Group #21448091 — subgroups

Subgroups — #21448091

Order 7808.

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

normal subgroups only

This group has 178 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, complemented
2	C₂×#14519721	C₂	1	2	yes	maximal
3	#16840142	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#495	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	#14519721	—	2	4	no	—
11	C₂×#11758185	C₂²	1	2	yes	—
12	C₂×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×SD₁₆×C₆₁	—	2	1	no	—
14	C₂×D₈×C₆₁	C₂²	1	1	yes	characteristic
15	#124×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	—	2	1	no	—
18	C₂×D₄×C₆₁	—	2	1	no	—
19	C₂×Dic₁₂₂	—	2	2	no	—
20	Q₁₆×C₆₁	—	2	2	no	—
21	SD₁₆×C₆₁	—	4	2	no	—
22	D₈×C₆₁	—	2	2	no	—
23	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
25	C₂²⋊C₄×C₆₁	—	4	2	no	—
26	C₄²×C₆₁	D₄	1	1	yes	characteristic
27	C₄⋊Dic₆₁	—	4	2	no	—
28	Dic₂₄₄	—	2	2	no	—
29	Dic₂₄₄	—	2	2	no	—
30	Dic₂₄₄	—	4	2	no	—
31	#11758185	D₄	1	4	yes	—
32	C₂³×C₆₁	—	4	1	no	—
33	Q₈×C₆₁	—	4	1	no	—
34	Q₈×C₆₁	—	4	1	no	—
35	D₄×C₆₁	—	4	1	no	—
36	D₄×C₆₁	—	4	1	no	—
37	C₂×C₄×C₆₁	—	4	1	no	—
38	C₂×C₄×C₆₁	D₈	1	2	yes	—
39	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₆₁	—	4	2	no	—
41	Dic₁₂₂	—	4	2	no	—
42	Dic₁₂₂	—	4	2	no	—
43	C₈×C₆₁	D₈	1	2	yes	—
44	C₈×C₆₁	C₂×D₄	1	2	yes	—
45	C₂²×C₆₁	—	8	1	no	—
46	C₂²×C₆₁	—	8	2	no	—
47	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
48	C₄×C₆₁	—	2	2	no	—
49	C₄×C₆₁	—	8	1	no	—
50	C₄×C₆₁	#127	1	1	yes	characteristic
51	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
52	Dic₆₁	—	8	2	no	—
53	#2251	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	16	1	no	—
55	C₂×C₆₁	#493	1	1	yes	characteristic
56	C₂×C₆₁	#510	1	2	yes	—
57	C₂×Q₃₂	—	61	2	no	—
58	C₂×SD₃₂	—	61	2	no	—
59	#495	D₆₁	1	1	yes	characteristic
60	#494	—	61	1	no	—
61	#346	—	61	1	no	—
62	C₆₁	#2251	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	C₂×SD₁₆	—	2	1	no	—
67	C₂×D₈	C₂×D₆₁	1	1	yes	characteristic
68	C₄⋊Q₈	—	122	1	no	—
69	#124	—	2	1	no	—
70	Q₃₂	—	122	4	no	—
71	SD₃₂	—	122	4	no	—
72	C₂×C₁₆	—	61	2	no	—
73	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
74	C₂×Q₈	—	2	1	no	—
75	C₂×Q₈	—	122	2	no	—
76	C₂×D₄	—	2	1	no	—
77	Q₁₆	—	2	2	no	—
78	Q₁₆	—	122	2	no	—
79	Q₁₆	—	122	2	no	—
80	Q₁₆	—	244	2	no	—
81	SD₁₆	—	4	2	no	—
82	D₈	—	2	2	no	—
83	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
85	C₄⋊C₄	—	244	2	no	—
86	C₂²⋊C₄	—	4	2	no	—
87	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
88	C₁₆	—	61	4	no	—
89	C₂³	—	4	1	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	4	1	no	—
92	Q₈	—	244	2	no	—
93	Q₈	—	244	2	no	—
94	D₄	—	4	1	no	—
95	D₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	#11758199	1	2	yes	—
99	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
100	C₈	#11758199	1	2	yes	—
101	C₈	D₄×D₆₁	1	2	yes	—
102	C₂²	—	8	2	no	—
103	C₂²	—	8	1	no	—
104	C₂²	C₂×#11758199	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	8	1	no	—
107	C₄	—	488	2	no	—
108	C₄	#14519773	1	1	yes	characteristic
109	C₄	C₂×#11758199	1	1	yes	characteristic
110	C₂	—	16	1	no	—
111	C₂	#16840138	1	1	yes	characteristic
112	C₂	#16840202	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519723

C₂

yes

maximal, complemented

C₂×#14519721

C₂

yes

maximal

#16840142

C₂

yes

maximal, characteristic, complemented

#16839538

C₂

yes

maximal, characteristic, complemented

C₆₁×#495

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×Q₁₆×C₆₁

C₂²

yes

characteristic

C₂×SD₁₆×C₆₁

—

C₂×D₈×C₆₁

C₂²

yes

characteristic

#124×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×D₄×C₆₁

—

C₂×Dic₁₂₂

—

Q₁₆×C₆₁

—

SD₁₆×C₆₁

—

D₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

D₄

yes

characteristic

C₄⋊Dic₆₁

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

#11758185

D₄

yes

—

C₂³×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

D₈

yes

—

C₈×C₆₁

C₂×D₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

#2251

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#493

yes

characteristic

C₂×C₆₁

#510

yes

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

D₆₁

yes

characteristic

#494

—

#346

—

C₆₁

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

122

—

C₂×Q₁₆

C₂×D₆₁

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₆₁

yes

characteristic

C₄⋊Q₈

—

122

—

#124

—

Q₃₂

—

122

—

SD₃₂

—

122

—

C₂×C₁₆

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

122

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

122

—

Q₁₆

—

122

—

Q₁₆

—

244

—

SD₁₆

—

D₈

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

#11758199

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

100

C₈

#11758199

yes

—

101

C₈

D₄×D₆₁

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×#11758199

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

488

—

108

C₄

#14519773

yes

characteristic

109

C₄

C₂×#11758199

yes

characteristic

110

C₂

—

111

C₂

#16840138

yes

characteristic

112

C₂

#16840202

yes

—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#495	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#495	D₆₁
hypocenter	C₆₁	#2251
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#495

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#14519723	C₂	semidirect
3. #16840142	C₂	semidirect
4. #16839538	C₂	semidirect
62. C₆₁	#2251	semidirect

H ≅ G/N

type

1. C₂×#14519723

C₂

semidirect

3. #16840142

C₂

semidirect

4. #16839538

C₂

semidirect

62. C₆₁

#2251

semidirect

Subgroups — #21448091

Conjugacy classes of subgroups

Complements