Subgroups — #101×D₂₃ #13092395

Order 1472.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₃	C₂	1	2	yes	maximal
3	C₂₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625018	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625006	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
7	Q₈×D₂₃	—	2	2	no	—
8	Q₈×D₂₃	—	2	2	no	—
9	C₂×C₄×D₂₃	C₄	1	2	yes	—
10	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₆	C₄	1	2	yes	—
12	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
13	M₁₆×C₂₃	C₂²	1	2	yes	—
14	#67267	C₂²	1	2	yes	—
15	#67262	—	2	2	no	—
16	C₈×D₂₃	—	2	2	no	—
17	C₂²×D₂₃	C₂×C₄	1	1	yes	characteristic
18	Q₈×C₂₃	—	2	2	no	—
19	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
22	C₂×Dic₂₃	C₂×C₄	1	1	yes	characteristic
23	C₄×D₂₃	—	2	2	no	—
24	C₄×D₂₃	—	2	2	no	—
25	C₄×D₂₃	D₄	1	2	yes	—
26	C₄×D₂₃	D₄	1	2	yes	—
27	Dic₄₆	—	2	2	no	—
28	Dic₄₆	—	2	4	no	—
29	C₈×C₂₃	—	2	2	no	—
30	C₂₃⋊C₈	—	2	2	no	—
31	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₂₃	—	2	2	no	—
33	C₂×D₂₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×D₂₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₂₃	—	2	2	no	—
36	C₄×C₂₃	C₂×D₄	1	2	yes	—
37	Dic₂₃	—	2	2	no	—
38	Dic₂₃	C₂²⋊C₄	1	2	yes	—
39	C₂×#101	—	23	1	no	maximal, Sylow
40	C₂×C₂₃	—	2	1	no	—
41	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	D₂₃	—	2	1	no	—
43	D₂₃	#101	1	2	yes	direct product factor
44	C₂²×Q₈	—	23	1	no	—
45	C₂×M₁₆	—	23	2	no	—
46	#101	—	23	1	no	—
47	#101	—	23	2	no	—
48	#101	D₂₃	1	1	yes	characteristic, direct product factor
49	C₂₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	23	2	no	—
51	C₂×Q₈	—	23	1	no	—
52	C₂×Q₈	—	46	2	no	—
53	C₂×Q₈	—	46	2	no	—
54	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
55	C₂²×C₄	—	23	1	no	—
56	C₂²×C₄	—	23	2	no	—
57	M₁₆	—	23	2	no	—
58	M₁₆	—	46	2	no	—
59	M₁₆	C₂×D₂₃	1	2	yes	—
60	C₂×C₈	—	46	2	no	—
61	C₂³	—	23	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	46	4	no	—
64	Q₈	—	46	2	no	—
65	C₂×C₄	—	23	1	no	—
66	C₂×C₄	—	23	2	no	—
67	C₂×C₄	—	23	2	no	—
68	C₂×C₄	—	23	2	no	—
69	C₂×C₄	—	46	2	no	—
70	C₂×C₄	—	46	2	no	—
71	C₂×C₄	C₄×D₂₃	1	2	yes	—
72	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	—	46	2	no	—
75	C₂²	—	23	1	no	—
76	C₂²	—	23	1	no	—
77	C₂²	—	46	2	no	—
78	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	23	2	no	—
81	C₄	—	46	2	no	—
82	C₄	D₄×D₂₃	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	23	2	no	—
85	C₂	—	46	1	no	—
86	C₂	C₂²⋊C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#101	C₂
socle	C₂×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#101	D₂₃
hypocenter	C₂₃	C₂×#101
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
3. C₂₃×#101	C₂	semidirect
4. #10625018	C₂	semidirect
5. #10625006	C₂	semidirect
43. D₂₃	#101	direct (N × H)
48. #101	D₂₃	direct (N × H)
49. C₂₃	C₂×#101	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Q₈×D₂₃	2
M₁₆×D₂₃	2
C₂₃×#101	2
#10625018	2
#10625006	2
C₂×#101	23

Subgroups — #101×D23 #13092395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #101×D₂₃ #13092395