Subgroups — C₂₃×#7450 #19155076

Order 5888.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2252	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#500	—	2	1	no	—
5	C₂×C₂₃×C₃₂	—	2	1	no	—
6	C₂₃×#366	—	2	1	no	—
7	C₂₃×#366	C₄	1	2	yes	—
8	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#335	—	2	1	no	—
10	C₂₃×C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
13	C₂₃×#107	—	2	2	no	—
14	C₂₃×#107	—	4	1	no	—
15	C₂₃×C₄⋊C₈	—	4	1	no	—
16	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂₃×C₃₂	—	4	1	no	—
18	C₂×Q₈×C₂₃	—	8	1	no	—
19	C₂×C₈×C₂₃	—	8	1	no	—
20	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₂₃	SD₁₆	1	1	yes	characteristic
22	C₄⋊C₄×C₂₃	—	4	2	no	—
23	C₄⋊C₄×C₂₃	—	8	1	no	—
24	C₄²×C₂₃	D₈	1	1	yes	characteristic
25	C₁₆×C₂₃	—	2	1	no	—
26	C₁₆×C₂₃	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
28	#7450	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	Q₈×C₂₃	—	16	1	no	—
30	Q₈×C₂₃	—	16	1	no	—
31	C₂×C₄×C₂₃	—	8	2	no	—
32	C₂×C₄×C₂₃	#102	1	1	yes	characteristic
33	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
34	C₂×C₄×C₂₃	SD₃₂	1	1	yes	characteristic
35	C₈×C₂₃	—	2	1	no	—
36	C₈×C₂₃	—	16	1	no	—
37	C₈×C₂₃	#101	1	1	yes	characteristic
38	C₈×C₂₃	#103	1	1	yes	characteristic
39	#2252	C₂×C₂₃	1	1	yes	characteristic
40	C₄⋊C₃₂	C₂×C₂₃	1	1	yes	characteristic
41	#1371	C₂×C₂₃	1	1	yes	characteristic
42	C₂²×C₂₃	#357	1	1	yes	characteristic
43	C₄×C₂₃	—	2	1	no	—
44	C₄×C₂₃	—	16	2	no	—
45	C₄×C₂₃	#332	1	1	yes	characteristic
46	C₄×C₂₃	#362	1	1	yes	characteristic
47	C₄×C₂₃	D₃₂	1	1	yes	characteristic
48	C₄×C₂₃	SD₆₄	1	1	yes	characteristic
49	#500	—	2	1	no	—
50	C₂×C₃₂	—	2	1	no	—
51	#366	—	2	1	no	—
52	#366	C₄×C₂₃	1	2	yes	—
53	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
54	#335	—	2	1	no	—
55	C₂×C₂₃	#1364	1	1	yes	characteristic
56	C₂×C₂₃	#1415	1	1	yes	characteristic
57	C₂×C₂₃	#1420	1	1	yes	characteristic
58	C₄⋊Q₈	—	4	1	no	—
59	C₂×C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
60	C₂×C₁₆	D₄×C₂₃	1	1	yes	characteristic
61	#107	—	2	2	no	—
62	#107	—	4	1	no	—
63	C₄⋊C₈	—	4	1	no	—
64	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
65	C₃₂	—	4	1	no	—
66	C₂₃	#7450	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×Q₈	—	8	1	no	—
68	C₂×C₈	—	8	1	no	—
69	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
70	C₂×C₈	SD₁₆×C₂₃	1	1	yes	characteristic
71	C₄⋊C₄	—	4	2	no	—
72	C₄⋊C₄	—	8	1	no	—
73	C₄²	D₈×C₂₃	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	SD₁₆×C₂₃	1	1	yes	characteristic
76	C₁₆	Q₁₆×C₂₃	1	1	yes	characteristic
77	Q₈	—	16	1	no	—
78	Q₈	—	16	1	no	—
79	C₂×C₄	—	8	2	no	—
80	C₂×C₄	C₂₃×#102	1	1	yes	characteristic
81	C₂×C₄	C₂₃×D₁₆	1	1	yes	characteristic
82	C₂×C₄	C₂₃×SD₃₂	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	16	1	no	—
85	C₈	C₂₃×#101	1	1	yes	characteristic
86	C₈	C₂₃×#103	1	1	yes	characteristic
87	C₂²	C₂₃×#357	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	16	2	no	—
90	C₄	C₂₃×#332	1	1	yes	characteristic
91	C₄	C₂₃×#362	1	1	yes	characteristic
92	C₄	C₂₃×D₃₂	1	1	yes	characteristic
93	C₄	C₂₃×SD₆₄	1	1	yes	characteristic
94	C₂	C₂₃×#1364	1	1	yes	characteristic
95	C₂	C₂₃×#1415	1	1	yes	characteristic
96	C₂	C₂₃×#1420	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#357
commutator	C₂×C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₃
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ C₄×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
28. #7450	C₂₃	direct (N × H)
66. C₂₃	#7450	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2252	2
C₂₃×C₄⋊C₃₂	2
C₂₃×#1371	2
#7450	23

Subgroups — C23×#7450 #19155076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7450 #19155076