Group #21447633 — subgroups

Subgroups — #21447633

Order 7808.

122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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	#16839719	C₂	1	1	yes	maximal, characteristic
2	#16839582	C₂	1	2	yes	maximal, complemented
3	#16839543	C₂	1	2	yes	maximal
4	#16839540	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
8	#14519734	C₄	1	1	yes	characteristic
9	#14519717	C₂²	1	2	yes	—
10	#14519687	C₄	1	1	yes	characteristic
11	C₄×#92418	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	M₃₂×C₆₁	C₂²	1	2	yes	—
14	#97×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	#11758198	—	2	1	no	—
20	#11758196	—	2	1	no	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂×C₄	1	1	yes	characteristic
24	#11758189	—	2	2	no	—
25	C₈×D₆₁	—	2	2	no	—
26	C₁₆×C₆₁	—	2	2	no	—
27	#11758185	—	2	2	no	—
28	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	2	1	no	—
32	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
33	C₄×D₆₁	—	2	1	no	—
34	C₄×D₆₁	—	2	1	no	—
35	C₈×C₆₁	—	2	1	no	—
36	C₈×C₆₁	#41	1	2	yes	—
37	#92418	—	2	1	no	—
38	#92418	M₁₆	1	2	yes	—
39	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
40	C₂×D₆₁	—	2	1	no	—
41	C₂×D₆₁	—	4	1	no	—
42	C₄×C₆₁	—	4	1	no	—
43	C₄×C₆₁	#117	1	1	yes	characteristic
44	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
45	Dic₆₁	—	2	1	no	—
46	Dic₆₁	—	4	1	no	—
47	#2166	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	1	no	—
49	C₂×C₆₁	#432	1	1	yes	characteristic
50	D₆₁	—	4	1	no	—
51	#405	—	61	1	no	—
52	#364	—	61	2	no	—
53	#349	—	61	2	no	—
54	#347	—	61	1	no	—
55	#347	D₆₁	1	1	yes	characteristic, complemented
56	C₆₁	#2166	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	61	1	no	—
58	C₂²×C₈	—	61	1	no	—
59	#117	—	61	1	no	—
60	M₃₂	—	61	2	no	—
61	M₃₂	C₂×D₆₁	1	2	yes	—
62	#97	—	61	1	no	—
63	#97	C₂×D₆₁	1	1	yes	characteristic
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	—	61	1	no	—
66	C₂²×C₄	—	61	1	no	—
67	M₁₆	—	122	2	no	—
68	C₂×C₈	—	61	1	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	—	122	2	no	—
71	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
73	C₄⋊C₄	—	122	1	no	—
74	C₂²⋊C₄	—	122	1	no	—
75	C₄²	—	61	1	no	—
76	C₄²	C₄×D₆₁	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	122	2	no	—
79	C₂³	—	61	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	122	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	122	1	no	—
85	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	61	2	no	—
88	C₈	—	122	1	no	—
89	C₈	#11758222	1	2	yes	—
90	C₂²	—	122	1	no	—
91	C₂²	—	244	1	no	—
92	C₂²	M₁₆×D₆₁	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	122	1	no	—
95	C₄	—	244	1	no	—
96	C₄	#14519734	1	1	yes	characteristic
97	C₄	M₁₆×D₆₁	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	244	1	no	—
100	C₂	#16839817	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839719

C₂

yes

maximal, characteristic

#16839582

C₂

yes

maximal, complemented

#16839543

C₂

yes

maximal

#16839540

C₂

yes

maximal, characteristic, complemented

C₆₁×#347

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

#14519734

C₄

yes

characteristic

#14519717

C₂²

yes

—

#14519687

C₄

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

C₂²

yes

—

#97×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

#41

yes

—

#92418

—

#92418

M₁₆

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#2166

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#432

yes

characteristic

D₆₁

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#2166

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

C₂×D₆₁

yes

—

#97

—

#97

C₂×D₆₁

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

#11758222

yes

—

C₂²

—

122

—

C₂²

—

244

—

C₂²

M₁₆×D₆₁

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

244

—

C₄

#14519734

yes

characteristic

C₄

M₁₆×D₆₁

yes

characteristic

C₂

—

C₂

—

244

—

100

C₂

#16839817

yes

characteristic

	subgroup	G/H
center	C₄	#14519734
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#347	C₂
socle	C₂×C₆₁	#432
hypercenter	#347	D₆₁
hypocenter	C₆₁	#2166
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#14519734

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#347

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #16839582	C₂	semidirect
4. #16839540	C₂	semidirect
5. C₆₁×#347	C₂	semidirect
55. #347	D₆₁	semidirect
56. C₆₁	#2166	semidirect

H ≅ G/N

type

2. #16839582

C₂

semidirect

4. #16839540

C₂

semidirect

5. C₆₁×#347

C₂

semidirect

55. #347

D₆₁

semidirect

56. C₆₁

#2166

semidirect

Subgroups — #21447633

Conjugacy classes of subgroups

Complements