Subgroups — #15673571

Order 2944.

212 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×#10624985	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	#10624985	C₄	1	4	yes	—
13	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	M₁₆×C₂₃	—	2	4	no	—
16	C₂×C₈×C₂₃	—	2	2	no	—
17	C₄²×C₂₃	C₂×C₄	1	2	yes	—
18	C₄²×C₂₃	D₄	1	2	yes	—
19	#67267	—	2	4	no	—
20	C₂×C₂₃⋊C₈	—	2	2	no	—
21	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
22	C₂×C₂₃⋊C₈	D₄	1	4	yes	—
23	C₂×C₂₃⋊C₈	Q₈	1	4	yes	—
24	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₂₃	—	4	2	no	—
26	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
31	C₈×C₂₃	—	4	2	no	—
32	C₂₃⋊C₈	—	4	2	no	—
33	C₂₃⋊C₈	C₄⋊C₄	1	8	yes	—
34	#1849	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₂₃	C₄⋊Q₈	1	2	yes	—
38	C₄×C₂₃	—	2	4	no	—
39	C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
40	C₄×C₂₃	#127	1	1	yes	characteristic
41	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×#108	—	23	4	no	—
43	#423	—	23	1	no	—
44	#423	D₂₃	1	1	yes	characteristic
45	C₂×#97	—	23	1	no	—
46	C₂×C₂₃	—	2	2	no	—
47	C₂×C₂₃	#384	1	1	yes	characteristic
48	C₂×C₂₃	#430	1	2	yes	—
49	C₂×M₁₆	—	23	2	no	—
50	C₂×M₁₆	C₂×D₂₃	1	2	yes	—
51	C₂²×C₈	—	23	2	no	—
52	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
53	#108	—	46	8	no	—
54	C₄⋊C₈	—	2	2	no	—
55	C₄⋊C₈	—	46	2	no	—
56	#97	—	23	4	no	—
57	C₂₃	#1849	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₄₆	1	2	yes	—
59	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	M₁₆	—	2	4	no	—
61	M₁₆	—	46	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	23	4	no	—
64	C₂×C₈	—	23	4	no	—
65	C₂×C₈	—	23	4	no	—
66	C₂×C₈	—	46	2	no	—
67	C₄²	C₄×D₂₃	1	2	yes	—
68	C₄²	C₂²⋊D₂₃	1	2	yes	—
69	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	Dic₂₃⋊C₄	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
73	C₂×C₄	D₄×D₂₃	1	2	yes	—
74	C₂×C₄	Q₈×D₂₃	1	2	yes	—
75	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
76	C₈	—	4	2	no	—
77	C₈	—	23	8	no	—
78	C₈	—	92	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	#10625059	1	2	yes	—
81	C₂²	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	C₄⋊C₄×D₂₃	1	2	yes	—
84	C₄	#10625111	1	1	yes	characteristic
85	C₄	#10625115	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	#13092286	1	1	yes	characteristic
88	C₂	#13092465	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	#1849
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
57. C₂₃	#1849	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×#10624985	2
C₂₃×#423	2
#1849	23