Group #21461745 — subgroups

Subgroups — #21461745

Order 7808.

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

normal subgroups only

This group has 180 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	#16840767	C₂	1	1	yes	maximal, characteristic
2	#16840766	C₂	1	1	yes	maximal, characteristic
3	#16840638	C₂	1	4	yes	maximal
4	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758213	C₂²	1	2	yes	—
6	C₂×#11758213	C₂²	1	2	yes	—
7	#14519844	—	2	2	no	—
8	C₄⋊#92420	—	2	2	no	—
9	C₂×C₈×D₆₁	C₂²	1	2	yes	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519688	C₄	1	1	yes	characteristic
12	#14519687	C₄	1	2	yes	—
13	#97×C₆₁	C₄	1	1	yes	characteristic
14	C₂×C₄×D₆₁	Q₈	1	2	yes	—
15	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
16	C₂×#92420	—	2	2	no	—
17	C₂×#92420	—	2	2	no	—
18	#11758213	—	2	4	no	—
19	#11758213	—	2	4	no	—
20	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
21	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	D₄	1	2	yes	—
24	C₂×#92418	C₂×C₄	1	2	yes	—
25	C₈×D₆₁	—	2	2	no	—
26	C₈×D₆₁	—	2	2	no	—
27	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
32	C₄×D₆₁	—	4	2	no	—
33	C₄×D₆₁	#41	1	2	yes	—
34	C₄×D₆₁	#41	1	2	yes	—
35	#92420	—	4	2	no	—
36	#92420	—	4	2	no	—
37	C₈×C₆₁	—	2	2	no	—
38	#92418	—	2	2	no	—
39	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×D₆₁	—	2	2	no	—
41	C₂×D₆₁	#125	1	2	yes	—
42	C₄×C₆₁	—	2	2	no	—
43	C₄×C₆₁	#117	1	2	yes	—
44	Dic₆₁	—	2	2	no	—
45	Dic₆₁	#124	1	1	yes	characteristic
46	Dic₆₁	#124	1	1	yes	characteristic
47	#1838	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#382	1	1	yes	characteristic
49	C₂×C₆₁	#430	1	2	yes	—
50	D₆₁	—	2	2	no	—
51	#423	—	61	1	no	—
52	#423	—	61	1	no	—
53	C₂×#97	—	61	1	no	—
54	#341	—	61	4	no	—
55	C₆₁	#1838	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	61	2	no	—
57	C₂×M₁₆	—	61	2	no	—
58	C₂²×C₈	—	61	2	no	—
59	C₂×C₄²	—	61	1	no	—
60	C₄⋊C₈	—	122	2	no	—
61	C₄⋊C₈	—	122	2	no	—
62	#97	—	61	2	no	—
63	#97	—	61	1	no	—
64	#97	#6923	1	1	yes	characteristic
65	C₂²×C₄	—	61	1	no	—
66	C₂²×C₄	—	61	2	no	—
67	M₁₆	—	122	4	no	—
68	M₁₆	—	122	4	no	—
69	C₂×C₈	—	61	2	no	—
70	C₂×C₈	—	122	2	no	—
71	C₂×C₈	—	122	2	no	—
72	C₂×C₈	—	122	2	no	—
73	C₂×C₈	—	122	2	no	—
74	C₂×C₈	C₂×#6923	1	2	yes	—
75	C₄²	—	61	2	no	—
76	C₄²	—	61	1	no	—
77	C₄²	C₂×#6923	1	1	yes	characteristic
78	C₂³	—	61	1	no	—
79	C₂×C₄	—	61	1	no	—
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	61	2	no	—
82	C₂×C₄	—	61	2	no	—
83	C₂×C₄	—	244	2	no	—
84	C₂×C₄	C₄⋊#6923	1	2	yes	—
85	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	122	2	no	—
88	C₈	—	244	2	no	—
89	C₈	—	244	2	no	—
90	C₂²	—	61	2	no	—
91	C₂²	—	122	2	no	—
92	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	61	1	no	—
95	C₄	—	61	1	no	—
96	C₄	—	122	2	no	—
97	C₄	#14519856	1	2	yes	—
98	C₂	—	122	2	no	—
99	C₂	#16840706	1	1	yes	characteristic
100	C₂	#16840777	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840767

C₂

yes

maximal, characteristic

#16840766

C₂

yes

maximal, characteristic

#16840638

C₂

yes

maximal

#97×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

C₂×#11758213

C₂²

yes

—

#14519844

—

C₄⋊#92420

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic

#14519687

C₄

yes

—

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

#41

yes

—

C₄×D₆₁

#41

yes

—

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#125

yes

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

—

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

#423

—

#423

—

C₂×#97

—

#341

—

C₆₁

#1838

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

244

—

C₈

—

244

—

C₂²

—

C₂²

—

122

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

122

—

C₄

#14519856

yes

—

C₂

—

122

—

C₂

#16840706

yes

characteristic

100

C₂

#16840777

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1838
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
55. C₆₁	#1838	semidirect

H ≅ G/N

type

55. C₆₁

#1838

semidirect

Subgroups — #21461745

Conjugacy classes of subgroups

Complements