Group #21447329 — subgroups

Subgroups — #21447329

Order 7808.

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

normal subgroups only

This group has 176 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	#16839805	C₂	1	2	yes	maximal
2	C₂×#14519709	C₂	1	1	yes	maximal, characteristic
3	#16839530	C₂	1	2	yes	maximal
4	#16839527	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519710	—	2	2	no	—
9	#14519709	—	2	2	no	—
10	#14519708	—	2	2	no	—
11	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	#117×C₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	—	2	2	no	—
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	—	2	2	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	2	no	—
19	C₂×C₈×C₆₁	—	2	1	no	—
20	C₂×C₈×C₆₁	D₄	1	2	yes	—
21	C₄⋊C₄×C₆₁	D₄	1	2	yes	—
22	C₂²⋊C₄×C₆₁	—	2	1	no	—
23	C₄²×C₆₁	—	2	1	no	—
24	C₄⋊Dic₆₁	—	2	2	no	—
25	C₄⋊Dic₆₁	—	2	2	no	—
26	#11758194	—	2	2	no	—
27	#11758194	Q₈	1	4	yes	—
28	C₂×#92418	—	2	2	no	—
29	C₂³×C₆₁	#41	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	2	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×Q₈	1	2	yes	—
34	C₂×C₄×C₆₁	#41	1	2	yes	—
35	C₂×Dic₆₁	—	4	2	no	—
36	C₂×Dic₆₁	—	8	2	no	—
37	C₈×C₆₁	—	2	2	no	—
38	C₈×C₆₁	—	4	1	no	—
39	#92418	—	2	4	no	—
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	#121	1	1	yes	characteristic
42	C₂²×C₆₁	#125	1	2	yes	—
43	C₄×C₆₁	—	4	2	no	—
44	C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
45	C₄×C₆₁	#123	1	1	yes	characteristic
46	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
47	Dic₆₁	—	8	2	no	—
48	#2090	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	—	2	2	no	—
50	C₂×C₆₁	#398	1	1	yes	characteristic
51	C₂×C₆₁	#471	1	2	yes	—
52	#428	—	61	2	no	—
53	C₂×#106	—	61	1	no	—
54	#424	D₆₁	1	1	yes	characteristic
55	#343	—	61	2	no	—
56	#341	—	61	1	no	—
57	C₆₁	#2090	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	61	2	no	—
59	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	#117	C₂×D₆₁	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	61	2	no	—
63	#107	—	122	2	no	—
64	#106	—	122	2	no	—
65	#106	—	122	2	no	—
66	C₄⋊C₈	—	2	2	no	—
67	C₂²×C₄	—	122	2	no	—
68	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	61	4	no	—
71	M₁₆	—	122	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	122	2	no	—
75	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
76	C₄⋊C₄	—	122	2	no	—
77	C₄⋊C₄	—	122	2	no	—
78	C₄⋊C₄	D₂₄₄	1	2	yes	—
79	C₂²⋊C₄	—	2	1	no	—
80	C₄²	—	2	1	no	—
81	C₂³	#11758222	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	488	2	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
86	C₂×C₄	#11758224	1	2	yes	—
87	C₂×C₄	Q₈×D₆₁	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	4	1	no	—
91	C₈	—	122	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#14519751	1	1	yes	characteristic
94	C₂²	#14519767	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	488	2	no	—
97	C₄	#14519757	1	2	yes	—
98	C₄	#14519758	1	1	yes	characteristic
99	C₄	#14519775	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#16839692	1	1	yes	characteristic
102	C₂	#16840025	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839805

C₂

yes

maximal

C₂×#14519709

C₂

yes

maximal, characteristic

#16839530

C₂

yes

maximal

#16839527

C₂

yes

maximal, characteristic

C₆₁×#424

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519710

—

#14519709

—

#14519708

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

C₄⋊C₄×C₆₁

D₄

yes

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758194

—

#11758194

Q₈

yes

—

C₂×#92418

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

#121

yes

characteristic

C₂²×C₆₁

#125

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊Q₈

yes

—

C₄×C₆₁

#123

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

#2090

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#398

yes

characteristic

C₂×C₆₁

#471

yes

—

#428

—

C₂×#106

—

#424

D₆₁

yes

characteristic

#343

—

#341

—

C₆₁

#2090

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

122

—

#106

—

122

—

#106

—

122

—

C₄⋊C₈

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

D₂₄₄

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#11758222

yes

characteristic

C₂×C₄

—

C₂×C₄

—

488

—

C₂×C₄

—

244

—

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

#11758224

yes

—

C₂×C₄

Q₈×D₆₁

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₂²

—

C₂²

#14519751

yes

characteristic

C₂²

#14519767

yes

—

C₄

—

C₄

—

488

—

C₄

#14519757

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#16839692

yes

characteristic

102

C₂

#16840025

yes

—

	subgroup	G/H
center	C₂²	#14519751
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#424	C₂
socle	C₂²×C₆₁	#121
hypercenter	#424	D₆₁
hypocenter	C₆₁	#2090
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#14519751

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#424

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
57. C₆₁	#2090	semidirect

H ≅ G/N

type

57. C₆₁

#2090

semidirect

Subgroups — #21447329

Conjugacy classes of subgroups

Complements