Group #21460640 — subgroups

Subgroups — #21460640

Order 7808.

166 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 54 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	#16840628	C₂	1	2	yes	maximal
2	#16839667	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	—	2	2	no	—
4	C₂²×Dic₁₂₂	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
6	#14519684	—	2	2	no	—
7	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	—	2	1	no	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×Dic₆₁	—	2	1	no	—
11	C₂²×Dic₆₁	D₄	1	2	yes	—
12	C₂×Dic₁₂₂	—	2	1	no	—
13	C₂×Dic₁₂₂	—	4	1	no	—
14	C₂×Dic₁₂₂	—	4	1	no	—
15	C₂×Dic₁₂₂	C₈	1	2	yes	complemented
16	C₂×#92420	—	2	4	no	—
17	C₂×#92420	—	4	2	no	—
18	C₂×#92420	—	4	2	no	—
19	C₄⋊C₄×C₆₁	—	4	1	no	—
20	C₄×Dic₆₁	—	4	1	no	—
21	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	—	4	1	no	—
25	C₂×C₄×C₆₁	—	4	2	no	—
26	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	2	no	—
29	C₂×Dic₆₁	—	2	2	no	—
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	—	4	1	no	—
32	C₂×Dic₆₁	—	4	1	no	—
33	C₂×Dic₆₁	SD₁₆	1	2	yes	—
34	C₂×Dic₆₁	Q₁₆	1	2	yes	—
35	Dic₁₂₂	—	4	2	no	—
36	Dic₁₂₂	—	4	2	no	—
37	#92420	—	4	4	no	—
38	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₆₁	#99	1	1	yes	characteristic
40	C₂²×C₆₁	#100	1	1	yes	characteristic
41	C₂²×C₆₁	#103	1	2	yes	—
42	C₂²×C₆₁	#104	1	2	yes	—
43	C₄×C₆₁	—	2	1	no	—
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	—	8	1	no	—
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	—	2	2	no	—
48	Dic₆₁	—	4	2	no	—
49	#1272	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	#323	1	1	yes	characteristic
51	C₂×C₆₁	Q₈⋊C₈	1	2	yes	—
52	C₂×C₆₁	#328	1	2	yes	—
53	C₂×C₆₁	#329	1	1	yes	characteristic
54	C₂×C₆₁	#333	1	1	yes	characteristic
55	#391	—	61	1	no	—
56	#336	—	61	2	no	—
57	C₆₁	#1272	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	—	61	1	no	—
59	C₂²×C₈	—	122	2	no	—
60	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
61	C₂×C₄²	—	61	1	no	—
62	#95	—	122	2	no	—
63	C₂×Q₈	—	61	2	no	—
64	C₂×Q₈	—	122	1	no	—
65	C₂×Q₈	—	244	1	no	—
66	C₂×Q₈	—	244	1	no	—
67	C₂²×C₄	—	2	1	no	—
68	C₂²×C₄	—	61	2	no	—
69	C₂²×C₄	—	122	1	no	—
70	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
71	C₂×C₈	—	122	4	no	—
72	C₂×C₈	—	244	2	no	—
73	C₂×C₈	—	244	2	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	—	244	1	no	—
76	C₂³	C₂²⋊#6923	1	1	yes	characteristic
77	Q₈	—	244	2	no	—
78	Q₈	—	244	2	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	61	2	no	—
85	C₂×C₄	—	122	2	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	—	122	2	no	—
88	C₂×C₄	—	244	1	no	—
89	C₂×C₄	—	244	1	no	—
90	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
91	C₂×C₄	#11758213	1	1	yes	characteristic
92	C₈	—	244	4	no	—
93	C₂²	#14519834	1	1	yes	characteristic
94	C₂²	#14519836	1	1	yes	characteristic
95	C₂²	#14519837	1	1	yes	characteristic
96	C₂²	#14519840	1	2	yes	—
97	C₂²	#14519841	1	2	yes	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	8	1	no	—
101	C₄	—	122	2	no	—
102	C₄	—	122	2	no	—
103	C₄	—	244	2	no	—
104	C₂	#16840606	1	1	yes	characteristic
105	C₂	#16840612	1	2	yes	—
106	C₂	#16840615	1	2	yes	—
107	C₂	#16840617	1	1	yes	characteristic
108	C₂	#16840622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840628

C₂

yes

maximal

#16839667

C₂

yes

maximal, characteristic

C₂²×#92420

—

C₂²×Dic₁₂₂

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519684

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

C₈

yes

—

—

—

C₄⋊C₄×C₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

SD₁₆

yes

—

C₂×Dic₆₁

Q₁₆

yes

—

Dic₁₂₂

—

Dic₁₂₂

—

#92420

—

C₂²×C₆₁

C₂²⋊C₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₂²×C₆₁

#104

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

Q₈⋊C₈

yes

—

C₂×C₆₁

#328

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₆₁

#1272

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

122

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

#95

—

122

—

C₂×Q₈

—

C₂×Q₈

—

122

—

C₂×Q₈

—

244

—

C₂×Q₈

—

244

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄⋊C₄

—

C₄²

—

244

—

C₂³

C₂²⋊#6923

yes

characteristic

Q₈

—

244

—

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₆₁⋊C₈

yes

characteristic

C₂×C₄

#11758213

yes

characteristic

C₈

—

244

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14519841

yes

—

C₄

—

C₄

—

100

C₄

—

101

C₄

—

122

—

102

C₄

—

122

—

103

C₄

—

244

—

104

C₂

#16840606

yes

characteristic

105

C₂

#16840612

yes

—

106

C₂

#16840615

yes

—

107

C₂

#16840617

yes

characteristic

108

C₂

#16840622

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1272
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₂×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

socle

C₂³×C₆₁

C₂²⋊C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
15. C₂×Dic₁₂₂	C₈	semidirect
57. C₆₁	#1272	semidirect

H ≅ G/N

type

15. C₂×Dic₁₂₂

C₈

semidirect

57. C₆₁

#1272

semidirect

Subgroups — #21460640

Conjugacy classes of subgroups

Complements