Group #49095156 — subgroups

Subgroups — #49095156

Order 35968.

292 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 165 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×C₄⋊#14555886	C₂	1	2	yes	maximal
2	C₂×#22582790	C₂	1	2	yes	maximal
3	#31823218	C₂	1	2	yes	maximal
4	C₄³×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14555886	C₂²	1	4	yes	—
6	C₄⋊#14555886	C₄	1	8	yes	complemented
7	#22582790	—	2	4	no	—
8	C₂×C₄²×C₂₈₁	C₄	1	2	yes	—
9	C₂×C₄²×C₂₈₁	C₄	1	2	yes	—
10	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₂×#14555886	—	2	4	no	—
14	C₂×#14555886	—	2	4	no	—
15	C₂×#14555886	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₈₁	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₂₈₁	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
21	C₄²×C₂₈₁	—	2	4	no	—
22	C₄²×C₂₈₁	—	2	4	no	—
23	C₄²×C₂₈₁	—	2	2	no	—
24	C₄²×C₂₈₁	C₂×C₄	1	4	yes	—
25	C₄²×C₂₈₁	D₄	1	2	yes	—
26	C₄²×C₂₈₁	Q₈	1	2	yes	—
27	#14555886	—	2	8	no	—
28	C₂³×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	—	2	2	no	—
30	C₂×C₄×C₂₈₁	—	2	2	no	—
31	C₂×C₄×C₂₈₁	—	2	2	no	—
32	C₂×C₄×C₂₈₁	—	2	2	no	—
33	C₂×C₄×C₂₈₁	—	2	2	no	—
34	C₂×C₄×C₂₈₁	C₄²	1	2	yes	—
35	C₂×C₄×C₂₈₁	C₄²	1	2	yes	—
36	C₂×C₄×C₂₈₁	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₂₈₁	M₁₆	1	4	yes	—
38	C₂×C₄×C₂₈₁	M₁₆	1	4	yes	—
39	C₂×C₄×C₂₈₁	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₂₈₁	#41	1	2	yes	—
43	C₂²×C₂₈₁	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₂₈₁	#117	1	1	yes	characteristic
46	C₂²×C₂₈₁	C₂×M₁₆	1	2	yes	—
47	C₂²×C₂₈₁	C₂×M₁₆	1	2	yes	—
48	C₄×C₂₈₁	—	2	2	no	—
49	C₄×C₂₈₁	—	2	4	no	—
50	C₄×C₂₈₁	—	2	4	no	—
51	C₄×C₂₈₁	#97	1	4	yes	complemented
52	C₄×C₂₈₁	C₄×D₄	1	2	yes	—
53	C₄×C₂₈₁	C₄×Q₈	1	2	yes	—
54	C₂×C₂₈₁	C₄×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₂₈₁	C₂×#97	1	1	yes	characteristic
56	C₂×C₂₈₁	C₄×M₁₆	1	1	yes	characteristic
57	C₂×C₂₈₁	#423	1	2	yes	—
58	C₂×C₂₈₁	#432	1	2	yes	—
59	C₂₈₁	#1767	1	1	yes	characteristic, complemented, Sylow
60	#1767	—	281	1	no	maximal, Sylow
61	C₂×C₄⋊C₈	—	281	2	no	—
62	C₂×#97	—	281	2	no	—
63	C₄³	D₂₈₁	1	1	yes	characteristic
64	#336	—	281	2	no	—
65	C₂²×C₈	—	281	4	no	—
66	C₂×C₄²	Dic₂₈₁	1	2	yes	—
67	C₂×C₄²	Dic₂₈₁	1	2	yes	—
68	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
69	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
70	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
71	C₄⋊C₈	—	281	8	no	—
72	#97	—	562	4	no	—
73	C₂²×C₄	C₂×Dic₂₈₁	1	1	yes	characteristic
74	C₂²×C₄	C₂×Dic₂₈₁	1	2	yes	—
75	C₂²×C₄	C₂×Dic₂₈₁	1	2	yes	—
76	C₂²×C₄	C₂×Dic₂₈₁	1	1	yes	characteristic
77	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
78	C₂×C₈	—	281	8	no	—
79	C₂×C₈	—	562	4	no	—
80	C₂×C₈	—	562	4	no	—
81	C₄²	—	2	4	no	—
82	C₄²	—	2	4	no	—
83	C₄²	—	2	2	no	—
84	C₄²	C₄×D₂₈₁	1	4	yes	—
85	C₄²	D₁₁₂₄	1	2	yes	—
86	C₄²	Dic₅₆₂	1	2	yes	—
87	C₂³	C₂²×Dic₂₈₁	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	C₄×Dic₂₈₁	1	2	yes	—
94	C₂×C₄	C₄×Dic₂₈₁	1	2	yes	—
95	C₂×C₄	C₄⋊Dic₂₈₁	1	4	yes	—
96	C₂×C₄	#17985122	1	4	yes	—
97	C₂×C₄	#17985122	1	4	yes	—
98	C₂×C₄	C₂×C₄×D₂₈₁	1	2	yes	—
99	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
100	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
101	C₂×C₄	#17985138	1	2	yes	—
102	C₈	—	562	8	no	—
103	C₂²	C₂×C₄×Dic₂₈₁	1	1	yes	characteristic
104	C₂²	C₂×C₄⋊Dic₂₈₁	1	1	yes	characteristic
105	C₂²	#22582838	1	1	yes	characteristic
106	C₂²	C₂×#17985122	1	2	yes	—
107	C₂²	C₂×#17985122	1	2	yes	—
108	C₄	—	2	2	no	—
109	C₄	—	2	4	no	—
110	C₄	—	2	4	no	—
111	C₄	#22582790	1	4	yes	complemented
112	C₄	C₄×D₁₁₂₄	1	2	yes	—
113	C₄	C₄×Dic₅₆₂	1	2	yes	—
114	C₂	C₄×C₄⋊Dic₂₈₁	1	1	yes	characteristic
115	C₂	C₂×#22582790	1	1	yes	characteristic
116	C₂	C₄×#17985122	1	1	yes	characteristic
117	C₂	#31823487	1	2	yes	—
118	C₂	#31823520	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14555886

C₂

yes

maximal

C₂×#22582790

C₂

yes

maximal

#31823218

C₂

yes

maximal

C₄³×C₂₈₁

C₂

yes

maximal, characteristic

C₂²×#14555886

C₂²

yes

—

C₄⋊#14555886

C₄

yes

complemented

#22582790

—

C₂×C₄²×C₂₈₁

C₄

yes

—

C₂×C₄²×C₂₈₁

C₄

yes

—

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₂×C₄²×C₂₈₁

C₂²

yes

—

—

C₂×C₄

yes

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂×C₄

yes

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂³

yes

characteristic

C₄²×C₂₈₁

—

C₄²×C₂₈₁

—

C₄²×C₂₈₁

—

C₄²×C₂₈₁

C₂×C₄

yes

—

C₄²×C₂₈₁

D₄

yes

—

C₄²×C₂₈₁

Q₈

yes

—

#14555886

—

C₂³×C₂₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₄²

yes

—

C₂×C₄×C₂₈₁

C₄²

yes

—

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₈₁

M₁₆

yes

—

C₂×C₄×C₂₈₁

M₁₆

yes

—

C₂×C₄×C₂₈₁

C₂²×C₄

yes

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

#41

yes

—

C₂²×C₂₈₁

C₂×C₄²

yes

characteristic

C₂²×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₈₁

#117

yes

characteristic

C₂²×C₂₈₁

C₂×M₁₆

yes

—

C₂²×C₂₈₁

C₂×M₁₆

yes

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

#97

yes

complemented

C₄×C₂₈₁

C₄×D₄

yes

—

C₄×C₂₈₁

C₄×Q₈

yes

—

C₂×C₂₈₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₈₁

C₂×#97

yes

characteristic

C₂×C₂₈₁

C₄×M₁₆

yes

characteristic

C₂×C₂₈₁

#423

yes

—

C₂×C₂₈₁

#432

yes

—

C₂₈₁

#1767

yes

characteristic, complemented, Sylow

#1767

—

281

maximal, Sylow

C₂×C₄⋊C₈

—

281

—

C₂×#97

—

281

—

C₄³

D₂₈₁

yes

characteristic

#336

—

281

—

C₂²×C₈

—

281

—

C₂×C₄²

Dic₂₈₁

yes

—

C₂×C₄²

Dic₂₈₁

yes

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₄⋊C₈

—

281

—

#97

—

562

—

C₂²×C₄

C₂×Dic₂₈₁

yes

characteristic

C₂²×C₄

C₂×Dic₂₈₁

yes

—

C₂²×C₄

C₂×Dic₂₈₁

yes

—

C₂²×C₄

C₂×Dic₂₈₁

yes

characteristic

C₂²×C₄

C₂²×D₂₈₁

yes

characteristic

C₂×C₈

—

281

—

C₂×C₈

—

562

—

C₂×C₈

—

562

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₂₈₁

yes

—

C₄²

D₁₁₂₄

yes

—

C₄²

Dic₅₆₂

yes

—

C₂³

C₂²×Dic₂₈₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₂₈₁

yes

—

C₂×C₄

C₄×Dic₂₈₁

yes

—

C₂×C₄

C₄⋊Dic₂₈₁

yes

—

C₂×C₄

#17985122

yes

—

C₂×C₄

#17985122

yes

—

C₂×C₄

C₂×C₄×D₂₈₁

yes

—

C₂×C₄

C₂×D₁₁₂₄

yes

characteristic

100

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

101

C₂×C₄

#17985138

yes

—

102

C₈

—

562

—

103

C₂²

C₂×C₄×Dic₂₈₁

yes

characteristic

104

C₂²

C₂×C₄⋊Dic₂₈₁

yes

characteristic

105

C₂²

#22582838

yes

characteristic

106

C₂²

C₂×#17985122

yes

—

107

C₂²

C₂×#17985122

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#22582790

yes

complemented

112

C₄

C₄×D₁₁₂₄

yes

—

113

C₄

C₄×Dic₅₆₂

yes

—

114

C₂

C₄×C₄⋊Dic₂₈₁

yes

characteristic

115

C₂

C₂×#22582790

yes

characteristic

116

C₂

C₄×#17985122

yes

characteristic

117

C₂

#31823487

yes

—

118

C₂

#31823520

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₈₁
commutator	C₂²×C₂₈₁	C₂×C₄²
Fitting	C₄³×C₂₈₁	C₂
socle, prime radical	C₂³×C₂₈₁	C₂²×C₄
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₄³	D₂₈₁
hypocenter	C₂₈₁	#1767
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₈₁

commutator

C₂²×C₂₈₁

C₂×C₄²

Fitting

C₄³×C₂₈₁

C₂

socle, prime radical

C₂³×C₂₈₁

C₂²×C₄

cosocle

C₂²×C₄×C₂₈₁

C₂³

hypercenter

C₄³

D₂₈₁

C₂₈₁

G ▷ C₂²×C₂₈₁ ▷ C₂₈₁

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
6. C₄⋊#14555886	C₄	semidirect
51. C₄×C₂₈₁	#97	semidirect
59. C₂₈₁	#1767	semidirect
111. C₄	#22582790	semidirect

H ≅ G/N

type

6. C₄⋊#14555886

C₄

semidirect

51. C₄×C₂₈₁

#97

semidirect

59. C₂₈₁

#1767

semidirect

111. C₄

#22582790

semidirect

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

subgroup	index
C₂×C₄⋊#14555886	2
C₂×#22582790	2
#31823218	2
C₄³×C₂₈₁	2
#1767	281

subgroup

index

C₄³×C₂₈₁

281

Subgroups — #49095156

Conjugacy classes of subgroups

Complements

Maximal subgroups