Group #36441647 — subgroups

Subgroups — #36441647

Order 22784.

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

normal subgroups only

This group has 250 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	#26018576	C₂	1	2	yes	maximal
2	C₈₉×#1985	C₂	1	1	yes	maximal, characteristic
3	#19151651	—	2	2	no	—
4	#19151324	—	2	2	no	—
5	#19151324	C₄	1	4	yes	—
6	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₈₉	C₄	1	1	yes	characteristic
8	C₂×#97×C₈₉	C₄	1	1	yes	characteristic
9	#336×C₈₉	—	2	2	no	—
10	C₄⋊#10623494	—	4	2	no	—
11	C₂²⋊#10623494	—	2	4	no	—
12	C₄×#10623494	—	4	2	no	—
13	C₂²×Q₈×C₈₉	Q₈	1	1	yes	characteristic
14	C₂²×C₈×C₈₉	—	2	1	no	—
15	C₂²×C₈×C₈₉	—	2	1	no	—
16	C₄×Q₈×C₈₉	—	4	1	no	—
17	C₄×Q₈×C₈₉	—	4	1	no	—
18	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
19	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₈₉	D₄	1	2	yes	—
22	C₄⋊C₈×C₈₉	—	4	1	no	—
23	#97×C₈₉	—	4	1	no	—
24	C₂×#10623494	—	4	4	no	—
25	C₂×Q₈×C₈₉	—	2	4	no	—
26	C₂×Q₈×C₈₉	—	4	1	no	—
27	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
28	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₈₉	—	2	2	no	—
33	C₂×C₈×C₈₉	—	4	1	no	—
34	C₂×C₈×C₈₉	—	4	1	no	—
35	C₂×C₈×C₈₉	—	4	2	no	—
36	C₂×C₈×C₈₉	—	4	1	no	—
37	C₄⋊C₄×C₈₉	—	4	2	no	—
38	C₄⋊C₄×C₈₉	—	4	1	no	—
39	C₄²×C₈₉	—	2	1	no	—
40	C₄²×C₈₉	—	2	1	no	—
41	C₄²×C₈₉	—	2	2	no	—
42	C₄²×C₈₉	—	2	2	no	—
43	C₂³×C₈₉	#95	1	1	yes	characteristic
44	Q₈×C₈₉	—	4	4	no	—
45	C₂×C₄×C₈₉	—	2	2	no	—
46	C₂×C₄×C₈₉	—	2	2	no	—
47	C₂×C₄×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈₉	—	2	1	no	—
49	C₂×C₄×C₈₉	—	2	2	no	—
50	C₂×C₄×C₈₉	—	2	1	no	—
51	C₂×C₄×C₈₉	—	2	2	no	—
52	C₂×C₄×C₈₉	—	2	1	no	—
53	C₂×C₄×C₈₉	—	4	1	no	—
54	C₂×C₄×C₈₉	—	4	2	no	—
55	C₂×C₄×C₈₉	#99	1	1	yes	characteristic
56	C₂×C₄×C₈₉	#99	1	1	yes	characteristic
57	C₂×C₄×C₈₉	#108	1	4	yes	—
58	C₈×C₈₉	—	4	2	no	—
59	C₈×C₈₉	—	8	1	no	—
60	#10623494	—	8	4	no	—
61	C₂²×C₈₉	—	2	1	no	—
62	C₂²×C₈₉	—	2	1	no	—
63	C₂²×C₈₉	#341	1	2	yes	—
64	C₂²×C₈₉	#342	1	1	yes	characteristic
65	C₄×C₈₉	—	2	4	no	—
66	C₄×C₈₉	—	2	1	no	—
67	C₄×C₈₉	—	4	1	no	—
68	C₄×C₈₉	—	4	2	no	—
69	C₄×C₈₉	—	4	1	no	—
70	C₄×C₈₉	#355	1	1	yes	characteristic
71	C₄×C₈₉	#356	1	1	yes	characteristic
72	#7286	—	89	1	no	maximal, Sylow
73	C₂×C₈₉	—	2	2	no	—
74	C₂×C₈₉	#1298	1	1	yes	characteristic
75	C₂×C₈₉	#1391	1	1	yes	characteristic
76	C₂×C₈₉	#1394	1	1	yes	characteristic
77	#1985	D₈₉	1	1	yes	characteristic
78	#1461	—	89	2	no	—
79	C₈₉	#7286	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
81	#431	—	178	2	no	—
82	C₂×C₄⋊C₈	Dic₈₉	1	1	yes	characteristic
83	C₂×#97	Dic₈₉	1	1	yes	characteristic
84	#336	—	2	2	no	—
85	#324	—	89	4	no	—
86	#324	—	178	2	no	—
87	C₂²×Q₈	Dic₁₇₈	1	1	yes	characteristic
88	C₂²×C₈	—	2	1	no	—
89	C₂²×C₈	—	2	1	no	—
90	C₄×Q₈	—	4	1	no	—
91	C₄×Q₈	—	4	1	no	—
92	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
93	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
94	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
95	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
96	C₄⋊C₈	—	4	1	no	—
97	C₄⋊C₈	—	356	2	no	—
98	C₂²⋊C₈	—	178	4	no	—
99	#97	—	4	1	no	—
100	C₄×C₈	—	356	2	no	—
101	C₂×Q₈	—	2	4	no	—
102	C₂×Q₈	—	4	1	no	—
103	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
104	C₂²×C₄	#13083551	1	2	yes	—
105	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
106	C₂²×C₄	#13083553	1	2	yes	—
107	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	4	1	no	—
110	C₂×C₈	—	4	1	no	—
111	C₂×C₈	—	4	2	no	—
112	C₂×C₈	—	4	1	no	—
113	C₂×C₈	—	356	4	no	—
114	C₄⋊C₄	—	4	2	no	—
115	C₄⋊C₄	—	4	1	no	—
116	C₄²	—	2	1	no	—
117	C₄²	—	2	2	no	—
118	C₄²	—	2	2	no	—
119	C₄²	—	2	1	no	—
120	C₂³	#15667919	1	1	yes	characteristic
121	Q₈	—	4	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	#15667927	1	1	yes	characteristic
133	C₂×C₄	#15667927	1	1	yes	characteristic
134	C₂×C₄	#15667947	1	4	yes	—
135	C₈	—	4	2	no	—
136	C₈	—	8	1	no	—
137	C₈	—	712	4	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	#19151362	1	2	yes	—
141	C₂²	#19151365	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	4	no	—
144	C₄	—	4	2	no	—
145	C₄	—	4	1	no	—
146	C₄	—	4	1	no	—
147	C₄	#19151395	1	1	yes	characteristic
148	C₄	#19151397	1	1	yes	characteristic
149	C₂	—	2	2	no	—
150	C₂	#26018139	1	1	yes	characteristic
151	C₂	#26018373	1	1	yes	characteristic
152	C₂	#26018379	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26018576

C₂

yes

maximal

C₈₉×#1985

C₂

yes

maximal, characteristic

#19151651

—

#19151324

—

#19151324

C₄

yes

—

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₉

C₄

yes

characteristic

C₂×#97×C₈₉

C₄

yes

characteristic

#336×C₈₉

—

C₄⋊#10623494

—

C₂²⋊#10623494

—

C₄×#10623494

—

C₂²×Q₈×C₈₉

Q₈

yes

characteristic

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

—

C₄⋊C₈×C₈₉

—

#97×C₈₉

—

C₂×#10623494

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

C₄²

yes

characteristic

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

#95

yes

characteristic

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

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#341

yes

—

C₂²×C₈₉

#342

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

D₈₉

yes

characteristic

#1461

—

C₈₉

#7286

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

#431

—

178

—

C₂×C₄⋊C₈

Dic₈₉

yes

characteristic

C₂×#97

Dic₈₉

yes

—

—

—

178

—

C₂²×Q₈

Dic₁₇₈

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

C₄×D₈₉

yes

—

C₂×C₄⋊C₄

D₃₅₆

yes

characteristic

C₂×C₄²

C₂×Dic₈₉

yes

characteristic

C₂×C₄²

C₂²⋊D₈₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

356

—

C₂²⋊C₈

—

178

—

#97

—

100

C₄×C₈

—

356

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

C₄×Dic₈₉

yes

characteristic

104

C₂²×C₄

#13083551

yes

—

105

C₂²×C₄

C₂²⋊Dic₈₉

yes

characteristic

106

C₂²×C₄

#13083553

yes

—

107

C₂²×C₄

C₄⋊Dic₈₉

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

356

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₂³

#15667919

yes

characteristic

121

Q₈

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#15667927

yes

characteristic

133

C₂×C₄

#15667927

yes

characteristic

134

C₂×C₄

#15667947

yes

—

135

C₈

—

136

C₈

—

137

C₈

—

712

—

138

C₂²

—

139

C₂²

—

140

C₂²

#19151362

yes

—

141

C₂²

#19151365

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#19151395

yes

characteristic

148

C₄

#19151397

yes

characteristic

149

C₂

—

150

C₂

#26018139

yes

characteristic

151

C₂

#26018373

yes

characteristic

152

C₂

#26018379

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#15667927
commutator	C₂²×C₄×C₈₉	C₄²
Frattini	C₂×C₄×Q₈	C₂×D₈₉
Fitting	C₈₉×#1985	C₂
socle	C₂²×C₈₉	#342
prime radical	C₂³×C₈₉	#95
cosocle	C₂×C₄×Q₈×C₈₉	C₂²
hypercenter	#1985	D₈₉
hypocenter	C₈₉	#7286
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂³×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1985

subgroup

G/H

center

C₂×C₄

#15667927

commutator

C₂²×C₄×C₈₉

C₄²

Frattini

C₂×C₄×Q₈

C₂×D₈₉

Fitting

C₈₉×#1985

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄×Q₈×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂³×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1985

N	H ≅ G/N	type
79. C₈₉	#7286	semidirect

H ≅ G/N

type

79. C₈₉

#7286

semidirect

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

subgroup	index
#26018576	2
C₈₉×#1985	2
#7286	89

subgroup

index

#26018576

C₈₉×#1985

#7286

Subgroups — #36441647

Conjugacy classes of subgroups

Complements

Maximal subgroups