Group #19180925 — subgroups

Subgroups — C₂₃×#33299 #19180925

Order 5888.

662 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2859	C₂	1	2	yes	maximal
2	C₂₃×#1992	C₂	1	8	yes	maximal
3	C₂₃×#1835	C₂	1	4	yes	maximal
4	C₄×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#125	C₂²	1	4	yes	—
6	C₂×C₂₃×#97	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
8	C₂₃×#389	—	2	8	no	—
9	C₂₃×#384	C₂²	1	4	yes	—
10	C₂₃×#382	C₂²	1	4	yes	—
11	C₄³×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#340	C₂²	1	16	yes	—
13	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
14	C₂₃×#125	—	2	16	no	—
15	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
16	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
17	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
18	C₂×C₄²×C₂₃	D₄	1	4	yes	—
19	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
21	C₂₃×#97	—	2	8	no	—
22	C₄×C₈×C₂₃	Q₈	1	8	yes	—
23	C₂₃×#95	—	2	8	no	—
24	C₂²×C₄×C₂₃	—	2	8	no	—
25	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
26	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
27	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₈×C₂₃	—	2	8	no	—
29	C₂×C₈×C₂₃	C₂×Q₈	1	8	yes	—
30	C₄⋊C₄×C₂₃	—	2	16	no	—
31	C₄⋊C₄×C₂₃	—	4	16	no	—
32	C₄⋊C₄×C₂₃	—	4	16	no	—
33	C₄²×C₂₃	—	4	4	no	—
34	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
35	C₄²×C₂₃	#41	1	8	yes	—
36	#33299	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₃	—	2	8	no	—
39	C₂×C₄×C₂₃	—	2	4	no	—
40	C₂×C₄×C₂₃	—	4	8	no	—
41	C₂×C₄×C₂₃	—	4	16	no	—
42	C₂×C₄×C₂₃	#124	1	8	yes	—
43	C₂×C₄×C₂₃	C₄⋊Q₈	1	4	yes	—
44	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
45	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
46	C₈×C₂₃	—	2	8	no	—
47	#2859	C₂×C₂₃	1	2	yes	—
48	#1992	C₂×C₂₃	1	8	yes	—
49	#1835	C₂×C₂₃	1	4	yes	—
50	C₄×#97	C₂×C₂₃	1	1	yes	characteristic
51	C₂²×C₂₃	C₂×#124	1	2	yes	—
52	C₂²×C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
53	C₂²×C₂₃	#575	1	4	yes	—
54	C₄×C₂₃	—	2	8	no	—
55	C₄×C₂₃	—	2	4	no	—
56	C₄×C₂₃	—	8	8	no	—
57	C₄×C₂₃	#533	1	4	yes	—
58	C₂×#125	C₂²×C₂₃	1	4	yes	—
59	C₂×#97	C₂²×C₂₃	1	4	yes	—
60	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
61	#389	—	2	8	no	—
62	#384	C₂²×C₂₃	1	4	yes	—
63	#382	C₂²×C₂₃	1	4	yes	—
64	C₄³	C₂²×C₂₃	1	1	yes	characteristic
65	#340	C₂²×C₂₃	1	16	yes	—
66	C₂×C₂₃	#2862	1	1	yes	characteristic
67	C₂×C₂₃	#3142	1	4	yes	—
68	C₂×C₂₃	#3162	1	2	yes	—
69	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
70	#125	—	2	16	no	—
71	C₂×C₄⋊C₄	—	2	8	no	—
72	C₂×C₄⋊C₄	—	2	8	no	—
73	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
74	C₂×C₄²	D₄×C₂₃	1	4	yes	—
75	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
76	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
77	#97	—	2	8	no	—
78	C₄×C₈	Q₈×C₂₃	1	8	yes	—
79	#95	—	2	8	no	—
80	C₂₃	#33299	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₄	—	2	8	no	—
82	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
83	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
84	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
85	C₂×C₈	—	2	8	no	—
86	C₂×C₈	C₂×Q₈×C₂₃	1	8	yes	—
87	C₄⋊C₄	—	2	16	no	—
88	C₄⋊C₄	—	4	16	no	—
89	C₄⋊C₄	—	4	16	no	—
90	C₄²	—	4	4	no	—
91	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
92	C₄²	#41×C₂₃	1	8	yes	—
93	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	16	no	—
97	C₂×C₄	—	4	8	no	—
98	C₂×C₄	C₂₃×#124	1	8	yes	—
99	C₂×C₄	C₂₃×C₄⋊Q₈	1	4	yes	—
100	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
101	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
102	C₈	—	2	8	no	—
103	C₂²	C₂×C₂₃×#124	1	2	yes	—
104	C₂²	C₂×C₂₃×C₄⋊Q₈	1	1	yes	characteristic
105	C₂²	C₂₃×#575	1	4	yes	—
106	C₄	—	2	8	no	—
107	C₄	—	2	4	no	—
108	C₄	—	8	8	no	—
109	C₄	C₂₃×#533	1	4	yes	—
110	C₂	C₂₃×#2862	1	1	yes	characteristic
111	C₂	C₂₃×#3142	1	4	yes	—
112	C₂	C₂₃×#3162	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2859

C₂

yes

maximal

C₂₃×#1992

C₂

yes

maximal

C₂₃×#1835

C₂

yes

maximal

C₄×C₂₃×#97

C₂

yes

maximal, characteristic

C₂×C₂₃×#125

C₂²

yes

—

C₂×C₂₃×#97

C₂²

yes

—

C₂×C₄×C₈×C₂₃

C₂²

yes

—

C₂₃×#389

—

C₂₃×#384

C₂²

yes

—

C₂₃×#382

C₂²

yes

—

C₄³×C₂₃

C₂²

yes

characteristic

C₂₃×#340

C₂²

yes

—

C₂²×C₈×C₂₃

C₂³

yes

—

C₂₃×#125

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

C₂³

yes

—

C₂×C₄²×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂×C₄²×C₂₃

C₂³

yes

—

C₂₃×#97

—

C₄×C₈×C₂₃

Q₈

yes

—

C₂₃×#95

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂×D₄

yes

—

C₂²×C₄×C₂₃

C₂×D₄

yes

—

C₂²×C₄×C₂₃

C₂⁴

yes

characteristic

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

C₂×Q₈

yes

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×Q₈

yes

—

C₄²×C₂₃

#41

yes

—

#33299

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

#124

yes

—

C₂×C₄×C₂₃

C₄⋊Q₈

yes

—

C₂×C₄×C₂₃

C₂²×Q₈

yes

—

C₂×C₄×C₂₃

C₂×#41

yes

—

C₈×C₂₃

—

#2859

C₂×C₂₃

yes

—

#1992

C₂×C₂₃

yes

—

#1835

C₂×C₂₃

yes

—

C₄×#97

C₂×C₂₃

yes

characteristic

C₂²×C₂₃

C₂×#124

yes

—

C₂²×C₂₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₂₃

#575

yes

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

#533

yes

—

C₂×#125

C₂²×C₂₃

yes

—

C₂×#97

C₂²×C₂₃

yes

—

C₂×C₄×C₈

C₂²×C₂₃

yes

—

#389

—

#384

C₂²×C₂₃

yes

—

#382

C₂²×C₂₃

yes

—

C₄³

C₂²×C₂₃

yes

characteristic

#340

C₂²×C₂₃

yes

—

C₂×C₂₃

#2862

yes

characteristic

C₂×C₂₃

#3142

yes

—

C₂×C₂₃

#3162

yes

—

C₂²×C₈

C₂³×C₂₃

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³×C₂₃

yes

—

C₂×C₄²

D₄×C₂₃

yes

—

C₂×C₄²

C₂³×C₂₃

yes

characteristic

C₂×C₄²

C₂³×C₂₃

yes

—

#97

—

C₄×C₈

Q₈×C₂₃

yes

—

#95

—

C₂₃

#33299

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₂₃

yes

—

C₂²×C₄

C₂×D₄×C₂₃

yes

—

C₂²×C₄

C₂⁴×C₂₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Q₈×C₂₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×Q₈×C₂₃

yes

—

C₄²

#41×C₂₃

yes

—

C₂³

C₂²×D₄×C₂₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂₃×#124

yes

—

C₂×C₄

C₂₃×C₄⋊Q₈

yes

—

100

C₂×C₄

C₂²×Q₈×C₂₃

yes

—

101

C₂×C₄

C₂×#41×C₂₃

yes

—

102

C₈

—

103

C₂²

C₂×C₂₃×#124

yes

—

104

C₂²

C₂×C₂₃×C₄⋊Q₈

yes

characteristic

105

C₂²

C₂₃×#575

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

C₂₃×#533

yes

—

110

C₂

C₂₃×#2862

yes

characteristic

111

C₂

C₂₃×#3142

yes

—

112

C₂

C₂₃×#3162

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄³×C₂₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₂₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₂₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₂₃ ◁ C₄³×C₂₃ ◁ G

N	H ≅ G/N	type
36. #33299	C₂₃	direct (N × H)
80. C₂₃	#33299	direct (N × H)

H ≅ G/N

type

36. #33299

C₂₃

direct (N × H)

80. C₂₃

#33299

direct (N × H)

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

subgroup	index
C₂₃×#2859	2
C₂₃×#1992	2
C₂₃×#1835	2
C₄×C₂₃×#97	2
#33299	23

subgroup

index

C₂₃×#2859

C₂₃×#1992

C₂₃×#1835

C₄×C₂₃×#97

#33299

Subgroups — C₂₃×#33299 #19180925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#33299 #19180925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33299 #19180925