Group #36475396 — subgroups

Subgroups — #36475396

Order 22784.

202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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	#26022527	C₂	1	1	yes	maximal, characteristic, complemented
2	#26018430	C₂	1	4	yes	maximal, complemented
3	C₄×#15667918	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2246	C₂	1	1	yes	maximal, characteristic
5	#19152003	—	2	1	no	—
6	C₂×#15667918	C₂²	1	2	yes	—
7	#19151424	—	2	1	no	—
8	#19151424	C₂²	1	2	yes	—
9	C₂×D₁₆×C₈₉	—	2	1	no	—
10	C₂×D₁₆×C₈₉	C₂²	1	2	yes	—
11	#493×C₈₉	—	2	1	no	—
12	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	#15668012	—	4	1	no	—
14	#15667946	—	2	2	no	—
15	#15667946	—	4	1	no	—
16	#15667918	—	2	2	no	—
17	C₂×D₈×C₈₉	—	2	2	no	—
18	C₂×D₈×C₈₉	—	4	1	no	—
19	#127×C₈₉	—	4	1	no	—
20	D₁₆×C₈₉	—	2	4	no	—
21	D₁₆×C₈₉	—	4	2	no	—
22	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
24	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
25	C₂×Dic₁₇₈	—	8	1	no	—
26	C₄⋊Dic₈₉	—	4	2	no	—
27	C₄⋊Dic₈₉	—	8	1	no	—
28	C₂×D₄×C₈₉	—	4	2	no	—
29	C₂×D₄×C₈₉	—	8	1	no	—
30	C₂×D₄×C₈₉	—	8	1	no	—
31	D₈×C₈₉	—	4	2	no	—
32	D₈×C₈₉	—	4	2	no	—
33	D₈×C₈₉	—	8	2	no	—
34	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
35	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
36	C₄²×C₈₉	D₈	1	1	yes	characteristic
37	C₁₆×C₈₉	SD₁₆	1	2	yes	—
38	C₁₆×C₈₉	#41	1	2	yes	—
39	C₂³×C₈₉	—	8	2	no	—
40	D₄×C₈₉	—	8	2	no	—
41	D₄×C₈₉	—	8	2	no	—
42	D₄×C₈₉	—	16	2	no	—
43	D₄×C₈₉	—	16	2	no	—
44	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
45	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
46	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
47	C₂×Dic₈₉	—	8	2	no	—
48	Dic₁₇₈	—	16	2	no	—
49	C₈×C₈₉	SD₃₂	1	2	yes	—
50	C₈×C₈₉	#124	1	1	yes	characteristic
51	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
52	C₂²×C₈₉	—	16	2	no	—
53	C₂²×C₈₉	—	16	2	no	—
54	C₂²×C₈₉	—	16	2	no	—
55	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
56	C₄×C₈₉	D₃₂	1	2	yes	—
57	C₄×C₈₉	SD₆₄	1	2	yes	—
58	C₄×C₈₉	#486	1	1	yes	characteristic
59	C₄×C₈₉	C₂×SD₃₂	1	1	yes	characteristic
60	Dic₈₉	—	16	2	no	—
61	#13719	—	89	1	no	maximal, Sylow
62	C₂×C₈₉	—	32	2	no	—
63	C₂×C₈₉	#2240	1	1	yes	characteristic
64	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
65	C₂×C₈₉	C₂×SD₆₄	1	1	yes	characteristic
66	#2252	—	89	1	no	—
67	#2246	D₈₉	1	1	yes	characteristic
68	#1415	—	89	4	no	—
69	C₄×C₃₂	—	89	1	no	—
70	C₈₉	#13719	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₁₆	—	2	1	no	—
72	C₂×D₁₆	C₂×D₈₉	1	2	yes	—
73	#500	—	178	1	no	—
74	#493	—	2	1	no	—
75	C₂×C₃₂	—	89	2	no	—
76	#366	—	89	2	no	—
77	#366	—	178	1	no	—
78	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
79	C₂×D₈	—	2	2	no	—
80	C₂×D₈	—	4	1	no	—
81	C₄⋊Q₈	—	356	1	no	—
82	#127	—	4	1	no	—
83	D₁₆	—	2	4	no	—
84	D₁₆	—	4	2	no	—
85	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
86	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
87	#107	—	356	1	no	—
88	#107	—	178	2	no	—
89	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
90	C₃₂	—	178	2	no	—
91	C₂×Q₈	—	712	1	no	—
92	C₂×D₄	—	4	2	no	—
93	C₂×D₄	—	8	1	no	—
94	C₂×D₄	—	8	1	no	—
95	D₈	—	4	2	no	—
96	D₈	—	4	2	no	—
97	D₈	—	8	2	no	—
98	C₂×C₈	#13083559	1	1	yes	characteristic
99	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
100	C₄⋊C₄	—	356	2	no	—
101	C₄⋊C₄	—	712	1	no	—
102	C₄²	#13083559	1	1	yes	characteristic
103	C₁₆	#13083562	1	2	yes	—
104	C₁₆	#13083573	1	2	yes	—
105	C₂³	—	8	2	no	—
106	Q₈	—	1424	2	no	—
107	D₄	—	8	2	no	—
108	D₄	—	8	2	no	—
109	D₄	—	16	2	no	—
110	D₄	—	16	2	no	—
111	C₂×C₄	—	712	2	no	—
112	C₂×C₄	#15667953	1	1	yes	characteristic
113	C₂×C₄	#15667953	1	1	yes	characteristic
114	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
115	C₈	#15667956	1	2	yes	—
116	C₈	#15667999	1	1	yes	characteristic
117	C₈	C₂×#13083562	1	1	yes	characteristic
118	C₂²	—	16	2	no	—
119	C₂²	—	16	2	no	—
120	C₂²	—	16	2	no	—
121	C₂²	C₂×#15667953	1	1	yes	characteristic
122	C₄	—	1424	2	no	—
123	C₄	#19151433	1	2	yes	—
124	C₄	#19151436	1	2	yes	—
125	C₄	#19151944	1	1	yes	characteristic
126	C₄	C₂×#15667956	1	1	yes	characteristic
127	C₂	—	32	2	no	—
128	C₂	#26022475	1	1	yes	characteristic
129	C₂	C₂×#19151433	1	1	yes	characteristic
130	C₂	C₂×#19151436	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022527

C₂

yes

maximal, characteristic, complemented

#26018430

C₂

yes

maximal, complemented

C₄×#15667918

C₂

yes

maximal, characteristic, complemented

C₈₉×#2246

C₂

yes

maximal, characteristic

#19152003

—

C₂×#15667918

C₂²

yes

—

#19151424

—

#19151424

C₂²

yes

—

C₂×D₁₆×C₈₉

—

C₂×D₁₆×C₈₉

C₂²

yes

—

#493×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

—

—

—

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

#127×C₈₉

—

D₁₆×C₈₉

—

D₁₆×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

—

C₁₆×C₈₉

#41

yes

—

C₂³×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×Dic₈₉

—

Dic₁₇₈

—

C₈×C₈₉

SD₃₂

yes

—

C₈×C₈₉

#124

yes

characteristic

C₈×C₈₉

C₂×SD₁₆

yes

characteristic

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₁₆

yes

characteristic

C₄×C₈₉

D₃₂

yes

—

C₄×C₈₉

SD₆₄

yes

—

C₄×C₈₉

#486

yes

characteristic

C₄×C₈₉

C₂×SD₃₂

yes

characteristic

Dic₈₉

—

#13719

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#2240

yes

characteristic

C₂×C₈₉

C₂×D₃₂

yes

characteristic

C₂×C₈₉

C₂×SD₆₄

yes

characteristic

#2252

—

#2246

D₈₉

yes

characteristic

#1415

—

C₄×C₃₂

—

C₈₉

#13719

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₂×D₁₆

C₂×D₈₉

yes

—

#500

—

178

—

#493

—

C₂×C₃₂

—

#366

—

#366

—

178

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

356

—

#127

—

D₁₆

—

D₁₆

—

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

#107

—

356

—

#107

—

178

—

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₃₂

—

178

—

C₂×Q₈

—

712

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

#13083559

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

100

C₄⋊C₄

—

356

—

101

C₄⋊C₄

—

712

—

102

C₄²

#13083559

yes

characteristic

103

C₁₆

#13083562

yes

—

104

C₁₆

#13083573

yes

—

105

C₂³

—

106

Q₈

—

1424

—

107

D₄

—

108

D₄

—

109

D₄

—

110

D₄

—

111

C₂×C₄

—

712

—

112

C₂×C₄

#15667953

yes

characteristic

113

C₂×C₄

#15667953

yes

characteristic

114

C₂×C₄

C₂×#13083559

yes

characteristic

115

C₈

#15667956

yes

—

116

C₈

#15667999

yes

characteristic

117

C₈

C₂×#13083562

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×#15667953

yes

characteristic

122

C₄

—

1424

—

123

C₄

#19151433

yes

—

124

C₄

#19151436

yes

—

125

C₄

#19151944

yes

characteristic

126

C₄

C₂×#15667956

yes

characteristic

127

C₂

—

128

C₂

#26022475

yes

characteristic

129

C₂

C₂×#19151433

yes

characteristic

130

C₂

C₂×#19151436

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#15667953
commutator, cosocle	C₂×C₁₆×C₈₉	C₂³
Frattini	C₂×C₁₆	C₂²×D₈₉
Fitting, prime radical	C₈₉×#2246	C₂
socle	C₂²×C₈₉	C₂×D₁₆
hypercenter	#2246	D₈₉
hypocenter	C₈₉	#13719
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

subgroup

G/H

center

C₂²

C₂×#15667953

commutator, cosocle

C₂×C₁₆×C₈₉

C₂³

Frattini

C₂×C₁₆

C₂²×D₈₉

Fitting, prime radical

C₈₉×#2246

C₂

socle

C₂²×C₈₉

C₂×D₁₆

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

N	H ≅ G/N	type
1. #26022527	C₂	semidirect
2. #26018430	C₂	semidirect
3. C₄×#15667918	C₂	semidirect
70. C₈₉	#13719	semidirect

H ≅ G/N

type

1. #26022527

C₂

semidirect

2. #26018430

C₂

semidirect

3. C₄×#15667918

C₂

semidirect

70. C₈₉

#13719

semidirect

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

subgroup	index
#26022527	2
#26018430	2
C₄×#15667918	2
C₈₉×#2246	2
#13719	89

subgroup

index

C₈₉×#2246

Subgroups — #36475396

Conjugacy classes of subgroups

Complements

Maximal subgroups