Group #21460911 — subgroups

Subgroups — #21460911

Order 7808.

158 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 40 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	#16840748	C₂	1	2	yes	maximal
2	#16839730	C₂	1	1	yes	maximal, characteristic
3	D₆₁⋊M₁₆	—	2	2	no	—
4	#14519838	—	2	2	no	—
5	#14519837	C₄	1	4	yes	—
6	C₂×#11758222	C₂²	1	1	yes	characteristic
7	C₂²×#92418	C₄	1	1	yes	characteristic
8	#14519689	—	2	2	no	—
9	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
12	#11758222	—	4	1	no	—
13	#11758222	—	4	1	no	—
14	C₂×D₂₄₄	Q₈	1	1	yes	characteristic
15	C₂×C₄×D₆₁	D₄	1	2	yes	—
16	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
17	#11758217	—	2	4	no	—
18	#11758213	—	4	2	no	—
19	D₆₁⋊C₈	—	4	2	no	—
20	M₁₆×C₆₁	—	4	1	no	—
21	C₂×C₈×C₆₁	—	2	1	no	—
22	C₂×#92418	—	2	1	no	—
23	C₂×#92418	—	4	1	no	—
24	C₂³×C₆₁	C₄²	1	1	yes	characteristic
25	C₂²×D₆₁	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₆₁	—	4	2	no	—
31	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
32	D₂₄₄	—	4	1	no	—
33	C₄×D₆₁	—	2	2	no	—
34	C₄×D₆₁	—	2	2	no	—
35	Dic₁₂₂	—	4	1	no	—
36	#92420	—	4	4	no	—
37	C₈×C₆₁	—	4	1	no	—
38	#92418	—	4	1	no	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	4	1	no	—
41	C₂²×C₆₁	#95	1	1	yes	characteristic
42	C₂×D₆₁	—	2	2	no	—
43	C₂×D₆₁	—	4	2	no	—
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	#99	1	1	yes	characteristic
46	C₄×C₆₁	#99	1	1	yes	characteristic
47	Dic₆₁	—	2	2	no	—
48	#1392	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	—	2	1	no	—
50	C₂×C₆₁	—	4	1	no	—
51	C₂×C₆₁	#342	1	1	yes	characteristic
52	D₆₁	—	4	2	no	—
53	#413	—	61	2	no	—
54	#408	—	61	1	no	—
55	C₆₁	#1392	1	1	yes	characteristic, complemented, Sylow
56	C₂×#41	—	61	1	no	—
57	C₂×M₁₆	—	122	2	no	—
58	C₂×M₁₆	#6923	1	1	yes	characteristic
59	C₂²×C₈	—	61	1	no	—
60	#101	—	122	2	no	—
61	#100	—	61	4	no	—
62	C₂²⋊C₈	—	122	2	no	—
63	#41	—	244	1	no	—
64	#41	—	244	1	no	—
65	C₂×Q₈	—	61	1	no	—
66	C₂×D₄	—	61	2	no	—
67	C₂×D₄	—	61	1	no	—
68	C₂²×C₄	—	61	2	no	—
69	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
70	M₁₆	—	4	1	no	—
71	M₁₆	—	122	4	no	—
72	M₁₆	—	244	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	122	1	no	—
75	C₂×C₈	—	244	2	no	—
76	C₂×C₈	—	244	1	no	—
77	C₂³	—	61	2	no	—
78	C₂³	C₄×#6923	1	1	yes	characteristic
79	Q₈	—	244	1	no	—
80	D₄	—	244	1	no	—
81	D₄	—	244	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	61	2	no	—
85	C₂×C₄	—	122	2	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
88	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	244	4	no	—
91	C₈	—	244	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	—	122	2	no	—
95	C₂²	—	244	2	no	—
96	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
97	C₄	—	2	1	no	—
98	C₄	—	122	2	no	—
99	C₄	#14519835	1	1	yes	characteristic
100	C₄	#14519836	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	4	1	no	—
103	C₂	—	244	2	no	—
104	C₂	#16840640	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840748

C₂

yes

maximal

#16839730

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

—

#14519838

—

#14519837

C₄

yes

—

C₂×#11758222

C₂²

yes

characteristic

C₂²×#92418

C₄

yes

characteristic

#14519689

—

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₆₁

C₂×C₄

yes

—

#11758222

—

#11758222

—

C₂×D₂₄₄

Q₈

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

C₂×Dic₁₂₂

D₄

yes

characteristic

#11758217

—

#11758213

—

D₆₁⋊C₈

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

C₄²

yes

characteristic

C₂²×D₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

#1392

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#342

yes

characteristic

D₆₁

—

#413

—

#408

—

C₆₁

#1392

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

122

—

C₂×M₁₆

#6923

yes

characteristic

C₂²×C₈

—

#101

—

122

—

#100

—

C₂²⋊C₈

—

122

—

#41

—

244

—

#41

—

244

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂³

—

C₂³

C₄×#6923

yes

characteristic

Q₈

—

244

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₄⋊#6923

yes

characteristic

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

244

—

C₈

—

244

—

C₂²

—

C₂²

—

C₂²

—

122

—

C₂²

—

244

—

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

C₄

—

C₄

—

122

—

C₄

#14519835

yes

characteristic

100

C₄

#14519836

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

244

—

104

C₂

#16840640

yes

characteristic

	subgroup	G/H
center	C₄	#14519836
commutator	C₂³×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂×C₆₁	#342
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1392
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

#14519836

commutator

C₂³×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×M₁₆×C₆₁

C₄

C₂×C₆₁

C₂×M₁₆

C₆₁

G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
55. C₆₁	#1392	semidirect

H ≅ G/N

type

55. C₆₁

#1392

semidirect

Subgroups — #21460911

Conjugacy classes of subgroups

Complements