Group #21445708 — subgroups

Subgroups — C₄×#14519709 #21445708

Order 7808.

280 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519709	C₂	1	2	yes	maximal
2	C₄×C₄⋊Dic₆₁	C₂	1	2	yes	maximal
3	#16839525	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
6	C₂×C₄×Dic₆₁	—	2	2	no	—
7	#14519709	C₄	1	8	yes	direct product factor
8	#14519684	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₄	1	4	yes	complemented
13	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	—	2	4	no	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
21	C₄²×C₆₁	C₂×C₄	1	2	yes	—
22	C₄²×C₆₁	Q₈	1	2	yes	—
23	C₄⋊Dic₆₁	—	2	4	no	—
24	C₄⋊Dic₆₁	C₂×C₄	1	8	yes	—
25	C₄×Dic₆₁	—	4	4	no	—
26	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	2	2	no	—
28	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₆₁	SD₁₆	1	4	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	#41	1	2	yes	—
35	C₂×Dic₆₁	—	2	8	no	—
36	C₂×Dic₆₁	—	4	4	no	—
37	C₂×Dic₆₁	—	4	4	no	—
38	C₈×C₆₁	—	2	2	no	—
39	C₈×C₆₁	C₄²	1	4	yes	complemented
40	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₆₁	C₄×D₄	1	2	yes	—
42	C₂²×C₆₁	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₆₁	#135	1	2	yes	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	#106	1	4	yes	complemented
46	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₆₁	#117	1	1	yes	characteristic
48	C₄×C₆₁	C₄×Q₈	1	2	yes	—
49	Dic₆₁	—	4	8	no	—
50	C₄×#106	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
53	C₂×C₆₁	#427	1	1	yes	characteristic
54	C₂×C₆₁	C₄×SD₁₆	1	4	yes	—
55	C₂×#106	—	61	2	no	—
56	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
57	C₄×C₄⋊C₄	—	61	2	no	—
58	#340	—	61	2	no	—
59	C₆₁	C₄×#106	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	61	4	no	—
63	C₂×C₄²	—	122	2	no	—
64	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
65	#106	—	61	8	no	—
66	C₄×C₈	Dic₆₁	1	4	yes	complemented
67	#95	—	122	2	no	—
68	C₂²×C₄	—	122	4	no	—
69	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
70	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
71	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	C₄×D₆₁	1	4	yes	—
74	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
75	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
76	C₄⋊C₄	—	61	8	no	—
77	C₄⋊C₄	—	122	4	no	—
78	C₄²	—	244	4	no	—
79	C₄²	Dic₁₂₂	1	2	yes	—
80	C₄²	C₂×Dic₆₁	1	2	yes	—
81	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	122	8	no	—
84	C₂×C₄	—	244	4	no	—
85	C₂×C₄	—	244	4	no	—
86	C₂×C₄	#11758190	1	4	yes	—
87	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
88	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
89	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
91	C₂×C₄	#11758222	1	2	yes	—
92	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	C₄×Dic₆₁	1	4	yes	complemented
95	C₂²	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
96	C₂²	C₄×D₂₄₄	1	2	yes	—
97	C₂²	C₂×#11758190	1	2	yes	—
98	C₂²	#14519799	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	244	8	no	—
101	C₄	#14519709	1	4	yes	direct product factor
102	C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
103	C₄	#14519736	1	1	yes	characteristic
104	C₄	C₄×Dic₁₂₂	1	2	yes	—
105	C₂	C₄×C₄⋊Dic₆₁	1	1	yes	characteristic
106	C₂	C₂×#14519709	1	1	yes	characteristic
107	C₂	#16839800	1	1	yes	characteristic
108	C₂	C₄×#11758190	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519709

C₂

yes

maximal

C₄×C₄⋊Dic₆₁

C₂

yes

maximal

#16839525

C₂

yes

maximal

C₂×C₄×C₈×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×C₄×Dic₆₁

—

#14519709

C₄

yes

direct product factor

#14519684

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

complemented

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×D₄

yes

—

C₂²×C₆₁

C₂×SD₁₆

yes

—

C₂²×C₆₁

#135

yes

—

C₄×C₆₁

—

C₄×C₆₁

#106

yes

complemented

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

—

Dic₆₁

—

C₄×#106

—

maximal, Sylow

C₂×C₆₁

C₄×C₄⋊C₄

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

C₄×SD₁₆

yes

—

C₂×#106

—

C₂×C₄×C₈

D₆₁

yes

characteristic

C₄×C₄⋊C₄

—

#340

—

C₆₁

C₄×#106

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#106

—

C₄×C₈

Dic₆₁

yes

complemented

#95

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

244

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂×Dic₆₁

yes

—

C₂³

C₂×D₂₄₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758190

yes

—

C₂×C₄

C₄⋊Dic₆₁

yes

—

C₂×C₄

C₄⋊Dic₆₁

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

—

C₂×C₄

#11758222

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₈

C₄×Dic₆₁

yes

complemented

C₂²

C₂×C₄⋊Dic₆₁

yes

characteristic

C₂²

C₄×D₂₄₄

yes

—

C₂²

C₂×#11758190

yes

—

C₂²

#14519799

yes

—

C₄

—

100

C₄

—

244

—

101

C₄

#14519709

yes

direct product factor

102

C₄

C₂×C₄×Dic₆₁

yes

characteristic

103

C₄

#14519736

yes

characteristic

104

C₄

C₄×Dic₁₂₂

yes

—

105

C₂

C₄×C₄⋊Dic₆₁

yes

characteristic

106

C₂

C₂×#14519709

yes

characteristic

107

C₂

#16839800

yes

characteristic

108

C₂

C₄×#11758190

yes

—

	subgroup	G/H
center	C₂²×C₄	D₂₄₄
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	C₄×#106
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₄

D₂₄₄

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×C₄×C₈×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

hypercenter

C₂×C₄×C₈

D₆₁

hypocenter

C₆₁

C₄×#106

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
7. #14519709	C₄	direct (N × H)
12. C₄×C₈×C₆₁	C₄	semidirect
39. C₈×C₆₁	C₄²	semidirect
45. C₄×C₆₁	#106	semidirect
59. C₆₁	C₄×#106	semidirect
66. C₄×C₈	Dic₆₁	semidirect
94. C₈	C₄×Dic₆₁	semidirect
101. C₄	#14519709	direct (N × H)

H ≅ G/N

type

7. #14519709

C₄

direct (N × H)

12. C₄×C₈×C₆₁

C₄

semidirect

39. C₈×C₆₁

C₄²

semidirect

45. C₄×C₆₁

#106

semidirect

59. C₆₁

C₄×#106

semidirect

66. C₄×C₈

Dic₆₁

semidirect

94. C₈

C₄×Dic₆₁

semidirect

101. C₄

#14519709

direct (N × H)

Subgroups — C₄×#14519709 #21445708

Conjugacy classes of subgroups

Complements

Subgroups — C4×#14519709 #21445708

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14519709 #21445708