Group #21447613 — subgroups

Subgroups — #21447613

Order 7808.

140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14519713	C₂	1	1	yes	maximal, characteristic
3	#16839591	C₂	1	4	yes	maximal, complemented
4	C₂×#108×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	—	2	1	no	—
6	#14519717	C₄	1	2	yes	—
7	#14519717	C₄	1	2	yes	—
8	C₂×#11758185	C₂²	1	2	yes	—
9	#14519713	—	2	1	no	—
10	#14519713	C₂²	1	2	yes	—
11	C₂×M₁₆×C₆₁	—	2	1	no	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	#108×C₆₁	—	2	1	no	—
14	#108×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
16	M₁₆×C₆₁	—	2	2	no	—
17	M₁₆×C₆₁	—	4	1	no	—
18	C₂×C₈×C₆₁	—	4	1	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
23	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
24	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
25	#11758194	—	2	2	no	—
26	#11758194	—	4	1	no	—
27	C₂×#92418	—	4	1	no	—
28	#11758185	C₂×C₄	1	4	yes	—
29	C₂³×C₆₁	Q₁₆	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	Q₁₆	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₆₁	—	4	2	no	—
37	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
41	#92418	—	4	2	no	—
42	C₂²×C₆₁	—	4	1	no	—
43	C₂²×C₆₁	#107	1	1	yes	characteristic
44	C₂²×C₆₁	#107	1	1	yes	characteristic
45	C₂²×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₆₁	#107	1	1	yes	characteristic
47	C₄×C₆₁	#107	1	1	yes	characteristic
48	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
50	#2161	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	—	2	1	no	—
52	C₂×C₆₁	—	2	1	no	—
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
55	C₂×M₃₂	—	61	1	no	—
56	C₂×#108	—	61	1	no	—
57	C₂×#108	D₆₁	1	1	yes	characteristic
58	#368	—	61	4	no	—
59	C₆₁	#2161	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₁₆	—	2	1	no	—
61	C₂×M₁₆	—	122	1	no	—
62	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
63	M₃₂	—	61	2	no	—
64	M₃₂	—	61	2	no	—
65	C₂×C₁₆	—	61	2	no	—
66	#108	—	2	1	no	—
67	#108	—	61	2	no	—
68	#108	—	122	1	no	—
69	#108	C₂×D₆₁	1	2	yes	—
70	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	M₁₆	—	122	2	no	—
74	M₁₆	—	244	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	—	244	1	no	—
77	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
78	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
79	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
80	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
83	C₁₆	—	61	4	no	—
84	C₂³	#11758202	1	1	yes	characteristic
85	C₂×C₄	#11758196	1	1	yes	characteristic
86	C₂×C₄	#11758196	1	1	yes	characteristic
87	C₂×C₄	#11758199	1	1	yes	characteristic
88	C₂×C₄	#11758199	1	1	yes	characteristic
89	C₂×C₄	#11758202	1	1	yes	characteristic
90	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	244	2	no	—
93	C₈	#11758196	1	1	yes	characteristic
94	C₈	#11758196	1	1	yes	characteristic
95	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
96	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
97	C₂²	—	4	1	no	—
98	C₂²	#14519710	1	1	yes	characteristic
99	C₂²	#14519710	1	1	yes	characteristic
100	C₂²	C₂×#11758202	1	1	yes	characteristic
101	C₄	#14519710	1	1	yes	characteristic
102	C₄	#14519710	1	1	yes	characteristic
103	C₄	C₂×#11758196	1	1	yes	characteristic
104	C₄	C₂×#11758199	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	C₂×#14519710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×#14519713

C₂

yes

maximal, characteristic

#16839591

C₂

yes

maximal, complemented

C₂×#108×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

—

#14519717

C₄

yes

—

#14519717

C₄

yes

—

C₂×#11758185

C₂²

yes

—

#14519713

—

#14519713

C₂²

yes

—

C₂×M₁₆×C₆₁

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

#108×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

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

—

—

—

C₂×C₄

yes

—

C₂³×C₆₁

Q₁₆

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

Q₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

C₂×Q₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

#2161

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×#107

yes

characteristic

C₂×M₃₂

—

C₂×#108

—

C₂×#108

D₆₁

yes

characteristic

#368

—

C₆₁

#2161

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

122

—

#108

C₂×D₆₁

yes

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₁₆

—

C₂³

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

244

—

C₈

yes

C₈

yes

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

C₂×C₄×D₆₁

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

100

C₂²

C₂×#11758202

yes

characteristic

101

C₄

#14519710

yes

characteristic

102

C₄

#14519710

yes

characteristic

103

C₄

C₂×#11758196

yes

characteristic

104

C₄

C₂×#11758199

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

C₂×#14519710

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#11758199
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×#108×C₆₁	C₂
socle	C₂×C₆₁	C₂×#107
hypercenter	C₂×#108	D₆₁
hypocenter	C₆₁	#2161
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

C₂×#11758199

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×#108×C₆₁

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #16839591	C₂	semidirect
59. C₆₁	#2161	semidirect

H ≅ G/N

type

3. #16839591

C₂

semidirect

59. C₆₁

#2161

semidirect

Subgroups — #21447613

Conjugacy classes of subgroups

Complements