Group #21445219 — subgroups

Subgroups — #21445219

Order 7808.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16840167	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840053	C₂	1	2	yes	maximal
3	C₈×D₂₄₄	C₂	1	1	yes	maximal, characteristic
4	#16839510	C₂	1	2	yes	maximal, complemented
5	C₆₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₆₁	—	2	1	no	—
7	#14519777	C₂²	1	2	yes	—
8	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
9	#14519711	—	2	1	no	—
10	#14519711	—	2	1	no	—
11	#14519709	—	2	2	no	—
12	C₄⋊#92418	C₂²	1	1	yes	characteristic
13	#14519699	—	2	2	no	—
14	#14519689	—	2	1	no	—
15	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×D₂₄₄	D₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	—	2	1	no	—
19	C₂×Dic₁₂₂	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	#11758198	—	2	1	no	—
25	C₄⋊Dic₆₁	—	2	2	no	—
26	C₄⋊Dic₆₁	—	2	2	no	—
27	C₄⋊Dic₆₁	D₄	1	1	yes	characteristic
28	C₂×#92418	—	2	1	no	—
29	C₈×D₆₁	—	4	2	no	—
30	C₂²×D₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	—	4	2	no	—
36	D₂₄₄	—	2	1	no	—
37	D₂₄₄	Q₁₆	1	2	yes	—
38	C₄×D₆₁	—	4	1	no	—
39	C₄×D₆₁	—	4	1	no	—
40	Dic₁₂₂	—	8	2	no	—
41	C₈×C₆₁	—	2	1	no	—
42	C₈×C₆₁	—	4	2	no	—
43	C₈×C₆₁	SD₁₆	1	2	yes	—
44	#92418	—	4	1	no	—
45	C₂²×C₆₁	#121	1	1	yes	characteristic
46	C₂×D₆₁	—	2	2	no	—
47	C₂×D₆₁	—	4	1	no	—
48	C₂×D₆₁	—	4	1	no	—
49	C₄×C₆₁	—	2	1	no	—
50	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
51	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
52	C₄×C₆₁	#135	1	1	yes	characteristic
53	C₄×C₆₁	#137	1	1	yes	characteristic
54	Dic₆₁	—	4	1	no	—
55	Dic₆₁	—	8	2	no	—
56	#1675	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	#461	1	1	yes	characteristic
58	C₂×C₆₁	#467	1	1	yes	characteristic
59	C₂×C₆₁	#472	1	1	yes	characteristic
60	D₆₁	—	4	2	no	—
61	#500	—	61	1	no	—
62	#476	—	61	2	no	—
63	C₈×D₄	—	61	1	no	—
64	#335	D₆₁	1	1	yes	characteristic, complemented
65	#333	—	61	2	no	—
66	C₆₁	#1675	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	122	1	no	—
68	C₄⋊Q₈	—	61	2	no	—
69	C₄×D₄	—	61	1	no	—
70	#107	—	122	1	no	—
71	#107	—	122	1	no	—
72	#106	—	122	2	no	—
73	C₄⋊C₈	—	61	1	no	—
74	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
75	#102	—	122	2	no	—
76	C₂²⋊C₈	—	122	1	no	—
77	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
78	C₂×Q₈	—	122	2	no	—
79	C₂×D₄	—	61	1	no	—
80	C₂²×C₄	—	122	1	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	122	1	no	—
83	C₂×C₈	—	244	2	no	—
84	C₂×C₈	D₂₄₄	1	1	yes	characteristic
85	C₂×C₈	D₂₄₄	1	1	yes	characteristic
86	C₄⋊C₄	—	61	1	no	—
87	C₄⋊C₄	—	122	2	no	—
88	C₄⋊C₄	—	122	2	no	—
89	C₂²⋊C₄	—	122	1	no	—
90	C₄²	C₂²×D₆₁	1	1	yes	characteristic
91	C₂³	—	122	1	no	—
92	Q₈	—	488	2	no	—
93	D₄	—	61	2	no	—
94	D₄	—	122	1	no	—
95	C₂×C₄	—	122	1	no	—
96	C₂×C₄	—	244	2	no	—
97	C₂×C₄	—	244	1	no	—
98	C₂×C₄	—	244	1	no	—
99	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
100	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
101	C₂×C₄	#11758226	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	4	2	no	—
104	C₈	—	244	1	no	—
105	C₈	#11758190	1	2	yes	—
106	C₂²	—	122	2	no	—
107	C₂²	—	244	1	no	—
108	C₂²	—	244	1	no	—
109	C₂²	#14519752	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	488	2	no	—
112	C₄	—	244	1	no	—
113	C₄	C₂×#11758190	1	1	yes	characteristic
114	C₄	Q₁₆×D₆₁	1	1	yes	characteristic
115	C₄	#14519796	1	1	yes	characteristic
116	C₄	#14519810	1	1	yes	characteristic
117	C₂	—	244	2	no	—
118	C₂	#16839968	1	1	yes	characteristic
119	C₂	#16840004	1	1	yes	characteristic
120	C₂	#16840033	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840167

C₂

yes

maximal, characteristic, complemented

#16840053

C₂

yes

maximal

C₈×D₂₄₄

C₂

yes

maximal, characteristic

#16839510

C₂

yes

maximal, complemented

C₆₁×#335

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

—

#14519777

C₂²

yes

—

C₄×D₂₄₄

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14519699

—

#14519689

—

C₄⋊C₈×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

D₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

D₄

yes

characteristic

C₂×#92418

—

C₈×D₆₁

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

Q₁₆

yes

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

SD₁₆

yes

—

#92418

—

C₂²×C₆₁

#121

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×SD₁₆

yes

characteristic

C₄×C₆₁

C₂×Q₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#500

—

#476

—

C₈×D₄

—

#335

D₆₁

yes

characteristic, complemented

#333

—

C₆₁

#1675

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

122

—

#107

—

122

—

#106

—

122

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

—

#102

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

D₂₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

122

—

Q₈

—

488

—

D₄

—

D₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂×D₂₄₄

yes

characteristic

100

C₂×C₄

D₄×D₆₁

yes

characteristic

101

C₂×C₄

#11758226

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

244

—

105

C₈

#11758190

yes

—

106

C₂²

—

122

—

107

C₂²

—

244

—

108

C₂²

—

244

—

109

C₂²

#14519752

yes

characteristic

110

C₄

—

111

C₄

—

488

—

112

C₄

—

244

—

113

C₄

C₂×#11758190

yes

characteristic

114

C₄

Q₁₆×D₆₁

yes

characteristic

115

C₄

#14519796

yes

characteristic

116

C₄

#14519810

yes

characteristic

117

C₂

—

244

—

118

C₂

#16839968

yes

characteristic

119

C₂

#16840004

yes

characteristic

120

C₂

#16840033

yes

characteristic

	subgroup	G/H
center	C₂²	#14519752
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	#121
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1675
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #335

subgroup

G/H

center

C₂²

#14519752

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#335

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #335

N	H ≅ G/N	type
1. #16840167	C₂	semidirect
4. #16839510	C₂	semidirect
5. C₆₁×#335	C₂	semidirect
64. #335	D₆₁	semidirect
66. C₆₁	#1675	semidirect

H ≅ G/N

type

1. #16840167

C₂

semidirect

4. #16839510

C₂

semidirect

5. C₆₁×#335

C₂

semidirect

64. #335

D₆₁

semidirect

66. C₆₁

#1675

semidirect

Subgroups — #21445219

Conjugacy classes of subgroups

Complements