Group #19136456 — subgroups

Subgroups — #19136456

Order 5504.

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

normal subgroups only

This group has 160 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×#13063269	C₂	1	1	yes	maximal, characteristic
2	#14582993	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582724	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582704	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#357	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	#13063290	—	2	1	no	—
10	D₄×Dic₄₃	—	2	1	no	—
11	#13063269	C₄	1	4	yes	complemented
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13063259	C₂²	1	1	yes	characteristic
14	#13063248	—	2	1	no	—
15	#13063246	—	2	1	no	—
16	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	#107×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₄₃	—	2	1	no	—
21	C₂²×Dic₄₃	—	4	1	no	—
22	C₂×Dic₈₆	—	2	1	no	—
23	D₈×C₄₃	—	2	1	no	—
24	D₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₄₃	—	2	1	no	—
27	C₂²⋊Dic₄₃	—	4	1	no	—
28	C₄⋊Dic₄₃	—	2	1	no	—
29	Dic₄₃⋊C₄	—	4	1	no	—
30	C₄×Dic₄₃	—	4	1	no	—
31	C₄×Dic₄₃	D₄	1	1	yes	characteristic
32	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
33	Dic₁₇₂	—	2	1	no	—
34	Dic₁₇₂	C₂×C₄	1	2	yes	complemented
35	C₁₆×C₄₃	—	2	1	no	—
36	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	complemented
37	C₂³×C₄₃	—	4	1	no	—
38	D₄×C₄₃	—	2	2	no	—
39	D₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	C₂×Dic₄₃	—	8	2	no	—
45	C₂×Dic₄₃	D₈	1	1	yes	characteristic
46	C₂×Dic₄₃	D₈	1	1	yes	characteristic
47	Dic₈₆	—	2	2	no	—
48	Dic₈₆	—	4	1	no	—
49	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₈×C₄₃	#41	1	1	yes	characteristic
51	C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃	—	4	2	no	—
53	C₂²×C₄₃	—	8	1	no	—
54	C₂²×C₄₃	—	8	1	no	—
55	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
56	C₄×C₄₃	—	8	1	no	—
57	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
58	C₄×C₄₃	#135	1	1	yes	characteristic
59	Dic₄₃	—	2	1	no	—
60	Dic₄₃	—	2	1	no	—
61	Dic₄₃	—	4	2	no	—
62	Dic₄₃	—	8	1	no	—
63	#2175	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	—	8	2	no	—
65	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
66	C₂×C₄₃	#509	1	1	yes	characteristic
67	C₂×C₄₃	#510	1	1	yes	characteristic
68	C₂×SD₃₂	—	43	1	no	—
69	C₄×Q₁₆	—	43	1	no	—
70	C₄×D₈	—	43	1	no	—
71	#366	—	43	1	no	—
72	#358	—	43	1	no	—
73	#357	D₄₃	1	1	yes	characteristic
74	#346	—	43	1	no	—
75	C₄₃	#2175	1	1	yes	characteristic, complemented, Sylow
76	C₂×Q₁₆	—	43	1	no	—
77	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
78	C₄×Q₈	—	86	1	no	—
79	C₄×D₄	—	86	1	no	—
80	SD₃₂	—	43	4	no	—
81	C₂×C₁₆	—	43	1	no	—
82	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
83	#107	—	43	1	no	—
84	#107	C₂×D₄₃	1	1	yes	characteristic
85	#103	—	86	1	no	—
86	#102	—	86	1	no	—
87	C₄×C₈	—	43	1	no	—
88	C₂×Q₈	—	86	1	no	—
89	C₂×D₄	—	2	1	no	—
90	C₂²×C₄	—	172	1	no	—
91	Q₁₆	—	43	2	no	—
92	Q₁₆	—	86	1	no	—
93	D₈	—	2	1	no	—
94	D₈	C₄×D₄₃	1	2	yes	—
95	C₂×C₈	—	43	1	no	—
96	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
97	C₄⋊C₄	—	2	1	no	—
98	C₄⋊C₄	—	86	1	no	—
99	C₄⋊C₄	—	172	1	no	—
100	C₂²⋊C₄	—	172	1	no	—
101	C₄²	—	43	1	no	—
102	C₄²	—	172	1	no	—
103	C₁₆	—	2	1	no	—
104	C₁₆	—	43	2	no	—
105	C₂³	—	4	1	no	—
106	Q₈	—	86	2	no	—
107	Q₈	—	172	1	no	—
108	D₄	—	2	2	no	—
109	D₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	43	1	no	—
112	C₂×C₄	—	43	1	no	—
113	C₂×C₄	—	344	2	no	—
114	C₂×C₄	—	172	1	no	—
115	C₂×C₄	—	172	1	no	—
116	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
117	C₈	—	86	1	no	—
118	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
119	C₈	#10621900	1	1	yes	characteristic
120	C₂²	—	4	2	no	—
121	C₂²	—	8	1	no	—
122	C₂²	—	8	1	no	—
123	C₂²	D₈×D₄₃	1	1	yes	characteristic
124	C₄	—	8	1	no	—
125	C₄	—	86	1	no	—
126	C₄	—	86	1	no	—
127	C₄	—	344	1	no	—
128	C₄	—	172	2	no	—
129	C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
130	C₄	#13063346	1	1	yes	characteristic
131	C₂	—	8	2	no	—
132	C₂	#14582979	1	1	yes	characteristic
133	C₂	#14583333	1	1	yes	characteristic
134	C₂	#14583338	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063269

C₂

yes

maximal, characteristic

#14582993

C₂

yes

maximal, characteristic, complemented

D₈×Dic₄₃

C₂

yes

maximal, characteristic

#14582724

C₂

yes

maximal, characteristic, complemented

#14582704

C₂

yes

maximal, characteristic, complemented

#14582674

C₂

yes

maximal, characteristic, complemented

C₄₃×#357

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

#13063290

—

D₄×Dic₄₃

—

#13063269

C₄

yes

complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063248

—

#13063246

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

D₈×C₄₃

—

D₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

C₂×C₄

yes

complemented

C₁₆×C₄₃

—

C₄₃⋊C₁₆

C₂×C₄

yes

complemented

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2175

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×D₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×SD₃₂

—

C₄×Q₁₆

—

C₄×D₈

—

#366

—

#358

—

#357

D₄₃

yes

characteristic

#346

—

C₄₃

#2175

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×D₄

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#107

C₂×D₄₃

yes

characteristic

#103

—

#102

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

172

—

Q₁₆

—

Q₁₆

—

D₈

—

D₈

C₄×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

100

C₂²⋊C₄

—

172

—

101

C₄²

—

102

C₄²

—

172

—

103

C₁₆

—

104

C₁₆

—

105

C₂³

—

106

Q₈

—

107

Q₈

—

172

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

344

—

114

C₂×C₄

—

172

—

115

C₂×C₄

—

172

—

116

C₂×C₄

D₄×D₄₃

yes

characteristic

117

C₈

—

118

C₈

C₂×C₄×D₄₃

yes

characteristic

119

C₈

#10621900

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

D₈×D₄₃

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

344

—

128

C₄

—

172

—

129

C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

130

C₄

#13063346

yes

characteristic

131

C₂

—

132

C₂

#14582979

yes

characteristic

133

C₂

#14583333

yes

characteristic

134

C₂

#14583338

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#357	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#357	D₄₃
hypocenter	C₄₃	#2175
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#357

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
2. #14582993	C₂	semidirect
4. #14582724	C₂	semidirect
5. #14582704	C₂	semidirect
6. #14582674	C₂	semidirect
11. #13063269	C₄	semidirect
34. Dic₁₇₂	C₂×C₄	semidirect
36. C₄₃⋊C₁₆	C₂×C₄	semidirect
75. C₄₃	#2175	semidirect

H ≅ G/N

type

2. #14582993

C₂

semidirect

4. #14582724

C₂

semidirect

5. #14582704

C₂

semidirect

6. #14582674

C₂

semidirect

11. #13063269

C₄

semidirect

34. Dic₁₇₂

C₂×C₄

semidirect

36. C₄₃⋊C₁₆

C₂×C₄

semidirect

75. C₄₃

#2175

semidirect

Subgroups — #19136456

Conjugacy classes of subgroups

Complements