Subgroups — #15673527

Order 2944.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#13092283	C₂	1	1	yes	maximal, characteristic
3	#13092179	C₂	1	4	yes	maximal
4	C₂₃×#382	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	—
8	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	—
9	C₂₃×#95	—	2	2	no	—
10	C₂₃⋊#95	—	2	2	no	—
11	C₄×C₂₃⋊C₈	C₄	1	4	yes	complemented
12	C₂²×C₄×C₂₃	—	2	2	no	—
13	C₂²×C₄×C₂₃	D₄	1	2	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₃	—	2	2	no	—
16	C₄⋊C₄×C₂₃	—	2	4	no	—
17	C₄²×C₂₃	C₂×C₄	1	2	yes	—
18	C₄²×C₂₃	Q₈	1	2	yes	—
19	C₄⋊Dic₂₃	—	2	4	no	—
20	C₂×C₂₃⋊C₈	—	2	2	no	—
21	C₂×C₂₃⋊C₈	—	2	2	no	—
22	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
23	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	4	no	—
25	C₂×C₄×C₂₃	—	4	2	no	—
26	C₂×C₄×C₂₃	—	4	4	no	—
27	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₂₃	#41	1	2	yes	—
31	C₂×C₄×C₂₃	#41	1	2	yes	—
32	C₂×Dic₂₃	—	4	2	no	—
33	C₂×Dic₂₃	—	4	4	no	—
34	C₂₃⋊C₈	—	2	4	no	—
35	#1835	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₂₃	#124	1	1	yes	characteristic
38	C₂²×C₂₃	#124	1	1	yes	characteristic
39	C₂²×C₂₃	#135	1	4	yes	—
40	C₄×C₂₃	—	2	4	no	—
41	C₄×C₂₃	—	8	2	no	—
42	C₄×C₂₃	#117	1	2	yes	—
43	C₄×C₂₃	#125	1	2	yes	—
44	Dic₂₃	—	8	2	no	—
45	C₂×C₄×C₈	—	23	1	no	—
46	#382	—	23	1	no	—
47	#382	D₂₃	1	1	yes	characteristic
48	#340	—	23	4	no	—
49	C₂×C₂₃	#382	1	1	yes	characteristic
50	C₂×C₂₃	#427	1	2	yes	—
51	C₂×C₂₃	#488	1	2	yes	—
52	C₂×C₂₃	#488	1	2	yes	—
53	C₂²×C₈	—	23	2	no	—
54	C₂×C₄⋊C₄	—	23	2	no	—
55	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	—
56	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
57	C₄×C₈	—	23	4	no	—
58	#95	—	2	2	no	—
59	#95	—	46	2	no	—
60	C₂₃	#1835	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	46	2	no	—
63	C₂²×C₄	C₂²⋊D₂₃	1	2	yes	—
64	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
65	C₂×C₈	—	23	4	no	—
66	C₂×C₈	—	46	2	no	—
67	C₂×C₈	—	46	2	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	46	4	no	—
70	C₄²	Dic₄₆	1	2	yes	—
71	C₄²	C₄×D₂₃	1	2	yes	—
72	C₂³	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	92	2	no	—
77	C₂×C₄	—	92	4	no	—
78	C₂×C₄	Dic₂₃⋊C₄	1	4	yes	—
79	C₂×C₄	C₂×Dic₄₆	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
81	C₂×C₄	#67290	1	2	yes	—
82	C₂×C₄	#67292	1	2	yes	—
83	C₈	—	46	4	no	—
84	C₂²	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic
85	C₂²	#10625107	1	1	yes	characteristic
86	C₂²	#10625118	1	1	yes	characteristic
87	C₂²	#10625121	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	184	2	no	—
91	C₄	#10625061	1	2	yes	—
92	C₄	#10625063	1	2	yes	—
93	C₂	#13092282	1	1	yes	characteristic
94	C₂	#13092453	1	2	yes	—
95	C₂	#13092771	1	2	yes	—
96	C₂	#13092774	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₃
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂₃×#382	C₂
socle, prime radical	C₂³×C₂₃	C₂×D₄
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#382	D₂₃
hypocenter	C₂₃	#1835
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
11. C₄×C₂₃⋊C₈	C₄	semidirect
60. C₂₃	#1835	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₂₃⋊C₈	2
#13092283	2
#13092179	2
C₂₃×#382	2
#1835	23