Group #21445408 — subgroups

Subgroups — #21445408

Order 7808.

224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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	#16840167	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840134	C₂	1	2	yes	maximal, complemented
3	#16840108	C₂	1	2	yes	maximal, complemented
4	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#493	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758200	—	2	4	no	—
7	#14519777	C₂²	1	2	yes	—
8	#14519711	—	2	2	no	—
9	#14519698	—	2	4	no	—
10	C₄×#92418	C₂²	1	1	yes	characteristic
11	C₄×#92418	C₂²	1	1	yes	characteristic
12	C₂×D₈×C₆₁	—	2	2	no	—
13	#127×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₆₁	—	2	2	no	—
16	C₂×D₄×C₆₁	—	2	2	no	—
17	C₂×D₄×C₆₁	—	2	2	no	—
18	C₂×Dic₁₂₂	—	2	2	no	—
19	D₈×C₆₁	—	4	4	no	—
20	C₂×C₈×C₆₁	D₄	1	2	yes	—
21	C₄²×C₆₁	C₂³	1	1	yes	characteristic
22	#11758200	—	4	8	no	—
23	C₄⋊Dic₆₁	—	2	2	no	—
24	C₄⋊Dic₆₁	—	2	2	no	—
25	C₂×#92418	D₄	1	2	yes	—
26	C₂×#92418	D₄	1	2	yes	—
27	C₂³×C₆₁	—	4	2	no	—
28	D₄×C₆₁	—	4	4	no	—
29	D₄×C₆₁	—	4	4	no	—
30	D₄×C₆₁	—	4	4	no	—
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	4	2	no	—
35	Dic₁₂₂	—	4	4	no	—
36	C₈×C₆₁	SD₁₆	1	4	yes	complemented
37	#92418	—	2	2	no	—
38	#92418	D₈	1	4	yes	complemented
39	C₂²×C₆₁	—	8	2	no	—
40	C₂²×C₆₁	—	8	2	no	—
41	C₂²×C₆₁	—	8	2	no	—
42	C₂²×C₆₁	#127	1	1	yes	characteristic
43	C₄×C₆₁	C₂×D₈	1	2	yes	—
44	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
45	C₄×C₆₁	#135	1	2	yes	—
46	Dic₆₁	—	8	2	no	—
47	#1706	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	16	2	no	—
49	C₂×C₆₁	#492	1	1	yes	characteristic
50	C₂×C₆₁	#493	1	1	yes	characteristic
51	C₂×C₆₁	#495	1	1	yes	characteristic
52	#500	—	61	1	no	—
53	#493	D₆₁	1	1	yes	characteristic
54	#492	—	61	2	no	—
55	#486	—	61	2	no	—
56	C₈²	—	61	1	no	—
57	C₆₁	#1706	1	1	yes	characteristic, complemented, Sylow
58	C₂×SD₁₆	—	122	4	no	—
59	C₂×D₈	—	2	2	no	—
60	C₄⋊Q₈	—	61	2	no	—
61	#127	C₂×D₆₁	1	2	yes	—
62	#107	—	122	2	no	—
63	#102	—	122	4	no	—
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	—	61	1	no	—
66	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
67	C₂×Q₈	—	122	2	no	—
68	C₂×D₄	—	2	2	no	—
69	C₂×D₄	—	2	2	no	—
70	C₂×D₄	—	2	2	no	—
71	SD₁₆	—	244	8	no	—
72	D₈	—	4	4	no	—
73	C₂×C₈	—	61	2	no	—
74	C₂×C₈	—	61	2	no	—
75	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
76	C₄⋊C₄	—	122	2	no	—
77	C₄⋊C₄	—	122	2	no	—
78	C₄²	C₂²×D₆₁	1	1	yes	characteristic
79	C₂³	—	4	2	no	—
80	Q₈	—	244	4	no	—
81	D₄	—	4	4	no	—
82	D₄	—	4	4	no	—
83	D₄	—	4	4	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
86	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
87	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
88	C₈	—	61	4	no	—
89	C₈	—	122	2	no	—
90	C₈	#11758200	1	4	yes	complemented
91	C₂²	—	8	2	no	—
92	C₂²	—	8	2	no	—
93	C₂²	—	8	2	no	—
94	C₂²	#14519773	1	1	yes	characteristic
95	C₄	—	488	2	no	—
96	C₄	D₈×D₆₁	1	2	yes	—
97	C₄	C₂×#11758200	1	2	yes	—
98	C₄	#14519796	1	2	yes	—
99	C₂	—	16	2	no	—
100	C₂	#16840134	1	1	yes	characteristic
101	C₂	#16840137	1	1	yes	characteristic
102	C₂	#16840145	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840167

C₂

yes

maximal, characteristic, complemented

#16840134

C₂

yes

maximal, complemented

#16840108

C₂

yes

maximal, complemented

C₈×#92418

C₂

yes

maximal, characteristic, complemented

C₆₁×#493

C₂

yes

maximal, characteristic

C₂×#11758200

—

#14519777

C₂²

yes

—

#14519711

—

#14519698

—

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₂×D₈×C₆₁

—

#127×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×Dic₁₂₂

—

D₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758200

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

D₄

yes

—

C₂×#92418

D₄

yes

—

C₂³×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

Dic₁₂₂

—

C₈×C₆₁

SD₁₆

yes

complemented

#92418

—

#92418

D₈

yes

complemented

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

—

C₄×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

#135

yes

—

Dic₆₁

—

#1706

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

yes

characteristic

#492

—

#486

—

C₈²

—

C₆₁

#1706

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

122

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₆₁

yes

—

#107

—

122

—

#102

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

244

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

Q₈

—

244

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

244

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₈

#11758200

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

#14519773

yes

characteristic

C₄

—

488

—

C₄

D₈×D₆₁

yes

—

C₄

C₂×#11758200

yes

—

C₄

#14519796

yes

—

C₂

—

100

C₂

#16840134

yes

characteristic

101

C₂

#16840137

yes

characteristic

102

C₂

#16840145

yes

characteristic

	subgroup	G/H
center	C₂²	#14519773
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#493	C₂
socle	C₂²×C₆₁	#127
hypercenter	#493	D₆₁
hypocenter	C₆₁	#1706
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#14519773

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#493

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #16840167	C₂	semidirect
2. #16840134	C₂	semidirect
3. #16840108	C₂	semidirect
4. C₈×#92418	C₂	semidirect
36. C₈×C₆₁	SD₁₆	semidirect
38. #92418	D₈	semidirect
57. C₆₁	#1706	semidirect
90. C₈	#11758200	semidirect

H ≅ G/N

type

1. #16840167

C₂

semidirect

2. #16840134

C₂

semidirect

3. #16840108

C₂

semidirect

4. C₈×#92418

C₂

semidirect

36. C₈×C₆₁

SD₁₆

semidirect

38. #92418

D₈

semidirect

57. C₆₁

#1706

semidirect

90. C₈

#11758200

semidirect

Subgroups — #21445408

Conjugacy classes of subgroups

Complements