Group #20246681 — subgroups

Subgroups — #20246681

Order 6016.

504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 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×C₄×Dic₉₄	C₂	1	2	yes	maximal
2	#15689055	C₂	1	4	yes	maximal
3	#15689044	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₄₇	C₂	1	4	yes	maximal
5	C₄₇×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	2	yes	—
7	C₄×Dic₉₄	—	2	8	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	8	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	4	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
16	#95×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₇	C₂³	1	4	yes	—
21	C₂²×Dic₄₇	C₂³	1	4	yes	—
22	C₂×Dic₉₄	—	2	4	no	—
23	C₂×Dic₉₄	—	2	8	no	—
24	C₄²×C₄₇	D₄	1	4	yes	—
25	C₄²×C₄₇	Q₈	1	8	yes	complemented
26	C₄⋊Dic₄₇	—	2	4	no	—
27	C₄⋊Dic₄₇	—	2	16	no	—
28	Dic₄₇⋊C₄	—	2	8	no	—
29	C₄×Dic₄₇	—	2	8	no	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	2	8	no	—
32	C₂×C₄×C₄₇	—	2	4	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₄₇	C₂×Q₈	1	8	yes	—
36	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	2	4	no	—
39	C₂×Dic₄₇	—	2	4	no	—
40	C₂×Dic₄₇	—	2	8	no	—
41	C₂×Dic₄₇	#41	1	8	yes	—
42	Dic₉₄	—	2	16	no	—
43	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
44	C₂²×C₄₇	C₂²×Q₈	1	2	yes	—
45	C₂²×C₄₇	C₂×#41	1	4	yes	—
46	C₄×C₄₇	—	2	4	no	—
47	C₄×C₄₇	—	2	8	no	—
48	C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
49	Dic₄₇	—	2	8	no	—
50	Dic₄₇	—	4	4	no	—
51	#2399	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	#525	1	2	yes	—
53	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₄₇	#533	1	4	yes	—
55	C₂×C₄×Q₈	—	47	2	no	—
56	#398	—	47	4	no	—
57	#395	—	47	4	no	—
58	C₄×C₄⋊C₄	—	47	4	no	—
59	#376	D₄₇	1	1	yes	characteristic
60	C₄₇	#2399	1	1	yes	characteristic, complemented, Sylow
61	C₂²×Q₈	—	47	2	no	—
62	C₄×Q₈	—	94	8	no	—
63	C₂×C₄⋊C₄	—	47	4	no	—
64	C₂×C₄⋊C₄	—	47	2	no	—
65	C₂×C₄⋊C₄	—	47	8	no	—
66	C₂×C₄²	—	47	4	no	—
67	C₂×C₄²	C₂×D₄₇	1	2	yes	—
68	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
69	#95	—	47	4	no	—
70	#95	—	47	4	no	—
71	#95	C₂×D₄₇	1	4	yes	—
72	C₂×Q₈	—	94	8	no	—
73	C₂×Q₈	—	94	4	no	—
74	C₂²×C₄	—	47	4	no	—
75	C₂²×C₄	—	47	4	no	—
76	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
77	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
78	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
79	C₄⋊C₄	—	94	16	no	—
80	C₄⋊C₄	—	94	8	no	—
81	C₄⋊C₄	—	94	4	no	—
82	C₄²	—	94	8	no	—
83	C₄²	Dic₉₄	1	8	yes	complemented
84	C₄²	D₁₈₈	1	4	yes	—
85	C₂³	C₂³×D₄₇	1	1	yes	characteristic
86	Q₈	—	94	16	no	—
87	C₂×C₄	—	2	8	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	47	8	no	—
90	C₂×C₄	—	94	4	no	—
91	C₂×C₄	—	94	4	no	—
92	C₂×C₄	—	94	4	no	—
93	C₂×C₄	—	94	8	no	—
94	C₂×C₄	C₂×Dic₉₄	1	8	yes	—
95	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
96	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
97	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
98	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
99	C₂²	C₂²×Dic₉₄	1	2	yes	—
100	C₂²	#41×D₄₇	1	4	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	94	8	no	—
104	C₄	—	188	4	no	—
105	C₄	#13094024	1	4	yes	—
106	C₂	#15689635	1	2	yes	—
107	C₂	C₂×#13094024	1	1	yes	characteristic
108	C₂	#15689676	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₉₄

C₂

yes

maximal

#15689055

C₂

yes

maximal

#15689044

C₂

yes

maximal

C₄×C₄⋊Dic₄₇

C₂

yes

maximal

C₄₇×#376

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

Q₈

yes

complemented

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

Dic₉₄

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄⋊Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

#2399

—

maximal, Sylow

C₂×C₄₇

#525

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

#533

yes

—

C₂×C₄×Q₈

—

#398

—

#395

—

C₄×C₄⋊C₄

—

#376

D₄₇

yes

characteristic

C₄₇

#2399

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

—

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

Dic₉₄

yes

complemented

C₄²

D₁₈₈

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂²

C₂²×D₁₈₈

yes

characteristic

C₂²

C₂²×Dic₉₄

yes

—

100

C₂²

#41×D₄₇

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

188

—

105

C₄

#13094024

yes

—

106

C₂

#15689635

yes

—

107

C₂

C₂×#13094024

yes

characteristic

108

C₂

#15689676

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#2399
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₄₇×#376

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
25. C₄²×C₄₇	Q₈	semidirect
60. C₄₇	#2399	semidirect
83. C₄²	Dic₉₄	semidirect

H ≅ G/N

type

25. C₄²×C₄₇

Q₈

semidirect

60. C₄₇

#2399

semidirect

83. C₄²

Dic₉₄

semidirect

Subgroups — #20246681

Conjugacy classes of subgroups

Complements