Group #19136630 — subgroups

Subgroups — #19136630

Order 5504.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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	C₂×#13063266	C₂	1	2	yes	maximal, complemented
2	#14583276	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582699	C₂	1	2	yes	maximal, complemented
5	C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₄₄	—	2	1	no	—
7	C₂×D₃₄₄	C₂²	1	2	yes	—
8	#13063322	—	2	1	no	—
9	#13063266	—	2	4	no	—
10	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
11	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×D₄×C₄₃	—	2	1	no	—
13	#107×C₄₃	C₂²	1	1	yes	characteristic
14	#102×C₄₃	—	2	1	no	—
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	—	4	1	no	—
18	C₂×D₁₇₂	—	2	2	no	—
19	C₂×D₁₇₂	—	4	1	no	—
20	C₂×D₁₇₂	—	4	1	no	—
21	D₈×C₄₃	—	2	1	no	—
22	D₈×C₄₃	D₄	1	2	yes	complemented
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₃	—	2	1	no	—
26	C₂²⋊C₄×C₄₃	—	4	1	no	—
27	C₄²×C₄₃	D₄	1	1	yes	characteristic
28	D₃₄₄	—	2	2	no	—
29	D₃₄₄	—	2	2	no	—
30	D₃₄₄	—	4	2	no	—
31	C₄₃⋊C₁₆	—	2	2	no	—
32	C₂³×C₄₃	—	4	1	no	—
33	C₂²×D₄₃	—	4	2	no	—
34	D₄×C₄₃	—	2	2	no	—
35	D₄×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	8	2	no	—
38	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
39	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	D₁₇₂	—	4	2	no	—
42	D₁₇₂	—	4	2	no	—
43	D₁₇₂	—	8	2	no	—
44	D₁₇₂	—	8	2	no	—
45	C₈×C₄₃	—	2	1	no	—
46	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₈×C₄₃	#41	1	1	yes	characteristic
48	C₂²×C₄₃	—	4	2	no	—
49	C₂²×C₄₃	—	8	1	no	—
50	C₂²×C₄₃	—	8	1	no	—
51	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₂×D₄₃	—	8	2	no	—
53	C₂×D₄₃	—	8	2	no	—
54	C₂×D₄₃	—	8	2	no	—
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	—	8	1	no	—
57	C₄×C₄₃	D₁₆	1	2	yes	complemented
58	C₄×C₄₃	#121	1	1	yes	characteristic
59	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
60	#2206	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	—	8	2	no	—
62	C₂×C₄₃	#459	1	1	yes	characteristic
63	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
64	C₂×C₄₃	#509	1	1	yes	characteristic
65	D₄₃	—	16	2	no	—
66	C₂×D₁₆	—	43	2	no	—
67	#493	—	43	1	no	—
68	C₄×D₈	D₄₃	1	1	yes	characteristic, complemented
69	C₄⋊C₁₆	—	43	1	no	—
70	#357	—	43	2	no	—
71	C₄₃	#2206	1	1	yes	characteristic, complemented, Sylow
72	C₂×D₈	—	43	2	no	—
73	C₂×D₈	—	86	1	no	—
74	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
75	#127	—	86	1	no	—
76	C₄×D₄	—	2	1	no	—
77	D₁₆	—	86	4	no	—
78	C₂×C₁₆	—	43	2	no	—
79	#107	C₂×D₄₃	1	1	yes	characteristic
80	#102	—	2	1	no	—
81	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
82	C₂×D₄	—	2	1	no	—
83	C₂×D₄	—	86	2	no	—
84	C₂×D₄	—	172	1	no	—
85	C₂×D₄	—	172	1	no	—
86	C₂²×C₄	—	4	1	no	—
87	D₈	—	2	1	no	—
88	D₈	—	86	2	no	—
89	D₈	—	86	2	no	—
90	D₈	—	172	2	no	—
91	D₈	D₁₇₂	1	2	yes	complemented
92	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
94	C₄⋊C₄	—	2	1	no	—
95	C₂²⋊C₄	—	4	1	no	—
96	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
97	C₁₆	—	86	2	no	—
98	C₂³	—	4	1	no	—
99	C₂³	—	172	2	no	—
100	D₄	—	2	2	no	—
101	D₄	—	4	1	no	—
102	D₄	—	344	2	no	—
103	D₄	—	344	2	no	—
104	D₄	—	172	2	no	—
105	D₄	—	172	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	8	2	no	—
108	C₂×C₄	#10621882	1	1	yes	characteristic
109	C₂×C₄	#10621882	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
111	C₈	—	2	1	no	—
112	C₈	C₂×D₁₇₂	1	1	yes	characteristic
113	C₈	#10621898	1	1	yes	characteristic
114	C₂²	—	4	2	no	—
115	C₂²	—	8	1	no	—
116	C₂²	—	8	1	no	—
117	C₂²	—	344	2	no	—
118	C₂²	—	344	2	no	—
119	C₂²	—	344	2	no	—
120	C₂²	C₂×#10621882	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	8	1	no	—
123	C₄	#13063266	1	2	yes	complemented
124	C₄	#13063299	1	1	yes	characteristic
125	C₄	#13063350	1	1	yes	characteristic
126	C₂	—	8	2	no	—
127	C₂	—	688	2	no	—
128	C₂	#14583094	1	1	yes	characteristic
129	C₂	C₂×#13063266	1	1	yes	characteristic
130	C₂	#14583334	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063266

C₂

yes

maximal, complemented

#14583276

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#14582699

C₂

yes

maximal, complemented

C₄×D₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂²

yes

—

#13063322

—

#13063266

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

—

#107×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

D₈×C₄₃

—

D₈×C₄₃

D₄

yes

complemented

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

D₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

characteristic

C₂×C₄₃

#509

yes

characteristic

D₄₃

—

C₂×D₁₆

—

#493

—

C₄×D₈

D₄₃

yes

characteristic, complemented

C₄⋊C₁₆

—

#357

—

C₄₃

#2206

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

#127

—

C₄×D₄

—

D₁₆

—

C₂×C₁₆

—

#107

C₂×D₄₃

yes

characteristic

#102

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

C₂²×C₄

—

D₈

—

D₈

—

D₈

—

D₈

—

172

—

D₈

D₁₇₂

yes

complemented

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

172

—

100

D₄

—

101

D₄

—

102

D₄

—

344

—

103

D₄

—

344

—

104

D₄

—

172

—

105

D₄

—

172

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#10621882

yes

characteristic

109

C₂×C₄

#10621882

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

111

C₈

—

112

C₈

C₂×D₁₇₂

yes

characteristic

113

C₈

#10621898

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

344

—

118

C₂²

—

344

—

119

C₂²

—

344

—

120

C₂²

C₂×#10621882

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

#13063266

yes

complemented

124

C₄

#13063299

yes

characteristic

125

C₄

#13063350

yes

characteristic

126

C₂

—

127

C₂

—

688

—

128

C₂

#14583094

yes

characteristic

129

C₂

C₂×#13063266

yes

characteristic

130

C₂

#14583334

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×D₈	D₄₃
hypocenter	C₄₃	#2206
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×D₈×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₄×D₈

D₄₃

hypocenter

C₄₃

#2206

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. C₂×#13063266	C₂	semidirect
2. #14583276	C₂	semidirect
3. C₄⋊(C₄₃⋊C₁₆)	C₂	semidirect
4. #14582699	C₂	semidirect
5. C₄×D₈×C₄₃	C₂	semidirect
22. D₈×C₄₃	D₄	semidirect
57. C₄×C₄₃	D₁₆	semidirect
68. C₄×D₈	D₄₃	semidirect
71. C₄₃	#2206	semidirect
91. D₈	D₁₇₂	semidirect
123. C₄	#13063266	semidirect

H ≅ G/N

type

1. C₂×#13063266

C₂

semidirect

2. #14583276

C₂

semidirect

3. C₄⋊(C₄₃⋊C₁₆)

C₂

semidirect

4. #14582699

C₂

semidirect

5. C₄×D₈×C₄₃

C₂

semidirect

22. D₈×C₄₃

D₄

semidirect

57. C₄×C₄₃

D₁₆

semidirect

68. C₄×D₈

D₄₃

semidirect

71. C₄₃

#2206

semidirect

91. D₈

D₁₇₂

semidirect

123. C₄

#13063266

semidirect

Subgroups — #19136630

Conjugacy classes of subgroups

Complements