Group #21460832 — subgroups

Subgroups — #21460832

Order 7808.

102 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 32 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	#16840683	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840624	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840147	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	C₂×#11758201	—	2	1	no	—
7	C₂×D₄₈₈	C₄	1	1	yes	characteristic
8	#14519766	—	2	1	no	—
9	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₆₁	—	2	1	no	—
12	C₂×D₂₄₄	—	2	1	no	—
13	C₂×#92420	—	4	1	no	—
14	Q₁₆×C₆₁	—	4	1	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	#11758201	—	4	1	no	—
17	#11758201	—	4	1	no	—
18	#11758198	—	4	1	no	—
19	#11758198	—	4	1	no	—
20	C₄×Dic₆₁	D₄	1	1	yes	characteristic
21	C₂×#92418	D₄	1	1	yes	characteristic
22	D₄₈₈	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	C₂²×D₆₁	—	4	1	no	—
25	Q₈×C₆₁	—	4	1	no	—
26	Q₈×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	D₈	1	1	yes	characteristic
30	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
31	D₂₄₄	—	4	1	no	—
32	D₂₄₄	—	4	1	no	—
33	#92420	—	8	1	no	—
34	C₈×C₆₁	—	2	1	no	—
35	#92418	D₈	1	1	yes	characteristic
36	#92418	SD₁₆	1	1	yes	characteristic
37	C₂²×C₆₁	#102	1	1	yes	characteristic
38	C₂×D₆₁	—	8	1	no	—
39	C₂×D₆₁	—	8	1	no	—
40	C₂×D₆₁	—	8	1	no	—
41	C₄×C₆₁	—	8	1	no	—
42	C₄×C₆₁	#100	1	1	yes	characteristic
43	C₄×C₆₁	#102	1	1	yes	characteristic
44	Dic₆₁	—	2	1	no	—
45	Dic₆₁	—	2	1	no	—
46	#1360	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	#331	1	1	yes	characteristic
48	C₂×C₆₁	#359	1	1	yes	characteristic
49	C₂×C₆₁	#360	1	1	yes	characteristic
50	D₆₁	—	16	1	no	—
51	#495	—	61	1	no	—
52	C₄⋊C₁₆	—	61	1	no	—
53	#334	—	61	1	no	—
54	C₆₁	#1360	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	#6923	1	1	yes	characteristic
56	C₂×SD₁₆	—	122	1	no	—
57	C₂×D₈	—	61	1	no	—
58	#124	—	122	1	no	—
59	C₂×C₁₆	—	122	1	no	—
60	C₄⋊C₈	—	122	1	no	—
61	C₄×C₈	—	61	1	no	—
62	C₂×Q₈	—	2	1	no	—
63	C₂×D₄	—	122	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	244	1	no	—
66	SD₁₆	—	244	1	no	—
67	D₈	—	244	1	no	—
68	C₂×C₈	—	61	1	no	—
69	C₂×C₈	—	244	1	no	—
70	C₂×C₈	C₂×#6923	1	1	yes	characteristic
71	C₂²⋊C₄	—	244	1	no	—
72	C₂²⋊C₄	—	244	1	no	—
73	C₄²	—	61	1	no	—
74	C₁₆	—	244	1	no	—
75	C₂³	—	244	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	D₄	—	244	1	no	—
79	D₄	—	244	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	61	1	no	—
86	C₈	—	61	1	no	—
87	C₈	—	488	1	no	—
88	C₂²	—	488	1	no	—
89	C₂²	—	488	1	no	—
90	C₂²	—	488	1	no	—
91	C₂²	#14519839	1	1	yes	characteristic
92	C₄	—	8	1	no	—
93	C₄	—	122	1	no	—
94	C₄	—	122	1	no	—
95	C₄	#14519837	1	1	yes	characteristic
96	C₄	#14519839	1	1	yes	characteristic
97	C₂	—	976	1	no	—
98	C₂	#16840620	1	1	yes	characteristic
99	C₂	#16840677	1	1	yes	characteristic
100	C₂	#16840679	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840683

C₂

yes

maximal, characteristic, complemented

#16840624

C₂

yes

maximal, characteristic, complemented

#16840147

C₂

yes

maximal, characteristic

C₂×#11758187

—

C₄⋊#92420

—

C₂×#11758201

—

C₂×D₄₈₈

C₄

yes

characteristic

#14519766

—

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×Q₁₆×C₆₁

C₄

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×D₂₄₄

—

C₂×#92420

—

Q₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

—

—

—

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

D₄₈₈

—

#11758187

—

C₂²×D₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

D₈

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

D₂₄₄

—

D₂₄₄

—

#92420

—

C₈×C₆₁

—

#92418

D₈

yes

characteristic

#92418

SD₁₆

yes

characteristic

C₂²×C₆₁

#102

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#495

—

C₄⋊C₁₆

—

#334

—

C₆₁

#1360

yes

characteristic, complemented, Sylow

C₂×Q₁₆

#6923

yes

characteristic

C₂×SD₁₆

—

122

—

C₂×D₈

—

#124

—

122

—

C₂×C₁₆

—

122

—

C₄⋊C₈

—

122

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

122

—

Q₁₆

—

SD₁₆

—

244

—

SD₁₆

—

244

—

D₈

—

244

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

characteristic

C₂²⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₄²

—

C₁₆

—

244

—

C₂³

—

244

—

Q₈

—

Q₈

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

#14519839

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

yes

C₄

yes

C₂

—

976

—

C₂

yes

C₂

yes

100

C₂

#16840679

yes

characteristic

	subgroup	G/H
center	C₂²	#14519839
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#102
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1360
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂²

#14519839

commutator

C₂×C₈×C₆₁

C₂×C₄

Frattini

C₂×C₈

C₂×#6923

Fitting

C₂×Q₁₆×C₆₁

C₄

C₂²×C₆₁

C₂×Q₁₆

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

N	H ≅ G/N	type
1. #16840683	C₂	semidirect
2. #16840624	C₂	semidirect
54. C₆₁	#1360	semidirect

H ≅ G/N

type

1. #16840683

C₂

semidirect

2. #16840624

C₂

semidirect

54. C₆₁

#1360

semidirect

Subgroups — #21460832

Conjugacy classes of subgroups

Complements