Subgroups — C₂₃×#8803 #19156429

Order 5888.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1455	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1291	C₂	1	3	yes	maximal
3	C₂₃×#1288	C₂	1	3	yes	maximal
4	C₂₃×#432	C₂²	1	3	yes	—
5	C₄×M₁₆×C₂₃	C₂²	1	3	yes	—
6	C₂₃×#383	C₂²	1	1	yes	characteristic
7	C₂₃×#322	C₄	1	3	yes	complemented
8	C₈²×C₂₃	C₄	1	1	yes	characteristic, complemented
9	C₂×M₁₆×C₂₃	—	2	3	no	—
10	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
11	C₂₃×C₄⋊C₈	—	2	3	no	—
12	C₂₃×C₂²⋊C₈	—	2	3	no	—
13	C₂₃×#97	—	2	3	no	—
14	C₂₃×#97	—	2	3	no	—
15	C₄×C₈×C₂₃	C₂×C₄	1	3	yes	—
16	C₄×C₈×C₂₃	C₂×C₄	1	3	yes	—
17	C₂₃×#95	—	2	3	no	—
18	C₂²×C₄×C₂₃	—	4	1	no	—
19	C₂²×C₄×C₂₃	#41	1	3	yes	—
20	M₁₆×C₂₃	—	4	6	no	—
21	C₂×C₈×C₂₃	—	2	3	no	—
22	C₂×C₈×C₂₃	—	2	3	no	—
23	C₂×C₈×C₂₃	—	4	3	no	—
24	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₄²×C₂₃	#41	1	3	yes	—
26	#8803	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₂₃	#126	1	1	yes	characteristic
28	C₂×C₄×C₂₃	—	4	3	no	—
29	C₂×C₄×C₂₃	—	8	3	no	—
30	C₂×C₄×C₂₃	#117	1	3	yes	—
31	C₂×C₄×C₂₃	#126	1	3	yes	—
32	C₈×C₂₃	—	2	6	no	—
33	C₈×C₂₃	—	4	3	no	—
34	C₈×C₂₃	—	8	3	no	—
35	#1455	C₂×C₂₃	1	1	yes	characteristic
36	#1291	C₂×C₂₃	1	3	yes	—
37	#1288	C₂×C₂₃	1	3	yes	—
38	C₂²×C₂₃	—	2	3	no	—
39	C₂²×C₂₃	#383	1	1	yes	characteristic
40	C₄×C₂₃	—	2	3	no	—
41	C₄×C₂₃	—	2	3	no	—
42	C₄×C₂₃	—	16	1	no	—
43	#432	C₂²×C₂₃	1	3	yes	—
44	C₄×M₁₆	C₂²×C₂₃	1	3	yes	—
45	#383	C₂²×C₂₃	1	1	yes	characteristic
46	#322	C₄×C₂₃	1	3	yes	complemented
47	C₈²	C₄×C₂₃	1	1	yes	characteristic, complemented
48	C₂×C₂₃	—	4	1	no	—
49	C₂×C₂₃	#1841	1	3	yes	—
50	C₂×M₁₆	—	2	3	no	—
51	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
52	C₄⋊C₈	—	2	3	no	—
53	C₂²⋊C₈	—	2	3	no	—
54	#97	—	2	3	no	—
55	#97	—	2	3	no	—
56	C₄×C₈	C₂×C₄×C₂₃	1	3	yes	—
57	C₄×C₈	C₂×C₄×C₂₃	1	3	yes	—
58	#95	—	2	3	no	—
59	C₂₃	#8803	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²×C₄	—	4	1	no	—
61	C₂²×C₄	#41×C₂₃	1	3	yes	—
62	M₁₆	—	4	6	no	—
63	C₂×C₈	—	2	3	no	—
64	C₂×C₈	—	2	3	no	—
65	C₂×C₈	—	4	3	no	—
66	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
67	C₄²	#41×C₂₃	1	3	yes	—
68	C₂³	C₂₃×#126	1	1	yes	characteristic
69	C₂×C₄	—	4	3	no	—
70	C₂×C₄	—	8	3	no	—
71	C₂×C₄	C₂₃×#117	1	3	yes	—
72	C₂×C₄	C₂₃×#126	1	3	yes	—
73	C₈	—	2	6	no	—
74	C₈	—	4	3	no	—
75	C₈	—	8	3	no	—
76	C₂²	—	2	3	no	—
77	C₂²	C₂₃×#383	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	2	3	no	—
80	C₄	—	16	1	no	—
81	C₂	—	4	1	no	—
82	C₂	C₂₃×#1841	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#383
commutator	C₄²	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂³×C₂₃	#126
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂₃×#322	C₄	semidirect
8. C₈²×C₂₃	C₄	semidirect
26. #8803	C₂₃	direct (N × H)
46. #322	C₄×C₂₃	semidirect
47. C₈²	C₄×C₂₃	semidirect
59. C₂₃	#8803	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×#1455	2
C₂₃×#1291	2
C₂₃×#1288	2
#8803	23

Subgroups — C23×#8803 #19156429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8803 #19156429