Group #21447589 — subgroups

Subgroups — C₂×#16839586 #21447589

Order 7808.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519717	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519709	C₂	1	1	yes	maximal, characteristic
3	#16839586	C₂	1	4	yes	maximal, direct product factor
4	C₂×#108×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₆₁	—	2	1	no	—
6	#14519717	C₄	1	2	yes	complemented
7	#14519717	C₂²	1	2	yes	—
8	C₂×#11758185	C₄	1	2	yes	complemented
9	#14519709	—	2	1	no	—
10	#14519709	C₂²	1	2	yes	—
11	C₂×M₁₆×C₆₁	—	2	1	no	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	#108×C₆₁	—	2	1	no	—
14	#108×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	—	4	1	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	M₁₆×C₆₁	—	4	1	no	—
19	C₂×C₈×C₆₁	—	4	1	no	—
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
24	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
25	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₆₁	—	2	2	no	—
27	C₄⋊Dic₆₁	—	4	1	no	—
28	#11758185	C₂×C₄	1	4	yes	complemented
29	C₂³×C₆₁	SD₁₆	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₆₁	—	4	2	no	—
37	C₂×Dic₆₁	—	8	2	no	—
38	C₈×C₆₁	—	4	2	no	—
39	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₆₁	—	2	2	no	—
44	C₂²×C₆₁	#106	1	1	yes	characteristic
45	C₂²×C₆₁	#106	1	1	yes	characteristic
46	C₂²×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
47	C₄×C₆₁	#106	1	1	yes	characteristic
48	C₄×C₆₁	#106	1	1	yes	characteristic
49	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
51	Dic₆₁	—	8	2	no	—
52	C₂×#365	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	#365	1	2	yes	complemented
56	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
57	C₂×M₃₂	—	61	1	no	—
58	C₂×#108	D₆₁	1	1	yes	characteristic
59	C₂×#106	—	61	1	no	—
60	#365	—	61	4	no	—
61	C₆₁	C₂×#365	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₁₆	—	2	1	no	—
63	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	122	1	no	—
65	M₃₂	—	61	2	no	—
66	M₃₂	—	61	2	no	—
67	C₂×C₁₆	—	61	2	no	—
68	#108	—	2	1	no	—
69	#108	C₂×D₆₁	1	2	yes	—
70	#106	—	61	2	no	—
71	#106	—	122	1	no	—
72	C₂²×C₄	—	244	1	no	—
73	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
78	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
79	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
80	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
83	C₄⋊C₄	—	122	2	no	—
84	C₄⋊C₄	—	244	1	no	—
85	C₁₆	—	61	4	no	—
86	C₂³	#11758201	1	1	yes	characteristic
87	C₂×C₄	—	488	2	no	—
88	C₂×C₄	—	244	2	no	—
89	C₂×C₄	#11758196	1	1	yes	characteristic
90	C₂×C₄	#11758196	1	1	yes	characteristic
91	C₂×C₄	#11758200	1	1	yes	characteristic
92	C₂×C₄	#11758200	1	1	yes	characteristic
93	C₂×C₄	#11758201	1	1	yes	characteristic
94	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
95	C₈	—	4	2	no	—
96	C₈	#11758196	1	1	yes	characteristic
97	C₈	#11758196	1	1	yes	characteristic
98	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
99	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
100	C₂²	—	2	2	no	—
101	C₂²	#14519708	1	1	yes	characteristic
102	C₂²	#14519708	1	1	yes	characteristic
103	C₂²	C₂×#11758201	1	1	yes	characteristic
104	C₄	—	488	2	no	—
105	C₄	#14519708	1	1	yes	characteristic
106	C₄	#14519708	1	1	yes	characteristic
107	C₄	C₂×#11758196	1	1	yes	characteristic
108	C₄	C₂×#11758200	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#16839586	1	2	yes	direct product factor
112	C₂	C₂×#14519708	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×#14519709

C₂

yes

maximal, characteristic

#16839586

C₂

yes

maximal, direct product factor

C₂×#108×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

—

#14519717

C₄

yes

complemented

#14519717

C₂²

yes

—

C₂×#11758185

C₄

yes

complemented

#14519709

—

#14519709

C₂²

yes

—

C₂×M₁₆×C₆₁

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

#108×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758185

C₂×C₄

yes

complemented

C₂³×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

C₂×SD₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

characteristic

Dic₆₁

—

C₂×#365

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×M₃₂

—

C₂×#108

D₆₁

yes

characteristic

C₂×#106

—

#365

—

C₆₁

C₂×#365

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

122

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

C₂×D₆₁

yes

—

#106

—

#106

—

122

—

C₂²×C₄

—

244

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₁₆

—

C₂³

#11758201

yes

characteristic

C₂×C₄

—

488

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

C₂×C₄×D₆₁

yes

characteristic

100

C₂²

—

101

C₂²

#14519708

yes

characteristic

102

C₂²

#14519708

yes

characteristic

103

C₂²

C₂×#11758201

yes

characteristic

104

C₄

—

488

—

105

C₄

#14519708

yes

characteristic

106

C₄

#14519708

yes

characteristic

107

C₄

C₂×#11758196

yes

characteristic

108

C₄

C₂×#11758200

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#16839586

yes

direct product factor

112

C₂

C₂×#14519708

yes

characteristic

	subgroup	G/H
center	C₂²	#14519708
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×#108×C₆₁	C₂
socle	C₂²×C₆₁	#106
hypercenter	C₂×#108	D₆₁
hypocenter	C₆₁	C₂×#365
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₂²

#14519708

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×#108×C₆₁

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #16839586	C₂	direct (N × H)
6. #14519717	C₄	semidirect
8. C₂×#11758185	C₄	semidirect
28. #11758185	C₂×C₄	semidirect
55. C₂×C₆₁	#365	semidirect
61. C₆₁	C₂×#365	semidirect
111. C₂	#16839586	direct (N × H)

H ≅ G/N

type

3. #16839586

C₂

direct (N × H)

6. #14519717

C₄

semidirect

8. C₂×#11758185

C₄

semidirect

28. #11758185

C₂×C₄

semidirect

55. C₂×C₆₁

#365

semidirect

61. C₆₁

C₂×#365

semidirect

111. C₂

#16839586

direct (N × H)

Subgroups — C₂×#16839586 #21447589

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16839586 #21447589

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839586 #21447589