Group #34069283 — subgroups

Subgroups — #34069283

Order 19328.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×#18012675	C₂	1	1	yes	maximal, characteristic
2	C₂×#18012674	C₂	1	2	yes	maximal
3	#23752235	C₂	1	2	yes	maximal
4	C₂×#18012649	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#14558988	C₂²	1	2	yes	—
7	C₂²×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic
9	#18012675	—	2	2	no	—
10	#18012674	—	2	4	no	—
11	Dic₁₅₁⋊C₈	—	2	4	no	—
12	#18012649	C₄	1	4	yes	—
13	C₂×M₁₆×C₁₅₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
15	#108×C₁₅₁	—	2	2	no	—
16	C₂²×Dic₁₅₁	Q₈	1	2	yes	—
17	#14558988	—	2	2	no	—
18	#14558988	—	2	2	no	—
19	C₂×C₁₅₁⋊C₈	—	2	2	no	—
20	C₂×C₁₅₁⋊C₈	C₂×C₄	1	2	yes	—
21	C₂×C₁₅₁⋊C₈	D₄	1	2	yes	—
22	C₂×C₁₅₁⋊C₈	Q₈	1	2	yes	—
23	C₄×Dic₁₅₁	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₅₁	D₄	1	2	yes	—
25	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
26	M₁₆×C₁₅₁	—	2	2	no	—
27	M₁₆×C₁₅₁	—	2	2	no	—
28	C₂×C₈×C₁₅₁	—	2	2	no	—
29	C₂×C₈×C₁₅₁	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₅₁	D₄	1	2	yes	—
31	C₂×C₈×C₁₅₁	Q₈	1	2	yes	—
32	C₂×Dic₁₅₁	—	4	2	no	—
33	C₂×Dic₁₅₁	C₄⋊C₄	1	4	yes	—
34	C₁₅₁⋊C₈	—	4	2	no	—
35	C₁₅₁⋊C₈	C₄⋊C₄	1	4	yes	—
36	C₂³×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
43	C₈×C₁₅₁	—	4	2	no	—
44	C₈×C₁₅₁	C₄⋊C₄	1	4	yes	—
45	C₂²×C₁₅₁	—	2	2	no	—
46	C₂²×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
49	C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₁₅₁	#127	1	1	yes	characteristic
52	C₄×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₁₅₁	—	2	4	no	—
54	C₂×C₁₅₁	—	2	1	no	—
55	C₂×C₁₅₁	—	2	1	no	—
56	C₂×C₁₅₁	#384	1	1	yes	characteristic
57	C₂×C₁₅₁	#430	1	2	yes	—
58	C₁₅₁	#1849	1	1	yes	characteristic, complemented, Sylow
59	#1849	—	151	1	no	maximal, Sylow
60	C₂×#108	—	151	2	no	—
61	C₂×#108	—	151	1	no	—
62	C₂×#108	D₁₅₁	1	1	yes	characteristic
63	#423	—	151	2	no	—
64	C₂×#97	—	151	1	no	—
65	C₂×M₁₆	—	151	2	no	—
66	C₂×M₁₆	C₂×D₁₅₁	1	2	yes	—
67	C₂²×C₈	—	151	1	no	—
68	C₂²×C₈	C₂×D₁₅₁	1	1	yes	characteristic
69	C₂×C₄²	—	151	1	no	—
70	#108	—	2	2	no	—
71	#108	—	302	4	no	—
72	#108	—	302	2	no	—
73	C₄⋊C₈	—	302	4	no	—
74	#97	—	151	4	no	—
75	C₂²×C₄	—	151	2	no	—
76	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	302	2	no	—
80	M₁₆	—	302	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	302	2	no	—
83	C₂×C₈	—	151	2	no	—
84	C₂×C₈	—	151	2	no	—
85	C₂×C₈	—	151	2	no	—
86	C₂×C₈	C₄×D₁₅₁	1	2	yes	—
87	C₂×C₈	C₂²⋊D₁₅₁	1	2	yes	—
88	C₂×C₈	Dic₃₀₂	1	2	yes	—
89	C₄²	—	151	2	no	—
90	C₄²	—	151	2	no	—
91	C₂³	Q₈×D₁₅₁	1	1	yes	characteristic
92	C₂×C₄	—	604	2	no	—
93	C₂×C₄	—	151	4	no	—
94	C₂×C₄	C₂×C₄×D₁₅₁	1	1	yes	characteristic
95	C₂×C₄	D₄×D₁₅₁	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₅₁	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₁₅₁	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₁₅₁	1	1	yes	characteristic
99	C₂×C₄	C₂×Dic₃₀₂	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	604	2	no	—
102	C₈	—	151	4	no	—
103	C₈	Dic₁₅₁⋊C₄	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₁₅₁	1	1	yes	characteristic
106	C₂²	#18012737	1	1	yes	characteristic
107	C₂²	#18012738	1	1	yes	characteristic
108	C₄	—	302	4	no	—
109	C₄	C₄⋊C₄×D₁₅₁	1	1	yes	characteristic
110	C₄	C₂×Dic₁₅₁⋊C₄	1	1	yes	characteristic
111	C₄	#18012735	1	1	yes	characteristic
112	C₄	#18012738	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#23752081	1	1	yes	characteristic
116	C₂	#23752259	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18012675

C₂

yes

maximal, characteristic

C₂×#18012674

C₂

yes

maximal

#23752235

C₂

yes

maximal

C₂×#18012649

C₂

yes

maximal, characteristic

C₂×#108×C₁₅₁

C₂

yes

maximal, characteristic

C₂×#14558988

C₂²

yes

—

C₂²×C₁₅₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₁₅₁

C₂²

yes

characteristic

#18012675

—

#18012674

—

Dic₁₅₁⋊C₈

—

#18012649

C₄

yes

—

C₂×M₁₆×C₁₅₁

C₂²

yes

—

C₂²×C₈×C₁₅₁

C₂²

yes

characteristic

#108×C₁₅₁

—

C₂²×Dic₁₅₁

Q₈

yes

—

#14558988

—

#14558988

—

C₂×C₁₅₁⋊C₈

—

C₂×C₁₅₁⋊C₈

C₂×C₄

yes

—

C₂×C₁₅₁⋊C₈

D₄

yes

—

C₂×C₁₅₁⋊C₈

Q₈

yes

—

C₄×Dic₁₅₁

C₂×C₄

yes

—

C₄×Dic₁₅₁

D₄

yes

—

C₂²×C₄×C₁₅₁

C₂³

yes

characteristic

M₁₆×C₁₅₁

—

M₁₆×C₁₅₁

—

C₂×C₈×C₁₅₁

—

C₂×C₈×C₁₅₁

C₂×C₄

yes

—

C₂×C₈×C₁₅₁

D₄

yes

—

C₂×C₈×C₁₅₁

Q₈

yes

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

C₄⋊C₄

yes

—

C₁₅₁⋊C₈

—

C₁₅₁⋊C₈

C₄⋊C₄

yes

—

C₂³×C₁₅₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₅₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₅₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₅₁

C₂×Q₈

yes

characteristic

C₈×C₁₅₁

—

C₈×C₁₅₁

C₄⋊C₄

yes

—

C₂²×C₁₅₁

—

C₂²×C₁₅₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₅₁

C₄⋊Q₈

yes

characteristic

C₂²×C₁₅₁

C₄⋊Q₈

yes

characteristic

C₄×C₁₅₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₅₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₅₁

#127

yes

characteristic

C₄×C₁₅₁

C₄⋊Q₈

yes

characteristic

Dic₁₅₁

—

C₂×C₁₅₁

—

C₂×C₁₅₁

—

C₂×C₁₅₁

#384

yes

characteristic

C₂×C₁₅₁

#430

yes

—

C₁₅₁

#1849

yes

characteristic, complemented, Sylow

#1849

—

151

maximal, Sylow

C₂×#108

—

151

—

C₂×#108

—

151

—

C₂×#108

D₁₅₁

yes

characteristic

#423

—

151

—

C₂×#97

—

151

—

C₂×M₁₆

—

151

—

C₂×M₁₆

C₂×D₁₅₁

yes

—

C₂²×C₈

—

151

—

C₂²×C₈

C₂×D₁₅₁

yes

characteristic

C₂×C₄²

—

151

—

#108

—

#108

—

302

—

#108

—

302

—

C₄⋊C₈

—

302

—

#97

—

151

—

C₂²×C₄

—

151

—

C₂²×C₄

C₂²×D₁₅₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

302

—

M₁₆

—

302

—

C₂×C₈

—

C₂×C₈

—

302

—

C₂×C₈

—

151

—

C₂×C₈

—

151

—

C₂×C₈

—

151

—

C₂×C₈

C₄×D₁₅₁

yes

—

C₂×C₈

C₂²⋊D₁₅₁

yes

—

C₂×C₈

Dic₃₀₂

yes

—

C₄²

—

151

—

C₄²

—

151

—

C₂³

Q₈×D₁₅₁

yes

characteristic

C₂×C₄

—

604

—

C₂×C₄

—

151

—

C₂×C₄

C₂×C₄×D₁₅₁

yes

characteristic

C₂×C₄

D₄×D₁₅₁

yes

characteristic

C₂×C₄

D₄×D₁₅₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₅₁

yes

characteristic

C₂×C₄

Q₈×D₁₅₁

yes

characteristic

C₂×C₄

C₂×Dic₃₀₂

yes

characteristic

100

C₈

—

101

C₈

—

604

—

102

C₈

—

151

—

103

C₈

Dic₁₅₁⋊C₄

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₁₅₁

yes

characteristic

106

C₂²

#18012737

yes

characteristic

107

C₂²

#18012738

yes

characteristic

108

C₄

—

302

—

109

C₄

C₄⋊C₄×D₁₅₁

yes

characteristic

110

C₄

C₂×Dic₁₅₁⋊C₄

yes

characteristic

111

C₄

#18012735

yes

characteristic

112

C₄

#18012738

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#23752081

yes

characteristic

116

C₂

#23752259

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅₁
commutator	C₂×C₄×C₁₅₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅₁
Fitting	C₂×#108×C₁₅₁	C₂
socle	C₂²×C₁₅₁	C₂×C₄⋊C₄
prime radical	C₂³×C₁₅₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₅₁	C₂³
hypercenter	C₂×#108	D₁₅₁
hypocenter	C₁₅₁	#1849
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₅₁

commutator

C₂×C₄×C₁₅₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₅₁

Fitting

C₂×#108×C₁₅₁

C₂

socle

C₂²×C₁₅₁

C₂×C₄⋊C₄

prime radical

C₂³×C₁₅₁

C₂×Q₈

cosocle

C₂²×C₄×C₁₅₁

C₂³

D₁₅₁

C₁₅₁

G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
58. C₁₅₁	#1849	semidirect

H ≅ G/N

type

58. C₁₅₁

#1849

semidirect

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

subgroup	index
C₂×#18012675	2
C₂×#18012674	2
#23752235	2
C₂×#18012649	2
C₂×#108×C₁₅₁	2
#1849	151

subgroup

index

C₂×#108×C₁₅₁

151

Subgroups — #34069283

Conjugacy classes of subgroups

Complements

Maximal subgroups