Group #21447581 — subgroups

Subgroups — C₂×#16839582 #21447581

Order 7808.

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

normal subgroups only

This group has 168 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×#14519717	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839582	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	#14519717	—	2	1	no	—
8	#14519717	C₂²	1	2	yes	—
9	C₂×#11758185	—	2	1	no	—
10	C₈×Dic₆₁	C₄	1	2	yes	—
11	C₈×Dic₆₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	M₃₂×C₆₁	—	2	1	no	—
14	M₃₂×C₆₁	C₂²	1	2	yes	—
15	C₂×C₁₆×C₆₁	—	2	1	no	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	—	2	1	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
23	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
24	C₄×Dic₆₁	—	2	1	no	—
25	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
26	C₂×#92418	C₈	1	2	yes	—
27	C₂×#92418	C₈	1	2	yes	—
28	C₂×#92418	C₂×C₄	1	2	yes	—
29	C₁₆×C₆₁	—	2	2	no	—
30	#11758185	—	2	2	no	—
31	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	—	2	4	no	—
39	C₂×Dic₆₁	—	2	2	no	—
40	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
43	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
44	#92418	C₂×C₈	1	4	yes	—
45	C₂²×C₆₁	—	2	2	no	—
46	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
47	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
48	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
51	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
53	Dic₆₁	—	2	4	no	—
54	C₂×#364	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	—	2	1	no	—
57	C₂×C₆₁	#364	1	2	yes	complemented
58	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂×M₃₂	—	61	1	no	—
60	C₂×M₃₂	D₆₁	1	1	yes	characteristic
61	C₂×C₄×C₈	—	61	1	no	—
62	#364	—	61	4	no	—
63	C₆₁	C₂×#364	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	61	1	no	—
65	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
66	C₂×C₄²	—	61	1	no	—
67	M₃₂	—	2	1	no	—
68	M₃₂	—	61	2	no	—
69	M₃₂	—	122	1	no	—
70	M₃₂	C₂×D₆₁	1	2	yes	—
71	C₂×C₁₆	—	2	1	no	—
72	C₂×C₁₆	—	122	1	no	—
73	C₄×C₈	—	61	2	no	—
74	C₄×C₈	—	61	2	no	—
75	C₂²×C₄	—	122	1	no	—
76	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
77	C₂×C₈	—	61	2	no	—
78	C₂×C₈	—	61	2	no	—
79	C₂×C₈	—	61	2	no	—
80	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
81	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
82	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
84	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
85	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
86	C₄²	—	61	2	no	—
87	C₄²	—	122	1	no	—
88	C₁₆	—	2	2	no	—
89	C₁₆	—	122	2	no	—
90	C₂³	#11758189	1	1	yes	characteristic
91	C₂×C₄	—	122	4	no	—
92	C₂×C₄	—	122	2	no	—
93	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
94	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
95	C₂×C₄	#11758189	1	1	yes	characteristic
96	C₂×C₄	#11758196	1	1	yes	characteristic
97	C₂×C₄	#11758196	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
99	C₈	—	61	4	no	—
100	C₈	#11758196	1	1	yes	characteristic
101	C₈	#11758196	1	1	yes	characteristic
102	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
103	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
104	C₂²	—	2	2	no	—
105	C₂²	#14519706	1	1	yes	characteristic
106	C₂²	#14519706	1	1	yes	characteristic
107	C₂²	C₂×#11758189	1	1	yes	characteristic
108	C₄	—	122	4	no	—
109	C₄	#14519706	1	1	yes	characteristic
110	C₄	#14519706	1	1	yes	characteristic
111	C₄	C₂×#11758196	1	1	yes	characteristic
112	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#16839582	1	2	yes	direct product factor
116	C₂	C₂×#14519706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

#16839582

C₂

yes

maximal, direct product factor

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

#14519717

—

#14519717

C₂²

yes

—

C₂×#11758185

—

C₈×Dic₆₁

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

M₃₂×C₆₁

C₂²

yes

—

C₂×C₁₆×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

C₈

yes

—

C₂×#92418

C₈

yes

—

C₂×#92418

C₂×C₄

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

C₂×C₈

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

C₂×#364

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#364

yes

complemented

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

D₆₁

yes

characteristic

C₂×C₄×C₈

—

#364

—

C₆₁

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

122

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

122

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

122

—

C₁₆

—

C₁₆

—

122

—

C₂³

#11758189

yes

characteristic

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

characteristic

C₂×C₄

C₈×D₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

100

C₈

#11758196

yes

characteristic

101

C₈

#11758196

yes

characteristic

102

C₈

C₂×Dic₁₂₂

yes

characteristic

103

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

104

C₂²

—

105

C₂²

#14519706

yes

characteristic

106

C₂²

#14519706

yes

characteristic

107

C₂²

C₂×#11758189

yes

characteristic

108

C₄

—

122

—

109

C₄

#14519706

yes

characteristic

110

C₄

#14519706

yes

characteristic

111

C₄

C₂×#11758196

yes

characteristic

112

C₄

C₂×C₈×D₆₁

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#16839582

yes

direct product factor

116

C₂

C₂×#14519706

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×M₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₄⋊C₈
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	C₂×#364
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×M₃₂×C₆₁

C₂

socle

C₂²×C₆₁

C₄⋊C₈

hypercenter

C₂×M₃₂

D₆₁

hypocenter

C₆₁

C₂×#364

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #16839582	C₂	direct (N × H)
57. C₂×C₆₁	#364	semidirect
63. C₆₁	C₂×#364	semidirect
115. C₂	#16839582	direct (N × H)

H ≅ G/N

type

3. #16839582

C₂

direct (N × H)

57. C₂×C₆₁

#364

semidirect

63. C₆₁

C₂×#364

semidirect

115. C₂

#16839582

direct (N × H)

Subgroups — C₂×#16839582 #21447581

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16839582 #21447581

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839582 #21447581