Group #20245950 — subgroups

Subgroups — #20245950

Order 6016.

924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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×#13094021	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093986	C₂	1	6	yes	maximal, complemented
3	#15689024	C₂	1	6	yes	maximal, complemented
4	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	6	yes	—
7	C₂²×C₄×D₄₇	C₂²	1	4	yes	—
8	#13094021	C₄	1	8	yes	complemented
9	#13093986	—	2	24	no	—
10	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	6	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×D₄₇	C₂³	1	4	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
18	C₂²×Dic₄₇	C₂³	1	3	yes	—
19	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
20	C₂×D₁₈₈	—	2	12	no	—
21	C₂×D₁₈₈	—	2	12	no	—
22	C₂×D₁₈₈	C₂×C₄	1	24	yes	complemented
23	C₂×C₄×D₄₇	—	2	24	no	—
24	C₄⋊C₄×C₄₇	—	2	12	no	—
25	C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
26	(C₂×D₄₇)⋊C₄	—	2	24	no	—
27	C₄×Dic₄₇	—	2	6	no	—
28	C₄×Dic₄₇	D₄	1	12	yes	complemented
29	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
30	C₂²×D₄₇	—	2	12	no	—
31	C₂²×D₄₇	—	2	12	no	—
32	C₂²×D₄₇	C₂²×C₄	1	8	yes	—
33	C₂×C₄×C₄₇	—	2	12	no	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
36	C₂×C₄×C₄₇	#41	1	6	yes	—
37	C₂×Dic₄₇	—	2	6	no	—
38	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
39	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
40	D₁₈₈	—	2	48	no	—
41	C₄×D₄₇	—	4	16	no	—
42	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
43	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
44	C₂²×C₄₇	C₂×#41	1	3	yes	—
45	C₂×D₄₇	—	2	24	no	—
46	C₂×D₄₇	—	4	4	no	—
47	C₂×D₄₇	—	4	12	no	—
48	C₄×C₄₇	—	4	4	no	—
49	C₄×C₄₇	C₄×D₄	1	12	yes	complemented
50	Dic₄₇	—	2	6	no	—
51	Dic₄₇	#127	1	4	yes	complemented
52	C₄×#127	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	C₂×C₄×D₄	1	3	yes	—
54	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
55	C₂×C₄₇	#532	1	3	yes	—
56	D₄₇	—	4	8	no	—
57	C₂×#127	—	47	1	no	—
58	C₂×C₄×D₄	—	47	6	no	—
59	#390	—	47	6	no	—
60	#384	D₄₇	1	1	yes	characteristic, complemented
61	C₄³	—	47	1	no	—
62	C₄₇	C₄×#127	1	1	yes	characteristic, complemented, Sylow
63	C₂²×D₄	—	47	6	no	—
64	C₂³×C₄	—	47	4	no	—
65	#127	—	47	8	no	—
66	C₄×D₄	—	94	24	no	—
67	C₂×C₄⋊C₄	C₂×D₄₇	1	6	yes	—
68	C₂×C₂²⋊C₄	—	47	12	no	—
69	C₂×C₄²	—	47	3	no	—
70	C₂×C₄²	—	47	3	no	—
71	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
72	C₂⁴	—	47	4	no	—
73	C₂×D₄	—	47	24	no	—
74	C₂×D₄	—	94	12	no	—
75	C₂×D₄	—	94	12	no	—
76	C₂²×C₄	—	47	1	no	—
77	C₂²×C₄	—	47	3	no	—
78	C₂²×C₄	—	94	24	no	—
79	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
80	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
81	C₄⋊C₄	—	2	12	no	—
82	C₂²⋊C₄	—	94	24	no	—
83	C₄²	—	47	12	no	—
84	C₄²	—	94	6	no	—
85	C₄²	C₄×D₄₇	1	4	yes	complemented
86	C₂³	—	47	8	no	—
87	C₂³	—	94	12	no	—
88	C₂³	—	94	12	no	—
89	C₂³	C₂³×D₄₇	1	1	yes	characteristic
90	D₄	—	94	48	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	47	6	no	—
93	C₂×C₄	—	47	6	no	—
94	C₂×C₄	—	94	6	no	—
95	C₂×C₄	—	188	16	no	—
96	C₂×C₄	C₂×C₄×D₄₇	1	6	yes	—
97	C₂×C₄	D₄×D₄₇	1	6	yes	—
98	C₂×C₄	#10625354	1	6	yes	—
99	C₂²	—	94	24	no	—
100	C₂²	—	188	4	no	—
101	C₂²	—	188	12	no	—
102	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
103	C₂²	C₂×D₄×D₄₇	1	3	yes	—
104	C₂²	C₂×#10625354	1	3	yes	—
105	C₄	—	4	4	no	—
106	C₄	—	47	4	no	—
107	C₄	—	94	6	no	—
108	C₄	#13093986	1	12	yes	complemented
109	C₂	—	188	8	no	—
110	C₂	C₂×#13093986	1	3	yes	—
111	C₂	#127×D₄₇	1	1	yes	characteristic
112	C₂	#15689674	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094021

C₂

yes

maximal, characteristic

C₂×#13093986

C₂

yes

maximal, complemented

#15689024

C₂

yes

maximal, complemented

C₄²×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×#384

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

C₂²×C₄×D₄₇

C₂²

yes

—

#13094021

C₄

yes

complemented

#13093986

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

complemented

C₂×C₄×D₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

complemented

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

—

D₁₈₈

—

C₄×D₄₇

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

complemented

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

C₂×C₄×D₄

yes

—

C₂×C₄₇

C₂×#127

yes

characteristic

C₂×C₄₇

#532

yes

—

D₄₇

—

C₂×#127

—

C₂×C₄×D₄

—

#390

—

#384

D₄₇

yes

characteristic, complemented

C₄³

—

C₄₇

C₄×#127

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

#127

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₇

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

D₄×D₄₇

yes

—

C₂×C₄

#10625354

yes

—

C₂²

—

100

C₂²

—

188

—

101

C₂²

—

188

—

102

C₂²

C₂²×C₄×D₄₇

yes

characteristic

103

C₂²

C₂×D₄×D₄₇

yes

—

104

C₂²

C₂×#10625354

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#13093986

yes

complemented

109

C₂

—

188

—

110

C₂

C₂×#13093986

yes

—

111

C₂

#127×D₄₇

yes

characteristic

112

C₂

#15689674

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#384	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	#384	D₄₇
hypocenter	C₄₇	C₄×#127
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₄₇×#384

C₂

socle

C₂³×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
2. C₂×#13093986	C₂	semidirect
3. #15689024	C₂	semidirect
4. C₄²×Dic₄₇	C₂	semidirect
5. C₄₇×#384	C₂	semidirect
8. #13094021	C₄	semidirect
22. C₂×D₁₈₈	C₂×C₄	semidirect
25. C₄²×C₄₇	C₂×C₄	semidirect
28. C₄×Dic₄₇	D₄	semidirect
49. C₄×C₄₇	C₄×D₄	semidirect
51. Dic₄₇	#127	semidirect
60. #384	D₄₇	semidirect
62. C₄₇	C₄×#127	semidirect
85. C₄²	C₄×D₄₇	semidirect
108. C₄	#13093986	semidirect

H ≅ G/N

type

2. C₂×#13093986

C₂

semidirect

3. #15689024

C₂

semidirect

4. C₄²×Dic₄₇

C₂

semidirect

5. C₄₇×#384

C₂

semidirect

8. #13094021

C₄

semidirect

22. C₂×D₁₈₈

C₂×C₄

semidirect

25. C₄²×C₄₇

C₂×C₄

semidirect

28. C₄×Dic₄₇

D₄

semidirect

49. C₄×C₄₇

C₄×D₄

semidirect

51. Dic₄₇

#127

semidirect

60. #384

D₄₇

semidirect

62. C₄₇

C₄×#127

semidirect

85. C₄²

C₄×D₄₇

semidirect

108. C₄

#13093986

semidirect

Subgroups — #20245950

Conjugacy classes of subgroups

Complements