Group #20245608 — subgroups

Subgroups — #20245608

Order 6016.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#15689381	C₂	1	1	yes	maximal, characteristic
2	#15689172	C₂	1	1	yes	maximal, characteristic
3	#15688946	C₂	1	2	yes	maximal, complemented
4	#15688940	C₂	1	2	yes	maximal, complemented
5	C₄₇×#349	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	C₂×#10625329	—	2	1	no	—
8	#13094003	—	2	1	no	—
9	#13093960	—	2	1	no	—
10	#13093960	C₂²	1	2	yes	—
11	#13093956	C₂²	1	1	yes	characteristic
12	#13093949	—	2	1	no	—
13	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂×Dic₉₄	—	2	1	no	—
17	M₁₆×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²⋊Dic₄₇	—	4	1	no	—
21	C₄⋊Dic₄₇	—	2	1	no	—
22	Dic₄₇⋊C₄	—	4	1	no	—
23	#10625329	—	2	2	no	—
24	#10625329	—	4	1	no	—
25	C₂×C₄₇⋊C₈	—	4	1	no	—
26	Dic₁₈₈	—	2	2	no	—
27	C₁₆×C₄₇	—	2	2	no	—
28	C₂³×C₄₇	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₇	—	4	1	no	—
34	C₂×Dic₄₇	—	4	1	no	—
35	Dic₉₄	—	4	1	no	—
36	Dic₉₄	—	4	1	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	#41	1	2	yes	—
39	C₄₇⋊C₈	—	4	2	no	—
40	C₂²×C₄₇	—	2	1	no	—
41	C₂²×C₄₇	—	4	1	no	—
42	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₄₇	—	2	1	no	—
44	C₄×C₄₇	#123	1	1	yes	characteristic
45	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₄₇	—	8	1	no	—
47	Dic₄₇	—	8	1	no	—
48	#2239	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	—	2	1	no	—
50	C₂×C₄₇	—	4	1	no	—
51	C₂×C₄₇	#481	1	1	yes	characteristic
52	#470	—	47	1	no	—
53	#430	—	47	1	no	—
54	#365	—	47	2	no	—
55	#362	—	47	2	no	—
56	#349	D₄₇	1	1	yes	characteristic
57	C₄₇	#2239	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	47	1	no	—
59	C₂×M₁₆	—	94	1	no	—
60	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
61	C₂²⋊Q₈	—	94	1	no	—
62	M₃₂	C₂×D₄₇	1	2	yes	—
63	#108	—	47	2	no	—
64	#108	—	94	1	no	—
65	#106	—	47	1	no	—
66	#103	—	94	1	no	—
67	C₂×Q₈	—	94	1	no	—
68	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
69	Q₁₆	—	94	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	94	2	no	—
72	M₁₆	—	188	1	no	—
73	C₂×C₈	—	188	1	no	—
74	C₂×C₈	D₁₈₈	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
76	C₄⋊C₄	—	94	1	no	—
77	C₄⋊C₄	—	188	1	no	—
78	C₂²⋊C₄	—	188	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	#10625325	1	1	yes	characteristic
81	Q₈	—	188	1	no	—
82	Q₈	—	188	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	188	1	no	—
86	C₂×C₄	—	188	1	no	—
87	C₂×C₄	#10625325	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	188	2	no	—
91	C₈	#10625352	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#10625325	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	376	1	no	—
97	C₄	—	376	1	no	—
98	C₄	#13094008	1	1	yes	characteristic
99	C₄	#13094052	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#15689442	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689381

C₂

yes

maximal, characteristic

#15689172

C₂

yes

maximal, characteristic

#15688946

C₂

yes

maximal, complemented

#15688940

C₂

yes

maximal, complemented

C₄₇×#349

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

—

—

C₂²

yes

—

#13093956

C₂²

yes

characteristic

#13093949

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#2239

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²⋊Q₈

—

M₃₂

C₂×D₄₇

yes

—

—

—

—

—

C₂×Q₈

—

C₂²×C₄

D₁₈₈

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

188

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₁₆

—

C₂³

#10625325

yes

characteristic

Q₈

—

188

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625325

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

—

C₈

—

188

—

C₈

#10625352

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#10625325

yes

characteristic

C₄

—

C₄

—

376

—

C₄

—

376

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#15689442

yes

characteristic

	subgroup	G/H
center	C₂	#15689442
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#349	C₂
socle	C₂×C₄₇	#481
hypercenter	#349	D₄₇
hypocenter	C₄₇	#2239
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#15689442

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#349

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
3. #15688946	C₂	semidirect
4. #15688940	C₂	semidirect
57. C₄₇	#2239	semidirect

H ≅ G/N

type

3. #15688946

C₂

semidirect

4. #15688940

C₂

semidirect

57. C₄₇

#2239

semidirect

Subgroups — #20245608

Conjugacy classes of subgroups

Complements