C₂×C₂²⋊D₂₃	1	2	yes	—
67	C₂²	C₂³×D₂₃	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	23	8	no	—
70	C₄	—	46	4	no	—
71	C₄	C₂×C₂²⋊D₂₃	1	4	yes	—
72	C₂	#10625115	1	4	yes	direct product factor
73	C₂	C₂×Q₈×D₂₃	1	2	yes	—
74	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, prime radical	C₂³×C₂₃	C₂³
hypercenter	C₂²×Q₈	D₂₃
hypocenter	C₂₃	C₂×C₄⋊Q₈
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
3. #10625115	C₂	direct (N × H)
23. C₂×Dic₂₃	Q₈	semidirect
33. Dic₂₃	C₂×Q₈	semidirect
35. C₂×C₂₃	C₄⋊Q₈	semidirect
43. C₂₃	C₂×C₄⋊Q₈	semidirect
72. C₂	#10625115	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×Dic₄₆	2
#10625115	2
C₂×Dic₂₃⋊C₄	2
C₂×C₄×Dic₂₃	2
C₂×C₄⋊Q₈	23

Subgroups — C2×#10625115 #13092959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625115 #13092959