Group #21462164 — subgroups

Subgroups — C₂×#16840687 #21462164

Order 7808.

152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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	C₂×#14519847	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519845	C₂	1	1	yes	maximal, characteristic
3	#16840687	C₂	1	4	yes	maximal, direct product factor
4	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758213	—	2	1	no	—
6	C₂×C₄⋊#6923	—	2	1	no	—
7	#14519847	—	2	1	no	—
8	#14519847	C₂²	1	2	yes	—
9	#14519845	—	2	1	no	—
10	#14519845	C₂²	1	2	yes	—
11	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
12	#14519716	C₄	1	2	yes	complemented
13	#14519716	C₂²	1	2	yes	—
14	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
16	C₂²×#6923	—	4	1	no	—
17	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
18	C₂×#92420	—	4	1	no	—
19	C₄⋊#6923	—	2	2	no	—
20	C₄⋊#6923	—	4	1	no	—
21	#11758213	—	2	2	no	—
22	#11758213	—	4	1	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	Q₈	1	1	yes	characteristic
25	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	D₄	1	1	yes	characteristic
27	C₈×D₆₁	Q₈	1	1	yes	characteristic
28	C₈×D₆₁	C₂³	1	1	yes	characteristic
29	C₁₆×C₆₁	C₂×C₄	1	2	yes	complemented
30	#11758185	C₂×C₄	1	2	yes	complemented
31	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
32	C₂×#6923	—	4	2	no	—
33	C₂×#6923	—	8	2	no	—
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
36	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
38	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
39	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
40	#92420	—	4	2	no	—
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
43	#92418	C₄⋊C₄	1	1	yes	characteristic
44	#92418	C₂×Q₈	1	1	yes	characteristic
45	C₂²×C₆₁	#106	1	1	yes	characteristic
46	C₂×D₆₁	—	2	2	no	—
47	C₂×D₆₁	#106	1	1	yes	characteristic
48	C₂×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
49	#6923	—	8	2	no	—
50	C₄×C₆₁	#106	1	1	yes	characteristic
51	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
52	Dic₆₁	#106	1	1	yes	characteristic
53	Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
54	C₂×#365	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	#365	1	2	yes	complemented
56	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
57	D₆₁	—	2	1	no	—
58	D₆₁	—	2	1	no	—
59	C₂×M₃₂	—	61	1	no	—
60	C₂×#108	—	61	1	no	—
61	C₂×#106	—	61	1	no	—
62	#365	—	61	4	no	—
63	C₆₁	C₂×#365	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	122	1	no	—
65	C₂²×C₈	—	61	1	no	—
66	C₂×C₄⋊C₄	—	122	1	no	—
67	M₃₂	—	61	2	no	—
68	M₃₂	—	61	2	no	—
69	C₂×C₁₆	—	61	1	no	—
70	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
71	#108	—	61	2	no	—
72	#108	—	122	1	no	—
73	#106	—	61	2	no	—
74	#106	—	122	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	244	1	no	—
77	M₁₆	—	122	2	no	—
78	M₁₆	—	244	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	244	1	no	—
85	C₂×C₈	C₂×#6923	1	1	yes	characteristic
86	C₄⋊C₄	—	122	2	no	—
87	C₄⋊C₄	—	244	1	no	—
88	C₁₆	—	61	2	no	—
89	C₁₆	C₂×#6923	1	2	yes	complemented
90	C₂³	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	488	2	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
99	C₈	—	61	1	no	—
100	C₈	—	61	1	no	—
101	C₈	—	244	2	no	—
102	C₈	C₄⋊#6923	1	1	yes	characteristic
103	C₈	C₂²×#6923	1	1	yes	characteristic
104	C₂²	—	61	1	no	—
105	C₂²	—	61	1	no	—
106	C₂²	—	122	2	no	—
107	C₂²	#14519845	1	1	yes	characteristic
108	C₄	—	61	1	no	—
109	C₄	—	61	1	no	—
110	C₄	—	488	2	no	—
111	C₄	#14519845	1	1	yes	characteristic
112	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
113	C₂	—	122	1	no	—
114	C₂	—	122	1	no	—
115	C₂	#16840687	1	2	yes	direct product factor
116	C₂	C₂×#14519845	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519847

C₂

yes

maximal, characteristic

C₂×#14519845

C₂

yes

maximal, characteristic

#16840687

C₂

yes

maximal, direct product factor

C₂×#14519716

C₂

yes

maximal, characteristic

C₂×#11758213

—

C₂×C₄⋊#6923

—

#14519847

—

#14519847

C₂²

yes

—

#14519845

—

#14519845

C₂²

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519716

C₄

yes

complemented

#14519716

C₂²

yes

—

C₂×#11758185

C₄

yes

characteristic, complemented

C₂×C₁₆×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

D₄

yes

—

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

Q₈

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₈×D₆₁

C₂³

yes

characteristic

C₁₆×C₆₁

C₂×C₄

yes

complemented

#11758185

C₂×C₄

yes

complemented

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×#6923

—

C₂×#6923

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

#92420

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

#92418

C₂×Q₈

yes

characteristic

C₂²×C₆₁

#106

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#106

yes

characteristic

C₂×D₆₁

C₂×SD₁₆

yes

characteristic

#6923

—

C₄×C₆₁

#106

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

Dic₆₁

#106

yes

characteristic

Dic₆₁

C₂×SD₁₆

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

C₂×M₃₂

—

C₂×#108

—

C₂×#106

—

#365

—

C₆₁

C₂×#365

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

122

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

#6923

yes

characteristic, complemented

#108

—

#108

—

122

—

#106

—

#106

—

122

—

C₂²×C₄

—

C₂²×C₄

—

244

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₁₆

—

C₁₆

C₂×#6923

yes

complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

488

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

244

—

102

C₈

C₄⋊#6923

yes

characteristic

103

C₈

C₂²×#6923

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

122

—

107

C₂²

#14519845

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

488

—

111

C₄

#14519845

yes

characteristic

112

C₄

C₂×C₄⋊#6923

yes

characteristic

113

C₂

—

122

—

114

C₂

—

122

—

115

C₂

#16840687

yes

direct product factor

116

C₂

C₂×#14519845

yes

characteristic

	subgroup	G/H
center	C₂²	#14519845
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₈	C₂²×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#106
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	C₂×#365
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₂²

#14519845

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₈

C₂²×#6923

Fitting

C₂×C₁₆×C₆₁

C₄

C₂²×C₆₁

C₂×C₁₆

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
3. #16840687	C₂	direct (N × H)
12. #14519716	C₄	semidirect
14. C₂×#11758185	C₄	semidirect
15. C₂×C₁₆×C₆₁	C₄	semidirect
29. C₁₆×C₆₁	C₂×C₄	semidirect
30. #11758185	C₂×C₄	semidirect
55. C₂×C₆₁	#365	semidirect
63. C₆₁	C₂×#365	semidirect
70. C₂×C₁₆	#6923	semidirect
89. C₁₆	C₂×#6923	semidirect
115. C₂	#16840687	direct (N × H)

H ≅ G/N

type

3. #16840687

C₂

direct (N × H)

12. #14519716

C₄

semidirect

14. C₂×#11758185

C₄

semidirect

15. C₂×C₁₆×C₆₁

C₄

semidirect

29. C₁₆×C₆₁

C₂×C₄

semidirect

30. #11758185

C₂×C₄

semidirect

55. C₂×C₆₁

#365

semidirect

63. C₆₁

C₂×#365

semidirect

70. C₂×C₁₆

#6923

semidirect

89. C₁₆

C₂×#6923

semidirect

115. C₂

#16840687

direct (N × H)

Subgroups — C₂×#16840687 #21462164

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16840687 #21462164

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840687 #21462164