Group #21447869 — subgroups

Subgroups — #21447869

Order 7808.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14519723	C₂	1	2	yes	maximal
2	#16840142	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic
4	#16839565	C₂	1	2	yes	maximal
5	C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	—	2	1	no	—
7	C₂×Dic₂₄₄	C₂²	1	2	yes	—
8	#14519777	—	2	1	no	—
9	#14519723	—	2	4	no	—
10	C₂×#11758185	C₂²	1	2	yes	—
11	C₂×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×Q₈×C₆₁	—	2	1	no	—
13	#107×C₆₁	C₂²	1	1	yes	characteristic
14	#103×C₆₁	—	2	1	no	—
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₆₁	—	2	1	no	—
17	C₂×Dic₁₂₂	—	2	2	no	—
18	Q₁₆×C₆₁	—	2	1	no	—
19	Q₁₆×C₆₁	D₄	1	2	yes	—
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₄⋊C₄×C₆₁	—	4	1	no	—
24	C₄²×C₆₁	—	4	1	no	—
25	C₄²×C₆₁	D₄	1	1	yes	characteristic
26	C₄⋊Dic₆₁	—	4	1	no	—
27	C₄⋊Dic₆₁	—	4	1	no	—
28	Dic₂₄₄	—	2	2	no	—
29	Dic₂₄₄	—	2	2	no	—
30	Dic₂₄₄	—	4	2	no	—
31	#11758185	—	2	2	no	—
32	Q₈×C₆₁	—	2	2	no	—
33	Q₈×C₆₁	—	4	1	no	—
34	C₂×C₄×C₆₁	—	4	1	no	—
35	C₂×C₄×C₆₁	—	4	1	no	—
36	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
37	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₆₁	—	4	2	no	—
40	Dic₁₂₂	—	4	2	no	—
41	Dic₁₂₂	—	4	2	no	—
42	C₈×C₆₁	—	2	1	no	—
43	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
44	C₈×C₆₁	#41	1	1	yes	characteristic
45	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	—	4	2	no	—
48	C₄×C₆₁	—	8	1	no	—
49	C₄×C₆₁	Q₃₂	1	2	yes	complemented
50	C₄×C₆₁	#121	1	1	yes	characteristic
51	C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
52	Dic₆₁	—	8	2	no	—
53	#2209	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	#459	1	1	yes	characteristic
55	C₂×C₆₁	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₆₁	#510	1	1	yes	characteristic
57	C₂×Q₃₂	—	61	2	no	—
58	#494	—	61	1	no	—
59	C₄×Q₁₆	D₆₁	1	1	yes	characteristic
60	C₄⋊C₁₆	—	61	1	no	—
61	#358	—	61	2	no	—
62	C₆₁	#2209	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	61	2	no	—
64	C₂×Q₁₆	—	122	1	no	—
65	C₂×Q₁₆	C₂×D₆₁	1	1	yes	characteristic
66	C₄⋊Q₈	—	122	1	no	—
67	C₄×Q₈	—	2	1	no	—
68	Q₃₂	—	122	4	no	—
69	C₂×C₁₆	—	61	2	no	—
70	#107	C₂×D₆₁	1	1	yes	characteristic
71	#103	—	2	1	no	—
72	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	122	2	no	—
75	Q₁₆	—	2	1	no	—
76	Q₁₆	—	122	2	no	—
77	Q₁₆	—	122	2	no	—
78	Q₁₆	—	244	2	no	—
79	Q₁₆	D₂₄₄	1	2	yes	—
80	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	4	1	no	—
84	C₄⋊C₄	—	244	1	no	—
85	C₄⋊C₄	—	244	1	no	—
86	C₄²	—	4	1	no	—
87	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
88	C₁₆	—	122	2	no	—
89	Q₈	—	2	2	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	244	2	no	—
92	Q₈	—	244	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	244	2	no	—
96	C₂×C₄	#11758199	1	1	yes	characteristic
97	C₂×C₄	#11758199	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	C₂×D₂₄₄	1	1	yes	characteristic
101	C₈	#11758222	1	1	yes	characteristic
102	C₂²	C₂×#11758199	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	8	1	no	—
106	C₄	—	488	2	no	—
107	C₄	#14519723	1	2	yes	complemented
108	C₄	#14519751	1	1	yes	characteristic
109	C₄	#14519802	1	1	yes	characteristic
110	C₂	#16839957	1	1	yes	characteristic
111	C₂	C₂×#14519723	1	1	yes	characteristic
112	C₂	#16840202	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519723

C₂

yes

maximal

#16840142

C₂

yes

maximal, characteristic

C₄⋊#11758185

C₂

yes

maximal, characteristic

#16839565

C₂

yes

maximal

C₄×Q₁₆×C₆₁

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

C₂²

yes

—

#14519777

—

#14519723

—

C₂×#11758185

C₂²

yes

—

C₂×Q₁₆×C₆₁

C₂²

yes

characteristic

C₄×Q₈×C₆₁

—

#107×C₆₁

C₂²

yes

characteristic

#103×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×Dic₁₂₂

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

D₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

#11758185

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

#41

yes

characteristic

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

Q₃₂

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂×Q₃₂

yes

characteristic

C₂×C₆₁

#510

yes

characteristic

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

D₆₁

yes

characteristic

C₄⋊C₁₆

—

#358

—

C₆₁

#2209

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

122

—

C₂×Q₁₆

C₂×D₆₁

yes

characteristic

C₄⋊Q₈

—

122

—

C₄×Q₈

—

Q₃₂

—

122

—

C₂×C₁₆

—

#107

C₂×D₆₁

yes

characteristic

#103

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

122

—

Q₁₆

—

Q₁₆

—

122

—

Q₁₆

—

122

—

Q₁₆

—

244

—

Q₁₆

D₂₄₄

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

122

—

Q₈

—

Q₈

—

Q₈

—

244

—

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

100

C₈

C₂×D₂₄₄

yes

characteristic

101

C₈

#11758222

yes

characteristic

102

C₂²

C₂×#11758199

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

488

—

107

C₄

#14519723

yes

complemented

108

C₄

#14519751

yes

characteristic

109

C₄

#14519802

yes

characteristic

110

C₂

#16839957

yes

characteristic

111

C₂

C₂×#14519723

yes

characteristic

112

C₂

#16840202

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₄×Q₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₄×Q₁₆	D₆₁
hypocenter	C₆₁	#2209
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₄×Q₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₄×Q₁₆

D₆₁

hypocenter

C₆₁

#2209

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
49. C₄×C₆₁	Q₃₂	semidirect
62. C₆₁	#2209	semidirect
107. C₄	#14519723	semidirect

H ≅ G/N

type

49. C₄×C₆₁

Q₃₂

semidirect

62. C₆₁

#2209

semidirect

107. C₄

#14519723

semidirect

Subgroups — #21447869

Conjugacy classes of subgroups

Complements