Subgroups — #15673569

Order 2944.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625001	C₂	1	4	yes	maximal
2	#13092441	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×#67267	C₂²	1	4	yes	—
7	C₄×C₈×C₂₃	C₄	1	2	yes	—
8	C₄×C₈×C₂₃	C₄	1	2	yes	—
9	#10625001	—	2	8	no	—
10	C₄⋊(C₂₃⋊C₈)	—	2	4	no	—
11	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
12	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₂₃	D₄	1	4	yes	—
15	C₂×C₈×C₂₃	Q₈	1	4	yes	—
16	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₂₃	D₄	1	2	yes	—
19	#67267	—	2	8	no	—
20	C₂×C₂₃⋊C₈	—	2	4	no	—
21	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₂₃	—	2	4	no	—
23	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
29	C₈×C₂₃	C₄⋊C₄	1	8	yes	—
30	C₂₃⋊C₈	—	4	4	no	—
31	#1848	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	—	2	2	no	—
33	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₂₃	C₄⋊Q₈	1	2	yes	—
35	C₄×C₂₃	—	2	2	no	—
36	C₄×C₂₃	#108	1	4	yes	complemented
37	C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
38	C₄×C₂₃	#127	1	1	yes	characteristic
39	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×#108	—	23	4	no	—
41	#423	—	23	2	no	—
42	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
43	C₂×C₂₃	—	2	2	no	—
44	C₂×C₂₃	#384	1	1	yes	characteristic
45	C₂×C₂₃	C₂×#108	1	2	yes	—
46	C₂×M₁₆	—	23	4	no	—
47	C₂²×C₈	C₂×D₂₃	1	2	yes	—
48	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
49	#108	—	46	8	no	—
50	C₄⋊C₈	—	46	4	no	—
51	C₄×C₈	Dic₂₃	1	2	yes	—
52	C₄×C₈	Dic₂₃	1	2	yes	—
53	C₂₃	#1848	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	Dic₄₆	1	2	yes	—
55	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
56	M₁₆	—	46	8	no	—
57	C₂×C₈	—	46	4	no	—
58	C₂×C₈	Dic₄₆	1	4	yes	—
59	C₂×C₈	D₉₂	1	4	yes	—
60	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
61	C₄²	D₉₂	1	2	yes	—
62	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
63	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
64	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
68	C₂×C₄	C₂×Dic₄₆	1	2	yes	—
69	C₂×C₄	C₂×D₉₂	1	2	yes	—
70	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
72	C₈	—	92	4	no	—
73	C₈	C₄⋊Dic₂₃	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	#10625040	1	2	yes	—
76	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	#10625001	1	4	yes	complemented
79	C₄	#10625040	1	1	yes	characteristic
80	C₄	#10625045	1	1	yes	characteristic
81	C₄	C₂×C₄⋊Dic₂₃	1	2	yes	—
82	C₂	—	2	2	no	—
83	C₂	#13092287	1	1	yes	characteristic
84	C₂	C₂×#10625001	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	#1848
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
36. C₄×C₂₃	#108	semidirect
53. C₂₃	#1848	semidirect
78. C₄	#10625001	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625001	2
#13092441	2
C₂×C₄×C₈×C₂₃	2
#1848	23