Group #36441093 — subgroups

Subgroups — #36441093

Order 22784.

132 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 55 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	#26019150	C₂	1	1	yes	maximal, characteristic
2	#26018322	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1312	C₂	1	1	yes	maximal, characteristic
4	#19151728	—	2	1	no	—
5	C₄×Dic₃₅₆	C₄	1	1	yes	characteristic
6	C₄⋊#13083549	—	2	1	no	—
7	#19151351	C₄	1	1	yes	characteristic
8	#19151330	—	2	1	no	—
9	C₄×C₁₆×C₈₉	—	2	1	no	—
10	C₈²×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₅₆	C₈	1	1	yes	characteristic
12	C₄×Dic₁₇₈	—	2	1	no	—
13	C₂×#13083549	—	4	1	no	—
14	#15667946	C₈	1	1	yes	characteristic
15	C₄⋊#10623494	—	2	1	no	—
16	#15667941	—	4	1	no	—
17	#15667937	—	2	1	no	—
18	#15667922	—	4	1	no	—
19	C₂×C₁₆×C₈₉	—	2	2	no	—
20	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
22	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
23	C₂×Dic₁₇₈	—	2	1	no	—
24	Dic₃₅₆	—	4	1	no	—
25	C₂×#10623494	—	4	1	no	—
26	C₄⋊Dic₈₉	—	2	1	no	—
27	#13083553	—	4	1	no	—
28	C₄×Dic₈₉	—	4	1	no	—
29	#13083549	—	8	1	no	—
30	C₂×C₈×C₈₉	—	2	1	no	—
31	C₂×C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₈₉	M₁₆	1	1	yes	characteristic
33	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
34	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
35	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₁₆×C₈₉	—	4	2	no	—
37	C₂×C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
39	C₂×C₄×C₈₉	#104	1	1	yes	characteristic
40	C₂×Dic₈₉	—	4	1	no	—
41	C₂×Dic₈₉	—	4	1	no	—
42	Dic₁₇₈	—	4	1	no	—
43	Dic₁₇₈	—	4	1	no	—
44	C₈×C₈₉	—	2	2	no	—
45	C₈×C₈₉	—	2	1	no	—
46	C₈×C₈₉	—	2	1	no	—
47	C₈×C₈₉	—	2	1	no	—
48	C₈×C₈₉	SD₃₂	1	1	yes	characteristic
49	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
50	#10623494	—	8	1	no	—
51	C₂²×C₈₉	D₄⋊C₈	1	1	yes	characteristic
52	C₄×C₈₉	—	2	1	no	—
53	C₄×C₈₉	#349	1	1	yes	characteristic
54	C₄×C₈₉	#350	1	1	yes	characteristic
55	C₄×C₈₉	#358	1	1	yes	characteristic
56	C₄×C₈₉	#359	1	1	yes	characteristic
57	Dic₈₉	—	8	1	no	—
58	Dic₈₉	—	8	1	no	—
59	#7073	—	89	1	no	maximal, Sylow
60	C₂×C₈₉	#1330	1	1	yes	characteristic
61	C₂×C₈₉	#1332	1	1	yes	characteristic
62	C₂×C₈₉	#1336	1	1	yes	characteristic
63	#1591	—	89	1	no	—
64	#1370	—	89	1	no	—
65	#1312	D₈₉	1	1	yes	characteristic
66	C₈₉	#7073	1	1	yes	characteristic, complemented, Sylow
67	#446	—	178	1	no	—
68	C₄×Q₁₆	—	89	1	no	—
69	C₄⋊C₁₆	—	178	1	no	—
70	C₄×C₁₆	—	2	1	no	—
71	#335	—	89	1	no	—
72	Q₈⋊C₈	—	178	1	no	—
73	C₈²	C₂×D₈₉	1	1	yes	characteristic
74	C₂×Q₁₆	—	89	1	no	—
75	C₄×Q₈	—	178	1	no	—
76	C₂×C₁₆	—	2	2	no	—
77	C₂×C₁₆	—	356	1	no	—
78	#107	—	89	1	no	—
79	C₄⋊C₈	—	356	1	no	—
80	C₄⋊C₈	—	178	1	no	—
81	#103	—	178	1	no	—
82	#97	—	356	1	no	—
83	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
84	C₄×C₈	D₃₅₆	1	1	yes	characteristic
85	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
86	C₂×Q₈	—	178	1	no	—
87	Q₁₆	—	356	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	356	1	no	—
90	C₂×C₈	C₈×D₈₉	1	1	yes	characteristic
91	C₂×C₈	#13083557	1	1	yes	characteristic
92	C₂×C₈	D₇₁₂	1	1	yes	characteristic
93	C₂×C₈	#13083563	1	1	yes	characteristic
94	C₄⋊C₄	—	356	1	no	—
95	C₄⋊C₄	—	178	1	no	—
96	C₄²	—	356	1	no	—
97	C₄²	#13083551	1	1	yes	characteristic
98	C₁₆	—	4	2	no	—
99	C₁₆	—	712	1	no	—
100	Q₈	—	356	1	no	—
101	Q₈	—	356	1	no	—
102	C₂×C₄	—	356	1	no	—
103	C₂×C₄	—	356	1	no	—
104	C₂×C₄	#15667924	1	1	yes	characteristic
105	C₂×C₄	#15667934	1	1	yes	characteristic
106	C₂×C₄	#15667940	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	2	1	no	—
111	C₈	—	712	1	no	—
112	C₈	#15667957	1	1	yes	characteristic
113	C₈	Dic₇₁₂	1	1	yes	characteristic
114	C₂²	#19151327	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	712	1	no	—
117	C₄	—	712	1	no	—
118	C₄	#19151379	1	1	yes	characteristic
119	C₄	#19151383	1	1	yes	characteristic
120	C₄	#19151403	1	1	yes	characteristic
121	C₄	#19151406	1	1	yes	characteristic
122	C₂	#26018211	1	1	yes	characteristic
123	C₂	#26018217	1	1	yes	characteristic
124	C₂	#26018229	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26019150

C₂

yes

maximal, characteristic

#26018322

C₂

yes

maximal, characteristic

C₈₉×#1312

C₂

yes

maximal, characteristic

#19151728

—

C₄×Dic₃₅₆

C₄

yes

characteristic

C₄⋊#13083549

—

#19151351

C₄

yes

characteristic

#19151330

—

C₄×C₁₆×C₈₉

—

C₈²×C₈₉

C₂²

yes

characteristic

C₂×Dic₃₅₆

C₈

yes

characteristic

C₄×Dic₁₇₈

—

C₂×#13083549

—

#15667946

C₈

yes

—

—

—

—

C₂×C₁₆×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

Dic₃₅₆

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

#13083553

—

C₄×Dic₈₉

—

#13083549

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×C₈

yes

characteristic

C₂×C₈×C₈₉

M₁₆

yes

characteristic

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₄²×C₈₉

C₂²⋊C₄

yes

characteristic

C₁₆×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

SD₃₂

yes

characteristic

C₈×C₈₉

Q₃₂

yes

characteristic

#10623494

—

C₂²×C₈₉

D₄⋊C₈

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

Dic₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

—

D₈₉

yes

characteristic

C₈₉

#7073

yes

characteristic, complemented, Sylow

#446

—

178

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

178

—

C₄×C₁₆

—

#335

—

Q₈⋊C₈

—

178

—

C₈²

C₂×D₈₉

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

178

—

C₂×C₁₆

—

C₂×C₁₆

—

356

—

#107

—

C₄⋊C₈

—

356

—

C₄⋊C₈

—

178

—

#103

—

178

—

#97

—

356

—

C₄×C₈

C₄×D₈₉

yes

characteristic

C₄×C₈

D₃₅₆

yes

characteristic

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₂×Q₈

—

178

—

Q₁₆

—

356

—

C₂×C₈

—

C₂×C₈

—

356

—

C₂×C₈

C₈×D₈₉

yes

characteristic

C₂×C₈

#13083557

yes

characteristic

C₂×C₈

D₇₁₂

yes

characteristic

C₂×C₈

#13083563

yes

characteristic

C₄⋊C₄

—

356

—

C₄⋊C₄

—

178

—

C₄²

—

356

—

C₄²

#13083551

yes

characteristic

C₁₆

—

C₁₆

—

712

—

100

Q₈

—

356

—

101

Q₈

—

356

—

102

C₂×C₄

—

356

—

103

C₂×C₄

—

356

—

104

C₂×C₄

#15667924

yes

characteristic

105

C₂×C₄

#15667934

yes

characteristic

106

C₂×C₄

#15667940

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

712

—

112

C₈

#15667957

yes

characteristic

113

C₈

Dic₇₁₂

yes

characteristic

114

C₂²

#19151327

yes

characteristic

115

C₄

—

116

C₄

—

712

—

117

C₄

—

712

—

118

C₄

#19151379

yes

characteristic

119

C₄

#19151383

yes

characteristic

120

C₄

#19151403

yes

characteristic

121

C₄

#19151406

yes

characteristic

122

C₂

#26018211

yes

characteristic

123

C₂

#26018217

yes

characteristic

124

C₂

#26018229

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#15667934
commutator	C₂×C₈×C₈₉	C₂×C₈
Frattini	C₈²	C₂×D₈₉
Fitting	C₈₉×#1312	C₂
socle, prime radical	C₂²×C₈₉	D₄⋊C₈
cosocle	C₈²×C₈₉	C₂²
hypercenter	#1312	D₈₉
hypocenter	C₈₉	#7073
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1312

subgroup

G/H

center

C₂×C₄

#15667934

commutator

C₂×C₈×C₈₉

C₂×C₈

Frattini

C₈²

C₂×D₈₉

Fitting

C₈₉×#1312

C₂

socle, prime radical

C₂²×C₈₉

D₄⋊C₈

cosocle

C₈²×C₈₉

C₂²

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1312

N	H ≅ G/N	type
66. C₈₉	#7073	semidirect

H ≅ G/N

type

66. C₈₉

#7073

semidirect

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

subgroup	index
#26019150	2
#26018322	2
C₈₉×#1312	2
#7073	89

subgroup

index

#26019150

#26018322

C₈₉×#1312

#7073

Subgroups — #36441093

Conjugacy classes of subgroups

Complements

Maximal subgroups