Group #24983920 — subgroups

Subgroups — #24983920

Order 11008.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19132929	C₂	1	2	yes	maximal
2	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic
3	#14582956	—	2	2	no	—
4	#14582625	C₄	1	4	yes	—
5	#14582623	—	2	2	no	—
6	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊C₈×C₄₃	C₄	1	2	yes	—
8	C₄₃×#336	—	2	2	no	—
9	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
10	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
11	#13063236	—	4	2	no	—
12	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	—	2	2	no	—
14	#117×C₄₃	—	4	2	no	—
15	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
16	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₄₃	Q₈	1	1	yes	characteristic
18	C₂×C₄²×C₄₃	D₄	1	2	yes	—
19	C₂²⋊C₈×C₄₃	—	4	2	no	—
20	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	—	2	2	no	—
22	C₂²×C₄×C₄₃	—	4	2	no	—
23	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₄₃	—	4	4	no	—
28	C₂×C₈×C₄₃	—	4	2	no	—
29	C₄⋊C₄×C₄₃	—	4	2	no	—
30	C₂²⋊C₄×C₄₃	—	4	1	no	—
31	C₂²⋊C₄×C₄₃	—	4	1	no	—
32	C₄²×C₄₃	—	2	2	no	—
33	C₄²×C₄₃	—	2	2	no	—
34	C₂×C₄₃⋊C₈	—	4	4	no	—
35	C₂³×C₄₃	—	2	1	no	—
36	C₂³×C₄₃	—	2	2	no	—
37	C₂³×C₄₃	—	4	2	no	—
38	C₂³×C₄₃	#95	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	4	4	no	—
45	C₂×C₄×C₄₃	—	4	2	no	—
46	C₂×C₄×C₄₃	—	4	2	no	—
47	C₂×C₄×C₄₃	#99	1	2	yes	—
48	C₈×C₄₃	—	8	2	no	—
49	C₄₃⋊C₈	—	8	4	no	—
50	#7327	—	43	1	no	maximal, Sylow
51	C₂²×C₄₃	—	2	2	no	—
52	C₂²×C₄₃	—	4	1	no	—
53	C₂²×C₄₃	—	4	2	no	—
54	C₂²×C₄₃	—	8	2	no	—
55	C₂²×C₄₃	#342	1	1	yes	characteristic
56	C₂²×C₄₃	#344	1	2	yes	—
57	C₄×C₄₃	—	2	2	no	—
58	C₄×C₄₃	—	4	1	no	—
59	C₄×C₄₃	—	4	2	no	—
60	C₄×C₄₃	—	4	2	no	—
61	#1818	D₄₃	1	1	yes	characteristic
62	#1464	—	43	2	no	—
63	C₂×C₄₃	—	2	2	no	—
64	C₂×C₄₃	—	8	1	no	—
65	C₂×C₄₃	#1306	1	1	yes	characteristic
66	C₂×C₄₃	#1395	1	2	yes	—
67	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
68	#432	—	86	2	no	—
69	C₂×C₂²⋊C₈	Dic₄₃	1	2	yes	—
70	#336	—	2	2	no	—
71	#324	—	43	4	no	—
72	#323	—	86	2	no	—
73	C₄₃	#7327	1	1	yes	characteristic, complemented, Sylow
74	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
75	C₂²×C₈	—	2	2	no	—
76	#117	—	4	2	no	—
77	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
78	C₂×C₂²⋊C₄	Dic₈₆	1	1	yes	characteristic
79	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
80	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
81	C₄⋊C₈	—	172	2	no	—
82	C₂²⋊C₈	—	4	2	no	—
83	C₂²⋊C₈	—	86	4	no	—
84	#97	—	172	2	no	—
85	C₂⁴	C₄⋊Dic₄₃	1	1	yes	characteristic
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	—	4	2	no	—
88	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
89	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
90	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
91	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
92	C₂×C₈	—	4	4	no	—
93	C₂×C₈	—	4	2	no	—
94	C₂×C₈	—	172	4	no	—
95	C₄⋊C₄	—	4	2	no	—
96	C₂²⋊C₄	—	4	1	no	—
97	C₂²⋊C₄	—	4	1	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	2	2	no	—
100	C₂³	—	2	1	no	—
101	C₂³	—	2	2	no	—
102	C₂³	—	4	2	no	—
103	C₂³	C₄₃⋊#95	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	4	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	2	no	—
112	C₂×C₄	#13063240	1	2	yes	—
113	C₈	—	8	2	no	—
114	C₈	—	344	4	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	4	1	no	—
118	C₂²	—	8	2	no	—
119	C₂²	#14582666	1	1	yes	characteristic
120	C₂²	#14582669	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	2	no	—
123	C₄	—	4	2	no	—
124	C₄	—	4	1	no	—
125	C₂	—	2	2	no	—
126	C₂	—	8	1	no	—
127	C₂	#19132503	1	1	yes	characteristic
128	C₂	#19132724	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19132929

C₂

yes

maximal

C₄₃×#1818

C₂

yes

maximal, characteristic

#14582956

—

#14582625

C₄

yes

—

#14582623

—

C₂×#117×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₃

C₄

yes

—

C₄₃×#336

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

—

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

Q₈

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#95

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#99

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#7327

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#342

yes

characteristic

C₂²×C₄₃

#344

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1818

D₄₃

yes

characteristic

#1464

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1306

yes

characteristic

C₂×C₄₃

#1395

yes

—

C₂×#117

C₂×D₄₃

yes

characteristic

#432

—

C₂×C₂²⋊C₈

Dic₄₃

yes

—

#336

—

#324

—

#323

—

C₄₃

#7327

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

C₄×D₄₃

yes

—

C₂×C₂²⋊C₄

Dic₈₆

yes

characteristic

C₂×C₂²⋊C₄

D₁₇₂

yes

characteristic

C₂×C₄²

C₂²⋊D₄₃

yes

—

C₄⋊C₈

—

172

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

172

—

C₂⁴

C₄⋊Dic₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂²×C₄

Dic₄₃⋊C₄

yes

—

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

C₄₃⋊#95

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

#13063240

yes

—

113

C₈

—

114

C₈

—

344

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

#14582666

yes

characteristic

120

C₂²

#14582669

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₂

—

126

C₂

—

127

C₂

#19132503

yes

characteristic

128

C₂

#19132724

yes

—

	subgroup	G/H
center	C₂²	#14582666
commutator	C₂²×C₄×C₄₃	C₄²
Frattini	C₂×#117	C₂×D₄₃
Fitting	C₄₃×#1818	C₂
socle	C₂²×C₄₃	#342
prime radical	C₂⁴×C₄₃	C₄⋊C₄
cosocle	C₂×#117×C₄₃	C₂²
hypercenter	#1818	D₄₃
hypocenter	C₄₃	#7327
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

subgroup

G/H

center

C₂²

#14582666

commutator

C₂²×C₄×C₄₃

C₄²

Frattini

C₂×#117

C₂×D₄₃

Fitting

C₄₃×#1818

C₂

socle

C₂²×C₄₃

#342

prime radical

C₂⁴×C₄₃

C₄⋊C₄

cosocle

C₂×#117×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

N	H ≅ G/N	type
73. C₄₃	#7327	semidirect

H ≅ G/N

type

73. C₄₃

#7327

semidirect

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

subgroup	index
#19132929	2
C₄₃×#1818	2
#7327	43

subgroup

index

#19132929

C₄₃×#1818

#7327

Subgroups — #24983920

Conjugacy classes of subgroups

Complements

Maximal subgroups