Subgroups — C₂₃×#7458 #19155084

Order 5888.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₄⋊C₃₂	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×C₃₂	—	2	2	no	—
4	C₄×C₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₈²×C₂₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₂₃	—	2	1	no	—
8	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₂₃	C₈	1	1	yes	characteristic
11	C₄×C₈×C₂₃	C₈	1	1	yes	characteristic
12	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂₃×C₃₂	—	4	2	no	—
14	C₂×C₈×C₂₃	—	2	1	no	—
15	C₂×C₈×C₂₃	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	M₁₆	1	1	yes	characteristic
19	C₄²×C₂₃	C₂×C₈	1	1	yes	characteristic
20	C₁₆×C₂₃	—	2	2	no	—
21	C₁₆×C₂₃	—	2	1	no	—
22	C₁₆×C₂₃	D₈	1	1	yes	characteristic
23	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
24	#7458	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
27	C₂×C₄×C₂₃	M₃₂	1	1	yes	characteristic
28	C₈×C₂₃	—	2	2	no	—
29	C₈×C₂₃	—	2	1	no	—
30	C₈×C₂₃	—	2	1	no	—
31	C₈×C₂₃	C₃₂	1	2	yes	complemented
32	C₈×C₂₃	#107	1	1	yes	characteristic
33	C₈×C₂₃	#108	1	1	yes	characteristic
34	C₄⋊C₃₂	C₂×C₂₃	1	2	yes	—
35	C₈×C₁₆	C₂×C₂₃	1	1	yes	characteristic
36	C₂²×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
37	C₄×C₂₃	—	2	1	no	—
38	C₄×C₂₃	#335	1	1	yes	characteristic
39	C₄×C₂₃	#364	1	1	yes	characteristic
40	C₄×C₂₃	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₂₃	M₆₄	1	1	yes	characteristic
42	C₂×C₃₂	—	2	2	no	—
43	C₄×C₁₆	C₄×C₂₃	1	1	yes	characteristic
44	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
45	C₈²	C₄×C₂₃	1	1	yes	characteristic
46	C₂×C₂₃	#1370	1	1	yes	characteristic
47	C₂×C₂₃	C₄⋊C₃₂	1	1	yes	characteristic
48	C₂×C₂₃	#1422	1	1	yes	characteristic
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	D₄×C₂₃	1	1	yes	characteristic
51	C₂×C₁₆	Q₈×C₂₃	1	1	yes	characteristic
52	C₄×C₈	C₈×C₂₃	1	1	yes	characteristic
53	C₄×C₈	C₈×C₂₃	1	1	yes	characteristic
54	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
55	C₃₂	—	4	2	no	—
56	C₂₃	#7458	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	C₁₆×C₂₃	1	1	yes	characteristic
59	C₂×C₈	C₁₆×C₂₃	1	1	yes	characteristic
60	C₂×C₈	C₄⋊C₄×C₂₃	1	1	yes	characteristic
61	C₂×C₈	M₁₆×C₂₃	1	1	yes	characteristic
62	C₄²	C₂×C₈×C₂₃	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	D₈×C₂₃	1	1	yes	characteristic
66	C₁₆	Q₁₆×C₂₃	1	1	yes	characteristic
67	C₂×C₄	C₂₃×C₄⋊C₈	1	1	yes	characteristic
68	C₂×C₄	C₂×C₁₆×C₂₃	1	1	yes	characteristic
69	C₂×C₄	C₂₃×M₃₂	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₈	C₂₃×C₃₂	1	2	yes	complemented
74	C₈	C₂₃×#107	1	1	yes	characteristic
75	C₈	C₂₃×#108	1	1	yes	characteristic
76	C₂²	C₂₃×C₄⋊C₁₆	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	C₂₃×#335	1	1	yes	characteristic
79	C₄	C₂₃×#364	1	1	yes	characteristic
80	C₄	C₂×C₂₃×C₃₂	1	1	yes	characteristic
81	C₄	C₂₃×M₆₄	1	1	yes	characteristic
82	C₂	C₂₃×#1370	1	1	yes	characteristic
83	C₂	C₂₃×C₄⋊C₃₂	1	1	yes	characteristic
84	C₂	C₂₃×#1422	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆×C₂₃	D₄
commutator	C₄	C₂×C₂₃×C₃₂
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	C₄⋊C₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₂₃ ◁ C₄×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
24. #7458	C₂₃	direct (N × H)
31. C₈×C₂₃	C₃₂	semidirect
56. C₂₃	#7458	direct (N × H)
73. C₈	C₂₃×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×C₄⋊C₃₂	2
C₈×C₁₆×C₂₃	2
#7458	23

Subgroups — C23×#7458 #19155084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7458 #19155084