Group #21448085 — subgroups

Subgroups — #21448085

Order 7808.

198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14519722	C₂	1	2	yes	maximal, complemented
2	C₂×D₉₇₆	C₂	1	2	yes	maximal, complemented
3	#16840146	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
7	C₂×#11758190	—	2	1	no	—
8	C₂×D₄₈₈	—	2	1	no	—
9	C₂×D₄₈₈	C₂²	1	2	yes	—
10	C₂×D₄₈₈	C₂²	1	1	yes	characteristic
11	#14519774	—	2	1	no	—
12	#14519765	—	2	1	no	—
13	#14519722	—	2	4	no	—
14	D₉₇₆	—	2	4	no	—
15	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×D₂₄₄	—	2	1	no	—
18	C₂×D₂₄₄	—	2	2	no	—
19	C₂×D₂₄₄	—	4	2	no	—
20	C₂×Dic₁₂₂	—	2	1	no	—
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
23	C₄²×C₆₁	D₄	1	1	yes	characteristic
24	#11758198	—	4	2	no	—
25	Dic₂₄₄	—	2	2	no	—
26	D₄₈₈	—	2	2	no	—
27	D₄₈₈	—	2	2	no	—
28	D₄₈₈	—	2	2	no	—
29	D₄₈₈	—	4	2	no	—
30	#11758190	—	4	2	no	—
31	C₁₆×C₆₁	D₄	1	4	yes	complemented
32	C₂²×D₆₁	—	4	1	no	—
33	C₂²×D₆₁	—	4	2	no	—
34	C₂×C₄×C₆₁	D₈	1	2	yes	—
35	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₆₁	—	4	1	no	—
37	D₂₄₄	—	4	1	no	—
38	D₂₄₄	—	4	2	no	—
39	D₂₄₄	—	4	1	no	—
40	D₂₄₄	—	4	2	no	—
41	D₂₄₄	—	8	4	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	C₂×D₈	1	1	yes	characteristic
47	C₂×D₆₁	—	8	1	no	—
48	C₂×D₆₁	—	8	2	no	—
49	C₂×D₆₁	—	8	4	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	#493	1	1	yes	characteristic
57	C₂×C₆₁	#509	1	2	yes	—
58	D₆₁	—	16	2	no	—
59	D₆₁	—	16	1	no	—
60	C₂×SD₃₂	—	61	2	no	—
61	C₂×D₁₆	—	61	2	no	—
62	#495	—	61	1	no	—
63	#493	—	61	1	no	—
64	#346	D₆₁	1	1	yes	characteristic, complemented
65	C₆₁	#2250	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₁₆	—	61	1	no	—
67	C₂×SD₁₆	—	122	1	no	—
68	C₂×D₈	—	61	2	no	—
69	C₂×D₈	—	61	1	no	—
70	C₂×D₈	—	122	1	no	—
71	#127	—	122	1	no	—
72	#124	—	122	1	no	—
73	SD₃₂	—	122	4	no	—
74	D₁₆	—	122	4	no	—
75	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
76	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
77	C₂×Q₈	—	122	1	no	—
78	C₂×D₄	—	122	1	no	—
79	C₂×D₄	—	122	2	no	—
80	C₂×D₄	—	244	2	no	—
81	Q₁₆	—	122	2	no	—
82	SD₁₆	—	244	2	no	—
83	D₈	—	122	2	no	—
84	D₈	—	122	2	no	—
85	D₈	—	122	2	no	—
86	D₈	—	244	2	no	—
87	C₂×C₈	D₂₄₄	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
89	C₂²⋊C₄	—	244	2	no	—
90	C₄²	D₂₄₄	1	1	yes	characteristic
91	C₁₆	D₂₄₄	1	4	yes	complemented
92	C₂³	—	244	1	no	—
93	C₂³	—	244	2	no	—
94	Q₈	—	244	1	no	—
95	Q₈	—	244	1	no	—
96	D₄	—	488	4	no	—
97	D₄	—	244	1	no	—
98	D₄	—	244	2	no	—
99	D₄	—	244	2	no	—
100	D₄	—	244	1	no	—
101	C₂×C₄	—	244	1	no	—
102	C₂×C₄	D₄₈₈	1	2	yes	—
103	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
104	C₈	D₄₈₈	1	2	yes	—
105	C₈	C₂×D₂₄₄	1	2	yes	—
106	C₂²	—	488	4	no	—
107	C₂²	—	488	2	no	—
108	C₂²	—	488	2	no	—
109	C₂²	—	488	1	no	—
110	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	488	1	no	—
113	C₄	#14519774	1	1	yes	characteristic
114	C₄	C₂×D₄₈₈	1	1	yes	characteristic
115	C₂	—	976	2	no	—
116	C₂	—	976	1	no	—
117	C₂	#16840139	1	1	yes	characteristic
118	C₂	#16840200	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519722

C₂

yes

maximal, complemented

C₂×D₉₇₆

C₂

yes

maximal, complemented

#16840146

C₂

yes

maximal, characteristic, complemented

#16840139

C₂

yes

maximal, characteristic, complemented

C₆₁×#346

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₄₄

C₂²

yes

characteristic

C₂×#11758190

—

C₂×D₄₈₈

—

C₂×D₄₈₈

C₂²

yes

—

C₂×D₄₈₈

C₂²

yes

—

—

—

D₉₇₆

—

C₂×C₁₆×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

#11758198

—

Dic₂₄₄

—

D₄₈₈

—

D₄₈₈

—

D₄₈₈

—

D₄₈₈

—

#11758190

—

C₁₆×C₆₁

D₄

yes

complemented

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

D₈

yes

—

C₈×C₆₁

C₂×D₄

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

D₆₁

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#493

—

#346

D₆₁

yes

characteristic, complemented

C₆₁

#2250

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

122

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

122

—

#127

—

122

—

#124

—

122

—

SD₃₂

—

122

—

D₁₆

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

122

—

D₈

—

122

—

D₈

—

122

—

D₈

—

244

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₂²⋊C₄

—

244

—

C₄²

D₂₄₄

yes

characteristic

C₁₆

D₂₄₄

yes

complemented

C₂³

—

244

—

C₂³

—

244

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

D₄

—

244

—

100

D₄

—

244

—

101

C₂×C₄

—

244

—

102

C₂×C₄

D₄₈₈

yes

—

103

C₂×C₄

C₂×D₂₄₄

yes

characteristic

104

C₈

D₄₈₈

yes

—

105

C₈

C₂×D₂₄₄

yes

—

106

C₂²

—

488

—

107

C₂²

—

488

—

108

C₂²

—

488

—

109

C₂²

—

488

—

110

C₂²

C₂×D₄₈₈

yes

characteristic

111

C₄

—

112

C₄

—

488

—

113

C₄

#14519774

yes

characteristic

114

C₄

C₂×D₄₈₈

yes

characteristic

115

C₂

—

976

—

116

C₂

—

976

—

117

C₂

#16840139

yes

characteristic

118

C₂

#16840200

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#346	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#346	D₆₁
hypocenter	C₆₁	#2250
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×D₄₈₈

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#346

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
1. C₂×#14519722	C₂	semidirect
2. C₂×D₉₇₆	C₂	semidirect
3. #16840146	C₂	semidirect
4. #16840139	C₂	semidirect
5. C₆₁×#346	C₂	semidirect
31. C₁₆×C₆₁	D₄	semidirect
64. #346	D₆₁	semidirect
65. C₆₁	#2250	semidirect
91. C₁₆	D₂₄₄	semidirect

H ≅ G/N

type

1. C₂×#14519722

C₂

semidirect

2. C₂×D₉₇₆

C₂

semidirect

3. #16840146

C₂

semidirect

4. #16840139

C₂

semidirect

5. C₆₁×#346

C₂

semidirect

31. C₁₆×C₆₁

D₄

semidirect

64. #346

D₆₁

semidirect

65. C₆₁

#2250

semidirect

91. C₁₆

D₂₄₄

semidirect

Subgroups — #21448085

Conjugacy classes of subgroups

Complements