Group #36441751 — subgroups

Subgroups — #36441751

Order 22784.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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	#26018586	C₂	1	2	yes	maximal
2	C₈₉×#1818	C₂	1	1	yes	maximal, characteristic
3	#19151655	—	2	2	no	—
4	#19151324	C₄	1	4	yes	—
5	#19151322	—	2	2	no	—
6	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊C₈×C₈₉	C₄	1	2	yes	—
8	#336×C₈₉	—	2	2	no	—
9	C₄⋊#10623494	—	4	2	no	—
10	C₂²⋊#10623494	—	2	4	no	—
11	#15667923	—	4	2	no	—
12	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₈₉	—	2	2	no	—
14	#117×C₈₉	—	4	2	no	—
15	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
16	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₈₉	Q₈	1	1	yes	characteristic
18	C₂×C₄²×C₈₉	D₄	1	2	yes	—
19	C₂²⋊C₈×C₈₉	—	4	2	no	—
20	C₂×#10623494	—	4	4	no	—
21	C₂⁴×C₈₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₈₉	—	2	2	no	—
23	C₂²×C₄×C₈₉	—	4	2	no	—
24	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
27	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₈₉	—	4	4	no	—
29	C₂×C₈×C₈₉	—	4	2	no	—
30	C₄⋊C₄×C₈₉	—	4	2	no	—
31	C₂²⋊C₄×C₈₉	—	4	1	no	—
32	C₂²⋊C₄×C₈₉	—	4	1	no	—
33	C₄²×C₈₉	—	2	2	no	—
34	C₄²×C₈₉	—	2	2	no	—
35	C₂³×C₈₉	—	2	1	no	—
36	C₂³×C₈₉	—	2	2	no	—
37	C₂³×C₈₉	—	4	2	no	—
38	C₂³×C₈₉	#95	1	1	yes	characteristic
39	C₂×C₄×C₈₉	—	2	2	no	—
40	C₂×C₄×C₈₉	—	2	2	no	—
41	C₂×C₄×C₈₉	—	2	2	no	—
42	C₂×C₄×C₈₉	—	2	1	no	—
43	C₂×C₄×C₈₉	—	2	2	no	—
44	C₂×C₄×C₈₉	—	4	4	no	—
45	C₂×C₄×C₈₉	—	4	2	no	—
46	C₂×C₄×C₈₉	—	4	2	no	—
47	C₂×C₄×C₈₉	#99	1	2	yes	—
48	C₈×C₈₉	—	8	2	no	—
49	#10623494	—	8	4	no	—
50	C₂²×C₈₉	—	2	2	no	—
51	C₂²×C₈₉	—	4	1	no	—
52	C₂²×C₈₉	—	4	2	no	—
53	C₂²×C₈₉	—	8	2	no	—
54	C₂²×C₈₉	#342	1	1	yes	characteristic
55	C₂²×C₈₉	#344	1	2	yes	—
56	C₄×C₈₉	—	2	2	no	—
57	C₄×C₈₉	—	4	1	no	—
58	C₄×C₈₉	—	4	2	no	—
59	C₄×C₈₉	—	4	2	no	—
60	#7327	—	89	1	no	maximal, Sylow
61	C₂×C₈₉	—	2	2	no	—
62	C₂×C₈₉	—	8	1	no	—
63	C₂×C₈₉	#1306	1	1	yes	characteristic
64	C₂×C₈₉	#1395	1	2	yes	—
65	#1818	D₈₉	1	1	yes	characteristic
66	#1464	—	89	2	no	—
67	C₈₉	#7327	1	1	yes	characteristic, complemented, Sylow
68	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
69	#432	—	178	2	no	—
70	C₂×C₂²⋊C₈	Dic₈₉	1	2	yes	—
71	#336	—	2	2	no	—
72	#324	—	89	4	no	—
73	#323	—	178	2	no	—
74	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
75	C₂²×C₈	—	2	2	no	—
76	#117	—	4	2	no	—
77	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
78	C₂×C₂²⋊C₄	Dic₁₇₈	1	1	yes	characteristic
79	C₂×C₂²⋊C₄	D₃₅₆	1	1	yes	characteristic
80	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
81	C₄⋊C₈	—	356	2	no	—
82	C₂²⋊C₈	—	4	2	no	—
83	C₂²⋊C₈	—	178	4	no	—
84	#97	—	356	2	no	—
85	C₂⁴	C₄⋊Dic₈₉	1	1	yes	characteristic
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	—	4	2	no	—
88	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
89	C₂²×C₄	#13083551	1	2	yes	—
90	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
91	C₂²×C₄	#13083553	1	2	yes	—
92	C₂×C₈	—	4	4	no	—
93	C₂×C₈	—	4	2	no	—
94	C₂×C₈	—	356	4	no	—
95	C₄⋊C₄	—	4	2	no	—
96	C₂²⋊C₄	—	4	1	no	—
97	C₂²⋊C₄	—	4	1	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	2	2	no	—
100	C₂³	—	2	1	no	—
101	C₂³	—	2	2	no	—
102	C₂³	—	4	2	no	—
103	C₂³	#15667919	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	4	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	2	no	—
112	C₂×C₄	#15667927	1	2	yes	—
113	C₈	—	8	2	no	—
114	C₈	—	712	4	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	4	1	no	—
118	C₂²	—	8	2	no	—
119	C₂²	#19151365	1	1	yes	characteristic
120	C₂²	#19151368	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	2	no	—
123	C₄	—	4	2	no	—
124	C₄	—	4	1	no	—
125	C₂	—	2	2	no	—
126	C₂	—	8	1	no	—
127	C₂	#26018160	1	1	yes	characteristic
128	C₂	#26018381	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26018586

C₂

yes

maximal

C₈₉×#1818

C₂

yes

maximal, characteristic

#19151655

—

#19151324

C₄

yes

—

#19151322

—

C₂×#117×C₈₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₈₉

C₄

yes

—

#336×C₈₉

—

C₄⋊#10623494

—

C₂²⋊#10623494

—

#15667923

—

C₂³×C₄×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

—

#117×C₈₉

—

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₈₉

Q₈

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

—

C₂²⋊C₈×C₈₉

—

C₂×#10623494

—

C₂⁴×C₈₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×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

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#95

yes

characteristic

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

#99

yes

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#342

yes

characteristic

C₂²×C₈₉

#344

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

#7327

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1306

yes

characteristic

C₂×C₈₉

#1395

yes

—

#1818

D₈₉

yes

characteristic

#1464

—

C₈₉

#7327

yes

characteristic, complemented, Sylow

C₂×#117

C₂×D₈₉

yes

characteristic

#432

—

178

—

C₂×C₂²⋊C₈

Dic₈₉

yes

—

#336

—

#324

—

#323

—

178

—

C₂³×C₄

C₂×Dic₈₉

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

C₄×D₈₉

yes

—

C₂×C₂²⋊C₄

Dic₁₇₈

yes

characteristic

C₂×C₂²⋊C₄

D₃₅₆

yes

characteristic

C₂×C₄²

C₂²⋊D₈₉

yes

—

C₄⋊C₈

—

356

—

C₂²⋊C₈

—

C₂²⋊C₈

—

178

—

#97

—

356

—

C₂⁴

C₄⋊Dic₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×Dic₈₉

yes

characteristic

C₂²×C₄

#13083551

yes

—

C₂²×C₄

C₂²⋊Dic₈₉

yes

characteristic

C₂²×C₄

#13083553

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

356

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

#15667919

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

#15667927

yes

—

113

C₈

—

114

C₈

—

712

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

#19151365

yes

characteristic

120

C₂²

#19151368

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₂

—

126

C₂

—

127

C₂

#26018160

yes

characteristic

128

C₂

#26018381

yes

—

	subgroup	G/H
center	C₂²	#19151365
commutator	C₂²×C₄×C₈₉	C₄²
Frattini	C₂×#117	C₂×D₈₉
Fitting	C₈₉×#1818	C₂
socle	C₂²×C₈₉	#342
prime radical	C₂⁴×C₈₉	C₄⋊C₄
cosocle	C₂×#117×C₈₉	C₂²
hypercenter	#1818	D₈₉
hypocenter	C₈₉	#7327
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂³×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

subgroup

G/H

center

C₂²

#19151365

commutator

C₂²×C₄×C₈₉

C₄²

Frattini

C₂×#117

C₂×D₈₉

Fitting

C₈₉×#1818

C₂

socle

C₂²×C₈₉

#342

prime radical

C₂⁴×C₈₉

C₄⋊C₄

cosocle

C₂×#117×C₈₉

C₂²

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

N	H ≅ G/N	type
67. C₈₉	#7327	semidirect

H ≅ G/N

type

67. C₈₉

#7327

semidirect

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

subgroup	index
#26018586	2
C₈₉×#1818	2
#7327	89

subgroup

index

#26018586

C₈₉×#1818

#7327

Subgroups — #36441751

Conjugacy classes of subgroups

Complements

Maximal subgroups