Group #46812605 — subgroups

Subgroups — #46812605

Order 34432.

220 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22575393	C₂	1	1	yes	maximal, characteristic
2	#31770643	C₂	1	1	yes	maximal, characteristic
3	#31770409	C₂	1	4	yes	maximal, complemented
4	C₂²×Q₁₆×C₂₆₉	C₂	1	1	yes	maximal, characteristic
5	#22575412	—	2	1	no	—
6	#22575393	—	2	2	no	—
7	C₂×#16864377	C₂²	1	2	yes	—
8	#22575387	C₂²	1	2	yes	—
9	#22575385	—	2	1	no	—
10	C₂²×Q₈×C₂₆₉	—	2	1	no	—
11	C₂×Q₁₆×C₂₆₉	—	2	1	no	—
12	C₂×Q₁₆×C₂₆₉	—	2	2	no	—
13	C₂×Q₁₆×C₂₆₉	C₄	1	4	yes	complemented
14	C₂×Q₁₆×C₂₆₉	C₂²	1	2	yes	—
15	C₂²×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₂₆₉	—	2	2	no	—
17	C₂²⋊Dic₂₆₉	—	4	1	no	—
18	C₄×Dic₂₆₉	—	4	1	no	—
19	#16864377	—	2	2	no	—
20	C₂×Q₈×C₂₆₉	—	2	4	no	—
21	C₂×Q₈×C₂₆₉	—	2	2	no	—
22	C₂×Q₈×C₂₆₉	—	4	1	no	—
23	C₂×Q₈×C₂₆₉	—	4	2	no	—
24	C₂²×C₄×C₂₆₉	—	4	1	no	—
25	C₂²×C₄×C₂₆₉	D₄	1	1	yes	characteristic
26	Q₁₆×C₂₆₉	—	2	4	no	—
27	Q₁₆×C₂₆₉	—	2	2	no	—
28	Q₁₆×C₂₆₉	C₂×C₄	1	4	yes	—
29	C₂×C₈×C₂₆₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
31	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
32	C₂×C₈×C₂₆₉	C₂³	1	1	yes	characteristic
33	C₂×Dic₂₆₉	—	4	2	no	—
34	C₂³×C₂₆₉	D₈	1	1	yes	characteristic
35	Q₈×C₂₆₉	—	2	4	no	—
36	Q₈×C₂₆₉	—	4	4	no	—
37	Q₈×C₂₆₉	—	4	2	no	—
38	C₂×C₄×C₂₆₉	—	4	4	no	—
39	C₂×C₄×C₂₆₉	—	4	2	no	—
40	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
42	C₂×C₄×C₂₆₉	SD₁₆	1	2	yes	—
43	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₂₆₉	C₂²⋊C₄	1	2	yes	—
45	C₈×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₂₆₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₂₆₉	—	2	2	no	—
48	C₂²×C₂₆₉	#102	1	2	yes	—
49	C₂²×C₂₆₉	C₂×D₈	1	1	yes	characteristic
50	C₄×C₂₆₉	—	4	4	no	—
51	C₄×C₂₆₉	#102	1	2	yes	—
52	C₄×C₂₆₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₄×C₂₆₉	C₂×SD₁₆	1	1	yes	characteristic
54	Dic₂₆₉	—	8	2	no	—
55	C₂×C₂₆₉	—	2	2	no	—
56	C₂×C₂₆₉	C₂×#102	1	1	yes	characteristic
57	C₂×C₂₆₉	#510	1	2	yes	—
58	C₂₆₉	#2141	1	1	yes	characteristic, complemented, Sylow
59	#2141	—	269	1	no	maximal, Sylow
60	C₂²×Q₁₆	D₂₆₉	1	1	yes	characteristic
61	C₂×M₃₂	—	269	1	no	—
62	#427	—	269	1	no	—
63	#358	—	269	4	no	—
64	C₂²×Q₈	—	2	1	no	—
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	—	2	2	no	—
67	C₂×Q₁₆	Dic₂₆₉	1	4	yes	complemented
68	C₂×Q₁₆	C₂×D₂₆₉	1	2	yes	—
69	C₂²×C₈	C₂×D₂₆₉	1	1	yes	characteristic
70	#117	—	538	1	no	—
71	M₃₂	—	538	2	no	—
72	C₂×C₁₆	—	269	2	no	—
73	#107	—	269	2	no	—
74	#106	—	538	1	no	—
75	C₂×Q₈	—	2	4	no	—
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	—	4	1	no	—
78	C₂×Q₈	—	4	2	no	—
79	C₂²×C₄	—	4	1	no	—
80	C₂²×C₄	C₂²⋊D₂₆₉	1	1	yes	characteristic
81	Q₁₆	—	2	4	no	—
82	Q₁₆	—	2	2	no	—
83	Q₁₆	C₂×Dic₂₆₉	1	4	yes	—
84	C₂×C₈	C₂×Dic₂₆₉	1	2	yes	—
85	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₂₆₉	1	2	yes	—
87	C₂×C₈	C₂²×D₂₆₉	1	1	yes	characteristic
88	C₄⋊C₄	—	538	2	no	—
89	C₂²⋊C₄	—	1076	1	no	—
90	C₄²	—	1076	1	no	—
91	C₁₆	—	538	2	no	—
92	C₂³	#16864387	1	1	yes	characteristic
93	Q₈	—	2	4	no	—
94	Q₈	—	4	4	no	—
95	Q₈	—	4	2	no	—
96	C₂×C₄	—	4	4	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	1076	2	no	—
99	C₂×C₄	C₂²⋊Dic₂₆₉	1	2	yes	—
100	C₂×C₄	#16864387	1	1	yes	characteristic
101	C₂×C₄	#16864390	1	2	yes	—
102	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
103	C₈	C₂²⋊Dic₂₆₉	1	2	yes	—
104	C₈	C₂²×Dic₂₆₉	1	1	yes	characteristic
105	C₈	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
106	C₂²	—	2	2	no	—
107	C₂²	#22575374	1	2	yes	—
108	C₂²	C₂×#16864387	1	1	yes	characteristic
109	C₄	—	4	4	no	—
110	C₄	—	2152	2	no	—
111	C₄	#22575374	1	2	yes	—
112	C₄	C₂×C₂²⋊Dic₂₆₉	1	1	yes	characteristic
113	C₄	C₂×#16864390	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	C₂×#22575374	1	1	yes	characteristic
116	C₂	#31771046	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22575393

C₂

yes

maximal, characteristic

#31770643

C₂

yes

maximal, characteristic

#31770409

C₂

yes

maximal, complemented

C₂²×Q₁₆×C₂₆₉

C₂

yes

maximal, characteristic

#22575412

—

#22575393

—

C₂×#16864377

C₂²

yes

—

#22575387

C₂²

yes

—

#22575385

—

C₂²×Q₈×C₂₆₉

—

C₂×Q₁₆×C₂₆₉

—

C₂×Q₁₆×C₂₆₉

—

C₂×Q₁₆×C₂₆₉

C₄

yes

complemented

C₂×Q₁₆×C₂₆₉

C₂²

yes

—

C₂²×C₈×C₂₆₉

C₂²

yes

characteristic

C₄⋊Dic₂₆₉

—

C₂²⋊Dic₂₆₉

—

C₄×Dic₂₆₉

—

#16864377

—

C₂×Q₈×C₂₆₉

—

C₂×Q₈×C₂₆₉

—

C₂×Q₈×C₂₆₉

—

C₂×Q₈×C₂₆₉

—

C₂²×C₄×C₂₆₉

—

C₂²×C₄×C₂₆₉

D₄

yes

characteristic

Q₁₆×C₂₆₉

—

Q₁₆×C₂₆₉

—

Q₁₆×C₂₆₉

C₂×C₄

yes

—

C₂×C₈×C₂₆₉

C₂×C₄

yes

—

C₂×C₈×C₂₆₉

D₄

yes

characteristic

C₂×C₈×C₂₆₉

D₄

yes

—

C₂×C₈×C₂₆₉

C₂³

yes

characteristic

C₂×Dic₂₆₉

—

C₂³×C₂₆₉

D₈

yes

characteristic

Q₈×C₂₆₉

—

Q₈×C₂₆₉

—

Q₈×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₆₉

D₈

yes

characteristic

C₂×C₄×C₂₆₉

SD₁₆

yes

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₈×C₂₆₉

C₂²⋊C₄

yes

—

C₈×C₂₆₉

C₂²×C₄

yes

characteristic

C₈×C₂₆₉

C₂×D₄

yes

characteristic

C₂²×C₂₆₉

—

C₂²×C₂₆₉

#102

yes

—

C₂²×C₂₆₉

C₂×D₈

yes

characteristic

C₄×C₂₆₉

—

C₄×C₂₆₉

#102

yes

—

C₄×C₂₆₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₆₉

C₂×SD₁₆

yes

characteristic

Dic₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

C₂×#102

yes

characteristic

C₂×C₂₆₉

#510

yes

—

C₂₆₉

#2141

yes

characteristic, complemented, Sylow

#2141

—

269

maximal, Sylow

C₂²×Q₁₆

D₂₆₉

yes

characteristic

C₂×M₃₂

—

269

—

#427

—

269

—

#358

—

269

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

Dic₂₆₉

yes

complemented

C₂×Q₁₆

C₂×D₂₆₉

yes

—

C₂²×C₈

C₂×D₂₆₉

yes

characteristic

#117

—

538

—

M₃₂

—

538

—

C₂×C₁₆

—

269

—

#107

—

269

—

#106

—

538

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₆₉

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

C₂×Dic₂₆₉

yes

—

C₂×C₈

C₂×Dic₂₆₉

yes

—

C₂×C₈

C₂²⋊D₂₆₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₆₉

yes

—

C₂×C₈

C₂²×D₂₆₉

yes

characteristic

C₄⋊C₄

—

538

—

C₂²⋊C₄

—

1076

—

C₄²

—

1076

—

C₁₆

—

538

—

C₂³

#16864387

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1076

—

C₂×C₄

C₂²⋊Dic₂₆₉

yes

—

100

C₂×C₄

#16864387

yes

characteristic

101

C₂×C₄

#16864390

yes

—

102

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

103

C₈

C₂²⋊Dic₂₆₉

yes

—

104

C₈

C₂²×Dic₂₆₉

yes

characteristic

105

C₈

C₂×C₂²⋊D₂₆₉

yes

characteristic

106

C₂²

—

107

C₂²

#22575374

yes

—

108

C₂²

C₂×#16864387

yes

characteristic

109

C₄

—

110

C₄

—

2152

—

111

C₄

#22575374

yes

—

112

C₄

C₂×C₂²⋊Dic₂₆₉

yes

characteristic

113

C₄

C₂×#16864390

yes

characteristic

114

C₂

—

115

C₂

C₂×#22575374

yes

characteristic

116

C₂

#31771046

yes

—

	subgroup	G/H
center	C₂²	C₂×#16864387
commutator	C₈×C₂₆₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₆₉
Fitting	C₂²×Q₁₆×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂×D₈
prime radical	C₂³×C₂₆₉	D₈
cosocle	C₂×C₈×C₂₆₉	C₂³
hypercenter	C₂²×Q₁₆	D₂₆₉
hypocenter	C₂₆₉	#2141
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

C₂×#16864387

commutator

C₈×C₂₆₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₂₆₉

Fitting

C₂²×Q₁₆×C₂₆₉

C₂

socle

C₂²×C₂₆₉

C₂×D₈

prime radical

C₂³×C₂₆₉

D₈

cosocle

C₂×C₈×C₂₆₉

C₂³

hypercenter

C₂²×Q₁₆

D₂₆₉

hypocenter

C₂₆₉

#2141

LCS

G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
3. #31770409	C₂	semidirect
13. C₂×Q₁₆×C₂₆₉	C₄	semidirect
58. C₂₆₉	#2141	semidirect
67. C₂×Q₁₆	Dic₂₆₉	semidirect

H ≅ G/N

type

3. #31770409

C₂

semidirect

13. C₂×Q₁₆×C₂₆₉

C₄

semidirect

58. C₂₆₉

#2141

semidirect

67. C₂×Q₁₆

Dic₂₆₉

semidirect

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

subgroup	index
C₂×#22575393	2
#31770643	2
#31770409	2
C₂²×Q₁₆×C₂₆₉	2
#2141	269

subgroup

index

C₂²×Q₁₆×C₂₆₉

269

Subgroups — #46812605

Conjugacy classes of subgroups

Complements

Maximal subgroups