Group #21460704 — subgroups

Subgroups — #21460704

Order 7808.

150 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 46 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	#16840780	C₂	1	1	yes	maximal, characteristic
2	#16840767	C₂	1	1	yes	maximal, characteristic
3	#16839714	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	C₄	1	2	yes	—
5	#14519844	—	2	1	no	—
6	#14519844	—	2	1	no	—
7	#14519844	C₄	1	2	yes	—
8	#14519834	—	2	1	no	—
9	C₄×#92420	—	2	1	no	—
10	C₂×#11758189	—	2	1	no	—
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	#14519688	C₄	1	1	yes	characteristic
13	C₈×Dic₆₁	—	2	1	no	—
14	#97×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
18	C₂×#92420	—	2	2	no	—
19	C₂×#92420	—	2	2	no	—
20	#11758213	—	4	2	no	—
21	C₂×C₈×C₆₁	—	2	1	no	—
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	D₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₂×#92418	—	2	1	no	—
27	#11758189	—	2	4	no	—
28	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₄×D₆₁	—	2	1	no	—
36	C₄×D₆₁	—	2	1	no	—
37	C₄×D₆₁	—	2	2	no	—
38	C₄×D₆₁	—	2	2	no	—
39	#92420	—	4	2	no	—
40	#92420	—	4	2	no	—
41	C₈×C₆₁	—	2	2	no	—
42	#92418	—	2	2	no	—
43	C₂²×C₆₁	#95	1	1	yes	characteristic
44	C₂×D₆₁	—	2	1	no	—
45	C₂×D₆₁	—	2	1	no	—
46	C₂×D₆₁	—	2	1	no	—
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	—	2	1	no	—
50	Dic₆₁	#100	1	1	yes	characteristic
51	Dic₆₁	#101	1	1	yes	characteristic
52	Dic₆₁	#104	1	2	yes	—
53	Dic₆₁	#108	1	2	yes	—
54	#1299	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	#339	1	1	yes	characteristic
56	C₂×C₆₁	#341	1	1	yes	characteristic
57	C₂×C₆₁	#343	1	1	yes	characteristic
58	D₆₁	—	4	1	no	—
59	#431	—	61	1	no	—
60	#423	—	61	1	no	—
61	C₄×M₁₆	—	61	1	no	—
62	C₆₁	#1299	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	61	2	no	—
64	C₂×M₁₆	—	122	1	no	—
65	C₂×C₄²	—	61	1	no	—
66	C₄⋊C₈	—	61	2	no	—
67	C₄⋊C₈	—	122	1	no	—
68	C₄⋊C₈	—	122	1	no	—
69	C₂²⋊C₈	—	122	1	no	—
70	#97	—	61	1	no	—
71	#97	#6923	1	1	yes	characteristic
72	C₄×C₈	—	122	1	no	—
73	C₄×C₈	—	122	1	no	—
74	C₂²×C₄	—	61	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	M₁₆	—	122	4	no	—
78	M₁₆	—	244	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	122	1	no	—
81	C₂×C₈	—	122	2	no	—
82	C₂×C₈	—	122	2	no	—
83	C₄²	—	61	1	no	—
84	C₄²	—	61	1	no	—
85	C₄²	—	61	1	no	—
86	C₄²	C₂×#6923	1	1	yes	characteristic
87	C₂³	—	61	1	no	—
88	C₂×C₄	—	61	1	no	—
89	C₂×C₄	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	122	2	no	—
92	C₂×C₄	—	122	1	no	—
93	C₂×C₄	—	122	2	no	—
94	C₂×C₄	—	122	1	no	—
95	C₂×C₄	C₄×#6923	1	1	yes	characteristic
96	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
97	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
98	C₈	—	2	2	no	—
99	C₈	—	122	2	no	—
100	C₈	—	244	2	no	—
101	C₈	—	244	2	no	—
102	C₂²	—	122	1	no	—
103	C₂²	—	122	1	no	—
104	C₂²	—	122	1	no	—
105	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	61	2	no	—
110	C₄	—	61	2	no	—
111	C₄	—	61	1	no	—
112	C₄	—	61	1	no	—
113	C₂	—	244	1	no	—
114	C₂	#16840633	1	1	yes	characteristic
115	C₂	#16840637	1	1	yes	characteristic
116	C₂	#16840641	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840780

C₂

yes

maximal, characteristic

#16840767

C₂

yes

maximal, characteristic

#16839714

C₂

yes

maximal, characteristic

C₂×#11758213

C₄

yes

—

#14519844

—

#14519844

—

#14519844

C₄

yes

—

#14519834

—

C₄×#92420

—

C₂×#11758189

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic

C₈×Dic₆₁

—

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

—

—

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

—

#11758189

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

yes

Dic₆₁

yes

Dic₆₁

yes

—

Dic₆₁

#108

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#431

—

#423

—

C₄×M₁₆

—

C₆₁

#1299

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

—

yes

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

100

C₈

—

244

—

101

C₈

—

244

—

102

C₂²

—

122

—

103

C₂²

—

122

—

104

C₂²

—

122

—

105

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₂

—

244

—

114

C₂

#16840633

yes

characteristic

115

C₂

#16840637

yes

characteristic

116

C₂

#16840641

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₄²	C₂×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	#97	#6923
hypocenter	C₆₁	#1299
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₄²

C₂×#6923

Fitting

#97×C₆₁

C₄

C₂²×C₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
62. C₆₁	#1299	semidirect

H ≅ G/N

type

62. C₆₁

#1299

semidirect

Subgroups — #21460704

Conjugacy classes of subgroups

Complements