Group #21443704 — subgroups

Subgroups — #21443704

Order 7808.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₄×C₂²⋊Dic₆₁	C₂	1	2	yes	maximal
2	C₆₁×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊Dic₆₁	—	2	2	no	—
4	C₂×C₄×Dic₆₁	—	2	2	no	—
5	#14519684	C₄	1	4	yes	complemented
6	C₂³×C₄×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₆₁	C₄	1	2	yes	complemented
8	C₂²⋊C₈×C₆₁	—	2	2	no	—
9	C₂⁴×C₆₁	D₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	4	2	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₆₁	D₄	1	2	yes	—
14	C₂²×C₄×C₆₁	Q₈	1	1	yes	characteristic
15	C₂²×Dic₆₁	—	2	4	no	—
16	M₁₆×C₆₁	—	4	2	no	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂²⋊Dic₆₁	—	2	8	no	—
19	C₄×Dic₆₁	—	4	4	no	—
20	C₂³×C₆₁	—	2	4	no	—
21	C₂³×C₆₁	—	4	1	no	—
22	C₂³×C₆₁	C₂²⋊C₄	1	2	yes	—
23	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	2	4	no	—
25	C₂×C₄×C₆₁	—	2	2	no	—
26	C₂×C₄×C₆₁	—	4	2	no	—
27	C₂×C₄×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₆₁	—	2	8	no	—
32	C₂×Dic₆₁	—	4	4	no	—
33	C₂×Dic₆₁	—	4	4	no	—
34	C₈×C₆₁	—	4	2	no	—
35	C₂²×C₆₁	—	2	2	no	—
36	C₂²×C₆₁	—	2	2	no	—
37	C₂²×C₆₁	—	2	2	no	—
38	C₂²×C₆₁	—	2	1	no	—
39	C₂²×C₆₁	—	4	4	no	—
40	C₂²×C₆₁	#95	1	1	yes	characteristic
41	C₂²×C₆₁	#104	1	4	yes	—
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	#99	1	2	yes	—
45	Dic₆₁	—	4	8	no	—
46	#1297	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	4	no	—
48	C₂×C₆₁	—	4	1	no	—
49	C₂×C₆₁	#339	1	2	yes	—
50	C₂×C₆₁	#342	1	1	yes	characteristic
51	#407	D₆₁	1	1	yes	characteristic
52	C₄×C₂²⋊C₄	—	61	2	no	—
53	C₆₁	#1297	1	1	yes	characteristic, complemented, Sylow
54	C₂³×C₄	C₂×D₆₁	1	1	yes	characteristic
55	C₂×M₁₆	Dic₆₁	1	2	yes	complemented
56	C₂×C₂²⋊C₄	—	122	2	no	—
57	C₂×C₄²	—	122	2	no	—
58	C₂²⋊C₈	—	2	2	no	—
59	#95	—	61	4	no	—
60	C₂⁴	D₂₄₄	1	1	yes	characteristic
61	C₂²×C₄	—	4	2	no	—
62	C₂²×C₄	—	122	4	no	—
63	C₂²×C₄	Dic₁₂₂	1	1	yes	characteristic
64	C₂²×C₄	C₄×D₆₁	1	2	yes	—
65	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
66	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
67	M₁₆	—	4	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂²⋊C₄	—	122	8	no	—
70	C₄²	—	244	4	no	—
71	C₂³	—	2	4	no	—
72	C₂³	—	4	1	no	—
73	C₂³	C₄⋊Dic₆₁	1	1	yes	characteristic
74	C₂³	#11758198	1	2	yes	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	122	8	no	—
80	C₂×C₄	—	244	4	no	—
81	C₂×C₄	—	244	4	no	—
82	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
83	C₂×C₄	#11758196	1	2	yes	—
84	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
85	C₈	—	4	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	4	no	—
91	C₂²	#14519684	1	1	yes	characteristic
92	C₂²	#14519703	1	4	yes	—
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	244	8	no	—
96	C₄	#14519692	1	2	yes	—
97	C₂	—	2	4	no	—
98	C₂	—	4	1	no	—
99	C₂	#16839523	1	2	yes	—
100	C₂	#16839529	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₂²⋊Dic₆₁

C₂

yes

maximal

C₆₁×#407

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₆₁

—

C₂×C₄×Dic₆₁

—

#14519684

C₄

yes

complemented

C₂³×C₄×C₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₄

yes

complemented

C₂²⋊C₈×C₆₁

—

C₂⁴×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

Q₈

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂²⋊Dic₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

#104

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#99

yes

—

Dic₆₁

—

#1297

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#339

yes

—

C₂×C₆₁

#342

yes

characteristic

#407

D₆₁

yes

characteristic

C₄×C₂²⋊C₄

—

C₆₁

#1297

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₆₁

yes

characteristic

C₂×M₁₆

Dic₆₁

yes

complemented

C₂×C₂²⋊C₄

—

122

—

C₂×C₄²

—

122

—

C₂²⋊C₈

—

#95

—

C₂⁴

D₂₄₄

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

Dic₁₂₂

yes

characteristic

C₂²×C₄

C₄×D₆₁

yes

—

C₂²×C₄

C₂×Dic₆₁

yes

characteristic

C₂²×C₄

C₂²⋊D₆₁

yes

—

M₁₆

—

C₂×C₈

—

C₂²⋊C₄

—

122

—

C₄²

—

244

—

C₂³

—

C₂³

—

C₂³

C₄⋊Dic₆₁

yes

characteristic

C₂³

#11758198

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₄×Dic₆₁

yes

characteristic

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂²⋊Dic₆₁

yes

characteristic

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14519684

yes

characteristic

C₂²

#14519703

yes

—

C₄

—

C₄

—

C₄

—

244

—

C₄

#14519692

yes

—

C₂

—

C₂

—

C₂

#16839523

yes

—

100

C₂

#16839529

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₆₁
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂³×C₄	C₂×D₆₁
Fitting	C₆₁×#407	C₂
socle	C₂²×C₆₁	#95
hypercenter	#407	D₆₁
hypocenter	C₆₁	#1297
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₆₁

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂³×C₄

C₂×D₆₁

Fitting

C₆₁×#407

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
5. #14519684	C₄	semidirect
7. C₂×M₁₆×C₆₁	C₄	semidirect
53. C₆₁	#1297	semidirect
55. C₂×M₁₆	Dic₆₁	semidirect

H ≅ G/N

type

5. #14519684

C₄

semidirect

7. C₂×M₁₆×C₆₁

C₄

semidirect

53. C₆₁

#1297

semidirect

55. C₂×M₁₆

Dic₆₁

semidirect

Subgroups — #21443704

Conjugacy classes of subgroups

Complements