Subgroups — #108×D₂₃ #13092461

Order 1472.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₂₃	C₂	1	2	yes	maximal
2	C₂×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625004	C₂	1	2	yes	maximal, complemented
5	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
7	M₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	#67267	C₂²	1	2	yes	—
10	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
11	#67262	—	2	2	no	—
12	C₈×D₂₃	—	2	2	no	—
13	C₈×D₂₃	C₄	1	2	yes	—
14	C₈×D₂₃	C₄	1	2	yes	—
15	C₂²×D₂₃	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₃	Q₈	1	1	yes	characteristic
18	C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
20	C₄×D₂₃	D₄	1	1	yes	characteristic
21	C₄×D₂₃	D₄	1	1	yes	characteristic
22	C₈×C₂₃	—	2	2	no	—
23	C₈×C₂₃	C₂×C₄	1	2	yes	—
24	C₂₃⋊C₈	—	2	2	no	—
25	C₂₃⋊C₈	C₂×C₄	1	2	yes	—
26	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
27	C₂×D₂₃	—	2	2	no	—
28	C₂×D₂₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₂₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
32	Dic₂₃	C₄⋊C₄	1	1	yes	characteristic
33	Dic₂₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×#108	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	—	2	1	no	—
36	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₂₃	—	2	1	no	—
38	D₂₃	#108	1	2	yes	direct product factor
39	C₂×M₁₆	—	23	2	no	—
40	C₂²×C₈	—	23	1	no	—
41	#108	—	23	2	no	—
42	#108	—	23	1	no	—
43	#108	D₂₃	1	1	yes	characteristic, direct product factor
44	C₂₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	—	23	1	no	—
46	M₁₆	—	23	2	no	—
47	M₁₆	—	46	2	no	—
48	M₁₆	C₂×D₂₃	1	2	yes	—
49	C₂×C₈	—	23	1	no	—
50	C₂×C₈	—	23	2	no	—
51	C₂×C₈	—	23	2	no	—
52	C₂×C₈	—	46	2	no	—
53	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
54	C₂³	—	23	1	no	—
55	C₂×C₄	—	23	1	no	—
56	C₂×C₄	—	23	1	no	—
57	C₂×C₄	—	23	1	no	—
58	C₂×C₄	—	23	1	no	—
59	C₂×C₄	—	23	1	no	—
60	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	—	23	2	no	—
63	C₈	—	46	2	no	—
64	C₈	C₄×D₂₃	1	2	yes	—
65	C₂²	—	23	1	no	—
66	C₂²	—	23	1	no	—
67	C₂²	—	46	2	no	—
68	C₂²	Q₈×D₂₃	1	1	yes	characteristic
69	C₄	—	23	1	no	—
70	C₄	—	23	1	no	—
71	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
72	C₄	D₄×D₂₃	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	23	2	no	—
75	C₂	—	46	1	no	—
76	C₂	C₄⋊C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#108	C₂
socle	C₂×C₂₃	C₂×C₄⋊C₄
prime radical	C₂²×D₂₃	Q₈
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#108	D₂₃
hypocenter	C₂₃	C₂×#108
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₂₃×#108	C₂	semidirect
4. #10625004	C₂	semidirect
5. #10625001	C₂	semidirect
38. D₂₃	#108	direct (N × H)
43. #108	D₂₃	direct (N × H)
44. C₂₃	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₂₃	2
C₂×C₈×D₂₃	2
C₂₃×#108	2
#10625004	2
#10625001	2
C₂×#108	23

Subgroups — #108×D23 #13092461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #108×D₂₃ #13092461