Group #21447539 — subgroups

Subgroups — #21447539

Order 7808.

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×#14519717	C₂	1	1	yes	maximal, characteristic
2	#16839800	C₂	1	1	yes	maximal, characteristic
3	#16839566	C₂	1	4	yes	maximal, complemented
4	C₂²×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519736	—	2	1	no	—
6	#14519717	—	2	2	no	—
7	C₂×#11758185	C₂²	1	2	yes	—
8	#14519711	C₂²	1	2	yes	—
9	#14519709	—	2	1	no	—
10	C₂²×Q₈×C₆₁	—	2	1	no	—
11	C₂×Q₁₆×C₆₁	—	2	1	no	—
12	C₂×Q₁₆×C₆₁	—	2	2	no	—
13	C₂×Q₁₆×C₆₁	C₄	1	4	yes	complemented
14	C₂×Q₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₆₁	—	2	4	no	—
17	C₂×Q₈×C₆₁	—	2	2	no	—
18	C₂×Q₈×C₆₁	—	4	1	no	—
19	C₂×Q₈×C₆₁	—	4	2	no	—
20	C₂²×C₄×C₆₁	—	4	1	no	—
21	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
22	Q₁₆×C₆₁	—	2	4	no	—
23	Q₁₆×C₆₁	—	2	2	no	—
24	Q₁₆×C₆₁	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
27	C₂×C₈×C₆₁	D₄	1	2	yes	—
28	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
29	C₂²⋊Dic₆₁	—	4	1	no	—
30	C₄⋊Dic₆₁	—	2	2	no	—
31	C₄×Dic₆₁	—	4	1	no	—
32	#11758185	—	2	2	no	—
33	C₂³×C₆₁	D₈	1	1	yes	characteristic
34	Q₈×C₆₁	—	2	4	no	—
35	Q₈×C₆₁	—	4	4	no	—
36	Q₈×C₆₁	—	4	2	no	—
37	C₂×C₄×C₆₁	—	4	4	no	—
38	C₂×C₄×C₆₁	—	4	2	no	—
39	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
41	C₂×C₄×C₆₁	SD₁₆	1	2	yes	—
42	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
43	C₂×Dic₆₁	—	4	2	no	—
44	C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
45	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₆₁	—	2	2	no	—
48	C₂²×C₆₁	#102	1	2	yes	—
49	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
50	C₄×C₆₁	—	4	4	no	—
51	C₄×C₆₁	#102	1	2	yes	—
52	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
54	Dic₆₁	—	8	2	no	—
55	#2141	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	2	2	no	—
57	C₂×C₆₁	C₂×#102	1	1	yes	characteristic
58	C₂×C₆₁	#510	1	2	yes	—
59	C₂²×Q₁₆	D₆₁	1	1	yes	characteristic
60	C₂×M₃₂	—	61	1	no	—
61	#427	—	61	1	no	—
62	#358	—	61	4	no	—
63	C₆₁	#2141	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	2	1	no	—
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	—	2	2	no	—
67	C₂×Q₁₆	Dic₆₁	1	4	yes	complemented
68	C₂×Q₁₆	C₂×D₆₁	1	2	yes	—
69	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
70	#117	—	122	1	no	—
71	M₃₂	—	122	2	no	—
72	C₂×C₁₆	—	61	2	no	—
73	#107	—	61	2	no	—
74	#106	—	122	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⋊D₆₁	1	1	yes	characteristic
81	Q₁₆	—	2	4	no	—
82	Q₁₆	—	2	2	no	—
83	Q₁₆	C₂×Dic₆₁	1	4	yes	—
84	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
85	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
87	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
88	C₄⋊C₄	—	122	2	no	—
89	C₂²⋊C₄	—	244	1	no	—
90	C₄²	—	244	1	no	—
91	C₁₆	—	122	2	no	—
92	C₂³	#11758199	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	—	244	2	no	—
99	C₂×C₄	#11758199	1	1	yes	characteristic
100	C₂×C₄	#11758200	1	2	yes	—
101	C₂×C₄	C₂²⋊Dic₆₁	1	2	yes	—
102	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
103	C₈	C₂²⋊Dic₆₁	1	2	yes	—
104	C₈	C₂²×Dic₆₁	1	1	yes	characteristic
105	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
106	C₂²	—	2	2	no	—
107	C₂²	#14519698	1	2	yes	—
108	C₂²	C₂×#11758199	1	1	yes	characteristic
109	C₄	—	4	4	no	—
110	C₄	—	488	2	no	—
111	C₄	#14519698	1	2	yes	—
112	C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
113	C₄	C₂×#11758200	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	C₂×#14519698	1	1	yes	characteristic
116	C₂	#16840203	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

#16839800

C₂

yes

maximal, characteristic

#16839566

C₂

yes

maximal, complemented

C₂²×Q₁₆×C₆₁

C₂

yes

maximal, characteristic

#14519736

—

#14519717

—

C₂×#11758185

C₂²

yes

—

#14519711

C₂²

yes

—

#14519709

—

C₂²×Q₈×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

C₄

yes

complemented

C₂×Q₁₆×C₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758185

—

C₂³×C₆₁

D₈

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₈×C₆₁

C₂²⋊C₄

yes

—

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

#102

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#102

yes

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

characteristic

Dic₆₁

—

#2141

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×#102

yes

characteristic

C₂×C₆₁

#510

yes

—

C₂²×Q₁₆

D₆₁

yes

characteristic

C₂×M₃₂

—

#427

—

#358

—

C₆₁

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

Dic₆₁

yes

complemented

C₂×Q₁₆

C₂×D₆₁

yes

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

122

—

M₃₂

—

122

—

C₂×C₁₆

—

#107

—

#106

—

122

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

C₂×Dic₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₁₆

—

122

—

C₂³

#11758199

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

#11758199

yes

characteristic

100

C₂×C₄

#11758200

yes

—

101

C₂×C₄

C₂²⋊Dic₆₁

yes

—

102

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

103

C₈

C₂²⋊Dic₆₁

yes

—

104

C₈

C₂²×Dic₆₁

yes

characteristic

105

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

106

C₂²

—

107

C₂²

#14519698

yes

—

108

C₂²

C₂×#11758199

yes

characteristic

109

C₄

—

110

C₄

—

488

—

111

C₄

#14519698

yes

—

112

C₄

C₂×C₂²⋊Dic₆₁

yes

characteristic

113

C₄

C₂×#11758200

yes

characteristic

114

C₂

—

115

C₂

C₂×#14519698

yes

characteristic

116

C₂

#16840203

yes

—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂²×Q₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₂²×Q₁₆	D₆₁
hypocenter	C₆₁	#2141
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂²×Q₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₂²×Q₁₆

D₆₁

hypocenter

C₆₁

#2141

LCS

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
3. #16839566	C₂	semidirect
13. C₂×Q₁₆×C₆₁	C₄	semidirect
63. C₆₁	#2141	semidirect
67. C₂×Q₁₆	Dic₆₁	semidirect

H ≅ G/N

type

3. #16839566

C₂

semidirect

13. C₂×Q₁₆×C₆₁

C₄

semidirect

63. C₆₁

#2141

semidirect

67. C₂×Q₁₆

Dic₆₁

semidirect

Subgroups — #21447539

Conjugacy classes of subgroups

Complements