Group #20242917 — subgroups

Subgroups — #20242917

Order 6016.

140 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 55 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	#15689528	C₂	1	1	yes	maximal, characteristic
2	#15689419	C₂	1	2	yes	maximal
3	#15689253	C₂	1	1	yes	maximal, characteristic
4	#15688871	C₂	1	2	yes	maximal
5	C₄₇×#334	C₂	1	1	yes	maximal, characteristic
6	#13094024	C₂²	1	2	yes	—
7	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
8	#13093958	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	#13093958	—	2	2	no	—
11	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₄₇⋊C₈	—	2	1	no	—
13	#13093949	—	2	2	no	—
14	#13093934	—	2	1	no	—
15	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Dic₉₄	—	2	2	no	—
18	C₂×Dic₉₄	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₄²×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
26	Dic₄₇⋊C₄	—	2	1	no	—
27	C₄×Dic₄₇	—	2	1	no	—
28	C₂×C₄₇⋊C₈	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
32	C₂×Dic₄₇	—	2	1	no	—
33	C₂×Dic₄₇	—	2	1	no	—
34	C₂×Dic₄₇	—	4	2	no	—
35	Dic₉₄	—	2	2	no	—
36	Dic₉₄	—	8	2	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	—	4	2	no	—
39	C₈×C₄₇	Q₁₆	1	2	yes	—
40	C₄₇⋊C₈	—	4	1	no	—
41	C₂²×C₄₇	#121	1	1	yes	characteristic
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
44	C₄×C₄₇	#137	1	2	yes	—
45	C₄×C₄₇	#137	1	1	yes	characteristic
46	Dic₄₇	—	4	1	no	—
47	Dic₄₇	—	4	1	no	—
48	Dic₄₇	—	8	2	no	—
49	#1696	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	#462	1	1	yes	characteristic
51	C₂×C₄₇	#470	1	1	yes	characteristic
52	C₂×C₄₇	#472	1	1	yes	characteristic
53	#500	—	47	1	no	—
54	#477	—	47	2	no	—
55	#446	—	47	1	no	—
56	#334	D₄₇	1	1	yes	characteristic
57	#333	—	47	2	no	—
58	C₄₇	#1696	1	1	yes	characteristic, complemented, Sylow
59	C₄⋊Q₈	—	47	2	no	—
60	C₄×Q₈	—	47	1	no	—
61	#107	—	94	2	no	—
62	#107	—	94	1	no	—
63	#107	—	94	1	no	—
64	C₄⋊C₈	—	47	1	no	—
65	C₄⋊C₈	—	94	1	no	—
66	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
67	#103	—	94	2	no	—
68	#97	—	94	1	no	—
69	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
70	C₂×Q₈	—	47	1	no	—
71	C₂×Q₈	—	94	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	94	1	no	—
74	C₂×C₈	D₁₈₈	1	1	yes	characteristic
75	C₂×C₈	D₁₈₈	1	1	yes	characteristic
76	C₄⋊C₄	—	47	1	no	—
77	C₄⋊C₄	—	94	1	no	—
78	C₄⋊C₄	—	94	2	no	—
79	C₄⋊C₄	—	94	2	no	—
80	C₄²	—	94	1	no	—
81	C₄²	C₂²×D₄₇	1	1	yes	characteristic
82	Q₈	—	94	2	no	—
83	Q₈	—	376	2	no	—
84	C₂×C₄	—	94	1	no	—
85	C₂×C₄	—	94	1	no	—
86	C₂×C₄	—	188	2	no	—
87	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
88	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
89	C₂×C₄	#10625354	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	4	2	no	—
92	C₈	—	188	1	no	—
93	C₈	Dic₁₈₈	1	2	yes	—
94	C₂²	#13093999	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	376	2	no	—
97	C₄	—	188	1	no	—
98	C₄	—	188	1	no	—
99	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
100	C₄	#13094053	1	2	yes	—
101	C₄	#13094057	1	1	yes	characteristic
102	C₂	#15689334	1	1	yes	characteristic
103	C₂	#15689382	1	1	yes	characteristic
104	C₂	#15689394	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

#15689419

C₂

yes

maximal

#15689253

C₂

yes

maximal, characteristic

#15688871

C₂

yes

maximal

C₄₇×#334

C₂

yes

maximal, characteristic

#13094024

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

—

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

#13093949

—

#13093934

—

C₄⋊C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

characteristic

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

Q₁₆

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

#137

yes

—

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

D₄₇

yes

characteristic

#333

—

C₄₇

#1696

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

—

376

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₈

Dic₁₈₈

yes

—

C₂²

#13093999

yes

characteristic

C₄

—

C₄

—

376

—

C₄

—

188

—

C₄

—

188

—

C₄

C₂×Dic₁₈₈

yes

characteristic

100

C₄

#13094053

yes

—

101

C₄

#13094057

yes

characteristic

102

C₂

#15689334

yes

characteristic

103

C₂

#15689382

yes

characteristic

104

C₂

#15689394

yes

characteristic

	subgroup	G/H
center	C₂²	#13093999
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#334	C₂
socle	C₂²×C₄₇	#121
hypercenter	#334	D₄₇
hypocenter	C₄₇	#1696
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13093999

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#334

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
58. C₄₇	#1696	semidirect

H ≅ G/N

type

58. C₄₇

#1696

semidirect

Subgroups — #20242917

Conjugacy classes of subgroups

Complements