Group #36441835 — subgroups

Subgroups — #36441835

Order 22784.

158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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	#26018196	C₂	1	2	yes	maximal
2	C₈₉×#1835	C₂	1	1	yes	maximal, characteristic
3	#19151324	—	2	2	no	—
4	C₂×C₄×C₈×C₈₉	C₄	1	1	yes	characteristic
5	#382×C₈₉	C₄	1	1	yes	characteristic
6	#382×C₈₉	C₂²	1	1	yes	characteristic
7	#340×C₈₉	—	2	2	no	—
8	C₂²⋊#10623494	—	4	2	no	—
9	C₂²×C₈×C₈₉	—	2	1	no	—
10	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
11	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
12	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈×C₈₉	—	2	1	no	—
14	C₄×C₈×C₈₉	C₈	1	2	yes	complemented
15	#95×C₈₉	—	4	1	no	—
16	#95×C₈₉	—	4	1	no	—
17	C₂×#10623494	—	8	2	no	—
18	C₂²×C₄×C₈₉	—	2	1	no	—
19	C₂²×C₄×C₈₉	—	2	2	no	—
20	C₂²×C₄×C₈₉	—	4	1	no	—
21	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₉	—	2	2	no	—
23	C₂×C₈×C₈₉	—	4	1	no	—
24	C₂×C₈×C₈₉	—	4	1	no	—
25	C₄⋊C₄×C₈₉	—	4	2	no	—
26	C₄⋊C₄×C₈₉	—	4	2	no	—
27	C₄²×C₈₉	—	2	1	no	—
28	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
29	C₄²×C₈₉	M₁₆	1	1	yes	characteristic
30	C₂³×C₈₉	#99	1	1	yes	characteristic
31	C₂×C₄×C₈₉	—	2	1	no	—
32	C₂×C₄×C₈₉	—	2	1	no	—
33	C₂×C₄×C₈₉	—	2	1	no	—
34	C₂×C₄×C₈₉	—	2	1	no	—
35	C₂×C₄×C₈₉	—	4	2	no	—
36	C₂×C₄×C₈₉	—	4	2	no	—
37	C₂×C₄×C₈₉	—	8	2	no	—
38	C₂×C₄×C₈₉	—	8	2	no	—
39	C₂×C₄×C₈₉	—	8	1	no	—
40	C₂×C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₈₉	#101	1	1	yes	characteristic
42	C₈×C₈₉	—	4	2	no	—
43	#10623494	—	16	2	no	—
44	C₂²×C₈₉	—	2	2	no	—
45	C₂²×C₈₉	#324	1	1	yes	characteristic
46	C₂²×C₈₉	#354	1	1	yes	characteristic
47	C₂²×C₈₉	#355	1	1	yes	characteristic
48	C₄×C₈₉	—	2	1	no	—
49	C₄×C₈₉	—	2	1	no	—
50	C₄×C₈₉	—	4	1	no	—
51	C₄×C₈₉	—	4	1	no	—
52	C₄×C₈₉	—	8	2	no	—
53	C₄×C₈₉	—	16	1	no	—
54	#7366	—	89	1	no	maximal, Sylow
55	C₂×C₈₉	—	2	1	no	—
56	C₂×C₈₉	—	2	1	no	—
57	C₂×C₈₉	#1324	1	1	yes	characteristic
58	C₂×C₈₉	#1414	1	2	yes	—
59	#1835	D₈₉	1	1	yes	characteristic
60	#1324	—	89	2	no	—
61	C₈₉	#7366	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₄×C₈	Dic₈₉	1	1	yes	characteristic
63	#382	Dic₈₉	1	1	yes	characteristic
64	#382	C₂×D₈₉	1	1	yes	characteristic
65	#340	—	2	2	no	—
66	#324	—	178	2	no	—
67	C₂²×C₈	—	2	1	no	—
68	C₂×C₄⋊C₄	—	2	1	no	—
69	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
70	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
71	C₂²⋊C₈	—	356	2	no	—
72	C₄×C₈	—	2	1	no	—
73	C₄×C₈	#10623494	1	2	yes	complemented
74	#95	—	4	1	no	—
75	#95	—	4	1	no	—
76	C₂²×C₄	—	2	1	no	—
77	C₂²×C₄	—	2	2	no	—
78	C₂²×C₄	—	4	1	no	—
79	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	4	1	no	—
82	C₂×C₈	—	4	1	no	—
83	C₂×C₈	—	712	2	no	—
84	C₄⋊C₄	—	4	2	no	—
85	C₄⋊C₄	—	4	2	no	—
86	C₄²	—	2	1	no	—
87	C₄²	C₂×#10623494	1	1	yes	characteristic
88	C₄²	#13083558	1	1	yes	characteristic
89	C₂³	#15667927	1	1	yes	characteristic
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	4	2	no	—
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	—	8	2	no	—
98	C₂×C₄	—	8	1	no	—
99	C₂×C₄	C₂²⋊#10623494	1	1	yes	characteristic
100	C₂×C₄	#15667931	1	1	yes	characteristic
101	C₈	—	4	2	no	—
102	C₈	—	1424	2	no	—
103	C₂²	—	2	2	no	—
104	C₂²	#19151324	1	1	yes	characteristic
105	C₂²	#19151393	1	1	yes	characteristic
106	C₂²	#19151395	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	4	1	no	—
110	C₄	—	4	1	no	—
111	C₄	—	8	2	no	—
112	C₄	—	16	1	no	—
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#26018196	1	1	yes	characteristic
116	C₂	#26018427	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26018196

C₂

yes

maximal

C₈₉×#1835

C₂

yes

maximal, characteristic

#19151324

—

C₂×C₄×C₈×C₈₉

C₄

yes

characteristic

#382×C₈₉

C₄

yes

characteristic

#382×C₈₉

C₂²

yes

characteristic

#340×C₈₉

—

C₂²⋊#10623494

—

C₂²×C₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₈

yes

complemented

#95×C₈₉

—

#95×C₈₉

—

C₂×#10623494

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×C₈

yes

characteristic

C₄²×C₈₉

M₁₆

yes

characteristic

C₂³×C₈₉

#99

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

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₉

#101

yes

characteristic

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

#7366

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1324

yes

characteristic

C₂×C₈₉

#1414

yes

—

#1835

D₈₉

yes

characteristic

#1324

—

C₈₉

#7366

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

Dic₈₉

yes

characteristic

#382

Dic₈₉

yes

characteristic

#382

C₂×D₈₉

yes

characteristic

#340

—

#324

—

178

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

characteristic

C₂²⋊C₈

—

356

—

C₄×C₈

—

C₄×C₈

yes

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₈₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

712

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

yes

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#10623494

yes

characteristic

100

C₂×C₄

#15667931

yes

characteristic

101

C₈

—

102

C₈

—

1424

—

103

C₂²

—

104

C₂²

#19151324

yes

characteristic

105

C₂²

#19151393

yes

characteristic

106

C₂²

#19151395

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₂

—

114

C₂

—

115

C₂

#26018196

yes

characteristic

116

C₂

#26018427

yes

—

	subgroup	G/H
center	C₂²	#19151393
commutator	C₄²×C₈₉	C₂×C₈
Frattini	#382	C₂×D₈₉
Fitting	C₈₉×#1835	C₂
socle	C₂²×C₈₉	#354
prime radical	C₂³×C₈₉	#99
cosocle	#382×C₈₉	C₂²
hypercenter	#1835	D₈₉
hypocenter	C₈₉	#7366
LCS	G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1835

subgroup

G/H

center

C₂²

#19151393

commutator

C₄²×C₈₉

C₂×C₈

Frattini

#382

C₂×D₈₉

Fitting

C₈₉×#1835

C₂

C₂²×C₈₉

C₂³×C₈₉

#382×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1835

N	H ≅ G/N	type
14. C₄×C₈×C₈₉	C₈	semidirect
61. C₈₉	#7366	semidirect
73. C₄×C₈	#10623494	semidirect

H ≅ G/N

type

14. C₄×C₈×C₈₉

C₈

semidirect

61. C₈₉

#7366

semidirect

73. C₄×C₈

#10623494

semidirect

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

subgroup	index
#26018196	2
C₈₉×#1835	2
#7366	89

subgroup

index

#26018196

C₈₉×#1835

#7366

Subgroups — #36441835

Conjugacy classes of subgroups

Complements

Maximal subgroups