Group #20251811 — subgroups

Subgroups — C₄×#13094031 #20251811

Order 6016.

572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 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×#13094031	C₂	1	2	yes	maximal
2	#15689079	C₂	1	6	yes	maximal, complemented
3	C₄×#10625329	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×C₄₇⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#13094031	C₄	1	16	yes	direct product factor
7	C₂×#10625329	C₂²	1	6	yes	—
8	C₂²×C₄₇⋊C₈	C₂²	1	6	yes	—
9	#13093935	C₂²	1	6	yes	—
10	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
12	C₄×C₄₇⋊C₈	C₂²	1	6	yes	—
13	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₄₇	C₄	1	2	yes	—
15	C₄×D₄×C₄₇	C₄	1	6	yes	—
16	#117×C₄₇	C₂²	1	3	yes	—
17	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
18	#41×C₄₇	C₂×C₄	1	8	yes	—
19	C₂×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₄₇	C₂×C₄	1	3	yes	—
21	C₂²×C₄×C₄₇	C₂×C₄	1	6	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
23	C₄⋊C₄×C₄₇	C₂×C₄	1	6	yes	—
24	C₂²⋊C₄×C₄₇	C₂×C₄	1	6	yes	—
25	C₄²×C₄₇	C₂×C₄	1	6	yes	—
26	C₄²×C₄₇	C₂³	1	3	yes	—
27	C₄²×C₄₇	C₂³	1	1	yes	characteristic
28	#10625329	C₂×C₄	1	24	yes	complemented
29	C₂×C₄₇⋊C₈	C₂×C₄	1	24	yes	complemented
30	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
31	C₂×C₄₇⋊C₈	C₂³	1	6	yes	—
32	C₂³×C₄₇	C₂²×C₄	1	3	yes	—
33	Q₈×C₄₇	C₄²	1	4	yes	—
34	D₄×C₄₇	C₄²	1	12	yes	—
35	C₂×C₄×C₄₇	—	2	12	no	—
36	C₂×C₄×C₄₇	C₂²×C₄	1	12	yes	—
37	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
38	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
39	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
41	C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
42	C₄₇⋊C₈	C₂²×C₄	1	12	yes	—
43	C₂²×C₄₇	—	2	6	no	—
44	C₂²×C₄₇	C₂×C₄²	1	6	yes	—
45	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
46	C₄×C₄₇	—	2	6	no	—
47	C₄×C₄₇	C₂×C₄²	1	6	yes	—
48	C₄×C₄₇	#131	1	4	yes	complemented
49	C₄×C₄₇	C₂³×C₄	1	2	yes	—
50	C₄×#131	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	—	2	6	no	—
52	C₂×C₄₇	C₂²×C₄²	1	1	yes	characteristic
53	C₂×C₄₇	C₂×#131	1	2	yes	—
54	C₂×#131	—	47	2	no	—
55	C₄×#41	D₄₇	1	1	yes	characteristic
56	#405	—	47	6	no	—
57	C₄×M₁₆	—	47	3	no	—
58	C₂×C₄×C₈	—	47	3	no	—
59	C₄₇	C₄×#131	1	1	yes	characteristic, complemented, Sylow
60	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
61	#131	—	47	16	no	—
62	C₂×M₁₆	—	47	6	no	—
63	C₂²×C₈	—	47	6	no	—
64	C₄×Q₈	Dic₄₇	1	2	yes	—
65	C₄×D₄	Dic₄₇	1	6	yes	—
66	#117	C₂×D₄₇	1	3	yes	—
67	C₂×C₄²	C₂×D₄₇	1	3	yes	—
68	#97	—	47	6	no	—
69	C₄×C₈	—	47	6	no	—
70	C₄×C₈	—	47	1	no	—
71	C₄×C₈	—	47	3	no	—
72	#41	C₄×D₄₇	1	8	yes	—
73	C₂×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
74	C₂×D₄	C₂×Dic₄₇	1	3	yes	—
75	C₂²×C₄	C₂×Dic₄₇	1	6	yes	—
76	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
77	M₁₆	—	47	24	no	—
78	C₂×C₈	—	47	24	no	—
79	C₂×C₈	—	47	2	no	—
80	C₂×C₈	—	47	6	no	—
81	C₄⋊C₄	C₂×Dic₄₇	1	6	yes	—
82	C₂²⋊C₄	C₂×Dic₄₇	1	6	yes	—
83	C₄²	C₂×Dic₄₇	1	6	yes	—
84	C₄²	C₂²×D₄₇	1	3	yes	—
85	C₄²	C₂²×D₄₇	1	1	yes	characteristic
86	C₂³	C₂²×Dic₄₇	1	3	yes	—
87	Q₈	C₄×Dic₄₇	1	4	yes	—
88	D₄	C₄×Dic₄₇	1	12	yes	—
89	C₂×C₄	—	2	12	no	—
90	C₂×C₄	C₂×C₄×D₄₇	1	12	yes	—
91	C₂×C₄	C₂²×Dic₄₇	1	6	yes	—
92	C₂×C₄	C₂²×Dic₄₇	1	3	yes	—
93	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
94	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
95	C₈	—	47	4	no	—
96	C₈	—	47	12	no	—
97	C₂²	—	2	6	no	—
98	C₂²	C₂×C₄×Dic₄₇	1	6	yes	—
99	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
100	C₄	—	2	6	no	—
101	C₄	C₂×C₄×Dic₄₇	1	6	yes	—
102	C₄	#13094031	1	4	yes	direct product factor
103	C₄	C₂²×C₄×D₄₇	1	2	yes	—
104	C₂	—	2	6	no	—
105	C₂	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
106	C₂	C₂×#13094031	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094031

C₂

yes

maximal

#15689079

C₂

yes

maximal, complemented

C₄×#10625329

C₂

yes

maximal, complemented

C₂×C₄×C₄₇⋊C₈

C₂

yes

maximal, complemented

C₄×#41×C₄₇

C₂

yes

maximal, characteristic

#13094031

C₄

yes

direct product factor

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

—

#13093935

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

—

C₂×#41×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₄

yes

—

C₄×D₄×C₄₇

C₄

yes

—

#117×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

#41×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

C₂×C₄

yes

characteristic

C₂×D₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂²⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625329

C₂×C₄

yes

complemented

C₂×C₄₇⋊C₈

C₂×C₄

yes

complemented

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂²×C₄

yes

—

Q₈×C₄₇

C₄²

yes

—

D₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₄₇⋊C₈

C₂²×C₄

yes

—

C₄₇⋊C₈

C₂²×C₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄²

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

—

C₄×C₄₇

#131

yes

complemented

C₄×C₄₇

C₂³×C₄

yes

—

C₄×#131

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂²×C₄²

yes

characteristic

C₂×C₄₇

C₂×#131

yes

—

C₂×#131

—

C₄×#41

D₄₇

yes

characteristic

#405

—

C₄×M₁₆

—

C₂×C₄×C₈

—

C₄₇

C₄×#131

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₇

yes

characteristic

#131

—

C₂×M₁₆

—

C₂²×C₈

—

C₄×Q₈

Dic₄₇

yes

—

C₄×D₄

Dic₄₇

yes

—

#117

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

#41

C₄×D₄₇

yes

—

C₂×Q₈

C₂×Dic₄₇

yes

characteristic

C₂×D₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₂²⋊C₄

C₂×Dic₄₇

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₄²

C₂²×D₄₇

yes

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

C₂²×Dic₄₇

yes

—

Q₈

C₄×Dic₄₇

yes

—

D₄

C₄×Dic₄₇

yes

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂³×D₄₇

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

C₂×C₄×Dic₄₇

yes

—

C₂²

C₂³×Dic₄₇

yes

characteristic

100

C₄

—

101

C₄

C₂×C₄×Dic₄₇

yes

—

102

C₄

#13094031

yes

direct product factor

103

C₄

C₂²×C₄×D₄₇

yes

—

104

C₂

—

105

C₂

C₂²×C₄×Dic₄₇

yes

characteristic

106

C₂

C₂×#13094031

yes

—

	subgroup	G/H
center	C₄²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×C₄
hypercenter	C₄×#41	D₄₇
hypocenter	C₄₇	C₄×#131
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₄×#41

subgroup

G/H

center

C₄²

C₂²×D₄₇

commutator

C₂×C₄₇

C₂²×C₄²

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄×#41×C₄₇

C₂

socle

C₂²×C₄₇

C₂³×C₄

hypercenter

C₄×#41

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₄² ◁ C₄×#41

N	H ≅ G/N	type
2. #15689079	C₂	semidirect
3. C₄×#10625329	C₂	semidirect
4. C₂×C₄×C₄₇⋊C₈	C₂	semidirect
6. #13094031	C₄	direct (N × H)
28. #10625329	C₂×C₄	semidirect
29. C₂×C₄₇⋊C₈	C₂×C₄	semidirect
48. C₄×C₄₇	#131	semidirect
59. C₄₇	C₄×#131	semidirect
102. C₄	#13094031	direct (N × H)

H ≅ G/N

type

2. #15689079

C₂

semidirect

3. C₄×#10625329

C₂

semidirect

4. C₂×C₄×C₄₇⋊C₈

C₂

semidirect

6. #13094031

C₄

direct (N × H)

28. #10625329

C₂×C₄

semidirect

29. C₂×C₄₇⋊C₈

C₂×C₄

semidirect

48. C₄×C₄₇

#131

semidirect

59. C₄₇

C₄×#131

semidirect

102. C₄

#13094031

direct (N × H)

Subgroups — C₄×#13094031 #20251811

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13094031 #20251811

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13094031 #20251811