Group #20241273 — subgroups

Subgroups — #20241273

Order 6016.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
2	C₄₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
4	C₂×C₄×Dic₄₇	—	2	2	no	—
5	C₄₇⋊#95	C₄	1	4	yes	complemented
6	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₄₇	C₄	1	2	yes	complemented
8	C₂²⋊C₈×C₄₇	—	2	2	no	—
9	C₂⁴×C₄₇	D₄	1	1	yes	characteristic
10	C₂²×C₄×C₄₇	—	4	2	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₄₇	D₄	1	2	yes	—
14	C₂²×C₄×C₄₇	Q₈	1	1	yes	characteristic
15	C₂²×Dic₄₇	—	2	4	no	—
16	M₁₆×C₄₇	—	4	2	no	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂²⋊Dic₄₇	—	2	8	no	—
19	C₄×Dic₄₇	—	4	4	no	—
20	C₂³×C₄₇	—	2	4	no	—
21	C₂³×C₄₇	—	4	1	no	—
22	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
23	C₂³×C₄₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	—	2	4	no	—
25	C₂×C₄×C₄₇	—	2	2	no	—
26	C₂×C₄×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	—	4	1	no	—
28	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₄₇	—	2	8	no	—
32	C₂×Dic₄₇	—	4	4	no	—
33	C₂×Dic₄₇	—	4	4	no	—
34	C₈×C₄₇	—	4	2	no	—
35	C₂²×C₄₇	—	2	2	no	—
36	C₂²×C₄₇	—	2	2	no	—
37	C₂²×C₄₇	—	2	2	no	—
38	C₂²×C₄₇	—	2	1	no	—
39	C₂²×C₄₇	—	4	4	no	—
40	C₂²×C₄₇	#95	1	1	yes	characteristic
41	C₂²×C₄₇	#104	1	4	yes	—
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	—	2	2	no	—
44	C₄×C₄₇	#99	1	2	yes	—
45	Dic₄₇	—	4	8	no	—
46	#1297	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	2	4	no	—
48	C₂×C₄₇	—	4	1	no	—
49	C₂×C₄₇	#339	1	2	yes	—
50	C₂×C₄₇	#342	1	1	yes	characteristic
51	#407	D₄₇	1	1	yes	characteristic
52	C₄×C₂²⋊C₄	—	47	2	no	—
53	C₄₇	#1297	1	1	yes	characteristic, complemented, Sylow
54	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
55	C₂×M₁₆	Dic₄₇	1	2	yes	complemented
56	C₂×C₂²⋊C₄	—	94	2	no	—
57	C₂×C₄²	—	94	2	no	—
58	C₂²⋊C₈	—	2	2	no	—
59	#95	—	47	4	no	—
60	C₂⁴	D₁₈₈	1	1	yes	characteristic
61	C₂²×C₄	—	4	2	no	—
62	C₂²×C₄	—	94	4	no	—
63	C₂²×C₄	Dic₉₄	1	1	yes	characteristic
64	C₂²×C₄	C₄×D₄₇	1	2	yes	—
65	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
66	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
67	M₁₆	—	4	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂²⋊C₄	—	94	8	no	—
70	C₄²	—	188	4	no	—
71	C₂³	—	2	4	no	—
72	C₂³	—	4	1	no	—
73	C₂³	C₄⋊Dic₄₇	1	1	yes	characteristic
74	C₂³	(C₂×D₄₇)⋊C₄	1	2	yes	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	94	8	no	—
80	C₂×C₄	—	188	4	no	—
81	C₂×C₄	—	188	4	no	—
82	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
83	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
84	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
85	C₈	—	4	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	4	no	—
91	C₂²	C₄₇⋊#95	1	1	yes	characteristic
92	C₂²	#13093950	1	4	yes	—
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	188	8	no	—
96	C₄	#13093939	1	2	yes	—
97	C₂	—	2	4	no	—
98	C₂	—	4	1	no	—
99	C₂	#15688884	1	2	yes	—
100	C₂	#15688890	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal

C₄₇×#407

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄₇⋊#95

C₄

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₄

yes

complemented

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂²⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#95

yes

characteristic

C₂²×C₄₇

#104

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#99

yes

—

Dic₄₇

—

#1297

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#339

yes

—

C₂×C₄₇

#342

yes

characteristic

#407

D₄₇

yes

characteristic

C₄×C₂²⋊C₄

—

C₄₇

#1297

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

Dic₄₇

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

#95

—

C₂⁴

D₁₈₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

—

M₁₆

—

C₂×C₈

—

C₂²⋊C₄

—

C₄²

—

188

—

C₂³

—

C₂³

—

C₂³

C₄⋊Dic₄₇

yes

characteristic

C₂³

(C₂×D₄₇)⋊C₄

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

—

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄₇⋊#95

yes

characteristic

C₂²

#13093950

yes

—

C₄

—

C₄

—

C₄

—

188

—

C₄

#13093939

yes

—

C₂

—

C₂

—

C₂

#15688884

yes

—

100

C₂

#15688890

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₄²
Frattini	C₂³×C₄	C₂×D₄₇
Fitting	C₄₇×#407	C₂
socle	C₂²×C₄₇	#95
hypercenter	#407	D₄₇
hypocenter	C₄₇	#1297
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₄₇

commutator

C₂×C₄×C₄₇

C₄²

Frattini

C₂³×C₄

C₂×D₄₇

Fitting

C₄₇×#407

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
5. C₄₇⋊#95	C₄	semidirect
7. C₂×M₁₆×C₄₇	C₄	semidirect
53. C₄₇	#1297	semidirect
55. C₂×M₁₆	Dic₄₇	semidirect

H ≅ G/N

type

5. C₄₇⋊#95

C₄

semidirect

7. C₂×M₁₆×C₄₇

C₄

semidirect

53. C₄₇

#1297

semidirect

55. C₂×M₁₆

Dic₄₇

semidirect

Subgroups — #20241273

Conjugacy classes of subgroups

Complements