Subgroups — #15671992

Order 2944.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#67267	C₂	1	2	yes	maximal
2	#13092159	C₂	1	4	yes	maximal, complemented
3	C₂₃×#533	C₂	1	1	yes	maximal, characteristic
4	C₂₃×C₄⋊Q₈	C₄	1	2	yes	—
5	C₂₃×#125	C₂²	1	2	yes	—
6	C₂₃×C₂²⋊Q₈	—	2	2	no	—
7	C₄×Q₈×C₂₃	—	2	2	no	—
8	C₂₃×#117	C₄	1	2	yes	—
9	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×#67267	—	2	2	no	—
11	#10624985	C₂²	1	4	yes	—
12	C₄×C₂₃⋊C₈	—	2	2	no	—
13	C₂×Q₈×C₂₃	—	2	2	no	—
14	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₂₃	—	2	2	no	—
17	C₄⋊C₄×C₂₃	—	2	4	no	—
18	C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
19	C₂²⋊C₄×C₂₃	—	2	2	no	—
20	C₄²×C₂₃	—	2	2	no	—
21	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₃	D₄	1	2	yes	—
23	C₄²×C₂₃	C₂³	1	1	yes	characteristic
24	#67267	—	2	8	no	—
25	C₂×C₂₃⋊C₈	—	2	4	no	—
26	C₂³×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
27	Q₈×C₂₃	—	4	4	no	—
28	C₂×C₄×C₂₃	—	2	2	no	—
29	C₂×C₄×C₂₃	—	2	4	no	—
30	C₂×C₄×C₂₃	—	2	4	no	—
31	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
35	C₂₃⋊C₈	—	2	8	no	—
36	#1526	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	2	2	no	—
39	C₂²×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	—	4	4	no	—
43	C₄×C₂₃	#101	1	2	yes	—
44	C₄×C₂₃	#104	1	4	yes	—
45	#533	D₂₃	1	1	yes	characteristic
46	C₄×M₁₆	—	23	2	no	—
47	#330	—	23	4	no	—
48	C₂×C₂₃	—	4	1	no	—
49	C₂×C₂₃	C₂×#101	1	1	yes	characteristic
50	C₂×C₂₃	C₂×#104	1	2	yes	—
51	C₂×M₁₆	—	46	2	no	—
52	C₄⋊Q₈	Dic₂₃	1	2	yes	—
53	#125	C₂×D₂₃	1	2	yes	—
54	C₂²⋊Q₈	—	2	2	no	—
55	C₄×Q₈	—	2	2	no	—
56	#117	Dic₂₃	1	2	yes	—
57	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
58	#97	—	23	4	no	—
59	C₄×C₈	—	46	2	no	—
60	C₂₃	#1526	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₈	—	2	2	no	—
62	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
63	C₂²×C₄	C₂²⋊D₂₃	1	2	yes	—
64	M₁₆	—	46	8	no	—
65	C₂×C₈	—	46	4	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	C₂×Dic₂₃	1	4	yes	—
69	C₂²⋊C₄	—	2	2	no	—
70	C₄²	—	2	2	no	—
71	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
72	C₄²	C₂²⋊D₂₃	1	2	yes	—
73	C₄²	C₂²×D₂₃	1	1	yes	characteristic
74	C₂³	C₂²⋊Dic₂₃	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	C₂²⋊Dic₂₃	1	2	yes	—
80	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
82	C₂×C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
83	C₈	—	46	8	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	2	no	—
86	C₂²	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	#10625018	1	2	yes	—
91	C₄	#10625019	1	4	yes	—
92	C₂	—	4	1	no	—
93	C₂	C₂×#10625018	1	1	yes	characteristic
94	C₂	C₂×#10625019	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₂₃
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₄²	C₂²×D₂₃
Fitting	C₂₃×#533	C₂
socle	C₂²×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₃	C₂²⋊C₄
cosocle	C₄²×C₂₃	C₂³
hypercenter	#533	D₂₃
hypocenter	C₂₃	#1526
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

Complements

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

N	H ≅ G/N	type
2. #13092159	C₂	semidirect
60. C₂₃	#1526	semidirect

Maximal subgroups

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

subgroup	index
C₄×#67267	2
#13092159	2
C₂₃×#533	2
#1526	23