Group #21461541 — subgroups

Subgroups — #21461541

Order 7808.

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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	#16840725	C₂	1	2	yes	maximal
2	#16840631	C₂	1	1	yes	maximal, characteristic
3	#16840630	C₂	1	1	yes	maximal, characteristic
4	#16840629	C₂	1	2	yes	maximal
5	#16839719	C₂	1	1	yes	maximal, characteristic
6	D₆₁⋊M₁₆	C₂²	1	2	yes	—
7	#14519856	C₂²	1	2	yes	—
8	#14519831	C₄	1	4	yes	complemented
9	C₈×#6923	C₄	1	4	yes	complemented
10	C₂×#11758189	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
12	#14519734	C₂²	1	1	yes	characteristic
13	#14519687	C₄	1	1	yes	characteristic, complemented
14	C₄×#92418	C₄	1	1	yes	characteristic, complemented
15	C₈×Dic₆₁	C₄	1	1	yes	characteristic, complemented
16	#97×C₆₁	C₄	1	1	yes	characteristic, complemented
17	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
18	C₂²⋊#6923	—	2	2	no	—
19	#11758217	—	2	2	no	—
20	C₄⋊#6923	—	2	2	no	—
21	C₄×#6923	C₂×C₄	1	4	yes	—
22	#11758213	—	2	2	no	—
23	D₆₁⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
27	#11758198	—	2	1	no	—
28	#11758196	—	2	1	no	—
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×#92418	C₂×C₄	1	1	yes	characteristic
31	C₂×#92418	C₂×C₄	1	1	yes	characteristic
32	#11758189	—	2	2	no	—
33	C₈×D₆₁	C₂×C₄	1	2	yes	—
34	C₈×D₆₁	C₂×C₄	1	2	yes	—
35	C₂²×D₆₁	#41	1	1	yes	characteristic
36	C₂×#6923	—	2	4	no	—
37	C₂×C₄×C₆₁	—	2	1	no	—
38	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	—	2	1	no	—
40	C₂×Dic₆₁	#41	1	1	yes	characteristic
41	C₄×D₆₁	C₂²×C₄	1	2	yes	—
42	C₄×D₆₁	#41	1	2	yes	—
43	#92420	—	2	4	no	—
44	C₈×C₆₁	—	2	1	no	—
45	C₈×C₆₁	C₄²	1	2	yes	—
46	#92418	—	2	1	no	—
47	#92418	C₄²	1	1	yes	characteristic
48	#92418	C₄²	1	1	yes	characteristic
49	C₂²×C₆₁	#117	1	1	yes	characteristic
50	C₂×D₆₁	—	4	1	no	—
51	C₂×D₆₁	#117	1	2	yes	—
52	#6923	—	4	4	no	—
53	C₄×C₆₁	—	4	1	no	—
54	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₆₁	#117	1	1	yes	characteristic
56	Dic₆₁	—	4	1	no	—
57	Dic₆₁	#117	1	2	yes	—
58	#1747	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	—	2	1	no	—
60	C₂×C₆₁	#376	1	1	yes	characteristic
61	D₆₁	—	2	2	no	—
62	#405	—	61	2	no	—
63	#405	—	61	1	no	—
64	#338	—	61	1	no	—
65	H(3,ℤ/4)	—	61	2	no	—
66	H(3,ℤ/4)	—	61	1	no	—
67	C₆₁	#1747	1	1	yes	characteristic, complemented, Sylow
68	C₂×M₁₆	—	61	2	no	—
69	C₂×M₁₆	—	61	1	no	—
70	C₂²×C₈	—	61	1	no	—
71	#117	—	61	2	no	—
72	#117	—	61	1	no	—
73	#97	—	61	4	no	—
74	#97	—	61	1	no	—
75	#97	#6923	1	1	yes	characteristic, complemented
76	C₄×C₈	—	61	4	no	—
77	C₄×C₈	—	61	1	no	—
78	C₄×C₈	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	M₁₆	—	122	2	no	—
81	M₁₆	—	122	2	no	—
82	M₁₆	—	122	2	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	61	2	no	—
86	C₂×C₈	—	61	4	no	—
87	C₂×C₈	—	61	1	no	—
88	C₂×C₈	C₂×#6923	1	1	yes	characteristic
89	C₂×C₈	C₂×#6923	1	1	yes	characteristic
90	C₄⋊C₄	—	122	1	no	—
91	C₄⋊C₄	—	122	2	no	—
92	C₂²⋊C₄	—	122	1	no	—
93	C₂²⋊C₄	—	122	2	no	—
94	C₄²	—	61	4	no	—
95	C₄²	—	61	1	no	—
96	C₄²	C₂×#6923	1	1	yes	characteristic
97	C₂³	—	61	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	2	no	—
101	C₂×C₄	—	61	2	no	—
102	C₂×C₄	—	122	4	no	—
103	C₂×C₄	—	122	1	no	—
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	61	1	no	—
107	C₈	—	61	1	no	—
108	C₈	—	122	4	no	—
109	C₈	—	122	1	no	—
110	C₈	C₄×#6923	1	2	yes	—
111	C₂²	—	61	2	no	—
112	C₂²	—	244	1	no	—
113	C₂²	#14519856	1	1	yes	characteristic
114	C₄	—	4	1	no	—
115	C₄	—	61	2	no	—
116	C₄	—	244	1	no	—
117	C₄	—	244	4	no	—
118	C₄	C₂×C₄×#6923	1	1	yes	characteristic
119	C₄	#14519856	1	1	yes	characteristic
120	C₂	—	2	1	no	—
121	C₂	—	122	2	no	—
122	C₂	#16840698	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840725

C₂

yes

maximal

#16840631

C₂

yes

maximal, characteristic

#16840630

C₂

yes

maximal, characteristic

#16840629

C₂

yes

maximal

#16839719

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₂²

yes

—

#14519856

C₂²

yes

—

#14519831

C₄

yes

complemented

C₈×#6923

C₄

yes

complemented

C₂×#11758189

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₂²

yes

characteristic

#14519687

C₄

yes

characteristic, complemented

C₄×#92418

C₄

yes

characteristic, complemented

C₈×Dic₆₁

C₄

yes

characteristic, complemented

#97×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂²⋊#6923

—

#11758217

—

C₄⋊#6923

—

C₄×#6923

C₂×C₄

yes

—

#11758213

—

D₆₁⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

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

C₂²×C₄

yes

—

C₄×D₆₁

#41

yes

—

#92420

—

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

—

#92418

—

#92418

C₄²

yes

characteristic

#92418

C₄²

yes

characteristic

C₂²×C₆₁

#117

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#117

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

Dic₆₁

—

Dic₆₁

#117

yes

—

#1747

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#376

yes

characteristic

D₆₁

—

—

—

—

—

—

C₆₁

#1747

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

122

—

109

C₈

—

122

—

110

C₈

C₄×#6923

yes

—

111

C₂²

—

112

C₂²

—

244

—

113

C₂²

#14519856

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

244

—

117

C₄

—

244

—

118

C₄

C₂×C₄×#6923

yes

characteristic

119

C₄

#14519856

yes

characteristic

120

C₂

—

121

C₂

—

122

—

122

C₂

#16840698

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂×C₆₁	#376
hypercenter	#97	#6923
hypocenter	C₆₁	#1747
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #97

subgroup

G/H

center

C₄

C₂×C₄×#6923

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

C₂×C₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ #97

N	H ≅ G/N	type
8. #14519831	C₄	semidirect
9. C₈×#6923	C₄	semidirect
13. #14519687	C₄	semidirect
14. C₄×#92418	C₄	semidirect
15. C₈×Dic₆₁	C₄	semidirect
16. #97×C₆₁	C₄	semidirect
67. C₆₁	#1747	semidirect
75. #97	#6923	semidirect

H ≅ G/N

type

8. #14519831

C₄

semidirect

9. C₈×#6923

C₄

semidirect

13. #14519687

C₄

semidirect

14. C₄×#92418

C₄

semidirect

15. C₈×Dic₆₁

C₄

semidirect

16. #97×C₆₁

C₄

semidirect

67. C₆₁

#1747

semidirect

75. #97

#6923

semidirect

Subgroups — #21461541

Conjugacy classes of subgroups

Complements