Group #36475404 — subgroups

Subgroups — #36475404

Order 22784.

180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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	#26022531	C₂	1	1	yes	maximal, characteristic, complemented
2	#26018433	C₂	1	2	yes	maximal, complemented
3	#26018430	C₂	1	2	yes	maximal
4	C₄×#15667918	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2249	C₂	1	1	yes	maximal, characteristic
6	#19152000	—	2	1	no	—
7	C₂×#15667918	C₂²	1	2	yes	—
8	#19151426	—	2	1	no	—
9	#19151424	C₂²	1	2	yes	—
10	C₂×Q₃₂×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×SD₃₂×C₈₉	—	2	1	no	—
12	C₂×D₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	#495×C₈₉	—	2	1	no	—
14	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
15	#15668004	—	4	1	no	—
16	#15667946	—	2	2	no	—
17	#15667944	—	4	1	no	—
18	#15667918	—	2	2	no	—
19	C₂×Q₁₆×C₈₉	—	2	1	no	—
20	C₂×SD₁₆×C₈₉	—	4	1	no	—
21	C₂×D₈×C₈₉	—	2	1	no	—
22	#124×C₈₉	—	4	1	no	—
23	Q₃₂×C₈₉	—	2	2	no	—
24	SD₃₂×C₈₉	—	4	2	no	—
25	D₁₆×C₈₉	—	2	2	no	—
26	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
27	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
28	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
29	C₄⋊Dic₈₉	—	4	2	no	—
30	#13083553	—	8	2	no	—
31	C₂×Q₈×C₈₉	—	4	1	no	—
32	C₂×D₄×C₈₉	—	4	1	no	—
33	Q₁₆×C₈₉	—	4	1	no	—
34	Q₁₆×C₈₉	—	4	1	no	—
35	SD₁₆×C₈₉	—	8	2	no	—
36	D₈×C₈₉	—	4	1	no	—
37	D₈×C₈₉	—	4	1	no	—
38	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
39	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
40	C₂²⋊C₄×C₈₉	—	8	2	no	—
41	C₄²×C₈₉	D₈	1	1	yes	characteristic
42	C₁₆×C₈₉	SD₁₆	1	2	yes	—
43	C₁₆×C₈₉	#41	1	2	yes	—
44	C₂³×C₈₉	—	8	1	no	—
45	Q₈×C₈₉	—	8	1	no	—
46	Q₈×C₈₉	—	8	1	no	—
47	D₄×C₈₉	—	8	1	no	—
48	D₄×C₈₉	—	8	1	no	—
49	C₂×C₄×C₈₉	—	8	1	no	—
50	C₂×C₄×C₈₉	D₁₆	1	2	yes	—
51	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
52	C₂×Dic₈₉	—	8	2	no	—
53	C₈×C₈₉	SD₃₂	1	2	yes	—
54	C₈×C₈₉	#124	1	1	yes	characteristic
55	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
56	C₂²×C₈₉	—	16	1	no	—
57	C₂²×C₈₉	—	16	2	no	—
58	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
59	C₄×C₈₉	—	2	2	no	—
60	C₄×C₈₉	—	16	1	no	—
61	C₄×C₈₉	#486	1	1	yes	characteristic
62	C₄×C₈₉	C₂×SD₃₂	1	1	yes	characteristic
63	Dic₈₉	—	16	2	no	—
64	#13721	—	89	1	no	maximal, Sylow
65	C₂×C₈₉	—	32	1	no	—
66	C₂×C₈₉	#2240	1	1	yes	characteristic
67	C₂×C₈₉	#2262	1	2	yes	—
68	#2253	—	89	1	no	—
69	#2249	D₈₉	1	1	yes	characteristic
70	#1416	—	89	2	no	—
71	#1415	—	89	2	no	—
72	C₄×C₃₂	—	89	1	no	—
73	C₈₉	#13721	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₃₂	C₂×D₈₉	1	1	yes	characteristic
75	C₂×SD₃₂	—	2	1	no	—
76	C₂×D₁₆	C₂×D₈₉	1	1	yes	characteristic
77	#499	—	178	1	no	—
78	#495	—	2	1	no	—
79	C₂×C₃₂	—	89	2	no	—
80	#367	—	178	1	no	—
81	#366	—	89	2	no	—
82	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
83	C₂×Q₁₆	—	2	1	no	—
84	C₂×SD₁₆	—	4	1	no	—
85	C₂×D₈	—	2	1	no	—
86	#125	—	356	1	no	—
87	#124	—	4	1	no	—
88	Q₃₂	—	2	2	no	—
89	SD₃₂	—	4	2	no	—
90	D₁₆	—	2	2	no	—
91	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
92	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
93	#107	—	178	2	no	—
94	#106	—	356	1	no	—
95	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
96	C₃₂	—	178	2	no	—
97	C₂×Q₈	—	4	1	no	—
98	C₂×D₄	—	4	1	no	—
99	Q₁₆	—	4	1	no	—
100	Q₁₆	—	4	1	no	—
101	SD₁₆	—	8	2	no	—
102	D₈	—	4	1	no	—
103	D₈	—	4	1	no	—
104	C₂×C₈	#13083559	1	1	yes	characteristic
105	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
106	C₄⋊C₄	—	356	2	no	—
107	C₄⋊C₄	—	712	2	no	—
108	C₂²⋊C₄	—	8	2	no	—
109	C₄²	#13083559	1	1	yes	characteristic
110	C₁₆	#13083562	1	2	yes	—
111	C₁₆	#13083573	1	2	yes	—
112	C₂³	—	8	1	no	—
113	Q₈	—	8	1	no	—
114	Q₈	—	8	1	no	—
115	D₄	—	8	1	no	—
116	D₄	—	8	1	no	—
117	C₂×C₄	—	8	1	no	—
118	C₂×C₄	—	712	2	no	—
119	C₂×C₄	#15667953	1	2	yes	—
120	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
121	C₈	#15667956	1	2	yes	—
122	C₈	#15667999	1	1	yes	characteristic
123	C₈	C₂×#13083562	1	1	yes	characteristic
124	C₂²	—	16	1	no	—
125	C₂²	—	16	2	no	—
126	C₂²	C₂×#15667953	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	16	1	no	—
129	C₄	—	1424	2	no	—
130	C₄	#19151944	1	1	yes	characteristic
131	C₄	C₂×#15667956	1	1	yes	characteristic
132	C₂	—	32	1	no	—
133	C₂	#26022475	1	1	yes	characteristic
134	C₂	#26022559	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26022531

C₂

yes

maximal, characteristic, complemented

#26018433

C₂

yes

maximal, complemented

#26018430

C₂

yes

maximal

C₄×#15667918

C₂

yes

maximal, characteristic, complemented

C₈₉×#2249

C₂

yes

maximal, characteristic

#19152000

—

C₂×#15667918

C₂²

yes

—

#19151426

—

#19151424

C₂²

yes

—

C₂×Q₃₂×C₈₉

C₂²

yes

characteristic

C₂×SD₃₂×C₈₉

—

C₂×D₁₆×C₈₉

C₂²

yes

characteristic

#495×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

—

—

—

—

C₂×Q₁₆×C₈₉

—

C₂×SD₁₆×C₈₉

—

C₂×D₈×C₈₉

—

#124×C₈₉

—

Q₃₂×C₈₉

—

SD₃₂×C₈₉

—

D₁₆×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄⋊Dic₈₉

—

#13083553

—

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

SD₁₆×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

—

C₁₆×C₈₉

#41

yes

—

C₂³×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₁₆

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×Dic₈₉

—

C₈×C₈₉

SD₃₂

yes

—

C₈×C₈₉

#124

yes

characteristic

C₈×C₈₉

C₂×SD₁₆

yes

characteristic

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₁₆

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#486

yes

characteristic

C₄×C₈₉

C₂×SD₃₂

yes

characteristic

Dic₈₉

—

#13721

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#2240

yes

characteristic

C₂×C₈₉

#2262

yes

—

#2253

—

#2249

D₈₉

yes

characteristic

#1416

—

#1415

—

C₄×C₃₂

—

C₈₉

#13721

yes

characteristic, complemented, Sylow

C₂×Q₃₂

C₂×D₈₉

yes

characteristic

C₂×SD₃₂

—

C₂×D₁₆

C₂×D₈₉

yes

characteristic

#499

—

178

—

#495

—

C₂×C₃₂

—

#367

—

178

—

#366

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#125

—

356

—

#124

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

#107

—

178

—

#106

—

356

—

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₃₂

—

178

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

100

Q₁₆

—

101

SD₁₆

—

102

D₈

—

103

D₈

—

104

C₂×C₈

#13083559

yes

characteristic

105

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

106

C₄⋊C₄

—

356

—

107

C₄⋊C₄

—

712

—

108

C₂²⋊C₄

—

109

C₄²

#13083559

yes

characteristic

110

C₁₆

#13083562

yes

—

111

C₁₆

#13083573

yes

—

112

C₂³

—

113

Q₈

—

114

Q₈

—

115

D₄

—

116

D₄

—

117

C₂×C₄

—

118

C₂×C₄

—

712

—

119

C₂×C₄

#15667953

yes

—

120

C₂×C₄

C₂×#13083559

yes

characteristic

121

C₈

#15667956

yes

—

122

C₈

#15667999

yes

characteristic

123

C₈

C₂×#13083562

yes

characteristic

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×#15667953

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

1424

—

130

C₄

#19151944

yes

characteristic

131

C₄

C₂×#15667956

yes

characteristic

132

C₂

—

133

C₂

#26022475

yes

characteristic

134

C₂

#26022559

yes

—

	subgroup	G/H
center	C₂²	C₂×#15667953
commutator, cosocle	C₂×C₁₆×C₈₉	C₂³
Frattini	C₂×C₁₆	C₂²×D₈₉
Fitting	C₈₉×#2249	C₂
socle	C₂²×C₈₉	C₂×D₁₆
prime radical	C₂×D₁₆×C₈₉	C₂²
hypercenter	#2249	D₈₉
hypocenter	C₈₉	#13721
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

subgroup

G/H

center

C₂²

C₂×#15667953

commutator, cosocle

C₂×C₁₆×C₈₉

C₂³

Frattini

C₂×C₁₆

C₂²×D₈₉

Fitting

C₈₉×#2249

C₂

socle

C₂²×C₈₉

C₂×D₁₆

prime radical

C₂×D₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

N	H ≅ G/N	type
1. #26022531	C₂	semidirect
2. #26018433	C₂	semidirect
4. C₄×#15667918	C₂	semidirect
73. C₈₉	#13721	semidirect

H ≅ G/N

type

1. #26022531

C₂

semidirect

2. #26018433

C₂

semidirect

4. C₄×#15667918

C₂

semidirect

73. C₈₉

#13721

semidirect

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

subgroup	index
#26022531	2
#26018433	2
#26018430	2
C₄×#15667918	2
C₈₉×#2249	2
#13721	89

subgroup

index

C₈₉×#2249

Subgroups — #36475404

Conjugacy classes of subgroups

Complements

Maximal subgroups