Subgroups — #15672035

Order 2944.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092474	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	C₂²⋊(C₂₃⋊C₈)	—	2	2	no	—
11	C₄⋊(C₂₃⋊C₈)	—	2	2	no	—
12	#10624985	C₂²	1	4	yes	—
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	C₂×C₂₃⋊C₈	—	2	4	no	—
25	C₂³×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈×C₂₃	—	4	4	no	—
27	C₂×C₄×C₂₃	—	2	2	no	—
28	C₂×C₄×C₂₃	—	2	4	no	—
29	C₂×C₄×C₂₃	—	4	2	no	—
30	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
34	C₂₃⋊C₈	—	4	4	no	—
35	#1537	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	—	2	1	no	—
37	C₂²×C₂₃	—	2	2	no	—
38	C₂²×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₄×C₂₃	—	2	1	no	—
40	C₄×C₂₃	—	2	2	no	—
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	—	4	4	no	—
43	C₄×C₂₃	#101	1	2	yes	—
44	#533	D₂₃	1	1	yes	characteristic
45	#432	—	23	2	no	—
46	#330	—	23	4	no	—
47	C₂×C₂₃	—	4	1	no	—
48	C₂×C₂₃	C₂×#101	1	1	yes	characteristic
49	C₂×C₂₃	#421	1	2	yes	—
50	C₄⋊Q₈	Dic₂₃	1	2	yes	—
51	#125	C₂×D₂₃	1	2	yes	—
52	C₂²⋊Q₈	—	2	2	no	—
53	C₄×Q₈	—	2	2	no	—
54	#117	Dic₂₃	1	2	yes	—
55	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
56	C₄⋊C₈	—	46	2	no	—
57	C₂²⋊C₈	—	46	2	no	—
58	#97	—	23	4	no	—
59	C₂₃	#1537	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	2	no	—
61	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
62	C₂²×C₄	C₂²⋊D₂₃	1	2	yes	—
63	C₂×C₈	—	46	4	no	—
64	C₄⋊C₄	—	2	2	no	—
65	C₄⋊C₄	—	2	4	no	—
66	C₄⋊C₄	C₂×Dic₂₃	1	4	yes	—
67	C₂²⋊C₄	—	2	2	no	—
68	C₄²	—	2	2	no	—
69	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
70	C₄²	C₂²⋊D₂₃	1	2	yes	—
71	C₄²	C₂²×D₂₃	1	1	yes	characteristic
72	C₂³	C₂²⋊Dic₂₃	1	1	yes	characteristic
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	C₂²⋊Dic₂₃	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
81	C₈	—	92	4	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	2	no	—
87	C₄	—	2	2	no	—
88	C₄	—	4	4	no	—
89	C₄	#10625018	1	2	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₂×#10625018	1	1	yes	characteristic
92	C₂	#13092434	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×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	#1537
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

Complements

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

N	H ≅ G/N	type
2. #13092159	C₂	semidirect
59. C₂₃	#1537	semidirect

Maximal subgroups

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

subgroup	index
#13092474	2
#13092159	2
C₂₃×#533	2
#1537	23