Subgroups — #15673303

Order 2944.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625001	C₂	1	2	yes	maximal
2	C₄×#67267	C₂	1	2	yes	maximal
3	#13092182	C₂	1	2	yes	maximal
4	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×#67267	C₂²	1	4	yes	—
9	C₂₃×#97	C₄	1	4	yes	—
10	#10625001	C₄	1	8	yes	complemented
11	#10624985	—	2	2	no	—
12	C₄×C₂₃⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₂₃	—	2	2	no	—
16	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
19	C₄²×C₂₃	C₂×C₄	1	2	yes	—
20	C₄²×C₂₃	D₄	1	2	yes	—
21	#67267	—	2	4	no	—
22	#67267	C₂×C₄	1	8	yes	—
23	C₂×C₂₃⋊C₈	—	2	4	no	—
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	2	yes	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₃	#41	1	2	yes	—
31	C₈×C₂₃	—	2	2	no	—
32	C₈×C₂₃	C₄²	1	4	yes	—
33	C₂₃⋊C₈	—	2	8	no	—
34	#1778	—	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×C₄²	1	1	yes	characteristic
40	C₄×C₂₃	#117	1	1	yes	characteristic
41	C₄×C₂₃	C₄×D₄	1	2	yes	—
42	C₂×#108	—	23	2	no	—
43	C₄×M₁₆	—	23	2	no	—
44	C₂×#97	D₂₃	1	1	yes	characteristic
45	#341	—	23	2	no	—
46	C₂×C₂₃	—	2	2	no	—
47	C₂×C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₂₃	#430	1	2	yes	—
49	C₂×M₁₆	—	23	4	no	—
50	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
51	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
52	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
53	#108	—	23	8	no	—
54	#97	—	46	2	no	—
55	#97	Dic₂₃	1	4	yes	—
56	C₄×C₈	—	46	2	no	—
57	C₂₃	#1778	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₄₆	1	2	yes	—
59	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	M₁₆	—	23	8	no	—
61	M₁₆	—	46	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	46	4	no	—
64	C₂×C₈	C₄×D₂₃	1	4	yes	—
65	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
66	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
67	C₄²	D₉₂	1	2	yes	—
68	C₄²	C₂×Dic₂₃	1	2	yes	—
69	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₂₃	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
73	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
74	C₂×C₄	#67288	1	2	yes	—
75	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	46	8	no	—
78	C₈	C₄×Dic₂₃	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₄×Dic₄₆	1	2	yes	—
81	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	C₄×D₉₂	1	2	yes	—
84	C₄	C₂×C₄×Dic₂₃	1	1	yes	characteristic
85	C₄	#10625097	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₂₃	1	1	yes	characteristic
88	C₂	#13092466	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator	C₄×C₂₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂×C₂₃×#97	C₂
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	#1778
LCS	G ▷ 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
10. #10625001	C₄	semidirect
57. C₂₃	#1778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625001	2
C₄×#67267	2
#13092182	2
C₂×C₂₃×#97	2
#1778	23