Group #36448082 — subgroups

Subgroups — #36448082

Order 22784.

262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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	#26019000	C₂	1	2	yes	maximal
2	#26018097	C₂	1	2	yes	maximal
3	#26018081	C₂	1	2	yes	maximal
4	C₈₉×#1746	C₂	1	1	yes	maximal, characteristic
5	#19151651	C₂²	1	4	yes	—
6	#19151351	—	2	2	no	—
7	#19151349	—	2	2	no	—
8	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	#376×C₈₉	C₂²	1	1	yes	characteristic
11	#336×C₈₉	C₄	1	4	yes	—
12	C₄⋊#10623494	—	2	4	no	—
13	C₂²⋊#10623494	—	2	4	no	—
14	C₄×#10623494	—	2	4	no	—
15	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
19	#97×C₈₉	—	2	2	no	—
20	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
21	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
22	C₄×C₈×C₈₉	Q₈	1	2	yes	—
23	#95×C₈₉	—	2	2	no	—
24	C₂×#10623494	—	4	4	no	—
25	C₂²×C₄×C₈₉	—	2	2	no	—
26	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₈₉	#41	1	2	yes	—
28	C₂×C₈×C₈₉	—	2	4	no	—
29	C₂×C₈×C₈₉	—	2	2	no	—
30	C₂×C₈×C₈₉	—	2	4	no	—
31	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
33	C₄²×C₈₉	—	2	4	no	—
34	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
35	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
36	C₄²×C₈₉	#41	1	2	yes	—
37	C₂³×C₈₉	#117	1	1	yes	characteristic
38	C₂×C₄×C₈₉	—	4	2	no	—
39	C₂×C₄×C₈₉	—	4	4	no	—
40	C₂×C₄×C₈₉	—	4	2	no	—
41	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
43	C₂×C₄×C₈₉	#124	1	2	yes	—
44	C₂×C₄×C₈₉	#125	1	2	yes	—
45	C₂×C₄×C₈₉	#131	1	4	yes	—
46	C₈×C₈₉	—	2	2	no	—
47	C₈×C₈₉	—	2	2	no	—
48	C₈×C₈₉	—	4	2	no	—
49	#10623494	—	8	4	no	—
50	C₂²×C₈₉	—	2	2	no	—
51	C₂²×C₈₉	#382	1	1	yes	characteristic
52	C₂²×C₈₉	#433	1	2	yes	—
53	C₄×C₈₉	—	2	2	no	—
54	C₄×C₈₉	—	2	2	no	—
55	C₄×C₈₉	—	8	2	no	—
56	C₄×C₈₉	#424	1	2	yes	—
57	C₄×C₈₉	#433	1	2	yes	—
58	#8782	—	89	1	no	maximal, Sylow
59	C₂×C₈₉	—	2	2	no	—
60	C₂×C₈₉	#1832	1	1	yes	characteristic
61	C₂×C₈₉	#1833	1	2	yes	—
62	#1746	D₈₉	1	1	yes	characteristic
63	#1564	—	89	2	no	—
64	#1281	—	89	2	no	—
65	#1274	—	89	2	no	—
66	C₈₉	#8782	1	1	yes	characteristic, complemented, Sylow
67	#431	—	89	4	no	—
68	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
70	#376	C₂×D₈₉	1	1	yes	characteristic
71	#336	Dic₈₉	1	4	yes	—
72	#335	—	178	2	no	—
73	#334	—	178	2	no	—
74	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
75	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
76	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
77	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
78	C₄⋊C₈	—	178	4	no	—
79	C₂²⋊C₈	—	178	4	no	—
80	#97	—	2	2	no	—
81	C₄×C₈	—	178	4	no	—
82	C₄×C₈	Dic₁₇₈	1	2	yes	—
83	C₄×C₈	D₃₅₆	1	1	yes	characteristic
84	C₄×C₈	D₃₅₆	1	1	yes	characteristic
85	#95	—	2	2	no	—
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
88	C₂²×C₄	#13083574	1	2	yes	—
89	C₂×C₈	—	2	4	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	356	4	no	—
93	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
94	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
95	C₄²	—	2	4	no	—
96	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
97	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
98	C₄²	#13083574	1	2	yes	—
99	C₂³	#15667971	1	1	yes	characteristic
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	4	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
104	C₂×C₄	#15667971	1	1	yes	characteristic
105	C₂×C₄	#15668000	1	2	yes	—
106	C₂×C₄	#15668004	1	2	yes	—
107	C₂×C₄	#15668019	1	4	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	2	2	no	—
110	C₈	—	4	2	no	—
111	C₈	—	712	4	no	—
112	C₂²	—	2	2	no	—
113	C₂²	#19151464	1	1	yes	characteristic
114	C₂²	#19151659	1	2	yes	—
115	C₄	—	2	2	no	—
116	C₄	—	2	2	no	—
117	C₄	—	8	2	no	—
118	C₄	#19151625	1	2	yes	—
119	C₄	#19151659	1	2	yes	—
120	C₂	—	2	2	no	—
121	C₂	#26020372	1	1	yes	characteristic
122	C₂	#26020376	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26019000

C₂

yes

maximal

#26018097

C₂

yes

maximal

#26018081

C₂

yes

maximal

C₈₉×#1746

C₂

yes

maximal, characteristic

#19151651

C₂²

yes

—

#19151351

—

#19151349

—

C₂×#97×C₈₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#376×C₈₉

C₂²

yes

characteristic

#336×C₈₉

C₄

yes

—

C₄⋊#10623494

—

C₂²⋊#10623494

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#97×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

Q₈

yes

—

#95×C₈₉

—

C₂×#10623494

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₄⋊C₄

yes

—

C₂×C₈×C₈₉

C₄⋊C₄

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

#125

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

#382

yes

characteristic

C₂²×C₈₉

#433

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#424

yes

—

C₄×C₈₉

#433

yes

—

#8782

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#1832

yes

characteristic

C₂×C₈₉

#1833

yes

—

#1746

D₈₉

yes

—

—

—

C₈₉

#8782

yes

characteristic, complemented, Sylow

#431

—

C₂×#97

C₂×D₈₉

yes

characteristic

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

#376

C₂×D₈₉

yes

characteristic

#336

Dic₈₉

yes

—

#335

—

178

—

#334

—

178

—

C₂²×C₈

C₂×Dic₈₉

yes

—

C₂²×C₈

C₂×Dic₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

C₄⋊C₈

—

178

—

C₂²⋊C₈

—

178

—

#97

—

C₄×C₈

—

178

—

C₄×C₈

Dic₁₇₈

yes

—

C₄×C₈

D₃₅₆

yes

characteristic

C₄×C₈

D₃₅₆

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

C₂²×C₄

#13083574

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

356

—

C₂×C₈

C₄⋊Dic₈₉

yes

—

C₂×C₈

C₄⋊Dic₈₉

yes

—

C₄²

—

C₄²

C₂×D₃₅₆

yes

characteristic

C₄²

C₂×Dic₁₇₈

yes

characteristic

C₄²

#13083574

yes

—

C₂³

#15667971

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₂×C₄⋊Dic₈₉

yes

characteristic

104

C₂×C₄

#15667971

yes

characteristic

105

C₂×C₄

#15668000

yes

—

106

C₂×C₄

#15668004

yes

—

107

C₂×C₄

#15668019

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

712

—

112

C₂²

—

113

C₂²

#19151464

yes

characteristic

114

C₂²

#19151659

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#19151625

yes

—

119

C₄

#19151659

yes

—

120

C₂

—

121

C₂

#26020372

yes

characteristic

122

C₂

#26020376

yes

—

	subgroup	G/H
center	C₂×C₄	#15667971
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1746	C₂
socle	C₂²×C₈₉	#382
prime radical	C₂³×C₈₉	#117
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1746	D₈₉
hypocenter	C₈₉	#8782
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

subgroup

G/H

center

C₂×C₄

#15667971

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1746

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

N	H ≅ G/N	type
66. C₈₉	#8782	semidirect

H ≅ G/N

type

66. C₈₉

#8782

semidirect

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

subgroup	index
#26019000	2
#26018097	2
#26018081	2
C₈₉×#1746	2
#8782	89

subgroup

index

C₈₉×#1746

Subgroups — #36448082

Conjugacy classes of subgroups

Complements

Maximal subgroups