Group #20245787 — subgroups

Subgroups — #384×D₄₇ #20245787

Order 6016.

888 conjugacy classes of subgroups; only the 365 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 365 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⋊C₄×D₄₇	C₂	1	6	yes	maximal
2	C₂×C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688993	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688992	C₂	1	6	yes	maximal, complemented
5	C₄₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₇	C₂²	1	4	yes	—
7	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	6	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	12	yes	—
10	C₄⋊C₄×D₄₇	—	2	24	no	—
11	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
12	C₄²×D₄₇	C₄	1	8	yes	complemented
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	6	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×D₄₇	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
18	C₂²×Dic₄₇	C₂³	1	4	yes	—
19	C₂²×Dic₄₇	C₂³	1	3	yes	—
20	C₂×C₄×D₄₇	—	2	24	no	—
21	C₂×C₄×D₄₇	C₂×C₄	1	12	yes	—
22	C₂×C₄×D₄₇	D₄	1	12	yes	—
23	C₂×C₄×D₄₇	Q₈	1	12	yes	—
24	C₄⋊C₄×C₄₇	—	2	12	no	—
25	C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
26	C₄⋊Dic₄₇	—	2	12	no	—
27	Dic₄₇⋊C₄	—	2	24	no	—
28	C₄×Dic₄₇	C₂×C₄	1	12	yes	complemented
29	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
30	C₂²×D₄₇	C₂²×C₄	1	2	yes	—
31	C₂²×D₄₇	C₂×D₄	1	6	yes	—
32	C₂²×D₄₇	C₂×Q₈	1	6	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	C₂×Q₈	1	6	yes	—
37	C₂×Dic₄₇	—	2	12	no	—
38	C₂×Dic₄₇	C₂²×C₄	1	6	yes	—
39	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
40	C₂×Dic₄₇	C₂×Q₈	1	6	yes	—
41	C₄×D₄₇	—	4	16	no	—
42	C₄×D₄₇	C₄⋊C₄	1	48	yes	complemented
43	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
44	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
45	C₂²×C₄₇	C₂²×Q₈	1	3	yes	—
46	C₂×D₄₇	C₂×C₄⋊C₄	1	12	yes	—
47	C₂×D₄₇	#127	1	4	yes	—
48	C₂×D₄₇	C₄⋊Q₈	1	12	yes	—
49	C₄×C₄₇	—	4	4	no	—
50	C₄×C₄₇	C₂×C₄⋊C₄	1	12	yes	complemented
51	Dic₄₇	—	4	4	no	—
52	Dic₄₇	C₂×C₄⋊C₄	1	12	yes	complemented
53	C₂×#384	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	C₂²×C₄⋊C₄	1	3	yes	—
55	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
56	C₂×C₄₇	C₂×C₄⋊Q₈	1	3	yes	—
57	D₄₇	#384	1	8	yes	direct product factor
58	C₂²×C₄⋊C₄	—	47	6	no	—
59	C₂²×C₄²	—	47	1	no	—
60	#384	—	47	6	no	—
61	#384	—	47	1	no	—
62	#384	D₄₇	1	1	yes	characteristic, direct product factor
63	C₄₇	C₂×#384	1	1	yes	characteristic, complemented, Sylow
64	C₂³×C₄	—	47	3	no	—
65	C₂³×C₄	—	47	4	no	—
66	C₂×C₄⋊C₄	—	47	12	no	—
67	C₂×C₄⋊C₄	—	47	6	no	—
68	C₂×C₄⋊C₄	—	94	24	no	—
69	C₂×C₄⋊C₄	C₂×D₄₇	1	6	yes	—
70	C₂×C₄²	—	47	3	no	—
71	C₂×C₄²	—	47	8	no	—
72	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
73	C₂⁴	—	47	1	no	—
74	C₂²×C₄	—	47	3	no	—
75	C₂²×C₄	—	47	12	no	—
76	C₂²×C₄	—	47	12	no	—
77	C₂²×C₄	—	47	12	no	—
78	C₂²×C₄	—	47	4	no	—
79	C₂²×C₄	—	94	24	no	—
80	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
81	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
82	C₄⋊C₄	—	2	12	no	—
83	C₄⋊C₄	—	94	24	no	—
84	C₄⋊C₄	—	94	12	no	—
85	C₄²	—	47	12	no	—
86	C₄²	C₄×D₄₇	1	4	yes	complemented
87	C₂³	—	47	2	no	—
88	C₂³	—	47	6	no	—
89	C₂³	—	47	6	no	—
90	C₂³	C₂³×D₄₇	1	1	yes	characteristic
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	47	6	no	—
93	C₂×C₄	—	47	6	no	—
94	C₂×C₄	—	47	6	no	—
95	C₂×C₄	—	47	48	no	—
96	C₂×C₄	—	94	12	no	—
97	C₂×C₄	—	188	16	no	—
98	C₂×C₄	C₂×C₄×D₄₇	1	6	yes	—
99	C₂×C₄	D₄×D₄₇	1	6	yes	—
100	C₂×C₄	Q₈×D₄₇	1	6	yes	—
101	C₂²	—	47	12	no	—
102	C₂²	—	47	4	no	—
103	C₂²	—	47	12	no	—
104	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
105	C₂²	C₂×D₄×D₄₇	1	3	yes	—
106	C₂²	C₂×Q₈×D₄₇	1	3	yes	—
107	C₄	—	4	4	no	—
108	C₄	—	47	12	no	—
109	C₄	—	188	4	no	—
110	C₄	C₄⋊C₄×D₄₇	1	12	yes	complemented
111	C₂	—	47	8	no	—
112	C₂	C₂×C₄⋊C₄×D₄₇	1	3	yes	—
113	C₂	#127×D₄₇	1	1	yes	characteristic
114	C₂	C₄⋊Q₈×D₄₇	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₄×D₄₇

C₂

yes

maximal

C₂×C₄²×D₄₇

C₂

yes

maximal, characteristic

#15688993

C₂

yes

maximal, characteristic, complemented

#15688992

C₂

yes

maximal, complemented

C₄₇×#384

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

—

C₂²×C₄×D₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄⋊C₄×D₄₇

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄²×D₄₇

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

Q₈

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

complemented

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

C₂×C₄

yes

complemented

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

C₂×D₄

yes

—

C₂²×D₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₄×D₄₇

—

C₄×D₄₇

C₄⋊C₄

yes

complemented

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂×D₄₇

C₂×C₄⋊C₄

yes

—

C₂×D₄₇

#127

yes

—

C₂×D₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

complemented

Dic₄₇

—

Dic₄₇

C₂×C₄⋊C₄

yes

complemented

C₂×#384

—

maximal, Sylow

C₂×C₄₇

C₂²×C₄⋊C₄

yes

—

C₂×C₄₇

C₂×#127

yes

characteristic

C₂×C₄₇

C₂×C₄⋊Q₈

yes

—

D₄₇

#384

yes

direct product factor

C₂²×C₄⋊C₄

—

C₂²×C₄²

—

#384

—

#384

—

#384

D₄₇

yes

characteristic, direct product factor

C₄₇

C₂×#384

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₄×D₄₇

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

D₄×D₄₇

yes

—

100

C₂×C₄

Q₈×D₄₇

yes

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂²×C₄×D₄₇

yes

characteristic

105

C₂²

C₂×D₄×D₄₇

yes

—

106

C₂²

C₂×Q₈×D₄₇

yes

—

107

C₄

—

108

C₄

—

109

C₄

—

188

—

110

C₄

C₄⋊C₄×D₄₇

yes

complemented

111

C₂

—

112

C₂

C₂×C₄⋊C₄×D₄₇

yes

—

113

C₂

#127×D₄₇

yes

characteristic

114

C₂

C₄⋊Q₈×D₄₇

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	C₂×#384
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
3. #15688993	C₂	semidirect
4. #15688992	C₂	semidirect
5. C₄₇×#384	C₂	semidirect
12. C₄²×D₄₇	C₄	semidirect
25. C₄²×C₄₇	C₂×C₄	semidirect
28. C₄×Dic₄₇	C₂×C₄	semidirect
42. C₄×D₄₇	C₄⋊C₄	semidirect
50. C₄×C₄₇	C₂×C₄⋊C₄	semidirect
52. Dic₄₇	C₂×C₄⋊C₄	semidirect
57. D₄₇	#384	direct (N × H)
62. #384	D₄₇	direct (N × H)
63. C₄₇	C₂×#384	semidirect
86. C₄²	C₄×D₄₇	semidirect
110. C₄	C₄⋊C₄×D₄₇	semidirect

H ≅ G/N

type

3. #15688993

C₂

semidirect

4. #15688992

C₂

semidirect

5. C₄₇×#384

C₂

semidirect

12. C₄²×D₄₇

C₄

semidirect

25. C₄²×C₄₇

C₂×C₄

semidirect

28. C₄×Dic₄₇

C₂×C₄

semidirect

42. C₄×D₄₇

C₄⋊C₄

semidirect

50. C₄×C₄₇

C₂×C₄⋊C₄

semidirect

52. Dic₄₇

C₂×C₄⋊C₄

semidirect

57. D₄₇

#384

direct (N × H)

62. #384

D₄₇

direct (N × H)

63. C₄₇

C₂×#384

semidirect

86. C₄²

C₄×D₄₇

semidirect

110. C₄

C₄⋊C₄×D₄₇

semidirect

Subgroups — #384×D₄₇ #20245787

Conjugacy classes of subgroups

Complements

Subgroups — #384×D47 #20245787

Conjugacy classes of subgroups

Complements

Subgroups — #384×D₄₇ #20245787