Group #21460858 — subgroups

Subgroups — #21460858

Order 7808.

160 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 86 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	C₂²×#11758187	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758187	—	2	2	no	—
4	C₂×#11758187	—	2	2	no	—
5	C₂×#11758187	C₄	1	4	yes	complemented
6	C₂²×#92418	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
8	C₈×Dic₆₁	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	C₈	1	2	yes	—
12	C₂×C₈×C₆₁	—	2	1	no	—
13	C₂×C₈×C₆₁	—	2	1	no	—
14	C₂×C₈×C₆₁	C₈	1	2	yes	—
15	C₄×Dic₆₁	—	2	1	no	—
16	C₄×Dic₆₁	—	2	1	no	—
17	C₂×#92418	C₂×C₄	1	2	yes	—
18	C₂×#92418	D₄	1	1	yes	characteristic
19	C₂×#92418	D₄	1	2	yes	—
20	C₂×#92418	Q₈	1	1	yes	characteristic
21	#11758187	—	2	4	no	—
22	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
29	C₂×Dic₆₁	—	2	2	no	—
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	C₁₆	1	4	yes	complemented
32	C₈×C₆₁	—	2	2	no	—
33	#92418	C₂²⋊C₄	1	2	yes	—
34	#92418	C₄⋊C₄	1	2	yes	—
35	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
36	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
38	C₂²×C₆₁	C₂×C₁₆	1	2	yes	—
39	C₂²×C₆₁	M₃₂	1	2	yes	—
40	C₄×C₆₁	#95	1	1	yes	characteristic
41	C₄×C₆₁	#97	1	1	yes	characteristic
42	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
44	Dic₆₁	—	2	4	no	—
45	#1374	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	#336	1	1	yes	characteristic
47	C₂×C₆₁	C₄×C₁₆	1	1	yes	characteristic
48	C₂×C₆₁	#346	1	1	yes	characteristic
49	C₂×C₆₁	C₂²⋊C₁₆	1	2	yes	—
50	C₂×C₆₁	C₄⋊C₁₆	1	2	yes	—
51	C₂²×C₁₆	—	61	2	no	—
52	C₂×C₄×C₈	—	61	1	no	—
53	C₆₁	#1374	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	61	1	no	—
55	C₂²×C₈	#6923	1	1	yes	characteristic
56	C₂×C₄²	—	61	1	no	—
57	C₂×C₁₆	—	61	4	no	—
58	C₂×C₁₆	—	122	2	no	—
59	C₂×C₁₆	—	122	2	no	—
60	C₄×C₈	—	122	2	no	—
61	C₂²×C₄	—	61	2	no	—
62	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
63	C₂×C₈	—	2	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	61	2	no	—
66	C₂×C₈	—	61	1	no	—
67	C₂×C₈	—	61	1	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	#92420	1	2	yes	—
70	C₄²	—	122	1	no	—
71	C₄²	—	122	1	no	—
72	C₁₆	—	122	4	no	—
73	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
74	C₂×C₄	—	61	4	no	—
75	C₂×C₄	—	122	2	no	—
76	C₂×C₄	—	122	2	no	—
77	C₂×C₄	#11758213	1	1	yes	characteristic
78	C₂×C₄	C₄×#6923	1	1	yes	characteristic
79	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
80	C₂×C₄	C₂×#92420	1	1	yes	characteristic
81	C₂×C₄	#11758217	1	1	yes	characteristic
82	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₈	—	61	2	no	—
85	C₈	—	61	2	no	—
86	C₂²	C₄×#92420	1	1	yes	characteristic
87	C₂²	#14519834	1	1	yes	characteristic
88	C₂²	#14519844	1	1	yes	characteristic
89	C₂²	D₆₁⋊C₁₆	1	2	yes	—
90	C₂²	#14519852	1	2	yes	—
91	C₄	—	122	4	no	—
92	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
93	C₄	#14519832	1	1	yes	characteristic
94	C₄	C₂²⋊#92420	1	1	yes	characteristic
95	C₄	C₄⋊#92420	1	1	yes	characteristic
96	C₂	#16840628	1	1	yes	characteristic
97	C₂	#16840648	1	1	yes	characteristic
98	C₂	#16840651	1	1	yes	characteristic
99	C₂	#16840657	1	2	yes	—
100	C₂	#16840683	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758187

C₂

yes

maximal

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

C₂×#11758187

—

C₂×#11758187

—

C₂×#11758187

C₄

yes

complemented

C₂²×#92418

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₈

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

D₄

yes

characteristic

C₂×#92418

D₄

yes

—

C₂×#92418

Q₈

yes

characteristic

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₁₆

yes

complemented

C₈×C₆₁

—

#92418

C₂²⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₂²×C₆₁

C₂×C₁₆

yes

—

C₂²×C₆₁

M₃₂

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×C₁₆

yes

characteristic

C₂×C₆₁

#346

yes

characteristic

C₂×C₆₁

C₂²⋊C₁₆

yes

—

C₂×C₆₁

C₄⋊C₁₆

yes

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₆₁

#1374

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#92420

yes

—

C₄²

—

122

—

C₄²

—

122

—

C₁₆

—

122

—

C₂³

D₆₁⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

D₆₁⋊C₁₆

yes

—

C₂²

#14519852

yes

—

C₄

—

122

—

C₄

yes

C₄

yes

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

100

C₂

#16840683

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×#6923
commutator	C₂×C₆₁	C₄×C₁₆
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂³×C₆₁	C₂×C₈
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1374
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂×#6923

commutator

C₂×C₆₁

C₄×C₁₆

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂³×C₆₁

C₂×C₈

C₂²×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
5. C₂×#11758187	C₄	semidirect
31. C₂×Dic₆₁	C₁₆	semidirect
53. C₆₁	#1374	semidirect

H ≅ G/N

type

5. C₂×#11758187

C₄

semidirect

31. C₂×Dic₆₁

C₁₆

semidirect

53. C₆₁

#1374

semidirect

Subgroups — #21460858

Conjugacy classes of subgroups

Complements