Group #21448083 — subgroups

Subgroups — #21448083

Order 7808.

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

normal subgroups only

This group has 198 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×#14519721	C₂	1	2	yes	maximal, complemented
2	C₂×#14519718	C₂	1	2	yes	maximal, complemented
3	#16840146	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
7	C₂×#11758190	—	2	1	no	—
8	C₂×D₄₈₈	C₂²	1	1	yes	characteristic
9	#14519765	—	2	1	no	—
10	#14519721	—	2	4	no	—
11	#14519718	—	2	4	no	—
12	C₂×#11758185	C₂²	1	2	yes	—
13	C₂×D₈×C₆₁	—	2	1	no	—
14	C₂×D₈×C₆₁	C₂²	1	2	yes	—
15	#127×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₆₁	—	2	2	no	—
18	C₂×D₄×C₆₁	—	4	2	no	—
19	C₂×D₂₄₄	—	2	1	no	—
20	C₂×Dic₁₂₂	—	2	1	no	—
21	D₈×C₆₁	—	2	2	no	—
22	D₈×C₆₁	—	2	2	no	—
23	D₈×C₆₁	—	4	2	no	—
24	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
26	C₄²×C₆₁	D₄	1	1	yes	characteristic
27	#11758198	—	4	2	no	—
28	Dic₂₄₄	—	2	2	no	—
29	D₄₈₈	—	2	2	no	—
30	#11758190	—	4	2	no	—
31	#11758185	D₄	1	4	yes	complemented
32	C₂³×C₆₁	—	4	2	no	—
33	C₂²×D₆₁	—	4	1	no	—
34	D₄×C₆₁	—	4	2	no	—
35	D₄×C₆₁	—	4	2	no	—
36	D₄×C₆₁	—	8	4	no	—
37	C₂×C₄×C₆₁	D₈	1	2	yes	—
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₆₁	—	4	1	no	—
40	D₂₄₄	—	4	1	no	—
41	D₂₄₄	—	4	1	no	—
42	Dic₁₂₂	—	4	1	no	—
43	Dic₁₂₂	—	4	1	no	—
44	C₈×C₆₁	D₈	1	2	yes	—
45	C₈×C₆₁	C₂×D₄	1	2	yes	—
46	C₂²×C₆₁	—	8	2	no	—
47	C₂²×C₆₁	—	8	4	no	—
48	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
49	C₂×D₆₁	—	8	1	no	—
50	C₂×D₆₁	—	8	2	no	—
51	C₄×C₆₁	—	2	2	no	—
52	C₄×C₆₁	#127	1	1	yes	characteristic
53	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
54	Dic₆₁	—	8	1	no	—
55	#2250	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	16	2	no	—
57	C₂×C₆₁	#493	1	1	yes	characteristic
58	C₂×C₆₁	#509	1	2	yes	—
59	D₆₁	—	16	1	no	—
60	C₂×SD₃₂	—	61	2	no	—
61	C₂×D₁₆	—	61	2	no	—
62	#495	—	61	1	no	—
63	#493	D₆₁	1	1	yes	characteristic, complemented
64	#346	—	61	1	no	—
65	C₆₁	#2250	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₁₆	—	61	1	no	—
67	C₂×SD₁₆	—	122	1	no	—
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	—	61	1	no	—
70	C₂×D₈	C₂×D₆₁	1	2	yes	—
71	#127	—	2	1	no	—
72	#124	—	122	1	no	—
73	SD₃₂	—	122	4	no	—
74	D₁₆	—	122	4	no	—
75	C₂×C₁₆	—	61	2	no	—
76	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
77	C₂×Q₈	—	122	1	no	—
78	C₂×D₄	—	2	2	no	—
79	C₂×D₄	—	4	2	no	—
80	C₂×D₄	—	122	1	no	—
81	Q₁₆	—	122	2	no	—
82	SD₁₆	—	244	2	no	—
83	D₈	—	2	2	no	—
84	D₈	—	2	2	no	—
85	D₈	—	4	2	no	—
86	D₈	—	122	2	no	—
87	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
89	C₂²⋊C₄	—	244	2	no	—
90	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
91	C₁₆	—	61	4	no	—
92	C₂³	—	4	2	no	—
93	C₂³	—	244	1	no	—
94	Q₈	—	244	1	no	—
95	Q₈	—	244	1	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	D₄	—	8	4	no	—
99	D₄	—	244	1	no	—
100	D₄	—	244	1	no	—
101	C₂×C₄	—	244	1	no	—
102	C₂×C₄	#11758199	1	2	yes	—
103	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
104	C₈	#11758199	1	2	yes	—
105	C₈	D₄×D₆₁	1	2	yes	—
106	C₂²	—	8	4	no	—
107	C₂²	—	8	2	no	—
108	C₂²	—	488	2	no	—
109	C₂²	—	488	1	no	—
110	C₂²	C₂×#11758199	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	488	1	no	—
113	C₄	#14519773	1	1	yes	characteristic
114	C₄	C₂×#11758199	1	1	yes	characteristic
115	C₂	—	16	2	no	—
116	C₂	—	976	1	no	—
117	C₂	#16840138	1	1	yes	characteristic
118	C₂	#16840198	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519721

C₂

yes

maximal, complemented

C₂×#14519718

C₂

yes

maximal, complemented

#16840146

C₂

yes

maximal, characteristic, complemented

#16839538

C₂

yes

maximal, characteristic, complemented

C₆₁×#493

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₄₄

C₂²

yes

characteristic

C₂×#11758190

—

C₂×D₄₈₈

C₂²

yes

—

—

—

C₂²

yes

—

C₂×D₈×C₆₁

—

C₂×D₈×C₆₁

C₂²

yes

—

#127×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₂₄₄

—

C₂×Dic₁₂₂

—

D₈×C₆₁

—

D₈×C₆₁

—

D₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

#11758198

—

Dic₂₄₄

—

D₄₈₈

—

#11758190

—

#11758185

D₄

yes

complemented

C₂³×C₆₁

—

C₂²×D₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

D₈

yes

—

C₈×C₆₁

C₂×D₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

#2250

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#493

yes

characteristic

C₂×C₆₁

#509

yes

—

D₆₁

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#493

D₆₁

yes

characteristic, complemented

#346

—

C₆₁

#2250

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

122

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₆₁

yes

—

#127

—

#124

—

122

—

SD₃₂

—

122

—

D₁₆

—

122

—

C₂×C₁₆

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

122

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

D₈

—

D₈

—

D₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₂²⋊C₄

—

244

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

244

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

D₄

—

D₄

—

D₄

—

244

—

100

D₄

—

244

—

101

C₂×C₄

—

244

—

102

C₂×C₄

#11758199

yes

—

103

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

104

C₈

#11758199

yes

—

105

C₈

D₄×D₆₁

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

488

—

109

C₂²

—

488

—

110

C₂²

C₂×#11758199

yes

characteristic

111

C₄

—

112

C₄

—

488

—

113

C₄

#14519773

yes

characteristic

114

C₄

C₂×#11758199

yes

characteristic

115

C₂

—

116

C₂

—

976

—

117

C₂

#16840138

yes

characteristic

118

C₂

#16840198

yes

—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#493	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#493	D₆₁
hypocenter	C₆₁	#2250
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#493

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#14519721	C₂	semidirect
2. C₂×#14519718	C₂	semidirect
3. #16840146	C₂	semidirect
4. #16839538	C₂	semidirect
5. C₆₁×#493	C₂	semidirect
31. #11758185	D₄	semidirect
63. #493	D₆₁	semidirect
65. C₆₁	#2250	semidirect

H ≅ G/N

type

1. C₂×#14519721

C₂

semidirect

2. C₂×#14519718

C₂

semidirect

3. #16840146

C₂

semidirect

4. #16839538

C₂

semidirect

5. C₆₁×#493

C₂

semidirect

31. #11758185

D₄

semidirect

63. #493

D₆₁

semidirect

65. C₆₁

#2250

semidirect

Subgroups — #21448083

Conjugacy classes of subgroups

Complements