Group #21444940 — subgroups

Subgroups — #21444940

Order 7808.

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

normal subgroups only

This group has 218 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	#16840134	C₂	1	1	yes	maximal, characteristic
2	#16840057	C₂	1	2	yes	maximal, complemented
3	#16839506	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊#92418	C₂	1	2	yes	maximal, complemented
5	C₆₁×#559	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758200	—	2	2	no	—
7	#14519777	C₂²	1	1	yes	characteristic
8	#14519710	—	2	2	no	—
9	C₄⋊#92418	C₂²	1	2	yes	—
10	#14519701	—	2	2	no	—
11	C₄×#92418	C₂²	1	1	yes	characteristic
12	#127×C₆₁	C₂²	1	1	yes	characteristic
13	#124×C₆₁	—	2	2	no	—
14	#123×C₆₁	—	2	2	no	—
15	C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₄×D₄×C₆₁	—	2	2	no	—
17	C₂×Q₈×C₆₁	D₄	1	2	yes	—
18	C₂×D₄×C₆₁	—	2	2	no	—
19	C₂×D₄×C₆₁	D₄	1	2	yes	—
20	C₂²×C₄×C₆₁	—	2	2	no	—
21	C₂×Dic₁₂₂	—	2	1	no	—
22	C₄⋊C₄×C₆₁	—	2	2	no	—
23	C₄⋊C₄×C₆₁	D₄	1	2	yes	—
24	C₂²⋊C₄×C₆₁	—	2	4	no	—
25	C₂²⋊C₄×C₆₁	—	2	2	no	—
26	C₄²×C₆₁	—	2	2	no	—
27	C₄²×C₆₁	C₂³	1	1	yes	characteristic
28	#11758200	—	4	4	no	—
29	C₄⋊Dic₆₁	—	2	2	no	—
30	C₂×#92418	—	2	1	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂³×C₆₁	—	2	2	no	—
33	Q₈×C₆₁	—	2	2	no	—
34	Q₈×C₆₁	—	2	2	no	—
35	D₄×C₆₁	—	4	2	no	—
36	D₄×C₆₁	—	4	2	no	—
37	D₄×C₆₁	—	4	2	no	—
38	C₂×C₄×C₆₁	—	2	2	no	—
39	C₂×C₄×C₆₁	—	2	2	no	—
40	C₂×C₄×C₆₁	—	8	2	no	—
41	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
43	C₂×Dic₆₁	—	4	1	no	—
44	Dic₁₂₂	—	4	2	no	—
45	#92418	—	2	2	no	—
46	#92418	—	4	2	no	—
47	C₂²×C₆₁	—	4	4	no	—
48	C₂²×C₆₁	—	4	2	no	—
49	C₂²×C₆₁	#120	1	1	yes	characteristic
50	C₄×C₆₁	—	2	1	no	—
51	C₄×C₆₁	—	4	2	no	—
52	C₄×C₆₁	—	4	2	no	—
53	C₄×C₆₁	#135	1	2	yes	—
54	C₄×C₆₁	#137	1	2	yes	—
55	Dic₆₁	—	8	1	no	—
56	#1630	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	8	2	no	—
58	C₂×C₆₁	#452	1	2	yes	—
59	C₂×C₆₁	#453	1	1	yes	characteristic
60	#559	D₆₁	1	1	yes	characteristic
61	#492	—	61	1	no	—
62	#477	—	61	2	no	—
63	#331	—	61	1	no	—
64	Q₈⋊C₈	—	61	2	no	—
65	C₆₁	#1630	1	1	yes	characteristic, complemented, Sylow
66	C₂×SD₁₆	—	122	2	no	—
67	C₄⋊Q₈	—	61	1	no	—
68	#127	C₂×D₆₁	1	1	yes	characteristic
69	#124	—	2	2	no	—
70	#123	—	2	2	no	—
71	C₄×Q₈	C₂×D₆₁	1	2	yes	—
72	C₄×D₄	—	2	2	no	—
73	#107	—	122	2	no	—
74	C₄⋊C₈	—	61	2	no	—
75	#103	—	122	2	no	—
76	C₄×C₈	—	61	1	no	—
77	C₂×Q₈	—	122	1	no	—
78	C₂×Q₈	C₂²⋊D₆₁	1	2	yes	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	C₂²⋊D₆₁	1	2	yes	—
81	C₂²×C₄	—	2	2	no	—
82	SD₁₆	—	244	4	no	—
83	C₂×C₈	—	122	1	no	—
84	C₂×C₈	—	122	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	—	122	2	no	—
87	C₄⋊C₄	C₂²⋊D₆₁	1	2	yes	—
88	C₂²⋊C₄	—	2	4	no	—
89	C₂²⋊C₄	—	2	2	no	—
90	C₄²	—	2	2	no	—
91	C₄²	C₂²×D₆₁	1	1	yes	characteristic
92	C₂³	—	2	2	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	244	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	8	2	no	—
102	C₂×C₄	—	244	1	no	—
103	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₆₁	1	2	yes	—
105	C₈	—	122	2	no	—
106	C₈	—	244	2	no	—
107	C₂²	—	4	4	no	—
108	C₂²	—	4	2	no	—
109	C₂²	#14519746	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	4	2	no	—
112	C₄	—	4	2	no	—
113	C₄	—	488	1	no	—
114	C₄	#14519797	1	2	yes	—
115	C₄	#14519807	1	2	yes	—
116	C₂	—	8	2	no	—
117	C₂	#16839924	1	2	yes	—
118	C₂	#16839930	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840134

C₂

yes

maximal, characteristic

#16840057

C₂

yes

maximal, complemented

#16839506

C₂

yes

maximal, characteristic

Q₈⋊#92418

C₂

yes

maximal, complemented

C₆₁×#559

C₂

yes

maximal, characteristic

C₂×#11758200

—

#14519777

C₂²

yes

characteristic

#14519710

—

C₄⋊#92418

C₂²

yes

—

#14519701

—

C₄×#92418

C₂²

yes

characteristic

#127×C₆₁

C₂²

yes

characteristic

#124×C₆₁

—

#123×C₆₁

—

C₄×Q₈×C₆₁

C₂²

yes

—

C₄×D₄×C₆₁

—

C₂×Q₈×C₆₁

D₄

yes

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

—

C₂×Dic₁₂₂

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

D₄

yes

—

C₂²⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758200

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×Dic₆₁

—

Dic₁₂₂

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#120

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#135

yes

—

C₄×C₆₁

#137

yes

—

Dic₆₁

—

#1630

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#452

yes

—

C₂×C₆₁

#453

yes

characteristic

#559

D₆₁

yes

—

—

—

Q₈⋊C₈

—

C₆₁

#1630

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

122

—

C₄⋊Q₈

—

#127

C₂×D₆₁

yes

characteristic

#124

—

#123

—

C₄×Q₈

C₂×D₆₁

yes

—

C₄×D₄

—

#107

—

122

—

C₄⋊C₈

—

#103

—

122

—

C₄×C₈

—

C₂×Q₈

—

122

—

C₂×Q₈

C₂²⋊D₆₁

yes

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

—

SD₁₆

—

244

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₂²⋊D₆₁

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

244

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

244

—

103

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₆₁

yes

—

105

C₈

—

122

—

106

C₈

—

244

—

107

C₂²

—

108

C₂²

—

109

C₂²

#14519746

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

488

—

114

C₄

#14519797

yes

—

115

C₄

#14519807

yes

—

116

C₂

—

117

C₂

#16839924

yes

—

118

C₂

#16839930

yes

characteristic

	subgroup	G/H
center	C₂²	#14519746
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#559	C₂
socle	C₂²×C₆₁	#120
hypercenter	#559	D₆₁
hypocenter	C₆₁	#1630
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #559

subgroup

G/H

center

C₂²

#14519746

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#559

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #559

N	H ≅ G/N	type
2. #16840057	C₂	semidirect
4. Q₈⋊#92418	C₂	semidirect
65. C₆₁	#1630	semidirect

H ≅ G/N

type

2. #16840057

C₂

semidirect

4. Q₈⋊#92418

C₂

semidirect

65. C₆₁

#1630

semidirect

Subgroups — #21444940

Conjugacy classes of subgroups

Complements