Group #21460749 — subgroups

Subgroups — #21460749

Order 7808.

134 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 36 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	#16840607	C₂	1	2	yes	maximal
2	#16839669	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#92420	—	2	2	no	—
4	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
6	#14519684	—	2	2	no	—
7	C₂²×Q₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₆₁	—	2	1	no	—
9	C₂×Q₈×C₆₁	—	4	1	no	—
10	C₂×Q₈×C₆₁	—	4	1	no	—
11	C₂×Q₈×C₆₁	C₈	1	2	yes	complemented
12	C₂²×C₄×C₆₁	—	2	1	no	—
13	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₆₁	—	2	1	no	—
15	C₂²×Dic₆₁	D₄	1	2	yes	—
16	C₂×#92420	—	4	2	no	—
17	C₄⋊Dic₆₁	—	4	1	no	—
18	C₄×Dic₆₁	—	4	1	no	—
19	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
20	Q₈×C₆₁	—	4	2	no	—
21	Q₈×C₆₁	—	4	2	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	—	2	2	no	—
25	C₂×C₄×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
29	C₂×Dic₆₁	—	2	2	no	—
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	—	4	1	no	—
32	C₂×Dic₆₁	—	4	1	no	—
33	C₂×Dic₆₁	—	4	2	no	—
34	#92420	—	8	2	no	—
35	C₂²×C₆₁	—	2	1	no	—
36	C₂²×C₆₁	—	2	1	no	—
37	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₆₁	#99	1	1	yes	characteristic
39	C₂²×C₆₁	#100	1	1	yes	characteristic
40	C₄×C₆₁	—	2	1	no	—
41	C₄×C₆₁	—	2	1	no	—
42	C₄×C₆₁	—	4	2	no	—
43	Dic₆₁	—	4	2	no	—
44	Dic₆₁	—	4	2	no	—
45	#1319	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	2	1	no	—
47	C₂×C₆₁	—	2	1	no	—
48	C₂×C₆₁	#323	1	1	yes	characteristic
49	C₂×C₆₁	#354	1	1	yes	characteristic
50	C₂×C₆₁	#356	1	1	yes	characteristic
51	#391	—	61	1	no	—
52	#324	—	61	2	no	—
53	C₆₁	#1319	1	1	yes	characteristic, complemented, Sylow
54	C₂²×Q₈	#6923	1	1	yes	characteristic
55	C₂×C₄⋊C₄	—	61	1	no	—
56	C₂×C₄²	—	61	1	no	—
57	C₂²⋊C₈	—	122	2	no	—
58	#95	—	122	2	no	—
59	C₂×Q₈	—	2	1	no	—
60	C₂×Q₈	—	4	1	no	—
61	C₂×Q₈	—	4	1	no	—
62	C₂×Q₈	#92420	1	2	yes	complemented
63	C₂²×C₄	—	2	1	no	—
64	C₂²×C₄	—	61	2	no	—
65	C₂²×C₄	—	122	1	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	C₂×C₈	—	244	2	no	—
68	C₄⋊C₄	—	244	1	no	—
69	C₄²	—	244	1	no	—
70	C₂³	C₂²⋊#6923	1	1	yes	characteristic
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	122	2	no	—
79	C₂×C₄	—	122	2	no	—
80	C₂×C₄	—	244	1	no	—
81	C₂×C₄	—	244	1	no	—
82	C₂×C₄	—	244	2	no	—
83	C₂×C₄	C₂×#92420	1	1	yes	characteristic
84	C₂×C₄	#11758217	1	1	yes	characteristic
85	C₈	—	488	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	C₂²⋊#92420	1	1	yes	characteristic
89	C₂²	#14519835	1	1	yes	characteristic
90	C₂²	#14519837	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	2	1	no	—
93	C₄	—	4	2	no	—
94	C₄	—	244	2	no	—
95	C₄	—	244	2	no	—
96	C₂	—	2	1	no	—
97	C₂	—	2	1	no	—
98	C₂	#16840605	1	1	yes	characteristic
99	C₂	#16840668	1	1	yes	characteristic
100	C₂	#16840672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840607

C₂

yes

maximal

#16839669

C₂

yes

maximal, characteristic

C₂²⋊#92420

—

C₂×C₄⋊Dic₆₁

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

#14519684

—

C₂²×Q₈×C₆₁

C₄

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

C₈

yes

complemented

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×#92420

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

#1319

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₆₁

#1319

yes

characteristic, complemented, Sylow

C₂²×Q₈

#6923

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

122

—

#95

—

122

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

#92420

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

244

—

C₂³

C₂²⋊#6923

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

488

—

C₂²

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

244

—

C₄

—

244

—

C₂

—

C₂

—

C₂

yes

C₂

yes

100

C₂

#16840672

yes

characteristic

	subgroup	G/H
center	C₂²	#14519835
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²×Q₈×C₆₁	C₄
socle	C₂²×C₆₁	#99
hypercenter	C₂²×Q₈	#6923
hypocenter	C₆₁	#1319
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

subgroup

G/H

center

C₂²

#14519835

commutator

C₂×C₄×C₆₁

C₂×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂²×Q₈×C₆₁

C₄

C₂²×C₆₁

C₂²×Q₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

N	H ≅ G/N	type
11. C₂×Q₈×C₆₁	C₈	semidirect
53. C₆₁	#1319	semidirect
62. C₂×Q₈	#92420	semidirect

H ≅ G/N

type

11. C₂×Q₈×C₆₁

C₈

semidirect

53. C₆₁

#1319

semidirect

62. C₂×Q₈

#92420

semidirect

Subgroups — #21460749

Conjugacy classes of subgroups

Complements