Group #20246597 — subgroups

Subgroups — C₂×#15689042 #20246597

Order 6016.

908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 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	C₂²×Dic₄₇⋊C₄	C₂	1	3	yes	maximal
2	#15689042	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₇⋊#95	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
6	C₂³×Dic₄₇	C₂²	1	3	yes	—
7	C₂×Dic₄₇⋊C₄	—	2	12	no	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	12	yes	—
9	C₄₇⋊#95	C₂²	1	12	yes	—
10	C₂²×Q₈×C₄₇	—	2	12	no	—
11	C₂²×Q₈×C₄₇	C₂²	1	4	yes	—
12	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
13	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
14	C₂×Q₈×C₄₇	—	2	32	no	—
15	C₂×Q₈×C₄₇	—	2	24	no	—
16	C₂²×C₄×C₄₇	—	2	12	no	—
17	C₂²×C₄×C₄₇	D₄	1	12	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	6	yes	—
19	C₂²×Dic₄₇	—	2	6	no	—
20	C₂²×Dic₄₇	—	2	6	no	—
21	C₂²×Dic₄₇	—	2	6	no	—
22	C₂²×Dic₄₇	Q₈	1	12	yes	complemented
23	C₂²×Dic₄₇	C₂³	1	2	yes	—
24	C₂²×Dic₄₇	C₂³	1	6	yes	—
25	Dic₄₇⋊C₄	—	2	24	no	—
26	C₂³×C₄₇	C₂×D₄	1	6	yes	—
27	C₂³×C₄₇	C₂×Q₈	1	6	yes	—
28	C₂³×C₄₇	#41	1	2	yes	—
29	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
30	Q₈×C₄₇	—	2	32	no	—
31	C₂×C₄×C₄₇	—	2	24	no	—
32	C₂×C₄×C₄₇	—	2	12	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	12	yes	—
34	C₂×Dic₄₇	—	2	24	no	—
35	C₂×Dic₄₇	—	2	6	no	—
36	C₂×Dic₄₇	—	2	6	no	—
37	C₂×Dic₄₇	—	2	6	no	—
38	C₂×Dic₄₇	—	4	4	no	—
39	C₂×Dic₄₇	C₂×Q₈	1	12	yes	complemented
40	C₂²×C₄₇	#120	1	4	yes	—
41	C₂²×C₄₇	C₂²⋊Q₈	1	12	yes	—
42	C₂²×C₄₇	C₄⋊Q₈	1	12	yes	—
43	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
44	C₂²×C₄₇	C₂²×Q₈	1	3	yes	—
45	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
46	C₄×C₄₇	—	2	12	no	—
47	Dic₄₇	—	2	12	no	—
48	Dic₄₇	—	4	2	no	—
49	C₂×#395	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	#395	1	8	yes	complemented
51	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
52	C₂×C₄₇	C₂×C₂²⋊Q₈	1	3	yes	—
53	C₂×C₄₇	C₂×C₄⋊Q₈	1	3	yes	—
54	C₂³×Q₈	D₄₇	1	1	yes	characteristic
55	C₂²×C₄⋊C₄	—	47	3	no	—
56	#395	—	47	8	no	—
57	C₂×#95	—	47	3	no	—
58	C₄₇	C₂×#395	1	1	yes	characteristic, complemented, Sylow
59	C₂²×Q₈	—	2	12	no	—
60	C₂²×Q₈	C₂×D₄₇	1	4	yes	—
61	C₂³×C₄	—	47	3	no	—
62	C₂³×C₄	—	47	1	no	—
63	C₂³×C₄	C₂×D₄₇	1	3	yes	—
64	C₂×C₄⋊C₄	—	47	12	no	—
65	C₂×C₄⋊C₄	—	94	12	no	—
66	#95	—	47	12	no	—
67	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
68	C₂×Q₈	—	2	32	no	—
69	C₂×Q₈	—	2	24	no	—
70	C₂²×C₄	—	2	12	no	—
71	C₂²×C₄	—	47	12	no	—
72	C₂²×C₄	—	47	6	no	—
73	C₂²×C₄	—	47	2	no	—
74	C₂²×C₄	—	94	6	no	—
75	C₂²×C₄	—	94	6	no	—
76	C₂²×C₄	—	94	6	no	—
77	C₂²×C₄	C₂²⋊D₄₇	1	12	yes	—
78	C₂²×C₄	C₂²×D₄₇	1	6	yes	—
79	C₄⋊C₄	—	94	24	no	—
80	C₂³	Q₈×D₄₇	1	6	yes	—
81	C₂³	#10625354	1	2	yes	—
82	C₂³	C₂×C₂²⋊D₄₇	1	6	yes	—
83	C₂³	C₂³×D₄₇	1	1	yes	characteristic
84	Q₈	—	2	32	no	—
85	C₂×C₄	—	2	24	no	—
86	C₂×C₄	—	2	12	no	—
87	C₂×C₄	—	47	12	no	—
88	C₂×C₄	—	94	24	no	—
89	C₂×C₄	—	94	6	no	—
90	C₂×C₄	—	94	6	no	—
91	C₂×C₄	—	94	6	no	—
92	C₂×C₄	—	188	4	no	—
93	C₂×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
94	C₂²	#13093993	1	4	yes	—
95	C₂²	#13094000	1	12	yes	—
96	C₂²	#13094022	1	12	yes	—
97	C₂²	C₂²×C₂²⋊D₄₇	1	3	yes	—
98	C₂²	C₂×Q₈×D₄₇	1	3	yes	—
99	C₂²	C₂×#10625354	1	1	yes	characteristic
100	C₄	—	2	12	no	—
101	C₄	—	94	12	no	—
102	C₄	—	188	2	no	—
103	C₂	#15689042	1	8	yes	direct product factor
104	C₂	C₂×#13093993	1	1	yes	characteristic
105	C₂	C₂×#13094000	1	3	yes	—
106	C₂	C₂×#13094022	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₄₇⋊C₄

C₂

yes

maximal

#15689042

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂³×Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

Q₈

yes

complemented

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×Q₈

yes

complemented

C₂²×C₄₇

#120

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

C₄⋊Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

—

C₂³×Q₈

D₄₇

yes

characteristic

C₂²×C₄⋊C₄

—

#395

—

C₂×#95

—

C₄₇

C₂×#395

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₇

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

#95

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₂³

Q₈×D₄₇

yes

—

C₂³

#10625354

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

C₂²

#13093993

yes

—

C₂²

#13094000

yes

—

C₂²

#13094022

yes

—

C₂²

C₂²×C₂²⋊D₄₇

yes

—

C₂²

C₂×Q₈×D₄₇

yes

—

C₂²

C₂×#10625354

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

188

—

103

C₂

#15689042

yes

direct product factor

104

C₂

C₂×#13093993

yes

characteristic

105

C₂

C₂×#13094000

yes

—

106

C₂

C₂×#13094022

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂³×Q₈×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂³×Q₈	D₄₇
hypocenter	C₄₇	C₂×#395
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂³×Q₈×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂³×Q₈

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #15689042	C₂	direct (N × H)
22. C₂²×Dic₄₇	Q₈	semidirect
39. C₂×Dic₄₇	C₂×Q₈	semidirect
50. C₂×C₄₇	#395	semidirect
58. C₄₇	C₂×#395	semidirect
103. C₂	#15689042	direct (N × H)

H ≅ G/N

type

2. #15689042

C₂

direct (N × H)

22. C₂²×Dic₄₇

Q₈

semidirect

39. C₂×Dic₄₇

C₂×Q₈

semidirect

50. C₂×C₄₇

#395

semidirect

58. C₄₇

C₂×#395

semidirect

103. C₂

#15689042

direct (N × H)

Subgroups — C₂×#15689042 #20246597

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689042 #20246597

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689042 #20246597