Group #21454201 — subgroups

Subgroups — #21454201

Order 7808.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#16839668	C₂	1	3	yes	maximal
2	#16839660	C₂	1	3	yes	maximal
3	#16839646	C₂	1	6	yes	maximal
4	#16839630	C₂	1	2	yes	maximal
5	C₄³×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₆₁	C₂²	1	3	yes	—
8	C₂×#11758196	C₂²	1	6	yes	—
9	#14519684	C₂²	1	6	yes	—
10	#14519684	C₂²	1	6	yes	—
11	#14519684	C₂²	1	6	yes	—
12	C₂×C₄²×C₆₁	C₂²	1	3	yes	—
13	C₂×C₄²×C₆₁	C₂²	1	3	yes	—
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₆₁	C₂³	1	2	yes	—
19	C₂²×Dic₆₁	C₂³	1	6	yes	—
20	C₂×Dic₁₂₂	—	2	6	no	—
21	C₄²×C₆₁	—	2	6	no	—
22	C₄²×C₆₁	—	2	6	no	—
23	C₄²×C₆₁	Q₈	1	4	yes	complemented
24	C₄⋊Dic₆₁	—	2	6	no	—
25	#11758196	—	2	12	no	—
26	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	2	3	no	—
28	C₂×C₄×C₆₁	—	2	3	no	—
29	C₂×C₄×C₆₁	—	2	3	no	—
30	C₂×C₄×C₆₁	—	2	3	no	—
31	C₂×C₄×C₆₁	C₂×Q₈	1	6	yes	—
32	C₂×C₄×C₆₁	#41	1	6	yes	—
33	C₂×C₄×C₆₁	#41	1	6	yes	—
34	C₂×Dic₆₁	—	2	12	no	—
35	C₂×Dic₆₁	—	2	6	no	—
36	C₂×Dic₆₁	—	2	6	no	—
37	Dic₁₂₂	—	4	4	no	—
38	C₂²×C₆₁	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₆₁	C₂×#41	1	3	yes	—
40	C₂²×C₆₁	C₂×#41	1	3	yes	—
41	C₄×C₆₁	—	2	6	no	—
42	C₄×C₆₁	—	2	6	no	—
43	C₄×C₆₁	#126	1	4	yes	—
44	Dic₆₁	—	4	2	no	—
45	Dic₆₁	—	4	6	no	—
46	#2863	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	C₂×#126	1	1	yes	characteristic
48	C₂×C₆₁	#529	1	3	yes	—
49	C₂×C₆₁	#533	1	3	yes	—
50	#391	—	61	3	no	—
51	#389	—	61	3	no	—
52	#387	—	61	6	no	—
53	#383	—	61	2	no	—
54	C₄³	D₆₁	1	1	yes	characteristic
55	C₆₁	#2863	1	1	yes	characteristic, complemented, Sylow
56	C₂²×Q₈	—	61	1	no	—
57	C₂×C₄⋊C₄	—	61	6	no	—
58	C₂×C₄⋊C₄	—	61	3	no	—
59	C₂×C₄²	C₂×D₆₁	1	3	yes	—
60	C₂×C₄²	C₂×D₆₁	1	3	yes	—
61	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
62	#95	—	61	6	no	—
63	#95	—	61	6	no	—
64	#95	—	61	6	no	—
65	C₂×Q₈	—	122	6	no	—
66	C₂²×C₄	—	61	2	no	—
67	C₂²×C₄	—	61	6	no	—
68	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
69	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
70	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	C₄⋊C₄	—	122	12	no	—
72	C₄⋊C₄	—	122	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₁₂₂	1	4	yes	complemented
76	C₂³	C₂³×D₆₁	1	1	yes	characteristic
77	Q₈	—	244	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	122	6	no	—
83	C₂×C₄	—	122	12	no	—
84	C₂×C₄	—	122	6	no	—
85	C₂×C₄	C₂×Dic₁₂₂	1	6	yes	—
86	C₂×C₄	#11758222	1	6	yes	—
87	C₂×C₄	#11758222	1	6	yes	—
88	C₂²	C₂²×Dic₁₂₂	1	1	yes	characteristic
89	C₂²	C₂×#11758222	1	3	yes	—
90	C₂²	C₂×#11758222	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	244	2	no	—
94	C₄	—	244	6	no	—
95	C₄	#14519771	1	4	yes	—
96	C₂	C₂×#14519771	1	1	yes	characteristic
97	C₂	#16840296	1	3	yes	—
98	C₂	#16840319	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839668

C₂

yes

maximal

#16839660

C₂

yes

maximal

#16839646

C₂

yes

maximal

#16839630

C₂

yes

maximal

C₄³×C₆₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₂₂

C₂²

yes

characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×#11758196

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

C₂³

yes

—

C₂²×Dic₆₁

C₂³

yes

—

C₂×Dic₁₂₂

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

Q₈

yes

complemented

C₄⋊Dic₆₁

—

#11758196

—

C₂³×C₆₁

C₂⁴

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

C₂²×C₆₁

C₂²×Q₈

yes

characteristic

C₂²×C₆₁

C₂×#41

yes

—

C₂²×C₆₁

C₂×#41

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#126

yes

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#533

yes

—

—

—

—

—

C₄³

D₆₁

yes

characteristic

C₆₁

#2863

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

—

—

—

C₂×Q₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄²

—

C₄²

—

C₄²

Dic₁₂₂

yes

complemented

C₂³

C₂³×D₆₁

yes

characteristic

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×Dic₁₂₂

yes

—

C₂×C₄

#11758222

yes

—

C₂×C₄

#11758222

yes

—

C₂²

C₂²×Dic₁₂₂

yes

characteristic

C₂²

C₂×#11758222

yes

—

C₂²

C₂×#11758222

yes

—

C₄

—

C₄

—

C₄

—

244

—

C₄

—

244

—

C₄

#14519771

yes

—

C₂

C₂×#14519771

yes

characteristic

C₂

#16840296

yes

—

C₂

#16840319

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₄³×C₆₁	C₂
hypercenter	C₄³	D₆₁
hypocenter	C₆₁	#2863
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₆₁

commutator, socle

C₂³×C₆₁

C₂⁴

Fitting

C₄³×C₆₁

C₂

hypercenter

C₄³

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
23. C₄²×C₆₁	Q₈	semidirect
55. C₆₁	#2863	semidirect
75. C₄²	Dic₁₂₂	semidirect

H ≅ G/N

type

23. C₄²×C₆₁

Q₈

semidirect

55. C₆₁

#2863

semidirect

75. C₄²

Dic₁₂₂

semidirect

Subgroups — #21454201

Conjugacy classes of subgroups

Complements