Group #21447601 — subgroups

Subgroups — #21447601

Order 7808.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#11758185	C₂	1	1	yes	maximal, characteristic
2	#16839800	C₂	1	1	yes	maximal, characteristic
3	#16839589	C₂	1	2	yes	maximal, complemented
4	#16839587	C₂	1	2	yes	maximal, complemented
5	C₆₁×#427	C₂	1	1	yes	maximal, characteristic
6	#14519736	—	2	1	no	—
7	C₂×#11758185	C₄	1	4	yes	complemented
8	C₂×#11758185	C₂²	1	1	yes	characteristic
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	#14519711	C₂²	1	2	yes	—
11	#14519709	—	2	1	no	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	#117×C₆₁	—	2	1	no	—
14	#107×C₆₁	C₂²	1	2	yes	—
15	#106×C₆₁	—	2	1	no	—
16	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	Q₈	1	2	yes	—
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₂²⋊C₄×C₆₁	—	4	1	no	—
23	C₄²×C₆₁	—	4	1	no	—
24	C₂²⋊Dic₆₁	—	4	1	no	—
25	C₄⋊Dic₆₁	—	2	2	no	—
26	C₄×Dic₆₁	—	4	1	no	—
27	#11758185	C₂×C₄	1	2	yes	—
28	#11758185	C₂×C₄	1	2	yes	—
29	C₂³×C₆₁	D₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	4	2	no	—
31	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	Q₁₆	1	2	yes	—
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	4	2	no	—
36	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
37	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₆₁	—	2	2	no	—
40	C₂²×C₆₁	#107	1	2	yes	—
41	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
42	C₄×C₆₁	—	8	2	no	—
43	C₄×C₆₁	#107	1	2	yes	—
44	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₆₁	—	8	2	no	—
47	#2158	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	2	no	—
49	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
50	C₂×C₆₁	#508	1	2	yes	—
51	C₂²×C₁₆	—	61	1	no	—
52	#427	—	61	1	no	—
53	#427	D₆₁	1	1	yes	characteristic
54	#367	—	61	2	no	—
55	#366	—	61	2	no	—
56	C₆₁	#2158	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
58	#117	—	2	1	no	—
59	#117	—	122	1	no	—
60	C₂×C₁₆	—	61	4	no	—
61	C₂×C₁₆	—	61	1	no	—
62	C₂×C₁₆	—	61	1	no	—
63	#107	—	61	2	no	—
64	#107	C₂×D₆₁	1	2	yes	—
65	#106	—	2	1	no	—
66	#106	—	122	1	no	—
67	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
68	C₂×C₈	Dic₁₂₂	1	2	yes	—
69	C₂×C₈	C₄×D₆₁	1	2	yes	—
70	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	122	2	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₂²⋊C₄	—	244	1	no	—
76	C₄²	—	4	1	no	—
77	C₄²	—	244	1	no	—
78	C₁₆	—	61	2	no	—
79	C₁₆	—	61	2	no	—
80	C₂³	#11758199	1	1	yes	characteristic
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	244	2	no	—
83	C₂×C₄	#11758196	1	2	yes	—
84	C₂×C₄	#11758199	1	1	yes	characteristic
85	C₂×C₄	#11758202	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
87	C₈	#11758196	1	2	yes	—
88	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
89	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14519710	1	2	yes	—
92	C₂²	C₂×#11758199	1	1	yes	characteristic
93	C₄	—	8	2	no	—
94	C₄	—	488	2	no	—
95	C₄	#14519710	1	2	yes	—
96	C₄	C₂×#11758196	1	1	yes	characteristic
97	C₄	C₂×#11758202	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#14519710	1	1	yes	characteristic
100	C₂	#16840192	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758185

C₂

yes

maximal, characteristic

#16839800

C₂

yes

maximal, characteristic

#16839589

C₂

yes

maximal, complemented

#16839587

C₂

yes

maximal, complemented

C₆₁×#427

C₂

yes

maximal, characteristic

#14519736

—

C₂×#11758185

C₄

yes

complemented

C₂×#11758185

C₂²

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

#14519711

C₂²

yes

—

#14519709

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

—

#107×C₆₁

C₂²

yes

—

#106×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758185

C₂×C₄

yes

—

#11758185

C₂×C₄

yes

—

C₂³×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

Q₁₆

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

#107

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#107

yes

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×Q₁₆

yes

characteristic

Dic₆₁

—

#2158

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×#107

yes

characteristic

C₂×C₆₁

#508

yes

—

C₂²×C₁₆

—

#427

—

#427

D₆₁

yes

characteristic

#367

—

#366

—

C₆₁

#2158

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

#117

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₆₁

yes

—

#106

—

#106

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

C₂²⋊C₄

—

244

—

C₄²

—

C₄²

—

244

—

C₁₆

—

C₁₆

—

C₂³

#11758199

yes

characteristic

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

#11758196

yes

—

C₂×C₄

#11758199

yes

characteristic

C₂×C₄

#11758202

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

#11758196

yes

—

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

C₂×C₄×D₆₁

yes

characteristic

C₂²

—

C₂²

#14519710

yes

—

C₂²

C₂×#11758199

yes

characteristic

C₄

—

C₄

—

488

—

C₄

#14519710

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#14519710

yes

characteristic

100

C₂

#16840192

yes

—

	subgroup	G/H
center	C₂×C₄	#11758199
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#427	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#427	D₆₁
hypocenter	C₆₁	#2158
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₂×C₄

#11758199

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#427

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #16839589	C₂	semidirect
4. #16839587	C₂	semidirect
7. C₂×#11758185	C₄	semidirect
56. C₆₁	#2158	semidirect

H ≅ G/N

type

3. #16839589

C₂

semidirect

4. #16839587

C₂

semidirect

7. C₂×#11758185

C₄

semidirect

56. C₆₁

#2158

semidirect

Subgroups — #21447601

Conjugacy classes of subgroups

Complements