Group #21448053 — subgroups

Subgroups — #21448053

Order 7808.

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

normal subgroups only

This group has 138 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	#16840146	C₂	1	1	yes	maximal, characteristic
2	#16839565	C₂	1	2	yes	maximal, complemented
3	#16839562	C₂	1	2	yes	maximal
4	C₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
7	C₂×#11758190	—	2	1	no	—
8	C₂×D₄₈₈	C₂²	1	1	yes	characteristic
9	#14519765	—	2	1	no	—
10	C₂×#11758185	C₂²	1	2	yes	—
11	#125×C₆₁	—	2	1	no	—
12	#107×C₆₁	C₂²	1	2	yes	—
13	#106×C₆₁	—	2	1	no	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×D₂₄₄	—	2	1	no	—
16	C₂×Dic₁₂₂	—	2	1	no	—
17	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₆₁	—	2	2	no	—
20	C₄⋊C₄×C₆₁	—	4	2	no	—
21	C₄²×C₆₁	D₄	1	1	yes	characteristic
22	#11758198	—	4	2	no	—
23	Dic₂₄₄	—	2	2	no	—
24	D₄₈₈	—	2	2	no	—
25	#11758190	—	4	2	no	—
26	#11758185	—	2	2	no	—
27	C₂²×D₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	D₈	1	2	yes	—
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	4	1	no	—
32	D₂₄₄	—	4	1	no	—
33	D₂₄₄	—	4	1	no	—
34	Dic₁₂₂	—	4	1	no	—
35	Dic₁₂₂	—	4	1	no	—
36	C₈×C₆₁	SD₁₆	1	2	yes	—
37	C₈×C₆₁	#41	1	2	yes	—
38	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
39	C₂×D₆₁	—	8	1	no	—
40	C₂×D₆₁	—	8	2	no	—
41	C₄×C₆₁	—	2	2	no	—
42	C₄×C₆₁	—	8	2	no	—
43	C₄×C₆₁	#124	1	1	yes	characteristic
44	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
45	Dic₆₁	—	8	1	no	—
46	#2242	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	#486	1	1	yes	characteristic
48	C₂×C₆₁	#508	1	2	yes	—
49	D₆₁	—	16	1	no	—
50	#499	D₆₁	1	1	yes	characteristic, complemented
51	#495	—	61	1	no	—
52	#358	—	61	2	no	—
53	#357	—	61	2	no	—
54	C₄×C₁₆	—	61	1	no	—
55	C₆₁	#2242	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	—	61	1	no	—
57	C₂×SD₁₆	—	122	1	no	—
58	C₂×D₈	—	61	1	no	—
59	#125	—	2	1	no	—
60	#124	—	122	1	no	—
61	C₂×C₁₆	—	61	2	no	—
62	#107	C₂×D₆₁	1	2	yes	—
63	#106	—	2	1	no	—
64	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
65	C₂×Q₈	—	122	1	no	—
66	C₂×D₄	—	122	1	no	—
67	Q₁₆	—	122	2	no	—
68	SD₁₆	—	244	2	no	—
69	D₈	—	122	2	no	—
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	—	4	2	no	—
74	C₂²⋊C₄	—	244	2	no	—
75	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
76	C₁₆	—	122	2	no	—
77	C₂³	—	244	1	no	—
78	Q₈	—	244	1	no	—
79	Q₈	—	244	1	no	—
80	D₄	—	244	1	no	—
81	D₄	—	244	1	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	244	1	no	—
84	C₂×C₄	#11758199	1	2	yes	—
85	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
86	C₈	#11758201	1	2	yes	—
87	C₈	#11758226	1	2	yes	—
88	C₂²	—	488	2	no	—
89	C₂²	—	488	1	no	—
90	C₂²	C₂×#11758199	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	8	2	no	—
93	C₄	—	488	1	no	—
94	C₄	#14519766	1	1	yes	characteristic
95	C₄	C₂×#11758201	1	1	yes	characteristic
96	C₂	—	976	1	no	—
97	C₂	#16840110	1	1	yes	characteristic
98	C₂	#16840192	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840146

C₂

yes

maximal, characteristic

#16839565

C₂

yes

maximal, complemented

#16839562

C₂

yes

maximal

C₄×#11758185

C₂

yes

maximal, characteristic, complemented

C₆₁×#499

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₄₄

C₂²

yes

characteristic

C₂×#11758190

—

C₂×D₄₈₈

C₂²

yes

characteristic

#14519765

—

C₂×#11758185

C₂²

yes

—

#125×C₆₁

—

#107×C₆₁

C₂²

yes

—

#106×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

D₄

yes

characteristic

#11758198

—

Dic₂₄₄

—

D₄₈₈

—

#11758190

—

#11758185

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

SD₁₆

yes

—

C₈×C₆₁

#41

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#124

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

characteristic

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

#499

D₆₁

yes

characteristic, complemented

#495

—

#358

—

#357

—

C₄×C₁₆

—

C₆₁

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

122

—

C₂×D₈

—

#125

—

#124

—

122

—

C₂×C₁₆

—

#107

C₂×D₆₁

yes

—

#106

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

122

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

244

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

122

—

C₂³

—

244

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

#11758199

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

#11758201

yes

—

C₈

#11758226

yes

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

C₂×#11758199

yes

characteristic

C₄

—

C₄

—

C₄

—

488

—

C₄

yes

C₄

yes

C₂

—

976

—

C₂

#16840110

yes

characteristic

C₂

#16840192

yes

—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#499	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#499	D₆₁
hypocenter	C₆₁	#2242
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#499

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

N	H ≅ G/N	type
2. #16839565	C₂	semidirect
4. C₄×#11758185	C₂	semidirect
5. C₆₁×#499	C₂	semidirect
50. #499	D₆₁	semidirect
55. C₆₁	#2242	semidirect

H ≅ G/N

type

2. #16839565

C₂

semidirect

4. C₄×#11758185

C₂

semidirect

5. C₆₁×#499

C₂

semidirect

50. #499

D₆₁

semidirect

55. C₆₁

#2242

semidirect

Subgroups — #21448053

Conjugacy classes of subgroups

Complements