Group #21445975 — subgroups

Subgroups — #21445975

Order 7808.

280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519708	C₂	1	4	yes	maximal
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	#16839632	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	—	2	2	no	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519708	—	2	8	no	—
9	C₄×#92418	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
11	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
12	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	—	2	2	no	—
14	C₂²×C₄×C₆₁	D₄	1	2	yes	—
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	—	2	2	no	—
17	C₄⋊C₄×C₆₁	—	2	4	no	—
18	C₄⋊C₄×C₆₁	—	4	4	no	—
19	C₄²×C₆₁	C₂×C₄	1	2	yes	—
20	C₄²×C₆₁	Q₈	1	2	yes	—
21	C₄⋊Dic₆₁	—	2	4	no	—
22	C₄⋊Dic₆₁	—	4	4	no	—
23	C₂×#92418	C₂×C₄	1	4	yes	—
24	C₂×#92418	D₄	1	4	yes	—
25	C₂×#92418	Q₈	1	4	yes	—
26	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	—	4	4	no	—
29	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₆₁	SD₁₆	1	4	yes	—
31	C₂×C₄×C₆₁	SD₁₆	1	4	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×Dic₆₁	—	4	2	no	—
37	C₂×Dic₆₁	—	4	4	no	—
38	#92418	C₄⋊C₄	1	8	yes	complemented
39	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₆₁	#127	1	1	yes	characteristic
41	C₂²×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₆₁	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₆₁	C₂×SD₁₆	1	2	yes	—
44	C₄×C₆₁	—	8	2	no	—
45	C₄×C₆₁	#106	1	8	yes	complemented
46	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
47	C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
48	Dic₆₁	—	8	2	no	—
49	#1844	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	#384	1	1	yes	characteristic
51	C₂×C₆₁	C₂×#106	1	2	yes	—
52	C₂×C₆₁	#492	1	1	yes	characteristic
53	C₂×C₆₁	#492	1	1	yes	characteristic
54	C₂×C₆₁	#498	1	2	yes	—
55	C₂×#106	—	61	4	no	—
56	C₂×C₄×C₈	—	61	1	no	—
57	#384	—	61	1	no	—
58	#384	D₆₁	1	1	yes	characteristic
59	C₆₁	#1844	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	61	2	no	—
61	C₂×C₄⋊C₄	—	2	2	no	—
62	C₂×C₄⋊C₄	—	61	2	no	—
63	C₂×C₄⋊C₄	—	122	2	no	—
64	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
65	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
66	#106	—	122	8	no	—
67	C₄×C₈	—	61	4	no	—
68	C₂²×C₄	—	2	2	no	—
69	C₂²×C₄	—	122	2	no	—
70	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
71	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
72	C₂×C₈	—	61	4	no	—
73	C₂×C₈	—	61	4	no	—
74	C₂×C₈	—	61	4	no	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	122	4	no	—
78	C₄⋊C₄	—	244	4	no	—
79	C₄²	Dic₁₂₂	1	2	yes	—
80	C₄²	C₄×D₆₁	1	2	yes	—
81	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	—	244	4	no	—
86	C₂×C₄	#11758196	1	4	yes	—
87	C₂×C₄	#11758200	1	4	yes	—
88	C₂×C₄	#11758201	1	4	yes	—
89	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
91	C₂×C₄	D₄×D₆₁	1	2	yes	—
92	C₂×C₄	Q₈×D₆₁	1	2	yes	—
93	C₈	—	61	8	no	—
94	C₂²	C₂×#11758196	1	1	yes	characteristic
95	C₂²	#14519773	1	1	yes	characteristic
96	C₂²	#14519775	1	1	yes	characteristic
97	C₂²	C₂×#11758201	1	2	yes	—
98	C₂²	C₂×#11758200	1	2	yes	—
99	C₄	—	8	2	no	—
100	C₄	—	488	2	no	—
101	C₄	#14519708	1	8	yes	complemented
102	C₄	C₄⋊C₄×D₆₁	1	2	yes	—
103	C₄	#14519776	1	2	yes	—
104	C₂	#16839631	1	1	yes	characteristic
105	C₂	C₂×#14519708	1	2	yes	—
106	C₂	#16840134	1	1	yes	characteristic
107	C₂	#16840136	1	1	yes	characteristic
108	C₂	#16840158	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519708

C₂

yes

maximal

C₂×C₄×#92418

C₂

yes

maximal, characteristic

#16839632

C₂

yes

maximal, characteristic

C₆₁×#384

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519708

—

C₄×#92418

C₄

yes

complemented

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

D₄

yes

—

C₂×#92418

Q₈

yes

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92418

C₄⋊C₄

yes

complemented

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#127

yes

characteristic

C₂²×C₆₁

C₄⋊Q₈

yes

characteristic

C₂²×C₆₁

C₂×SD₁₆

yes

—

C₂²×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

—

C₄×C₆₁

#106

yes

complemented

C₄×C₆₁

C₂×C₄⋊C₄

yes

—

C₄×C₆₁

C₄⋊Q₈

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×#106

—

C₂×C₄×C₈

—

#384

—

#384

D₆₁

yes

characteristic

C₆₁

#1844

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#106

—

122

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₄×D₆₁

yes

—

C₂³

C₂×C₂²⋊D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758196

yes

—

C₂×C₄

#11758200

yes

—

C₂×C₄

#11758201

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

—

C₂×C₄

Q₈×D₆₁

yes

—

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#11758200

yes

—

C₄

—

100

C₄

—

488

—

101

C₄

#14519708

yes

complemented

102

C₄

C₄⋊C₄×D₆₁

yes

—

103

C₄

#14519776

yes

—

104

C₂

#16839631

yes

characteristic

105

C₂

C₂×#14519708

yes

—

106

C₂

#16840134

yes

characteristic

107

C₂

#16840136

yes

characteristic

108

C₂

#16840158

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#384	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	#384	D₆₁
hypocenter	C₆₁	#1844
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#384

C₂

socle

C₂³×C₆₁

C₂×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×#92418	C₄	semidirect
38. #92418	C₄⋊C₄	semidirect
45. C₄×C₆₁	#106	semidirect
59. C₆₁	#1844	semidirect
101. C₄	#14519708	semidirect

H ≅ G/N

type

9. C₄×#92418

C₄

semidirect

38. #92418

C₄⋊C₄

semidirect

45. C₄×C₆₁

#106

semidirect

59. C₆₁

#1844

semidirect

101. C₄

#14519708

semidirect

Subgroups — #21445975

Conjugacy classes of subgroups

Complements