Group #36369795 — subgroups

Subgroups — #36369795

Order 22144.

228 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 82 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×#19149753	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14583829	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012386	C₂	1	4	yes	maximal, complemented
4	C₂×#19149687	C₂	1	1	yes	maximal, characteristic
5	#19149753	—	2	2	no	—
6	C₂×#14583829	—	2	2	no	—
7	C₂×#14583829	C₂²	1	2	yes	—
8	C₂×#14583829	C₂²	1	2	yes	—
9	C₂×#14583826	C₄	1	1	yes	characteristic
10	#19149687	—	2	2	no	—
11	#19149687	—	2	2	no	—
12	C₂×#14583809	C₄	1	2	yes	—
13	C₂²×#13063436	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₁₇₃	C₂²	1	2	yes	—
15	C₂×M₁₆×C₁₇₃	C₄	1	1	yes	characteristic
16	#14583829	—	2	2	no	—
17	#14583829	—	2	2	no	—
18	#14583826	—	2	2	no	—
19	#14583826	—	2	2	no	—
20	C₂×Dic₃₄₆	C₈	1	1	yes	characteristic
21	C₂×D₆₉₂	C₈	1	1	yes	characteristic
22	C₂×C₂²⋊D₁₇₃	C₈	1	2	yes	—
23	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
24	#14583809	—	2	4	no	—
25	C₂×#13063436	C₂×C₄	1	1	yes	characteristic
26	C₂×#13063436	D₄	1	2	yes	—
27	C₂×#13063436	D₄	1	2	yes	—
28	C₂×#13063436	C₂³	1	1	yes	characteristic
29	C₈×D₁₇₃	—	2	2	no	—
30	C₈×D₁₇₃	—	2	2	no	—
31	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
32	M₁₆×C₁₇₃	—	2	2	no	—
33	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
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	C₂²⋊C₄	1	2	yes	—
42	#13063436	C₂×D₄	1	1	yes	characteristic
43	#13063436	C₂×D₄	1	1	yes	characteristic
44	C₂³×C₁₇₃	C₂×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₇₃	M₁₆	1	2	yes	—
48	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
49	C₈×C₁₇₃	—	2	2	no	—
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	—	173	1	no	—
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	2	no	—
73	C₂×M₁₆	#10621924	1	1	yes	characteristic
74	C₂²×C₈	—	173	2	no	—
75	C₂²×C₈	—	173	1	no	—
76	M₃₂	—	346	2	no	—
77	C₂×C₁₆	—	346	2	no	—
78	C₂×C₁₆	—	173	2	no	—
79	C₂×C₁₆	—	173	2	no	—
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	C₂×#10621924	1	1	yes	characteristic
87	M₁₆	—	2	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	—	173	2	no	—
93	C₂×C₈	—	173	1	no	—
94	C₂×C₈	—	173	1	no	—
95	C₂×C₈	C₂×#10621924	1	2	yes	—
96	C₁₆	—	346	2	no	—
97	C₁₆	—	346	2	no	—
98	C₂³	—	173	2	no	—
99	C₂³	D₁₇₃⋊C₈	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	C₂²⋊#10621924	1	2	yes	—
107	C₂×C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
108	C₂×C₄	#14583836	1	2	yes	—
109	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	173	2	no	—
112	C₈	—	173	1	no	—
113	C₈	—	173	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	346	2	no	—
116	C₂²	—	346	4	no	—
117	C₂²	#19149736	1	2	yes	—
118	C₂²	C₂×D₁₇₃⋊C₈	1	1	yes	characteristic
119	C₄	—	346	2	no	—
120	C₄	#19149736	1	2	yes	—
121	C₄	C₂×C₂²⋊#10621924	1	1	yes	characteristic
122	C₄	C₂×#14583836	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	692	2	no	—
125	C₂	C₂×#19149736	1	1	yes	characteristic
126	C₂	#26012550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149753

C₂

yes

maximal, characteristic, complemented

C₂²×#14583829

C₂

yes

maximal, characteristic, complemented

#26012386

C₂

yes

maximal, complemented

C₂×#19149687

C₂

yes

maximal, characteristic

#19149753

—

C₂×#14583829

—

C₂×#14583829

C₂²

yes

—

C₂×#14583829

C₂²

yes

—

C₂×#14583826

C₄

yes

—

—

C₄

yes

—

C₂²×#13063436

C₂²

yes

characteristic

C₂×C₈×D₁₇₃

C₂²

yes

—

C₂×M₁₆×C₁₇₃

C₄

yes

—

—

—

—

C₂×Dic₃₄₆

C₈

yes

characteristic

C₂×D₆₉₂

C₈

yes

characteristic

C₂×C₂²⋊D₁₇₃

C₈

yes

—

C₂×C₄×D₁₇₃

C₂×C₄

yes

—

#14583809

—

C₂×#13063436

C₂×C₄

yes

characteristic

C₂×#13063436

D₄

yes

—

C₂×#13063436

D₄

yes

—

C₂×#13063436

C₂³

yes

characteristic

C₈×D₁₇₃

—

C₈×D₁₇₃

—

C₂²×C₄×C₁₇₃

C₂×C₄

yes

characteristic

M₁₆×C₁₇₃

—

C₂×C₈×C₁₇₃

C₂×C₄

yes

—

C₂²×D₁₇₃

C₂×C₈

yes

—

Dic₃₄₆

—

D₆₉₂

—

C₂²⋊D₁₇₃

—

C₂×Dic₁₇₃

C₂×C₈

yes

—

C₄×D₁₇₃

—

C₄×D₁₇₃

—

#13063436

C₂²⋊C₄

yes

—

#13063436

C₂×D₄

yes

characteristic

#13063436

C₂×D₄

yes

characteristic

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×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

—

173

—

C₂²⋊C₁₆

—

173

—

C₂×#41

—

173

—

#131

—

346

—

#131

—

346

—

C₂×M₁₆

—

173

—

C₂×M₁₆

#10621924

yes

characteristic

C₂²×C₈

—

173

—

C₂²×C₈

—

173

—

M₃₂

—

346

—

C₂×C₁₆

—

346

—

C₂×C₁₆

—

173

—

C₂×C₁₆

—

173

—

#41

—

346

—

#41

—

346

—

C₂×Q₈

—

173

—

C₂×D₄

—

173

—

C₂×D₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₂×#10621924

yes

characteristic

M₁₆

—

M₁₆

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

C₂×#10621924

yes

—

C₁₆

—

346

—

C₁₆

—

346

—

C₂³

—

173

—

C₂³

D₁₇₃⋊C₈

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

C₂²⋊#10621924

yes

—

107

C₂×C₄

D₁₇₃⋊C₈

yes

characteristic

108

C₂×C₄

#14583836

yes

—

109

C₂×C₄

C₂²×#10621924

yes

characteristic

110

C₈

—

111

C₈

—

173

—

112

C₈

—

173

—

113

C₈

—

173

—

114

C₂²

—

115

C₂²

—

346

—

116

C₂²

—

346

—

117

C₂²

#19149736

yes

—

118

C₂²

C₂×D₁₇₃⋊C₈

yes

characteristic

119

C₄

—

346

—

120

C₄

#19149736

yes

—

121

C₄

C₂×C₂²⋊#10621924

yes

characteristic

122

C₄

C₂×#14583836

yes

characteristic

123

C₂

—

124

C₂

—

692

—

125

C₂

C₂×#19149736

yes

characteristic

126

C₂

#26012550

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10621924
commutator, socle	C₂²×C₁₇₃	C₂²×C₈
Fitting	C₂×M₁₆×C₁₇₃	C₄
prime radical	C₂×#14583826	C₄
cosocle	C₂×#13063436	C₂³
hypercenter	C₂×M₁₆	#10621924
hypocenter	C₁₇₃	#2113
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#10621924

commutator, socle

C₂²×C₁₇₃

C₂²×C₈

Fitting

C₂×M₁₆×C₁₇₃

C₄

C₄

C₂³

C₂×M₁₆

C₁₇₃

G ▷ C₂²×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#19149753	C₂	semidirect
2. C₂²×#14583829	C₂	semidirect
3. #26012386	C₂	semidirect
63. C₁₇₃	#2113	semidirect

H ≅ G/N

type

1. C₂×#19149753

C₂

semidirect

2. C₂²×#14583829

C₂

semidirect

3. #26012386

C₂

semidirect

63. C₁₇₃

#2113

semidirect

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

subgroup	index
C₂×#19149753	2
C₂²×#14583829	2
#26012386	2
C₂×#19149687	2
#2113	173

subgroup

index

173

Subgroups — #36369795

Conjugacy classes of subgroups

Complements

Maximal subgroups