Group #36441609 — subgroups

Subgroups — #36441609

Order 22784.

208 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₂×#19151419	C₂	1	2	yes	maximal
2	C₈₉×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667952	—	2	2	no	—
4	#19151419	—	2	2	no	—
5	#19151419	C₄	1	4	yes	—
6	C₂×#108×C₈₉	—	2	2	no	—
7	#423×C₈₉	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
9	#15667952	—	2	4	no	—
10	#15667952	—	4	2	no	—
11	C₂×#13083549	—	4	2	no	—
12	C₂×M₁₆×C₈₉	—	2	2	no	—
13	C₂²×C₈×C₈₉	D₄	1	2	yes	—
14	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
15	#108×C₈₉	—	4	2	no	—
16	#108×C₈₉	—	4	2	no	—
17	C₄⋊C₈×C₈₉	—	4	2	no	—
18	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₈₉	Q₈	1	1	yes	characteristic
21	#13083549	—	4	4	no	—
22	C₂²×C₄×C₈₉	—	2	1	no	—
23	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₈₉	—	4	4	no	—
25	C₂×C₈×C₈₉	—	4	2	no	—
26	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₈₉	D₈	1	2	yes	—
29	C₂×C₈×C₈₉	SD₁₆	1	2	yes	—
30	C₂×C₈×C₈₉	SD₁₆	1	2	yes	—
31	C₂×C₈×C₈₉	Q₁₆	1	2	yes	—
32	C₄²×C₈₉	—	2	1	no	—
33	C₄²×C₈₉	C₄²	1	1	yes	characteristic
34	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂³×C₈₉	#101	1	1	yes	characteristic
36	C₂×C₄×C₈₉	—	2	1	no	—
37	C₂×C₄×C₈₉	—	2	1	no	—
38	C₂×C₄×C₈₉	—	4	2	no	—
39	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₈₉	#100	1	1	yes	characteristic
41	C₂×C₄×C₈₉	#102	1	2	yes	—
42	C₂×C₄×C₈₉	#103	1	2	yes	—
43	C₈×C₈₉	—	8	2	no	—
44	C₈×C₈₉	#102	1	2	yes	—
45	C₈×C₈₉	#103	1	2	yes	—
46	C₈×C₈₉	#106	1	2	yes	—
47	C₈×C₈₉	#107	1	2	yes	—
48	C₂²×C₈₉	—	4	1	no	—
49	C₂²×C₈₉	#332	1	2	yes	—
50	C₂²×C₈₉	#343	1	1	yes	characteristic
51	C₄×C₈₉	—	2	2	no	—
52	C₄×C₈₉	—	4	1	no	—
53	C₄×C₈₉	#331	1	1	yes	characteristic
54	C₄×C₈₉	#333	1	1	yes	characteristic
55	C₄×C₈₉	#340	1	2	yes	—
56	#7272	—	89	1	no	maximal, Sylow
57	C₂×C₈₉	—	2	1	no	—
58	C₂×C₈₉	—	2	2	no	—
59	C₂×C₈₉	#1296	1	1	yes	characteristic
60	C₂×#364	—	89	2	no	—
61	#1848	D₈₉	1	1	yes	characteristic
62	C₈₉	#7272	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	178	2	no	—
64	C₂×#108	—	2	2	no	—
65	#423	Dic₈₉	1	2	yes	—
66	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
67	#364	—	89	4	no	—
68	#364	—	178	2	no	—
69	C₂×M₁₆	—	2	2	no	—
70	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
71	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
72	M₃₂	—	356	2	no	—
73	M₃₂	—	178	4	no	—
74	C₂×C₁₆	—	356	2	no	—
75	#108	—	4	2	no	—
76	#108	—	4	2	no	—
77	C₄⋊C₈	—	4	2	no	—
78	C₄×C₈	Dic₁₇₈	1	1	yes	characteristic
79	C₄×C₈	C₄×D₈₉	1	2	yes	—
80	C₄×C₈	D₃₅₆	1	1	yes	characteristic
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
83	M₁₆	—	4	4	no	—
84	C₂×C₈	—	4	2	no	—
85	C₂×C₈	#13083551	1	2	yes	—
86	C₂×C₈	#13083553	1	2	yes	—
87	C₂×C₈	#13083559	1	2	yes	—
88	C₂×C₈	#13083561	1	2	yes	—
89	C₂×C₈	#13083562	1	2	yes	—
90	C₂×C₈	#13083564	1	2	yes	—
91	C₄²	—	2	1	no	—
92	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
93	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
94	C₁₆	—	356	4	no	—
95	C₂³	#15667931	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	#15667919	1	1	yes	characteristic
100	C₂×C₄	#15667929	1	1	yes	characteristic
101	C₂×C₄	#15667933	1	2	yes	—
102	C₂×C₄	#15667936	1	2	yes	—
103	C₈	—	8	2	no	—
104	C₈	#15667932	1	2	yes	—
105	C₈	#15667935	1	2	yes	—
106	C₈	#15667943	1	2	yes	—
107	C₈	#15667945	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#19151344	1	2	yes	—
110	C₂²	#19151367	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	4	1	no	—
113	C₄	#19151342	1	1	yes	characteristic
114	C₄	#19151347	1	1	yes	characteristic
115	C₄	#19151360	1	2	yes	—
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	#26018135	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151419

C₂

yes

maximal

C₈₉×#1848

C₂

yes

maximal, characteristic

C₂×#15667952

—

#19151419

—

#19151419

C₄

yes

—

C₂×#108×C₈₉

—

#423×C₈₉

C₄

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

—

—

C₂×M₁₆×C₈₉

—

C₂²×C₈×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

#108×C₈₉

—

#108×C₈₉

—

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

Q₈

yes

characteristic

#13083549

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₄⋊C₄

yes

—

C₂×C₈×C₈₉

D₈

yes

—

C₂×C₈×C₈₉

SD₁₆

yes

—

C₂×C₈×C₈₉

SD₁₆

yes

—

C₂×C₈×C₈₉

Q₁₆

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

C₄²

yes

characteristic

C₄²×C₈₉

C₄⋊C₄

yes

characteristic

C₂³×C₈₉

#101

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

#103

yes

—

C₈×C₈₉

—

C₈×C₈₉

#102

yes

—

C₈×C₈₉

#103

yes

—

C₈×C₈₉

#106

yes

—

C₈×C₈₉

#107

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

#332

yes

—

C₂²×C₈₉

#343

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

#7272

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

—

D₈₉

yes

characteristic

C₈₉

#7272

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

178

—

C₂×#108

—

#423

Dic₈₉

yes

—

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

#364

—

#364

—

178

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

characteristic

M₃₂

—

356

—

M₃₂

—

178

—

C₂×C₁₆

—

356

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₁₇₈

yes

characteristic

C₄×C₈

C₄×D₈₉

yes

—

C₄×C₈

D₃₅₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₈₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

#13083551

yes

—

C₂×C₈

#13083553

yes

—

C₂×C₈

#13083559

yes

—

C₂×C₈

#13083561

yes

—

C₂×C₈

#13083562

yes

—

C₂×C₈

#13083564

yes

—

C₄²

—

C₄²

C₄×Dic₈₉

yes

characteristic

C₄²

C₄⋊Dic₈₉

yes

characteristic

C₁₆

—

356

—

C₂³

#15667931

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#15667919

yes

characteristic

100

C₂×C₄

#15667929

yes

characteristic

101

C₂×C₄

#15667933

yes

—

102

C₂×C₄

#15667936

yes

—

103

C₈

—

104

C₈

#15667932

yes

—

105

C₈

#15667935

yes

—

106

C₈

#15667943

yes

—

107

C₈

#15667945

yes

—

108

C₂²

—

109

C₂²

#19151344

yes

—

110

C₂²

#19151367

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

#19151342

yes

characteristic

114

C₄

#19151347

yes

characteristic

115

C₄

#19151360

yes

—

116

C₂

—

117

C₂

—

118

C₂

#26018135

yes

characteristic

	subgroup	G/H
center	C₄	#19151347
commutator	C₄²×C₈₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₈₉
Fitting	C₈₉×#1848	C₂
socle	C₂×C₈₉	#1296
prime radical	C₂³×C₈₉	#101
cosocle	C₂×C₄×C₈×C₈₉	C₂²
hypercenter	#1848	D₈₉
hypocenter	C₈₉	#7272
LCS	G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₄

#19151347

commutator

C₄²×C₈₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₈₉

Fitting

C₈₉×#1848

C₂

C₂×C₈₉

C₂³×C₈₉

C₂×C₄×C₈×C₈₉

C₂²

D₈₉

C₈₉

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

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

N	H ≅ G/N	type
62. C₈₉	#7272	semidirect

H ≅ G/N

type

62. C₈₉

#7272

semidirect

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

subgroup	index
C₂×#19151419	2
C₈₉×#1848	2
#7272	89

subgroup

index

C₂×#19151419

C₈₉×#1848

#7272

Subgroups — #36441609

Conjugacy classes of subgroups

Complements

Maximal subgroups