Subgroups — #15673568

Order 2944.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625004	C₂	1	4	yes	maximal
2	#13092441	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×#67267	C₂²	1	2	yes	—
8	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	—
9	C₂₃×C₄⋊C₈	—	2	2	no	—
10	#10625004	—	2	8	no	—
11	C₄⋊(C₂₃⋊C₈)	—	2	2	no	—
12	C₄×C₂₃⋊C₈	C₄	1	2	yes	—
13	C₄×C₂₃⋊C₈	C₄	1	2	yes	—
14	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
15	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	M₁₆×C₂₃	—	2	4	no	—
17	C₂×C₈×C₂₃	—	2	2	no	—
18	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₃	D₄	1	2	yes	—
21	#67267	—	2	4	no	—
22	C₂×C₂₃⋊C₈	—	2	2	no	—
23	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₂₃⋊C₈	D₄	1	4	yes	—
25	C₂×C₂₃⋊C₈	Q₈	1	4	yes	—
26	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₂₃	—	2	4	no	—
28	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
34	C₈×C₂₃	—	4	2	no	—
35	C₂₃⋊C₈	—	4	2	no	—
36	C₂₃⋊C₈	C₄⋊C₄	1	8	yes	—
37	#1848	—	23	1	no	maximal, Sylow
38	C₂²×C₂₃	—	2	2	no	—
39	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₃	C₄⋊Q₈	1	2	yes	—
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	#108	1	4	yes	complemented
43	C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
44	C₄×C₂₃	#127	1	1	yes	characteristic
45	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×#108	—	23	4	no	—
47	#423	—	23	1	no	—
48	#423	D₂₃	1	1	yes	characteristic
49	C₂×C₄×C₈	—	23	1	no	—
50	C₂×C₂₃	—	2	2	no	—
51	C₂×C₂₃	#384	1	1	yes	characteristic
52	C₂×C₂₃	C₂×#108	1	2	yes	—
53	C₂×M₁₆	—	23	2	no	—
54	C₂×M₁₆	C₂×D₂₃	1	2	yes	—
55	C₂²×C₈	—	23	2	no	—
56	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
57	#108	—	46	8	no	—
58	C₄⋊C₈	—	2	2	no	—
59	C₄⋊C₈	—	46	2	no	—
60	C₄×C₈	—	23	2	no	—
61	C₄×C₈	—	23	2	no	—
62	C₂₃	#1848	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	Dic₄₆	1	2	yes	—
64	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
65	M₁₆	—	2	4	no	—
66	M₁₆	—	46	4	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	23	4	no	—
69	C₂×C₈	—	23	4	no	—
70	C₂×C₈	—	23	4	no	—
71	C₂×C₈	—	46	2	no	—
72	C₄²	C₄×D₂₃	1	1	yes	characteristic
73	C₄²	C₄×D₂₃	1	1	yes	characteristic
74	C₄²	C₂²⋊D₂₃	1	2	yes	—
75	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
78	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
80	C₂×C₄	D₄×D₂₃	1	2	yes	—
81	C₂×C₄	Q₈×D₂₃	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
83	C₈	—	4	2	no	—
84	C₈	—	23	8	no	—
85	C₈	—	92	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#10625059	1	2	yes	—
88	C₂²	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	#10625004	1	4	yes	complemented
91	C₄	C₄⋊C₄×D₂₃	1	2	yes	—
92	C₄	#10625111	1	1	yes	characteristic
93	C₄	#10625115	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	#13092286	1	1	yes	characteristic
96	C₂	C₂×#10625004	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₃
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂₃×#423	C₂
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#423	D₂₃
hypocenter	C₂₃	#1848
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
42. C₄×C₂₃	#108	semidirect
62. C₂₃	#1848	semidirect
90. C₄	#10625004	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625004	2
#13092441	2
C₂×C₄×C₂₃⋊C₈	2
C₂₃×#423	2
#1848	23