Group #36441809 — subgroups

Subgroups — #36441809

Order 22784.

204 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 47 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	#26018196	C₂	1	2	yes	maximal
2	C₈₉×#1960	C₂	1	1	yes	maximal, characteristic
3	#19151324	—	2	2	no	—
4	C₂×C₄⋊Q₈×C₈₉	C₄	1	1	yes	characteristic
5	C₂×#103×C₈₉	—	2	2	no	—
6	C₂×#97×C₈₉	C₄	1	1	yes	characteristic
7	#382×C₈₉	C₂²	1	1	yes	characteristic
8	C₂²⋊#10623494	—	4	2	no	—
9	C₂²×Q₈×C₈₉	—	2	1	no	—
10	C₂²×C₈×C₈₉	—	2	1	no	—
11	C₄⋊Q₈×C₈₉	—	2	1	no	—
12	C₄⋊Q₈×C₈₉	—	4	1	no	—
13	C₄⋊Q₈×C₈₉	C₈	1	2	yes	complemented
14	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
16	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
17	#103×C₈₉	—	4	4	no	—
18	#97×C₈₉	—	4	1	no	—
19	#95×C₈₉	—	4	1	no	—
20	C₂×#10623494	—	8	2	no	—
21	C₂×Q₈×C₈₉	—	2	2	no	—
22	C₂×Q₈×C₈₉	—	4	2	no	—
23	C₂×Q₈×C₈₉	—	4	2	no	—
24	C₂×Q₈×C₈₉	—	4	1	no	—
25	C₂²×C₄×C₈₉	—	2	1	no	—
26	C₂²×C₄×C₈₉	—	2	2	no	—
27	C₂²×C₄×C₈₉	—	4	1	no	—
28	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₈₉	—	2	2	no	—
30	C₂×C₈×C₈₉	—	4	1	no	—
31	C₂×C₈×C₈₉	—	4	1	no	—
32	C₄⋊C₄×C₈₉	—	4	2	no	—
33	C₄⋊C₄×C₈₉	—	4	2	no	—
34	C₄⋊C₄×C₈₉	—	4	2	no	—
35	C₄²×C₈₉	—	2	1	no	—
36	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₈₉	M₁₆	1	1	yes	characteristic
38	C₂³×C₈₉	#99	1	1	yes	characteristic
39	Q₈×C₈₉	—	4	4	no	—
40	Q₈×C₈₉	—	8	2	no	—
41	C₂×C₄×C₈₉	—	2	1	no	—
42	C₂×C₄×C₈₉	—	2	1	no	—
43	C₂×C₄×C₈₉	—	2	1	no	—
44	C₂×C₄×C₈₉	—	2	1	no	—
45	C₂×C₄×C₈₉	—	4	2	no	—
46	C₂×C₄×C₈₉	—	4	2	no	—
47	C₂×C₄×C₈₉	—	4	2	no	—
48	C₂×C₄×C₈₉	—	8	1	no	—
49	C₂×C₄×C₈₉	—	8	1	no	—
50	C₂×C₄×C₈₉	—	8	2	no	—
51	C₂×C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
52	C₂×C₄×C₈₉	#100	1	1	yes	characteristic
53	C₈×C₈₉	—	4	2	no	—
54	#10623494	—	16	2	no	—
55	C₂²×C₈₉	—	2	2	no	—
56	C₂²×C₈₉	#323	1	1	yes	characteristic
57	C₂²×C₈₉	#353	1	1	yes	characteristic
58	C₂²×C₈₉	#355	1	1	yes	characteristic
59	C₄×C₈₉	—	2	1	no	—
60	C₄×C₈₉	—	2	1	no	—
61	C₄×C₈₉	—	4	1	no	—
62	C₄×C₈₉	—	4	1	no	—
63	C₄×C₈₉	—	8	2	no	—
64	C₄×C₈₉	—	8	2	no	—
65	#7353	—	89	1	no	maximal, Sylow
66	C₂×C₈₉	—	2	1	no	—
67	C₂×C₈₉	—	2	1	no	—
68	C₂×C₈₉	#1318	1	1	yes	characteristic
69	C₂×C₈₉	#1407	1	2	yes	—
70	#1960	D₈₉	1	1	yes	characteristic
71	#1324	—	89	2	no	—
72	C₈₉	#7353	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₄⋊Q₈	Dic₈₉	1	1	yes	characteristic
74	C₂×#103	—	2	2	no	—
75	C₂×#97	Dic₈₉	1	1	yes	characteristic
76	#382	C₂×D₈₉	1	1	yes	characteristic
77	#324	—	178	2	no	—
78	C₂²×Q₈	—	2	1	no	—
79	C₂²×C₈	—	2	1	no	—
80	C₄⋊Q₈	—	2	1	no	—
81	C₄⋊Q₈	—	4	1	no	—
82	C₄⋊Q₈	#10623494	1	2	yes	complemented
83	C₂×C₄⋊C₄	—	4	1	no	—
84	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
85	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
86	#103	—	4	4	no	—
87	C₂²⋊C₈	—	356	2	no	—
88	#97	—	4	1	no	—
89	#95	—	4	1	no	—
90	C₂×Q₈	—	2	2	no	—
91	C₂×Q₈	—	4	2	no	—
92	C₂×Q₈	—	4	2	no	—
93	C₂×Q₈	—	4	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	4	1	no	—
97	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	4	1	no	—
100	C₂×C₈	—	4	1	no	—
101	C₂×C₈	—	712	2	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	2	no	—
105	C₄²	—	2	1	no	—
106	C₄²	C₂×#10623494	1	1	yes	characteristic
107	C₄²	#13083558	1	1	yes	characteristic
108	C₂³	#15667927	1	1	yes	characteristic
109	Q₈	—	4	4	no	—
110	Q₈	—	8	2	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	8	1	no	—
119	C₂×C₄	—	8	1	no	—
120	C₂×C₄	—	8	2	no	—
121	C₂×C₄	C₂²⋊#10623494	1	1	yes	characteristic
122	C₂×C₄	#15667929	1	1	yes	characteristic
123	C₈	—	4	2	no	—
124	C₈	—	1424	2	no	—
125	C₂²	—	2	2	no	—
126	C₂²	#19151322	1	1	yes	characteristic
127	C₂²	#19151391	1	1	yes	characteristic
128	C₂²	#19151395	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	2	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	8	2	no	—
134	C₄	—	8	2	no	—
135	C₂	—	2	1	no	—
136	C₂	—	2	1	no	—
137	C₂	#26018184	1	1	yes	characteristic
138	C₂	#26018412	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26018196

C₂

yes

maximal

C₈₉×#1960

C₂

yes

maximal, characteristic

#19151324

—

C₂×C₄⋊Q₈×C₈₉

C₄

yes

characteristic

C₂×#103×C₈₉

—

C₂×#97×C₈₉

C₄

yes

characteristic

#382×C₈₉

C₂²

yes

characteristic

C₂²⋊#10623494

—

C₂²×Q₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

C₈

yes

complemented

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

#103×C₈₉

—

#97×C₈₉

—

#95×C₈₉

—

C₂×#10623494

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×C₈

yes

characteristic

C₄²×C₈₉

M₁₆

yes

characteristic

C₂³×C₈₉

#99

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₉

#100

yes

characteristic

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

#7353

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1318

yes

characteristic

C₂×C₈₉

#1407

yes

—

#1960

D₈₉

yes

characteristic

#1324

—

C₈₉

#7353

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

Dic₈₉

yes

characteristic

C₂×#103

—

C₂×#97

Dic₈₉

yes

characteristic

#382

C₂×D₈₉

yes

characteristic

#324

—

178

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

#10623494

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

characteristic

#103

—

C₂²⋊C₈

—

356

—

#97

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₈₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

712

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄²

—

106

C₄²

C₂×#10623494

yes

characteristic

107

C₄²

#13083558

yes

characteristic

108

C₂³

#15667927

yes

characteristic

109

Q₈

—

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂²⋊#10623494

yes

characteristic

122

C₂×C₄

#15667929

yes

characteristic

123

C₈

—

124

C₈

—

1424

—

125

C₂²

—

126

C₂²

#19151322

yes

characteristic

127

C₂²

#19151391

yes

characteristic

128

C₂²

#19151395

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₂

—

136

C₂

—

137

C₂

#26018184

yes

characteristic

138

C₂

#26018412

yes

—

	subgroup	G/H
center	C₂²	#19151391
commutator	C₄²×C₈₉	C₂×C₈
Frattini	#382	C₂×D₈₉
Fitting	C₈₉×#1960	C₂
socle	C₂²×C₈₉	#353
prime radical	C₂³×C₈₉	#99
cosocle	#382×C₈₉	C₂²
hypercenter	#1960	D₈₉
hypocenter	C₈₉	#7353
LCS	G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1960

subgroup

G/H

center

C₂²

#19151391

commutator

C₄²×C₈₉

C₂×C₈

Frattini

#382

C₂×D₈₉

Fitting

C₈₉×#1960

C₂

C₂²×C₈₉

C₂³×C₈₉

#382×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1960

N	H ≅ G/N	type
13. C₄⋊Q₈×C₈₉	C₈	semidirect
72. C₈₉	#7353	semidirect
82. C₄⋊Q₈	#10623494	semidirect

H ≅ G/N

type

13. C₄⋊Q₈×C₈₉

C₈

semidirect

72. C₈₉

#7353

semidirect

82. C₄⋊Q₈

#10623494

semidirect

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

subgroup	index
#26018196	2
C₈₉×#1960	2
#7353	89

subgroup

index

#26018196

C₈₉×#1960

#7353

Subgroups — #36441809

Conjugacy classes of subgroups

Complements

Maximal subgroups