Subgroups — C₂₃×#8134 #19155760

Order 5888.

414 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1744	C₂	1	2	yes	maximal
2	C₄×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1273	C₂	1	4	yes	maximal
4	C₂×C₂₃×#97	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₂₃	C₂²	1	4	yes	—
7	C₄³×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#336	C₄	1	8	yes	—
9	C₂²×C₈×C₂₃	C₂×C₄	1	8	yes	—
10	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
14	C₂₃×#97	—	2	8	no	—
15	C₄×C₈×C₂₃	—	2	4	no	—
16	C₄×C₈×C₂₃	—	2	8	no	—
17	C₂²×C₄×C₂₃	C₄²	1	4	yes	—
18	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
20	C₂×C₈×C₂₃	—	2	4	no	—
21	C₂×C₈×C₂₃	—	2	4	no	—
22	C₂×C₈×C₂₃	—	2	8	no	—
23	C₂×C₈×C₂₃	—	2	16	no	—
24	C₂×C₈×C₂₃	M₁₆	1	8	yes	—
25	C₄²×C₂₃	—	2	4	no	—
26	C₄²×C₂₃	—	2	8	no	—
27	C₄²×C₂₃	#41	1	4	yes	—
28	#8134	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₂₃	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₄×C₂₃	—	2	4	no	—
31	C₂×C₄×C₂₃	—	2	8	no	—
32	C₂×C₄×C₂₃	#117	1	2	yes	—
33	C₂×C₄×C₂₃	#117	1	4	yes	—
34	C₂×C₄×C₂₃	C₂×M₁₆	1	4	yes	—
35	C₂×C₄×C₂₃	#131	1	8	yes	—
36	C₈×C₂₃	—	2	8	no	—
37	C₈×C₂₃	—	4	8	no	—
38	#1744	C₂×C₂₃	1	2	yes	—
39	C₄×#97	C₂×C₂₃	1	1	yes	characteristic
40	#1273	C₂×C₂₃	1	4	yes	—
41	C₂²×C₂₃	#376	1	1	yes	characteristic
42	C₂²×C₂₃	C₄×M₁₆	1	2	yes	—
43	C₂²×C₂₃	#405	1	4	yes	—
44	C₄×C₂₃	—	4	4	no	—
45	C₄×C₂₃	#432	1	4	yes	—
46	C₄×C₂₃	#433	1	8	yes	—
47	C₂×#97	C₄×C₂₃	1	4	yes	—
48	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
49	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	—
50	C₄³	C₂²×C₂₃	1	1	yes	characteristic
51	#336	C₄×C₂₃	1	8	yes	—
52	C₂×C₂₃	#1453	1	4	yes	—
53	C₂×C₂₃	#1745	1	1	yes	characteristic
54	C₂×C₂₃	#1746	1	2	yes	—
55	C₂²×C₈	C₂×C₄×C₂₃	1	8	yes	—
56	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
57	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
58	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
59	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
60	#97	—	2	8	no	—
61	C₄×C₈	—	2	4	no	—
62	C₄×C₈	—	2	8	no	—
63	C₂₃	#8134	1	1	yes	characteristic, direct product factor, Sylow
64	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
65	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
66	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
67	C₂×C₈	—	2	4	no	—
68	C₂×C₈	—	2	4	no	—
69	C₂×C₈	—	2	8	no	—
70	C₂×C₈	—	2	16	no	—
71	C₂×C₈	M₁₆×C₂₃	1	8	yes	—
72	C₄²	—	2	4	no	—
73	C₄²	—	2	8	no	—
74	C₄²	#41×C₂₃	1	4	yes	—
75	C₂³	C₂×C₄²×C₂₃	1	1	yes	characteristic
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	—	2	8	no	—
78	C₂×C₄	C₂₃×#117	1	2	yes	—
79	C₂×C₄	C₂₃×#117	1	4	yes	—
80	C₂×C₄	C₂×M₁₆×C₂₃	1	4	yes	—
81	C₂×C₄	C₂₃×#131	1	8	yes	—
82	C₈	—	2	8	no	—
83	C₈	—	4	8	no	—
84	C₂²	C₂₃×#376	1	1	yes	characteristic
85	C₂²	C₄×M₁₆×C₂₃	1	2	yes	—
86	C₂²	C₂₃×#405	1	4	yes	—
87	C₄	—	4	4	no	—
88	C₄	C₂₃×#432	1	4	yes	—
89	C₄	C₂₃×#433	1	8	yes	—
90	C₂	C₂₃×#1453	1	4	yes	—
91	C₂	C₂₃×#1745	1	1	yes	characteristic
92	C₂	C₂₃×#1746	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
28. #8134	C₂₃	direct (N × H)
63. C₂₃	#8134	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×#1744	2
C₄×C₂₃×#97	2
C₂₃×#1273	2
#8134	23

Subgroups — C23×#8134 #19155760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8134 #19155760