Group #22590188 — subgroups

Subgroups — C₄×D₁₁₃₆ #22590188

Order 9088.

174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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×D₁₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₄×D₅₆₈	C₂	1	2	yes	maximal, complemented
3	#17985825	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985801	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅₆₈	C₂²	1	2	yes	—
7	C₄×D₂₈₄	—	2	2	no	—
8	D₁₁₃₆	C₄	1	4	yes	direct product factor
9	#14556062	C₂²	1	2	yes	—
10	#14556050	—	2	2	no	—
11	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×D₂₈₄	—	2	2	no	—
15	C₂×C₄×D₇₁	—	4	2	no	—
16	D₅₆₈	—	2	2	no	—
17	D₅₆₈	C₂×C₄	1	4	yes	complemented
18	C₄⋊Dic₇₁	—	2	2	no	—
19	(C₂×D₇₁)⋊C₄	—	4	2	no	—
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
22	C₄²×C₇₁	D₄	1	1	yes	characteristic
23	C₁₆×C₇₁	—	2	1	no	—
24	C₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
25	C₂²×D₇₁	—	4	2	no	—
26	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₁	—	4	2	no	—
30	D₂₈₄	—	2	4	no	—
31	D₂₈₄	—	4	2	no	—
32	C₄×D₇₁	—	8	4	no	—
33	C₈×C₇₁	—	2	1	no	—
34	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₇₁	#41	1	1	yes	characteristic
36	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
37	C₂×D₇₁	—	4	4	no	—
38	C₂×D₇₁	—	8	2	no	—
39	C₂×D₇₁	—	8	2	no	—
40	C₄×C₇₁	—	2	1	no	—
41	C₄×C₇₁	D₁₆	1	2	yes	complemented
42	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₇₁	#135	1	1	yes	characteristic
44	Dic₇₁	—	8	2	no	—
45	C₂×C₇₁	C₄×D₈	1	1	yes	characteristic
46	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
47	C₂×C₇₁	#508	1	1	yes	characteristic
48	D₇₁	—	8	4	no	—
49	C₄×D₁₆	—	71	1	no	maximal, Sylow
50	C₇₁	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₁₆	—	71	1	no	—
52	C₄×D₈	—	71	2	no	—
53	#366	—	71	1	no	—
54	#357	—	71	2	no	—
55	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
56	C₂×D₈	—	71	2	no	—
57	C₄×D₄	—	142	2	no	—
58	D₁₆	—	71	4	no	—
59	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
61	#107	—	71	2	no	—
62	#102	—	142	2	no	—
63	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
64	C₂×D₄	—	142	2	no	—
65	C₂²×C₄	—	284	2	no	—
66	D₈	—	71	4	no	—
67	D₈	—	142	2	no	—
68	C₂×C₈	D₂₈₄	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
70	C₄⋊C₄	—	142	2	no	—
71	C₂²⋊C₄	—	284	2	no	—
72	C₄²	D₂₈₄	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	C₄×D₇₁	1	2	yes	complemented
75	C₂³	—	284	2	no	—
76	D₄	—	284	2	no	—
77	D₄	—	142	4	no	—
78	C₂×C₄	—	284	2	no	—
79	C₂×C₄	—	568	4	no	—
80	C₂×C₄	D₅₆₈	1	1	yes	characteristic
81	C₂×C₄	D₅₆₈	1	1	yes	characteristic
82	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
85	C₈	#11765865	1	1	yes	characteristic
86	C₂²	—	284	4	no	—
87	C₂²	—	568	2	no	—
88	C₂²	—	568	2	no	—
89	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	568	2	no	—
92	C₄	D₁₁₃₆	1	2	yes	direct product factor
93	C₄	C₄×D₂₈₄	1	1	yes	characteristic
94	C₄	#14556150	1	1	yes	characteristic
95	C₂	—	568	4	no	—
96	C₂	C₄×D₅₆₈	1	1	yes	characteristic
97	C₂	C₂×D₁₁₃₆	1	1	yes	characteristic
98	C₂	#17986431	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₁₃₆

C₂

yes

maximal, characteristic

C₄×D₅₆₈

C₂

yes

maximal, complemented

#17985825

C₂

yes

maximal, characteristic, complemented

#17985801

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×D₅₆₈

C₂²

yes

—

C₄×D₂₈₄

—

D₁₁₃₆

C₄

yes

direct product factor

#14556062

C₂²

yes

—

#14556050

—

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×D₂₈₄

—

C₂×C₄×D₇₁

—

D₅₆₈

—

D₅₆₈

C₂×C₄

yes

complemented

C₄⋊Dic₇₁

—

(C₂×D₇₁)⋊C₄

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

D₄

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

C₂×C₄

yes

complemented

C₂²×D₇₁

—

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

C₄×D₇₁

—

C₈×C₇₁

—

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

D₁₆

yes

complemented

C₄×C₇₁

C₄×D₄

yes

characteristic

C₄×C₇₁

#135

yes

characteristic

Dic₇₁

—

C₂×C₇₁

C₄×D₈

yes

characteristic

C₂×C₇₁

C₂×D₁₆

yes

characteristic

C₂×C₇₁

#508

yes

characteristic

D₇₁

—

C₄×D₁₆

—

maximal, Sylow

C₇₁

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂×D₈

—

C₄×D₄

—

142

—

D₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#107

—

#102

—

142

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×D₄

—

142

—

C₂²×C₄

—

284

—

D₈

—

D₈

—

142

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

284

—

C₄²

D₂₈₄

yes

characteristic

C₁₆

—

C₁₆

C₄×D₇₁

yes

complemented

C₂³

—

284

—

D₄

—

284

—

D₄

—

142

—

C₂×C₄

—

284

—

C₂×C₄

—

568

—

C₂×C₄

D₅₆₈

yes

characteristic

C₂×C₄

D₅₆₈

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

—

C₈

C₂×C₄×D₇₁

yes

characteristic

C₈

#11765865

yes

characteristic

C₂²

—

284

—

C₂²

—

568

—

C₂²

—

568

—

C₂²

C₂×D₅₆₈

yes

characteristic

C₄

—

C₄

—

568

—

C₄

D₁₁₃₆

yes

direct product factor

C₄

C₄×D₂₈₄

yes

characteristic

C₄

#14556150

yes

characteristic

C₂

—

568

—

C₂

C₄×D₅₆₈

yes

characteristic

C₂

C₂×D₁₁₃₆

yes

characteristic

C₂

#17986431

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₅₆₈
commutator	C₈×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	C₄×D₁₆
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₄

D₅₆₈

commutator

C₈×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

hypercenter

C₄×C₁₆

D₇₁

hypocenter

C₇₁

C₄×D₁₆

LCS

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄×D₅₆₈	C₂	semidirect
3. #17985825	C₂	semidirect
4. #17985801	C₂	semidirect
5. C₄×C₁₆×C₇₁	C₂	semidirect
8. D₁₁₃₆	C₄	direct (N × H)
17. D₅₆₈	C₂×C₄	semidirect
24. C₁₆×C₇₁	C₂×C₄	semidirect
41. C₄×C₇₁	D₁₆	semidirect
50. C₇₁	C₄×D₁₆	semidirect
55. C₄×C₁₆	D₇₁	semidirect
74. C₁₆	C₄×D₇₁	semidirect
92. C₄	D₁₁₃₆	direct (N × H)

H ≅ G/N

type

2. C₄×D₅₆₈

C₂

semidirect

3. #17985825

C₂

semidirect

4. #17985801

C₂

semidirect

5. C₄×C₁₆×C₇₁

C₂

semidirect

8. D₁₁₃₆

C₄

direct (N × H)

17. D₅₆₈

C₂×C₄

semidirect

24. C₁₆×C₇₁

C₂×C₄

semidirect

41. C₄×C₇₁

D₁₆

semidirect

50. C₇₁

C₄×D₁₆

semidirect

55. C₄×C₁₆

D₇₁

semidirect

74. C₁₆

C₄×D₇₁

semidirect

92. C₄

D₁₁₃₆

direct (N × H)

Subgroups — C₄×D₁₁₃₆ #22590188

Conjugacy classes of subgroups

Complements

Subgroups — C4×D1136 #22590188

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₁₁₃₆ #22590188