Subgroups — #15675181

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092455	C₂	1	2	yes	maximal
2	#13092245	C₂	1	2	yes	maximal, complemented
3	#13092243	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	#10625097	—	2	2	no	—
7	C₂×C₁₆×C₂₃	C₄	1	4	yes	complemented
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	#10625000	C₂²	1	4	yes	—
11	#10624999	—	2	2	no	—
12	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	Q₈	1	2	yes	—
16	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
17	C₂²⋊Dic₂₃	—	4	2	no	—
18	C₄⋊Dic₂₃	—	2	4	no	—
19	C₄×Dic₂₃	—	4	2	no	—
20	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
21	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
22	C₂³×C₂₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₂₃	Q₁₆	1	2	yes	—
26	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₃	—	4	4	no	—
28	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
29	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
31	#2158	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	—	2	2	no	—
33	C₂²×C₂₃	#107	1	2	yes	—
34	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
35	C₄×C₂₃	#107	1	2	yes	—
36	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
38	Dic₂₃	—	8	4	no	—
39	C₂²×C₁₆	D₂₃	1	1	yes	characteristic
40	#427	—	23	2	no	—
41	#367	—	23	2	no	—
42	#366	—	23	2	no	—
43	C₂×C₂₃	—	2	2	no	—
44	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
45	C₂×C₂₃	#508	1	2	yes	—
46	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
47	#117	—	46	2	no	—
48	C₂×C₁₆	Dic₂₃	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
50	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
51	#107	—	23	4	no	—
52	#106	—	46	2	no	—
53	C₂₃	#2158	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	D₉₂	1	1	yes	characteristic
55	C₂×C₈	Dic₄₆	1	2	yes	—
56	C₂×C₈	D₉₂	1	1	yes	characteristic
57	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
58	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	46	4	no	—
60	C₂²⋊C₄	—	92	2	no	—
61	C₄²	—	92	2	no	—
62	C₁₆	C₂×Dic₂₃	1	2	yes	—
63	C₁₆	C₂×Dic₂₃	1	2	yes	—
64	C₂³	D₁₈₄	1	1	yes	characteristic
65	C₂×C₄	—	92	4	no	—
66	C₂×C₄	D₁₈₄	1	1	yes	characteristic
67	C₂×C₄	Dic₉₂	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
69	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
70	C₈	C₄⋊Dic₂₃	1	2	yes	—
71	C₈	C₂×Dic₄₆	1	1	yes	characteristic
72	C₈	C₂²×Dic₂₃	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	#10625000	1	2	yes	—
75	C₂²	C₂×D₁₈₄	1	1	yes	characteristic
76	C₄	—	184	4	no	—
77	C₄	#10625000	1	2	yes	—
78	C₄	C₂×Dic₉₂	1	1	yes	characteristic
79	C₄	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×#10625000	1	1	yes	characteristic
82	C₂	#13092849	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₈₄
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂²×C₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₈
prime radical	C₂³×C₂₃	D₈
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	C₂²×C₁₆	D₂₃
hypocenter	C₂₃	#2158
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13092245	C₂	semidirect
3. #13092243	C₂	semidirect
7. C₂×C₁₆×C₂₃	C₄	semidirect
48. C₂×C₁₆	Dic₂₃	semidirect
53. C₂₃	#2158	semidirect

Maximal subgroups

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

subgroup	index
#13092455	2
#13092245	2
#13092243	2
C₂²×C₁₆×C₂₃	2
#2158	23