Subgroups — #15683921

Order 2944.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092974	C₂	1	2	yes	maximal
2	#13092826	C₂	1	8	yes	maximal, complemented
3	#13092455	C₂	1	4	yes	maximal
4	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	#10625097	C₂²	1	4	yes	—
8	#10625095	—	2	4	no	—
9	#10625041	C₂²	1	4	yes	—
10	#10625040	C₂²	1	4	yes	—
11	C₄×Dic₄₆	—	2	4	no	—
12	C₂₃×#97	C₂²	1	4	yes	—
13	#10625000	C₂²	1	8	yes	—
14	#10624999	C₂²	1	8	yes	—
15	C₂²×C₄×C₂₃	D₄	1	2	yes	—
16	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₆	—	2	4	no	—
18	C₂×C₈×C₂₃	Q₈	1	8	yes	complemented
19	C₂×C₈×C₂₃	C₂³	1	4	yes	—
20	C₄²×C₂₃	D₄	1	2	yes	—
21	C₄²×C₂₃	C₂³	1	2	yes	—
22	C₂²⋊Dic₂₃	—	2	4	no	—
23	C₄⋊Dic₂₃	—	2	4	no	—
24	C₄⋊Dic₂₃	C₂³	1	8	yes	—
25	Dic₂₃⋊C₄	—	2	8	no	—
26	C₄×Dic₂₃	—	2	4	no	—
27	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	—	4	2	no	—
29	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	—
32	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
33	C₂×Dic₂₃	—	2	8	no	—
34	Dic₄₆	—	4	8	no	—
35	C₈×C₂₃	C₂×Q₈	1	8	yes	—
36	#3162	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	2	no	—
38	C₂²×C₂₃	C₄⋊Q₈	1	2	yes	—
39	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₂₃	—	2	4	no	—
41	C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
42	C₄×C₂₃	C₂²×Q₈	1	2	yes	—
43	Dic₂₃	—	4	8	no	—
44	#533	—	23	2	no	—
45	#501	—	23	8	no	—
46	#427	—	23	4	no	—
47	C₂×#97	D₂₃	1	1	yes	characteristic
48	C₂×C₂₃	—	2	2	no	—
49	C₂×C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₂₃	#575	1	2	yes	—
51	C₂²×C₈	C₂×D₂₃	1	2	yes	—
52	C₄⋊Q₈	—	23	4	no	—
53	#125	—	23	4	no	—
54	C₂²⋊Q₈	—	46	4	no	—
55	C₄×Q₈	—	46	4	no	—
56	#117	—	23	4	no	—
57	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
58	#107	—	23	8	no	—
59	#106	—	23	8	no	—
60	#97	C₂×D₂₃	1	4	yes	—
61	C₂₃	#3162	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	46	4	no	—
63	C₂²×C₄	D₉₂	1	2	yes	—
64	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
65	C₂×C₈	Dic₄₆	1	8	yes	complemented
66	C₂×C₈	C₂²×D₂₃	1	4	yes	—
67	C₄⋊C₄	—	23	8	no	—
68	C₄⋊C₄	—	46	8	no	—
69	C₄⋊C₄	—	46	4	no	—
70	C₂²⋊C₄	—	46	4	no	—
71	C₄²	—	46	4	no	—
72	C₄²	D₉₂	1	2	yes	—
73	C₄²	C₂²×D₂₃	1	2	yes	—
74	C₂³	C₂×D₉₂	1	1	yes	characteristic
75	Q₈	—	92	8	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	46	8	no	—
78	C₂×C₄	C₂×Dic₄₆	1	4	yes	—
79	C₂×C₄	C₂×D₉₂	1	4	yes	—
80	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
81	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
82	C₈	C₂×Dic₄₆	1	8	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	#10625040	1	2	yes	—
85	C₂²	C₂²×D₉₂	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	92	8	no	—
88	C₄	#10625040	1	2	yes	—
89	C₄	C₂²×Dic₄₆	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	C₂×#10625040	1	1	yes	characteristic
92	C₂	#13093217	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂×C₂₃×#97	C₂
socle	C₂²×C₂₃	C₂²×D₄
prime radical	C₂³×C₂₃	C₂×D₄
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	#3162
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #13092826	C₂	semidirect
18. C₂×C₈×C₂₃	Q₈	semidirect
61. C₂₃	#3162	semidirect
65. C₂×C₈	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
#13092974	2
#13092826	2
#13092455	2
C₂×C₂₃×#97	2
#3162	23