Group #20249338 — subgroups

Subgroups — #20249338

Order 6016.

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

normal subgroups only

This group has 416 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×#13094016	C₂	1	1	yes	maximal, characteristic
2	#15689061	C₂	1	8	yes	maximal
3	#15689030	C₂	1	4	yes	maximal
4	#15688969	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#13094016	—	2	4	no	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
10	C₄₇⋊#95	C₂²	1	4	yes	—
11	C₄₇⋊#95	C₂²	1	16	yes	—
12	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
13	C₄⋊Q₈×C₄₇	—	2	4	no	—
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₇	—	2	4	no	—
17	C₂×Q₈×C₄₇	—	2	8	no	—
18	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₇	C₂³	1	4	yes	—
22	C₂²×Dic₄₇	C₂³	1	4	yes	—
23	C₄⋊C₄×C₄₇	—	2	8	no	—
24	C₄²×C₄₇	D₄	1	4	yes	—
25	C₄⋊Dic₄₇	—	2	4	no	—
26	Dic₄₇⋊C₄	—	2	8	no	—
27	C₄×Dic₄₇	—	2	4	no	—
28	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
29	Q₈×C₄₇	—	4	8	no	—
30	C₂×C₄×C₄₇	—	2	4	no	—
31	C₂×C₄×C₄₇	—	2	4	no	—
32	C₂×C₄×C₄₇	—	2	8	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₄₇	#41	1	4	yes	—
36	C₂×Dic₄₇	—	2	4	no	—
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	2	8	no	—
39	C₂×Dic₄₇	—	2	8	no	—
40	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₄₇	C₂×#41	1	2	yes	—
42	C₂²×C₄₇	2₋¹⁺⁴	1	4	yes	—
43	C₄×C₄₇	—	2	4	no	—
44	C₄×C₄₇	—	4	4	no	—
45	C₄×C₄₇	#124	1	4	yes	—
46	Dic₄₇	—	4	4	no	—
47	Dic₄₇	—	4	4	no	—
48	#2642	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
50	C₂×C₄₇	#536	1	2	yes	—
51	C₂×C₄₇	#541	1	4	yes	—
52	C₂×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
53	C₂×#125	—	47	1	no	—
54	#400	—	47	8	no	—
55	#391	—	47	4	no	—
56	#376	—	47	1	no	—
57	C₄₇	#2642	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
59	C₄⋊Q₈	—	2	4	no	—
60	#125	—	94	4	no	—
61	C₂×C₄⋊C₄	—	47	4	no	—
62	C₂×C₄⋊C₄	—	47	2	no	—
63	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
64	C₂×C₄²	—	47	2	no	—
65	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
66	#95	—	47	4	no	—
67	#95	—	47	16	no	—
68	C₂×Q₈	—	2	8	no	—
69	C₂×Q₈	—	2	4	no	—
70	C₂²×C₄	—	47	4	no	—
71	C₂²×C₄	—	47	4	no	—
72	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
73	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
74	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
75	C₄⋊C₄	—	2	8	no	—
76	C₄⋊C₄	—	94	8	no	—
77	C₄⋊C₄	—	94	4	no	—
78	C₄²	—	94	4	no	—
79	C₄²	C₂²⋊D₄₇	1	4	yes	—
80	C₂³	C₂³×D₄₇	1	1	yes	characteristic
81	Q₈	—	4	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	8	no	—
85	C₂×C₄	—	94	4	no	—
86	C₂×C₄	—	94	4	no	—
87	C₂×C₄	—	94	8	no	—
88	C₂×C₄	—	94	8	no	—
89	C₂×C₄	#10625352	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
91	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
92	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
93	C₂²	C₂×#10625352	1	2	yes	—
94	C₂²	#13094072	1	4	yes	—
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	188	4	no	—
98	C₄	—	188	4	no	—
99	C₄	#13094011	1	4	yes	—
100	C₂	C₂×#13094011	1	1	yes	characteristic
101	C₂	#15689697	1	2	yes	—
102	C₂	#15689734	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal, characteristic

#15689061

C₂

yes

maximal

#15689030

C₂

yes

maximal

#15688969

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#124

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#541

yes

—

C₂×C₄⋊Q₈

D₄₇

yes

—

—

—

—

C₄₇

#2642

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10625352

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

C₂²

C₂×#10625352

yes

—

C₂²

#13094072

yes

—

C₄

—

C₄

—

C₄

—

188

—

C₄

—

188

—

C₄

#13094011

yes

—

100

C₂

C₂×#13094011

yes

characteristic

101

C₂

#15689697

yes

—

102

C₂

#15689734

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×C₄⋊Q₈×C₄₇	C₂
hypercenter	C₂×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#2642
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×C₄⋊Q₈×C₄₇

C₂

hypercenter

C₂×C₄⋊Q₈

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
57. C₄₇	#2642	semidirect

H ≅ G/N

type

57. C₄₇

#2642

semidirect

Subgroups — #20249338

Conjugacy classes of subgroups

Complements