Group #21461039 — subgroups

Subgroups — #21461039

Order 7808.

190 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 84 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	#16840781	C₂	1	2	yes	maximal
2	#92420⋊C₈	C₂	1	2	yes	maximal, complemented
3	#16840603	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#92420	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839714	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#92420	C₄	1	4	yes	—
7	#14519834	C₄	1	4	yes	—
8	C₄×#92420	C₂²	1	2	yes	—
9	C₄×#92420	C₂²	1	2	yes	—
10	C₂×#11758189	C₄	1	1	yes	characteristic
11	C₂×#11758189	C₄	1	1	yes	characteristic
12	C₄²×D₆₁	C₂²	1	1	yes	characteristic
13	#14519688	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
16	#97×C₆₁	C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
19	C₂×#92420	C₂×C₄	1	4	yes	—
20	C₂×#92420	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
26	C₂×#92418	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	C₂×C₄	1	1	yes	characteristic
28	#11758189	—	2	2	no	—
29	#11758189	—	2	2	no	—
30	C₂²×D₆₁	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄²	1	2	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
35	C₄×D₆₁	—	2	1	no	—
36	C₄×D₆₁	—	2	1	no	—
37	C₄×D₆₁	—	2	4	no	—
38	#92420	—	2	4	no	—
39	#92420	—	2	4	no	—
40	C₈×C₆₁	—	2	1	no	—
41	C₈×C₆₁	M₁₆	1	2	yes	—
42	#92418	—	2	1	no	—
43	#92418	M₁₆	1	2	yes	—
44	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
45	C₂×D₆₁	—	2	1	no	—
46	C₂×D₆₁	—	2	2	no	—
47	C₄×C₆₁	—	2	2	no	—
48	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
50	Dic₆₁	—	2	1	no	—
51	Dic₆₁	#131	1	4	yes	—
52	#1453	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
54	C₂×C₆₁	#405	1	2	yes	—
55	D₆₁	—	4	1	no	—
56	#431	—	61	2	no	—
57	C₄×M₁₆	—	61	1	no	—
58	#322	—	61	1	no	—
59	#322	—	61	2	no	—
60	C₈²	—	61	1	no	—
61	C₆₁	#1453	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₁₆	—	61	1	no	—
63	C₂×M₁₆	—	61	1	no	—
64	C₂×C₄²	—	61	1	no	—
65	C₄⋊C₈	—	61	4	no	—
66	C₂²⋊C₈	—	61	4	no	—
67	#97	—	61	1	no	—
68	#97	#6923	1	1	yes	characteristic
69	C₄×C₈	—	61	2	no	—
70	C₄×C₈	—	61	2	no	—
71	C₄×C₈	—	61	1	no	—
72	C₄×C₈	—	61	1	no	—
73	C₂²×C₄	—	61	2	no	—
74	C₂²×C₄	—	61	1	no	—
75	M₁₆	—	122	2	no	—
76	M₁₆	—	122	2	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	—	61	4	no	—
79	C₂×C₈	—	61	4	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	C₂×#6923	1	1	yes	characteristic
82	C₂×C₈	C₂×#6923	1	1	yes	characteristic
83	C₄²	—	61	2	no	—
84	C₄²	—	61	1	no	—
85	C₄²	C₂×#6923	1	1	yes	characteristic
86	C₂³	—	61	1	no	—
87	C₂×C₄	—	61	2	no	—
88	C₂×C₄	—	61	1	no	—
89	C₂×C₄	—	122	4	no	—
90	C₂×C₄	—	122	1	no	—
91	C₂×C₄	—	122	1	no	—
92	C₂×C₄	C₄×#6923	1	2	yes	—
93	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	61	2	no	—
96	C₈	—	122	4	no	—
97	C₈	—	122	4	no	—
98	C₈	—	122	1	no	—
99	C₈	#11758213	1	2	yes	—
100	C₂²	—	122	1	no	—
101	C₂²	—	122	2	no	—
102	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	—	61	4	no	—
105	C₄	—	122	1	no	—
106	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
107	C₄	C₂×#11758213	1	1	yes	characteristic
108	C₂	—	244	1	no	—
109	C₂	C₄×#11758213	1	1	yes	characteristic
110	C₂	#16840728	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840781

C₂

yes

maximal

#92420⋊C₈

C₂

yes

maximal, complemented

#16840603

C₂

yes

maximal, characteristic, complemented

C₈×#92420

C₂

yes

maximal, characteristic, complemented

#16839714

C₂

yes

maximal, characteristic

C₄⋊#92420

C₄

yes

—

#14519834

C₄

yes

—

C₄×#92420

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₂×#11758189

C₄

yes

characteristic

C₂×#11758189

C₄

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

#11758189

—

C₂²×D₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

#92420

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

#92418

—

#92418

M₁₆

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

#131

yes

—

#1453

—

maximal, Sylow

C₂×C₆₁

C₄×M₁₆

yes

characteristic

C₂×C₆₁

#405

yes

—

D₆₁

—

#431

—

C₄×M₁₆

—

#322

—

#322

—

C₈²

—

C₆₁

#1453

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₄×#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

—

122

—

C₈

—

122

—

C₈

#11758213

yes

—

100

C₂²

—

122

—

101

C₂²

—

122

—

102

C₂²

C₂×C₄×#6923

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

122

—

106

C₄

D₆₁⋊M₁₆

yes

characteristic

107

C₄

C₂×#11758213

yes

characteristic

108

C₂

—

244

—

109

C₂

C₄×#11758213

yes

characteristic

110

C₂

#16840728

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	#97×C₆₁	C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1453
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂×C₄²

Fitting

#97×C₆₁

C₄

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
2. #92420⋊C₈	C₂	semidirect
3. #16840603	C₂	semidirect
4. C₈×#92420	C₂	semidirect
61. C₆₁	#1453	semidirect

H ≅ G/N

type

2. #92420⋊C₈

C₂

semidirect

3. #16840603

C₂

semidirect

4. C₈×#92420

C₂

semidirect

61. C₆₁

#1453

semidirect

Subgroups — #21461039

Conjugacy classes of subgroups

Complements