Group #20242793 — subgroups

Subgroups — #20242793

Order 6016.

144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 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	C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
4	#15688871	C₂	1	2	yes	maximal
5	C₄₇×#335	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	C₈×Dic₄₇	—	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	1	no	—
36	Dic₉₄	—	8	2	no	—
37	Dic₉₄	Q₁₆	1	2	yes	—
38	C₈×C₄₇	—	2	1	no	—
39	C₈×C₄₇	—	4	2	no	—
40	C₈×C₄₇	Q₁₆	1	2	yes	—
41	C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇	#121	1	1	yes	characteristic
43	C₄×C₄₇	—	2	1	no	—
44	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
45	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₇	#135	1	1	yes	characteristic
47	C₄×C₄₇	#137	1	1	yes	characteristic
48	Dic₄₇	—	2	2	no	—
49	Dic₄₇	—	4	1	no	—
50	Dic₄₇	—	8	2	no	—
51	#1676	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	#462	1	1	yes	characteristic
53	C₂×C₄₇	#467	1	1	yes	characteristic
54	C₂×C₄₇	#472	1	1	yes	characteristic
55	#500	—	47	1	no	—
56	#477	—	47	2	no	—
57	C₈×Q₈	—	47	1	no	—
58	#335	D₄₇	1	1	yes	characteristic
59	#333	—	47	2	no	—
60	C₄₇	#1676	1	1	yes	characteristic, complemented, Sylow
61	C₄⋊Q₈	—	47	2	no	—
62	C₄×Q₈	—	47	1	no	—
63	#107	—	94	2	no	—
64	#107	—	94	1	no	—
65	#107	—	94	1	no	—
66	C₄⋊C₈	—	47	1	no	—
67	C₄⋊C₈	—	94	1	no	—
68	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
69	#103	—	94	2	no	—
70	C₄×C₈	—	94	1	no	—
71	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
72	C₂×Q₈	—	47	1	no	—
73	C₂×Q₈	—	94	2	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	94	1	no	—
76	C₂×C₈	D₁₈₈	1	1	yes	characteristic
77	C₂×C₈	D₁₈₈	1	1	yes	characteristic
78	C₄⋊C₄	—	47	1	no	—
79	C₄⋊C₄	—	94	1	no	—
80	C₄⋊C₄	—	94	2	no	—
81	C₄⋊C₄	—	94	2	no	—
82	C₄²	—	94	1	no	—
83	C₄²	C₂²×D₄₇	1	1	yes	characteristic
84	Q₈	—	47	2	no	—
85	Q₈	—	94	1	no	—
86	Q₈	—	376	2	no	—
87	C₂×C₄	—	94	1	no	—
88	C₂×C₄	—	94	1	no	—
89	C₂×C₄	—	188	2	no	—
90	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
91	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
92	C₂×C₄	#10625354	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	4	2	no	—
95	C₈	—	188	1	no	—
96	C₈	Dic₁₈₈	1	2	yes	—
97	C₂²	#13093999	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	94	2	no	—
100	C₄	—	376	2	no	—
101	C₄	—	188	1	no	—
102	C₄	Q₁₆×D₄₇	1	1	yes	characteristic
103	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
104	C₄	#13094043	1	1	yes	characteristic
105	C₄	#13094057	1	1	yes	characteristic
106	C₂	#15689334	1	1	yes	characteristic
107	C₂	#15689365	1	1	yes	characteristic
108	C₂	#15689394	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

#15689419

C₂

yes

maximal

C₈×Dic₉₄

C₂

yes

maximal, characteristic

#15688871

C₂

yes

maximal

C₄₇×#335

C₂

yes

maximal, characteristic

#13094024

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

—

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

#13093949

—

C₈×Dic₄₇

—

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

—

Dic₉₄

Q₁₆

yes

—

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

C₂×Q₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

C₈×Q₈

—

#335

D₄₇

yes

characteristic

#333

—

C₄₇

#1676

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#103

—

C₄×C₈

—

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

—

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

—

100

C₄

—

376

—

101

C₄

—

188

—

102

C₄

Q₁₆×D₄₇

yes

characteristic

103

C₄

C₂×Dic₁₈₈

yes

characteristic

104

C₄

#13094043

yes

characteristic

105

C₄

#13094057

yes

characteristic

106

C₂

#15689334

yes

characteristic

107

C₂

#15689365

yes

characteristic

108

C₂

#15689394

yes

characteristic

	subgroup	G/H
center	C₂²	#13093999
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#335	C₂
socle	C₂²×C₄₇	#121
hypercenter	#335	D₄₇
hypocenter	C₄₇	#1676
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #335

subgroup

G/H

center

C₂²

#13093999

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#335

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #335

N	H ≅ G/N	type
60. C₄₇	#1676	semidirect

H ≅ G/N

type

60. C₄₇

#1676

semidirect

Subgroups — #20242793

Conjugacy classes of subgroups

Complements