Group #21461749 — subgroups

Subgroups — #21461749

Order 7808.

162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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	#16840644	C₂	1	2	yes	maximal
2	#16840633	C₂	1	2	yes	maximal
3	#16840631	C₂	1	1	yes	maximal, characteristic
4	#16840630	C₂	1	1	yes	maximal, characteristic
5	C₄×#11758189	C₂	1	1	yes	maximal, characteristic
6	D₆₁⋊M₁₆	C₂²	1	2	yes	—
7	#14519856	C₂²	1	2	yes	—
8	C₂×#11758189	C₂²	1	1	yes	characteristic
9	C₂×#11758189	C₂²	1	1	yes	characteristic
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519687	C₄	1	1	yes	characteristic, complemented
12	#14519687	C₄	1	1	yes	characteristic, complemented
13	C₄×#92418	C₄	1	1	yes	characteristic, complemented
14	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₆₁	—	2	1	no	—
16	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
17	C₂²⋊#6923	—	2	2	no	—
18	#11758217	—	2	2	no	—
19	C₄⋊#6923	—	2	2	no	—
20	C₄×#6923	—	2	2	no	—
21	#11758213	—	2	2	no	—
22	D₆₁⋊C₈	—	2	2	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	—	2	1	no	—
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂×C₄	1	1	yes	characteristic
30	#11758189	—	2	2	no	—
31	#11758189	—	2	2	no	—
32	C₂²×D₆₁	#41	1	1	yes	characteristic
33	C₂×#6923	—	4	2	no	—
34	C₂×C₄×C₆₁	—	2	1	no	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	#41	1	1	yes	characteristic
38	C₄×D₆₁	—	4	2	no	—
39	C₄×D₆₁	#41	1	2	yes	—
40	C₄×D₆₁	#41	1	2	yes	—
41	#92420	—	4	2	no	—
42	C₈×C₆₁	—	2	1	no	—
43	C₈×C₆₁	—	2	1	no	—
44	#92418	—	2	1	no	—
45	#92418	—	2	1	no	—
46	C₂²×C₆₁	#117	1	1	yes	characteristic
47	C₂×D₆₁	—	4	1	no	—
48	C₂×D₆₁	#126	1	2	yes	—
49	#6923	—	8	2	no	—
50	C₄×C₆₁	—	2	2	no	—
51	C₄×C₆₁	#117	1	1	yes	characteristic
52	C₄×C₆₁	#117	1	1	yes	characteristic
53	Dic₆₁	—	4	1	no	—
54	Dic₆₁	#126	1	2	yes	—
55	#1841	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	2	1	no	—
57	C₂×C₆₁	#383	1	1	yes	characteristic
58	D₆₁	—	2	2	no	—
59	C₄×M₁₆	—	61	1	no	—
60	#344	—	61	2	no	—
61	#339	—	61	2	no	—
62	#338	—	61	1	no	—
63	H(3,ℤ/4)	—	61	1	no	—
64	C₆₁	#1841	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	61	1	no	—
66	C₂×M₁₆	—	61	1	no	—
67	C₂×M₁₆	—	61	2	no	—
68	#117	—	61	2	no	—
69	C₂×C₄²	—	61	1	no	—
70	#97	—	61	1	no	—
71	#97	—	61	1	no	—
72	C₄×C₈	—	61	1	no	—
73	C₄×C₈	#6923	1	1	yes	characteristic, complemented
74	C₂²×C₄	—	61	1	no	—
75	C₂²×C₄	—	122	1	no	—
76	M₁₆	—	122	2	no	—
77	M₁₆	—	122	2	no	—
78	M₁₆	—	122	2	no	—
79	M₁₆	—	122	2	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	122	2	no	—
83	C₂×C₈	C₂×#6923	1	1	yes	characteristic
84	C₂×C₈	C₂×#6923	1	1	yes	characteristic
85	C₄⋊C₄	—	122	2	no	—
86	C₂²⋊C₄	—	122	2	no	—
87	C₄²	—	61	1	no	—
88	C₄²	—	122	1	no	—
89	C₄²	—	122	2	no	—
90	C₄²	C₂×#6923	1	1	yes	characteristic
91	C₂³	—	61	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	2	no	—
95	C₂×C₄	—	61	2	no	—
96	C₂×C₄	—	122	1	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	—	244	2	no	—
99	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	—	2	1	no	—
102	C₈	—	122	1	no	—
103	C₈	—	122	1	no	—
104	C₈	—	244	2	no	—
105	C₂²	—	61	2	no	—
106	C₂²	—	244	1	no	—
107	C₂²	#14519856	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	61	2	no	—
110	C₄	—	488	2	no	—
111	C₄	—	244	1	no	—
112	C₄	#14519856	1	1	yes	characteristic
113	C₄	#14519856	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	122	2	no	—
116	C₂	#16840707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840644

C₂

yes

maximal

#16840633

C₂

yes

maximal

#16840631

C₂

yes

maximal, characteristic

#16840630

C₂

yes

maximal, characteristic

C₄×#11758189

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₂²

yes

—

#14519856

C₂²

yes

—

C₂×#11758189

C₂²

yes

characteristic

C₂×#11758189

C₂²

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

#14519687

C₄

yes

characteristic, complemented

#14519687

C₄

yes

characteristic, complemented

C₄×#92418

C₄

yes

characteristic, complemented

C₄×C₈×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂²⋊#6923

—

—

—

—

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

#11758189

—

C₂²×D₆₁

#41

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

#41

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

#41

yes

—

C₄×D₆₁

#41

yes

—

#92420

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

#92418

—

C₂²×C₆₁

#117

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#126

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

#126

yes

—

#1841

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#383

yes

characteristic

D₆₁

—

C₄×M₁₆

—

—

—

—

—

C₆₁

#1841

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

#117

—

C₂×C₄²

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic, complemented

C₂²×C₄

—

C₂²×C₄

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂²×#6923

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

122

—

103

C₈

—

122

—

104

C₈

—

244

—

105

C₂²

—

106

C₂²

—

244

—

107

C₂²

#14519856

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

488

—

111

C₄

—

244

—

112

C₄

#14519856

yes

characteristic

113

C₄

#14519856

yes

characteristic

114

C₂

—

115

C₂

—

122

—

116

C₂

#16840707

yes

characteristic

	subgroup	G/H
center	C₄	#14519856
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂×C₆₁	#383
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1841
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₄

#14519856

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

C₂×C₆₁

C₄×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
11. #14519687	C₄	semidirect
12. #14519687	C₄	semidirect
13. C₄×#92418	C₄	semidirect
14. C₄×C₈×C₆₁	C₄	semidirect
64. C₆₁	#1841	semidirect
73. C₄×C₈	#6923	semidirect

H ≅ G/N

type

11. #14519687

C₄

semidirect

12. #14519687

C₄

semidirect

13. C₄×#92418

C₄

semidirect

14. C₄×C₈×C₆₁

C₄

semidirect

64. C₆₁

#1841

semidirect

73. C₄×C₈

#6923

semidirect

Subgroups — #21461749

Conjugacy classes of subgroups

Complements