Group #20242194 — subgroups

Subgroups — #20242194

Order 6016.

164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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	#15689247	C₂	1	2	yes	maximal
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688853	C₂	1	2	yes	maximal
4	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic
7	C₄×Dic₉₄	C₂²	1	2	yes	—
8	#13093958	C₄	1	1	yes	characteristic
9	Dic₄₇⋊C₈	—	2	2	no	—
10	#13093949	C₄	1	2	yes	—
11	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×Dic₄₇	—	2	2	no	—
14	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₇	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
22	Dic₄₇⋊C₄	—	2	2	no	—
23	C₄×Dic₄₇	—	2	2	no	—
24	C₂×C₄₇⋊C₈	—	2	1	no	—
25	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
26	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
27	Dic₁₈₈	C₈	1	4	yes	complemented
28	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
31	C₂×Dic₄₇	—	2	2	no	—
32	C₂×Dic₄₇	—	2	2	no	—
33	Dic₉₄	—	2	2	no	—
34	Dic₉₄	C₂×C₈	1	4	yes	—
35	C₈×C₄₇	—	2	1	no	—
36	C₈×C₄₇	—	4	2	no	—
37	C₈×C₄₇	C₂×C₈	1	2	yes	—
38	C₄₇⋊C₈	—	2	2	no	—
39	C₄₇⋊C₈	—	2	1	no	—
40	C₄₇⋊C₈	Q₁₆	1	2	yes	complemented
41	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₄₇	#131	1	1	yes	characteristic
45	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₇	#135	1	1	yes	characteristic
47	Dic₄₇	—	2	4	no	—
48	Dic₄₇	—	4	2	no	—
49	C₈×Q₁₆	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
51	C₂×C₄₇	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₇	#443	1	1	yes	characteristic
53	C₈×Q₈	—	47	2	no	—
54	C₄×Q₁₆	—	47	1	no	—
55	#335	D₄₇	1	1	yes	characteristic
56	Q₈⋊C₈	—	47	2	no	—
57	C₈²	—	47	1	no	—
58	C₄₇	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	47	1	no	—
60	C₄×Q₈	—	47	2	no	—
61	#107	—	47	1	no	—
62	C₄⋊C₈	—	94	2	no	—
63	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
64	#103	—	47	2	no	—
65	C₄×C₈	—	47	1	no	—
66	C₄×C₈	—	47	1	no	—
67	C₄×C₈	—	94	2	no	—
68	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
69	C₂×Q₈	—	47	2	no	—
70	Q₁₆	—	47	4	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	47	1	no	—
73	C₂×C₈	—	47	1	no	—
74	C₂×C₈	—	94	1	no	—
75	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
76	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
77	C₄⋊C₄	—	47	2	no	—
78	C₄⋊C₄	—	94	2	no	—
79	C₄²	—	94	2	no	—
80	C₄²	C₂²×D₄₇	1	1	yes	characteristic
81	Q₈	—	47	4	no	—
82	Q₈	—	94	2	no	—
83	C₂×C₄	—	94	2	no	—
84	C₂×C₄	—	94	2	no	—
85	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
86	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
87	C₂×C₄	#10625354	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	4	2	no	—
90	C₈	—	47	2	no	—
91	C₈	—	94	2	no	—
92	C₈	—	94	1	no	—
93	C₈	C₈×D₄₇	1	2	yes	—
94	C₂²	#13093986	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	94	4	no	—
97	C₄	—	188	2	no	—
98	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
99	C₄	#13094032	1	1	yes	characteristic
100	C₄	Q₁₆×D₄₇	1	1	yes	characteristic
101	C₄	#13094043	1	1	yes	characteristic
102	C₂	#15689188	1	1	yes	characteristic
103	C₂	#15689217	1	1	yes	characteristic
104	C₂	#15689239	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689247

C₂

yes

maximal

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688853

C₂

yes

maximal

C₈×C₄₇⋊C₈

C₂

yes

maximal, characteristic

C₄₇×#335

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₄

yes

characteristic

C₄×Dic₉₄

C₂²

yes

—

#13093958

C₄

yes

characteristic

Dic₄₇⋊C₈

—

#13093949

C₄

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

C₈

yes

complemented

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

C₂×C₈

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂×C₈

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

Q₁₆

yes

complemented

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

#131

yes

characteristic

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

#135

yes

characteristic

Dic₄₇

—

Dic₄₇

—

C₈×Q₁₆

—

maximal, Sylow

C₂×C₄₇

C₈×D₄

yes

characteristic

C₂×C₄₇

C₄×Q₁₆

yes

characteristic

C₂×C₄₇

#443

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

—

#335

D₄₇

yes

characteristic

Q₈⋊C₈

—

C₈²

—

C₄₇

C₈×Q₁₆

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₈×D₄₇

yes

—

C₂²

#13093986

yes

characteristic

C₄

—

C₄

—

C₄

—

188

—

C₄

C₂×C₈×D₄₇

yes

characteristic

C₄

#13094032

yes

characteristic

100

C₄

Q₁₆×D₄₇

yes

characteristic

101

C₄

#13094043

yes

characteristic

102

C₂

#15689188

yes

characteristic

103

C₂

#15689217

yes

characteristic

104

C₂

#15689239

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#335	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	#335	D₄₇
hypocenter	C₄₇	C₈×Q₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#335

C₂

socle

C₂²×C₄₇

C₄×D₄

hypercenter

#335

D₄₇

hypocenter

C₄₇

C₈×Q₁₆

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
27. Dic₁₈₈	C₈	semidirect
40. C₄₇⋊C₈	Q₁₆	semidirect
58. C₄₇	C₈×Q₁₆	semidirect

H ≅ G/N

type

27. Dic₁₈₈

C₈

semidirect

40. C₄₇⋊C₈

Q₁₆

semidirect

58. C₄₇

C₈×Q₁₆

semidirect

Subgroups — #20242194

Conjugacy classes of subgroups

Complements