Group #36466431 — subgroups

Subgroups — #36466431

Order 22784.

206 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 83 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	#26019149	C₂	1	2	yes	maximal
2	#26018326	C₂	1	1	yes	maximal, characteristic
3	#26018216	C₂	1	2	yes	maximal
4	#26018168	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
6	#19151729	—	2	2	no	—
7	C₄×#13083549	C₂²	1	1	yes	characteristic
8	#19151351	C₂²	1	2	yes	—
9	Q₈⋊#10623494	—	2	2	no	—
10	C₈×#10623494	C₂²	1	1	yes	characteristic
11	C₂×Q₃₂×C₈₉	C₄	1	1	yes	characteristic
12	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
13	#366×C₈₉	C₄	1	1	yes	characteristic
14	#358×C₈₉	C₄	1	2	yes	—
15	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#13083549	—	2	1	no	—
17	C₄⋊#10623494	—	2	2	no	—
18	C₄⋊#10623494	—	4	2	no	—
19	#15667923	—	4	2	no	—
20	C₄×#10623494	D₄	1	1	yes	characteristic
21	C₄×#10623494	D₄	1	1	yes	characteristic
22	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
23	C₄×Q₈×C₈₉	—	2	2	no	—
24	Q₃₂×C₈₉	—	2	2	no	—
25	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
27	#107×C₈₉	C₂×C₄	1	2	yes	—
28	#103×C₈₉	—	2	2	no	—
29	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
30	C₂×#10623494	—	2	1	no	—
31	C₂×#10623494	—	4	2	no	—
32	C₂×#10623494	D₈	1	2	yes	—
33	#13083549	—	2	2	no	—
34	C₂×Q₈×C₈₉	—	2	2	no	—
35	Q₁₆×C₈₉	—	2	2	no	—
36	Q₁₆×C₈₉	—	2	2	no	—
37	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
39	C₄⋊C₄×C₈₉	—	2	2	no	—
40	C₄⋊C₄×C₈₉	—	4	2	no	—
41	C₄²×C₈₉	—	4	2	no	—
42	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
43	C₁₆×C₈₉	—	2	1	no	—
44	C₁₆×C₈₉	M₁₆	1	2	yes	—
45	Q₈×C₈₉	—	4	2	no	—
46	Q₈×C₈₉	—	4	2	no	—
47	C₂×C₄×C₈₉	—	4	2	no	—
48	C₂×C₄×C₈₉	—	4	2	no	—
49	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
50	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
51	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
52	C₈×C₈₉	—	2	1	no	—
53	C₈×C₈₉	C₂×M₁₆	1	1	yes	characteristic
54	C₈×C₈₉	#131	1	1	yes	characteristic
55	#10623494	—	2	2	no	—
56	#10623494	—	4	1	no	—
57	#10623494	—	8	2	no	—
58	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
59	C₄×C₈₉	—	2	1	no	—
60	C₄×C₈₉	—	8	2	no	—
61	C₄×C₈₉	—	8	2	no	—
62	C₄×C₈₉	#436	1	1	yes	characteristic
63	C₄×C₈₉	#443	1	1	yes	characteristic
64	C₄×C₈₉	#510	1	2	yes	—
65	#12085	—	89	1	no	maximal, Sylow
66	C₂×C₈₉	#1589	1	1	yes	characteristic
67	C₂×C₈₉	#2176	1	1	yes	characteristic
68	C₂×C₈₉	#2179	1	1	yes	characteristic
69	C₄×Q₃₂	D₈₉	1	1	yes	characteristic
70	#1591	—	89	2	no	—
71	#1372	—	89	1	no	—
72	#1332	—	89	2	no	—
73	#1311	—	89	1	no	—
74	C₈₉	#12085	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₃₂	Dic₈₉	1	1	yes	characteristic
76	#446	—	178	2	no	—
77	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
78	#366	Dic₈₉	1	1	yes	characteristic
79	#358	Dic₈₉	1	2	yes	—
80	C₄×C₁₆	—	89	1	no	—
81	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
82	#335	—	89	2	no	—
83	Q₈⋊C₈	—	178	2	no	—
84	C₈²	—	89	1	no	—
85	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
86	C₄×Q₈	—	2	2	no	—
87	Q₃₂	—	2	2	no	—
88	C₂×C₁₆	—	178	1	no	—
89	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
90	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
91	#107	C₂×Dic₈₉	1	2	yes	—
92	C₄⋊C₈	—	356	2	no	—
93	C₄⋊C₈	—	178	2	no	—
94	#103	—	2	2	no	—
95	#97	—	356	2	no	—
96	C₄×C₈	—	89	1	no	—
97	C₄×C₈	—	89	1	no	—
98	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
99	C₂×Q₈	—	2	2	no	—
100	Q₁₆	—	2	2	no	—
101	Q₁₆	—	2	2	no	—
102	C₂×C₈	—	89	2	no	—
103	C₂×C₈	—	356	2	no	—
104	C₂×C₈	—	178	1	no	—
105	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
106	C₂×C₈	#13083573	1	1	yes	characteristic
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	4	2	no	—
109	C₄²	—	4	2	no	—
110	C₄²	D₄×D₈₉	1	1	yes	characteristic
111	C₁₆	—	2	1	no	—
112	C₁₆	—	178	2	no	—
113	C₁₆	#13083558	1	2	yes	—
114	Q₈	—	4	2	no	—
115	Q₈	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
119	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
120	C₂×C₄	#15668031	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	356	1	no	—
123	C₈	—	178	2	no	—
124	C₈	—	712	2	no	—
125	C₈	C₂×#13083558	1	1	yes	characteristic
126	C₈	#15668019	1	1	yes	characteristic
127	C₂²	D₈×Dic₈₉	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	8	2	no	—
130	C₄	—	8	2	no	—
131	C₄	#19151676	1	1	yes	characteristic
132	C₄	#19151715	1	1	yes	characteristic
133	C₄	#19152040	1	2	yes	—
134	C₂	#26019137	1	1	yes	characteristic
135	C₂	#26022123	1	1	yes	characteristic
136	C₂	#26022138	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26019149

C₂

yes

maximal

#26018326

C₂

yes

maximal, characteristic

#26018216

C₂

yes

maximal

#26018168

C₂

yes

maximal, characteristic

C₄×Q₃₂×C₈₉

C₂

yes

maximal, characteristic

#19151729

—

C₄×#13083549

C₂²

yes

characteristic

#19151351

C₂²

yes

—

Q₈⋊#10623494

—

C₈×#10623494

C₂²

yes

characteristic

C₂×Q₃₂×C₈₉

C₄

yes

characteristic

C₄×Q₁₆×C₈₉

C₂²

yes

—

#366×C₈₉

C₄

yes

characteristic

#358×C₈₉

C₄

yes

—

C₄×C₁₆×C₈₉

C₂²

yes

—

—

—

—

D₄

yes

characteristic

C₄×#10623494

D₄

yes

characteristic

C₂×Q₁₆×C₈₉

C₂×C₄

yes

—

C₄×Q₈×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

#107×C₈₉

C₂×C₄

yes

—

#103×C₈₉

—

C₄×C₈×C₈₉

C₂³

yes

—

—

D₈

yes

—

#13083549

—

C₂×Q₈×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

M₁₆

yes

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

C₂×M₁₆

yes

C₈×C₈₉

yes

—

—

—

C₂²×C₈₉

C₄×D₈

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

C₄×Q₃₂

D₈₉

yes

—

—

—

—

C₈₉

#12085

yes

characteristic, complemented, Sylow

C₂×Q₃₂

Dic₈₉

yes

characteristic

#446

—

178

—

C₄×Q₁₆

C₂×D₈₉

yes

—

#366

Dic₈₉

yes

characteristic

#358

Dic₈₉

yes

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

#335

—

Q₈⋊C₈

—

178

—

C₈²

—

C₂×Q₁₆

C₂×Dic₈₉

yes

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

178

—

C₂×C₁₆

C₂×Dic₈₉

yes

characteristic

C₂×C₁₆

C₂×Dic₈₉

yes

characteristic

#107

C₂×Dic₈₉

yes

—

C₄⋊C₈

—

356

—

C₄⋊C₈

—

178

—

#103

—

#97

—

356

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂²×D₈₉

yes

characteristic

C₂×Q₈

—

100

Q₁₆

—

101

Q₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

356

—

104

C₂×C₈

—

178

—

105

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

106

C₂×C₈

#13083573

yes

characteristic

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

D₄×D₈₉

yes

characteristic

111

C₁₆

—

112

C₁₆

—

178

—

113

C₁₆

#13083558

yes

—

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

D₄×Dic₈₉

yes

characteristic

119

C₂×C₄

D₈×D₈₉

yes

characteristic

120

C₂×C₄

#15668031

yes

characteristic

121

C₈

—

122

C₈

—

356

—

123

C₈

—

178

—

124

C₈

—

712

—

125

C₈

C₂×#13083558

yes

characteristic

126

C₈

#15668019

yes

characteristic

127

C₂²

D₈×Dic₈₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

#19151676

yes

characteristic

132

C₄

#19151715

yes

characteristic

133

C₄

#19152040

yes

—

134

C₂

#26019137

yes

characteristic

135

C₂

#26022123

yes

characteristic

136

C₂

#26022138

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₈₉
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₈₉
Fitting	C₄×Q₃₂×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₄×D₈
cosocle	C₄×C₈×C₈₉	C₂³
hypercenter	C₄×Q₃₂	D₈₉
hypocenter	C₈₉	#12085
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

subgroup

G/H

center

C₂×C₄

D₈×D₈₉

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₈₉

Fitting

C₄×Q₃₂×C₈₉

C₂

socle, prime radical

C₂²×C₈₉

C₄×D₈

cosocle

C₄×C₈×C₈₉

C₂³

hypercenter

C₄×Q₃₂

D₈₉

hypocenter

C₈₉

#12085

LCS

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

N	H ≅ G/N	type
74. C₈₉	#12085	semidirect

H ≅ G/N

type

74. C₈₉

#12085

semidirect

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

subgroup	index
#26019149	2
#26018326	2
#26018216	2
#26018168	2
C₄×Q₃₂×C₈₉	2
#12085	89

subgroup

index

C₄×Q₃₂×C₈₉

Subgroups — #36466431

Conjugacy classes of subgroups

Complements

Maximal subgroups