Subgroups — #15671479

Order 2944.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624994	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₂₃	—	2	2	no	—
7	#10624994	—	2	2	no	—
8	#10624994	C₄	1	4	yes	complemented
9	C₂×C₂₃⋊C₁₆	—	2	2	no	—
10	C₂²×C₄×C₂₃	—	2	1	no	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	1	no	—
13	C₂×C₈×C₂₃	—	2	1	no	—
14	C₂×C₈×C₂₃	C₈	1	2	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₃	D₄	1	2	yes	—
18	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
19	C₄²×C₂₃	—	2	1	no	—
20	C₄²×C₂₃	C₈	1	2	yes	—
21	C₂₃⋊C₁₆	—	2	4	no	—
22	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₃	—	2	4	no	—
24	C₂×C₄×C₂₃	—	2	2	no	—
25	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
31	C₈×C₂₃	—	2	2	no	—
32	C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
33	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
34	#1376	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	#97	1	1	yes	characteristic
37	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₂₃	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₂₃	—	2	4	no	—
40	C₄×C₂₃	#95	1	1	yes	characteristic
41	C₄×C₂₃	C₄×C₈	1	1	yes	characteristic
42	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	23	2	no	—
45	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	—	2	1	no	—
48	C₂×C₂₃	#336	1	1	yes	characteristic
49	C₂×C₂₃	#364	1	2	yes	—
50	C₂²×C₈	Dic₂₃	1	1	yes	characteristic
51	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
52	C₂×C₄²	Dic₂₃	1	1	yes	characteristic
53	M₃₂	—	23	4	no	—
54	M₃₂	—	46	2	no	—
55	C₂×C₁₆	—	46	2	no	—
56	C₄×C₈	—	2	2	no	—
57	C₂₃	#1376	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₂₃⋊C₈	1	2	yes	—
63	C₂×C₈	Dic₄₆	1	1	yes	characteristic
64	C₂×C₈	C₄×D₂₃	1	2	yes	—
65	C₂×C₈	D₉₂	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
67	C₄²	—	2	1	no	—
68	C₄²	C₂₃⋊C₈	1	2	yes	—
69	C₁₆	—	46	4	no	—
70	C₂³	#67267	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
75	C₂×C₄	#67267	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
77	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	Dic₂₃⋊C₄	1	2	yes	—
81	C₈	(C₂×D₂₃)⋊C₄	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#10624985	1	1	yes	characteristic
84	C₂²	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
85	C₂²	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄×C₂₃⋊C₈	1	1	yes	characteristic
88	C₄	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
89	C₄	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
90	C₄	C₂₃⋊#95	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#13092172	1	1	yes	characteristic
94	C₂	#13092238	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₉₂
commutator	C₄×C₂₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₄⋊C₈
prime radical	C₂³×C₂₃	M₁₆
cosocle	C₂²×C₈×C₂₃	C₂²
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	#1376
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. #10624994	C₄	semidirect
57. C₂₃	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624994	2
C₂×C₄×C₈×C₂₃	2
#1376	23