Group #36355176 — subgroups

Subgroups — #36355176

Order 22144.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19149685	C₂	1	1	yes	maximal, characteristic
2	C₂×#19149619	C₂	1	1	yes	maximal, characteristic, complemented
3	#26011270	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14583826	C₄	1	1	yes	characteristic
6	#19149685	—	2	2	no	—
7	#19149685	—	2	2	no	—
8	C₂×#14583810	C₄	1	1	yes	characteristic
9	C₂×#14583809	C₄	1	2	yes	—
10	C₂×C₈×D₁₇₃	C₂²	1	2	yes	—
11	#19149619	—	2	2	no	—
12	C₂×#14583801	C₂²	1	2	yes	—
13	C₂²×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₁₇₃	—	2	2	no	—
15	C₂×C₁₆×C₁₇₃	C₂²	1	2	yes	—
16	#14583826	—	2	2	no	—
17	#14583826	—	2	2	no	—
18	C₂×Dic₃₄₆	C₈	1	1	yes	characteristic
19	C₂×D₆₉₂	C₈	1	1	yes	characteristic
20	C₂×C₂²⋊D₁₇₃	C₈	1	2	yes	—
21	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
22	#14583810	—	2	2	no	—
23	#14583809	—	2	4	no	—
24	C₂×#13063436	C₂×C₄	1	2	yes	—
25	C₈×D₁₇₃	—	2	2	no	—
26	C₈×D₁₇₃	—	2	2	no	—
27	#14583801	—	2	2	no	—
28	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₇₃	D₄	1	2	yes	—
31	C₂×C₈×C₁₇₃	D₄	1	2	yes	—
32	C₂×C₈×C₁₇₃	C₂³	1	1	yes	characteristic
33	C₁₆×C₁₇₃	—	2	2	no	—
34	C₂²×D₁₇₃	C₂×C₈	1	2	yes	—
35	Dic₃₄₆	—	2	2	no	—
36	D₆₉₂	—	2	2	no	—
37	C₂²⋊D₁₇₃	—	2	4	no	—
38	C₂×Dic₁₇₃	C₂×C₈	1	2	yes	—
39	C₄×D₁₇₃	—	2	2	no	—
40	C₄×D₁₇₃	—	2	2	no	—
41	#13063436	—	2	2	no	—
42	C₂³×C₁₇₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₇₃	M₁₆	1	2	yes	—
46	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₈×C₁₇₃	C₂²⋊C₄	1	2	yes	—
48	C₈×C₁₇₃	C₂×D₄	1	1	yes	characteristic
49	C₈×C₁₇₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₁₇₃	—	2	2	no	—
51	C₂²×C₁₇₃	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₁₇₃	—	2	2	no	—
54	C₂×D₁₇₃	—	2	4	no	—
55	C₄×C₁₇₃	C₂²⋊C₈	1	2	yes	—
56	C₄×C₁₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₁₇₃	C₂×M₁₆	1	1	yes	characteristic
58	Dic₁₇₃	—	2	2	no	—
59	C₂×C₁₇₃	—	2	2	no	—
60	C₂×C₁₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
61	C₂×C₁₇₃	#504	1	2	yes	—
62	D₁₇₃	—	4	2	no	—
63	C₁₇₃	#2113	1	1	yes	characteristic, complemented, Sylow
64	#2113	—	173	1	no	maximal, Sylow
65	C₂×#131	—	173	1	no	—
66	C₂×M₃₂	—	173	1	no	—
67	C₂²×C₁₆	D₁₇₃	1	1	yes	characteristic, complemented
68	C₂²⋊C₁₆	—	173	4	no	—
69	C₂×#41	—	173	1	no	—
70	#131	—	346	2	no	—
71	#131	—	346	2	no	—
72	C₂×M₁₆	—	173	1	no	—
73	C₂×M₁₆	—	173	2	no	—
74	C₂²×C₈	—	173	2	no	—
75	C₂²×C₈	C₂×D₁₇₃	1	1	yes	characteristic
76	M₃₂	—	346	2	no	—
77	C₂×C₁₆	—	2	2	no	—
78	C₂×C₁₆	—	173	2	no	—
79	C₂×C₁₆	C₂×D₁₇₃	1	2	yes	—
80	#41	—	346	2	no	—
81	#41	—	346	2	no	—
82	C₂×Q₈	—	173	1	no	—
83	C₂×D₄	—	173	2	no	—
84	C₂×D₄	—	173	1	no	—
85	C₂²×C₄	—	173	2	no	—
86	C₂²×C₄	C₄×D₁₇₃	1	1	yes	characteristic
87	M₁₆	—	346	2	no	—
88	M₁₆	—	346	4	no	—
89	C₂×C₈	—	346	2	no	—
90	C₂×C₈	—	346	2	no	—
91	C₂×C₈	—	173	2	no	—
92	C₂×C₈	C₄×D₁₇₃	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₁₇₃	1	2	yes	—
94	C₂×C₈	D₆₉₂	1	2	yes	—
95	C₂×C₈	C₂²×D₁₇₃	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	346	2	no	—
98	C₂³	—	173	2	no	—
99	C₂³	C₈×D₁₇₃	1	1	yes	characteristic
100	Q₈	—	346	2	no	—
101	D₄	—	346	4	no	—
102	D₄	—	346	2	no	—
103	C₂×C₄	—	346	2	no	—
104	C₂×C₄	—	346	2	no	—
105	C₂×C₄	—	173	2	no	—
106	C₂×C₄	#14583803	1	2	yes	—
107	C₂×C₄	C₈×D₁₇₃	1	1	yes	characteristic
108	C₂×C₄	#14583809	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₁₇₃	1	1	yes	characteristic
110	C₈	—	346	2	no	—
111	C₈	#14583803	1	2	yes	—
112	C₈	C₂×C₂²⋊D₁₇₃	1	1	yes	characteristic
113	C₈	C₂×D₆₉₂	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	346	4	no	—
116	C₂²	—	346	2	no	—
117	C₂²	#19149591	1	2	yes	—
118	C₂²	C₂×C₈×D₁₇₃	1	1	yes	characteristic
119	C₄	—	346	2	no	—
120	C₄	#19149591	1	2	yes	—
121	C₄	C₂×#14583803	1	1	yes	characteristic
122	C₄	C₂×#14583809	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	692	2	no	—
125	C₂	C₂×#19149591	1	1	yes	characteristic
126	C₂	#26011907	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149685

C₂

yes

maximal, characteristic

C₂×#19149619

C₂

yes

maximal, characteristic, complemented

#26011270

C₂

yes

maximal, complemented

C₂²×C₁₆×C₁₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#14583826

C₄

yes

—

—

C₄

yes

characteristic

C₂×#14583809

C₄

yes

—

C₂×C₈×D₁₇₃

C₂²

yes

—

#19149619

—

C₂×#14583801

C₂²

yes

—

C₂²×C₈×C₁₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₁₇₃

—

C₂×C₁₆×C₁₇₃

C₂²

yes

—

#14583826

—

#14583826

—

C₂×Dic₃₄₆

C₈

yes

characteristic

C₂×D₆₉₂

C₈

yes

characteristic

C₂×C₂²⋊D₁₇₃

C₈

yes

—

C₂×C₄×D₁₇₃

C₂×C₄

yes

—

#14583810

—

#14583809

—

C₂×#13063436

C₂×C₄

yes

—

C₈×D₁₇₃

—

C₈×D₁₇₃

—

#14583801

—

C₂²×C₄×C₁₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇₃

D₄

yes

—

C₂×C₈×C₁₇₃

D₄

yes

—

C₂×C₈×C₁₇₃

C₂³

yes

characteristic

C₁₆×C₁₇₃

—

C₂²×D₁₇₃

C₂×C₈

yes

—

Dic₃₄₆

—

D₆₉₂

—

C₂²⋊D₁₇₃

—

C₂×Dic₁₇₃

C₂×C₈

yes

—

C₄×D₁₇₃

—

C₄×D₁₇₃

—

#13063436

—

C₂³×C₁₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇₃

M₁₆

yes

—

C₂×C₄×C₁₇₃

C₂²×C₄

yes

characteristic

C₈×C₁₇₃

C₂²⋊C₄

yes

—

C₈×C₁₇₃

C₂×D₄

yes

characteristic

C₈×C₁₇₃

C₂×D₄

yes

characteristic

C₂²×C₁₇₃

—

C₂²×C₁₇₃

C₂²⋊C₈

yes

—

C₂²×C₁₇₃

C₂²×C₈

yes

characteristic

C₂×D₁₇₃

—

C₂×D₁₇₃

—

C₄×C₁₇₃

C₂²⋊C₈

yes

—

C₄×C₁₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₇₃

C₂×M₁₆

yes

characteristic

Dic₁₇₃

—

C₂×C₁₇₃

—

C₂×C₁₇₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₇₃

#504

yes

—

D₁₇₃

—

C₁₇₃

#2113

yes

characteristic, complemented, Sylow

#2113

—

173

maximal, Sylow

C₂×#131

—

173

—

C₂×M₃₂

—

173

—

C₂²×C₁₆

D₁₇₃

yes

characteristic, complemented

C₂²⋊C₁₆

—

173

—

C₂×#41

—

173

—

#131

—

346

—

#131

—

346

—

C₂×M₁₆

—

173

—

C₂×M₁₆

—

173

—

C₂²×C₈

—

173

—

C₂²×C₈

C₂×D₁₇₃

yes

characteristic

M₃₂

—

346

—

C₂×C₁₆

—

C₂×C₁₆

—

173

—

C₂×C₁₆

C₂×D₁₇₃

yes

—

#41

—

346

—

#41

—

346

—

C₂×Q₈

—

173

—

C₂×D₄

—

173

—

C₂×D₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₄×D₁₇₃

yes

characteristic

M₁₆

—

346

—

M₁₆

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

173

—

C₂×C₈

C₄×D₁₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₇₃

yes

—

C₂×C₈

D₆₉₂

yes

—

C₂×C₈

C₂²×D₁₇₃

yes

characteristic

C₁₆

—

C₁₆

—

346

—

C₂³

—

173

—

C₂³

C₈×D₁₇₃

yes

characteristic

100

Q₈

—

346

—

101

D₄

—

346

—

102

D₄

—

346

—

103

C₂×C₄

—

346

—

104

C₂×C₄

—

346

—

105

C₂×C₄

—

173

—

106

C₂×C₄

#14583803

yes

—

107

C₂×C₄

C₈×D₁₇₃

yes

characteristic

108

C₂×C₄

#14583809

yes

—

109

C₂×C₄

C₂×C₄×D₁₇₃

yes

characteristic

110

C₈

—

346

—

111

C₈

#14583803

yes

—

112

C₈

C₂×C₂²⋊D₁₇₃

yes

characteristic

113

C₈

C₂×D₆₉₂

yes

characteristic

114

C₂²

—

115

C₂²

—

346

—

116

C₂²

—

346

—

117

C₂²

#19149591

yes

—

118

C₂²

C₂×C₈×D₁₇₃

yes

characteristic

119

C₄

—

346

—

120

C₄

#19149591

yes

—

121

C₄

C₂×#14583803

yes

characteristic

122

C₄

C₂×#14583809

yes

characteristic

123

C₂

—

124

C₂

—

692

—

125

C₂

C₂×#19149591

yes

characteristic

126

C₂

#26011907

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₇₃
commutator, socle	C₂²×C₁₇₃	C₂²×C₈
Fitting	C₂²×C₁₆×C₁₇₃	C₂
prime radical	C₂×#14583826	C₄
cosocle	C₂×C₈×C₁₇₃	C₂³
hypercenter	C₂²×C₁₆	D₁₇₃
hypocenter	C₁₇₃	#2113
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₇₃

commutator, socle

C₂²×C₁₇₃

C₂²×C₈

Fitting

C₂²×C₁₆×C₁₇₃

C₂

prime radical

C₂×#14583826

C₄

cosocle

C₂×C₈×C₁₇₃

C₂³

hypercenter

C₂²×C₁₆

D₁₇₃

C₁₇₃

G ▷ C₂²×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. C₂×#19149619	C₂	semidirect
3. #26011270	C₂	semidirect
4. C₂²×C₁₆×C₁₇₃	C₂	semidirect
63. C₁₇₃	#2113	semidirect
67. C₂²×C₁₆	D₁₇₃	semidirect

H ≅ G/N

type

2. C₂×#19149619

C₂

semidirect

3. #26011270

C₂

semidirect

4. C₂²×C₁₆×C₁₇₃

C₂

semidirect

63. C₁₇₃

#2113

semidirect

67. C₂²×C₁₆

D₁₇₃

semidirect

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

subgroup	index
C₂×#19149685	2
C₂×#19149619	2
#26011270	2
C₂²×C₁₆×C₁₇₃	2
#2113	173

subgroup

index

C₂²×C₁₆×C₁₇₃

173

Subgroups — #36355176

Conjugacy classes of subgroups

Complements

Maximal subgroups