Group #22598844 — subgroups

Subgroups — C₂×#17986401 #22598844

Order 9088.

360 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14556120	C₂	1	2	yes	maximal
2	#17986401	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14556062	C₂	1	2	yes	maximal
4	C₂×#14556060	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
6	#14556120	—	2	4	no	—
7	#14556120	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₇₁	C₂²	1	4	yes	—
9	C₂×Dic₇₁⋊C₄	—	2	4	no	—
10	#14556062	C₂²	1	8	yes	—
11	#14556060	C₂²	1	8	yes	—
12	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₁	C₂²	1	4	yes	—
16	C₂²×Dic₇₁	—	2	4	no	—
17	C₄⋊Dic₇₁	—	2	4	no	—
18	C₄⋊Dic₇₁	C₂³	1	8	yes	—
19	Dic₇₁⋊C₄	—	2	16	no	—
20	C₂²×C₄×C₇₁	D₄	1	2	yes	—
21	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₇₁	Q₈	1	4	yes	—
23	C₂×C₈×C₇₁	Q₈	1	4	yes	—
24	C₂×C₈×C₇₁	C₂³	1	2	yes	—
25	C₂×C₈×C₇₁	C₂³	1	2	yes	—
26	C₄²×C₇₁	D₄	1	2	yes	—
27	C₄²×C₇₁	C₂³	1	2	yes	—
28	C₂³×C₇₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	2	4	no	—
30	C₂×C₄×C₇₁	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₇₁	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
35	C₂×Dic₇₁	—	2	8	no	—
36	C₂×Dic₇₁	—	4	8	no	—
37	C₈×C₇₁	C₂×Q₈	1	4	yes	—
38	C₈×C₇₁	C₂×Q₈	1	4	yes	—
39	C₂²×C₇₁	C₄⋊Q₈	1	2	yes	—
40	C₂²×C₇₁	#135	1	4	yes	—
41	C₂²×C₇₁	C₂²×D₄	1	1	yes	characteristic
42	C₄×C₇₁	—	2	4	no	—
43	C₄×C₇₁	C₄⋊Q₈	1	2	yes	—
44	C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
45	C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
46	Dic₇₁	—	4	8	no	—
47	C₂×C₇₁	#499	1	4	yes	complemented
48	C₂×C₇₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
49	C₂×C₇₁	C₂×#135	1	2	yes	—
50	C₂×#499	—	71	1	no	maximal, Sylow
51	C₇₁	C₂×#499	1	1	yes	characteristic, complemented, Sylow
52	C₂×#125	—	71	2	no	—
53	#499	—	71	8	no	—
54	C₂×#107	—	71	2	no	—
55	C₂×#106	—	71	2	no	—
56	C₂×C₄×C₈	D₇₁	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
59	#125	—	71	8	no	—
60	#125	—	142	4	no	—
61	C₂×C₄⋊C₄	—	71	4	no	—
62	C₂×C₄⋊C₄	—	142	4	no	—
63	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic
64	#107	—	71	8	no	—
65	#106	—	71	8	no	—
66	C₄×C₈	C₂×D₇₁	1	4	yes	—
67	C₂²×C₄	—	142	4	no	—
68	C₂²×C₄	D₂₈₄	1	2	yes	—
69	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
70	C₂×C₈	Dic₁₄₂	1	4	yes	—
71	C₂×C₈	Dic₁₄₂	1	4	yes	—
72	C₂×C₈	C₂²×D₇₁	1	2	yes	—
73	C₂×C₈	C₂²×D₇₁	1	2	yes	—
74	C₄⋊C₄	—	71	8	no	—
75	C₄⋊C₄	—	142	16	no	—
76	C₄⋊C₄	—	142	4	no	—
77	C₄²	D₂₈₄	1	2	yes	—
78	C₄²	C₂²×D₇₁	1	2	yes	—
79	C₂³	C₂×D₂₈₄	1	1	yes	characteristic
80	C₂×C₄	—	2	4	no	—
81	C₂×C₄	—	284	8	no	—
82	C₂×C₄	—	142	8	no	—
83	C₂×C₄	C₂×D₂₈₄	1	4	yes	—
84	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
85	C₂×C₄	C₂×Dic₁₄₂	1	2	yes	—
86	C₂×C₄	C₂×Dic₁₄₂	1	2	yes	—
87	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
88	C₈	C₂×Dic₁₄₂	1	4	yes	—
89	C₈	C₂×Dic₁₄₂	1	4	yes	—
90	C₂²	#14556128	1	2	yes	—
91	C₂²	#14556150	1	4	yes	—
92	C₂²	C₂²×D₂₈₄	1	1	yes	characteristic
93	C₄	—	2	4	no	—
94	C₄	—	284	8	no	—
95	C₄	#14556128	1	2	yes	—
96	C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
97	C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
98	C₂	#17986401	1	4	yes	direct product factor
99	C₂	C₂×#14556128	1	1	yes	characteristic
100	C₂	C₂×#14556150	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556120

C₂

yes

maximal

#17986401

C₂

yes

maximal, direct product factor

C₂×#14556062

C₂

yes

maximal

C₂×#14556060

C₂

yes

maximal

C₂×C₄×C₈×C₇₁

C₂

yes

maximal, characteristic

#14556120

—

#14556120

C₂²

yes

—

C₂×C₄⋊Dic₇₁

C₂²

yes

—

C₂×Dic₇₁⋊C₄

—

#14556062

C₂²

yes

—

#14556060

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄²×C₇₁

C₂²

yes

characteristic

C₄×C₈×C₇₁

C₂²

yes

—

C₂²×Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₂³

yes

—

Dic₇₁⋊C₄

—

C₂²×C₄×C₇₁

D₄

yes

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

—

C₂×C₈×C₇₁

Q₈

yes

—

C₂×C₈×C₇₁

C₂³

yes

—

C₂×C₈×C₇₁

C₂³

yes

—

C₄²×C₇₁

D₄

yes

—

C₄²×C₇₁

C₂³

yes

—

C₂³×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₈

yes

—

C₂×C₄×C₇₁

C₂×Q₈

yes

—

C₂×C₄×C₇₁

C₂⁴

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

C₂×Q₈

yes

—

C₈×C₇₁

C₂×Q₈

yes

—

C₂²×C₇₁

C₄⋊Q₈

yes

—

C₂²×C₇₁

#135

yes

—

C₂²×C₇₁

C₂²×D₄

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

C₄⋊Q₈

yes

—

C₄×C₇₁

C₂²×Q₈

yes

characteristic

C₄×C₇₁

C₂²×Q₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

#499

yes

complemented

C₂×C₇₁

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₁

C₂×#135

yes

—

C₂×#499

—

maximal, Sylow

C₇₁

C₂×#499

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×C₄×C₈

D₇₁

yes

characteristic

C₂²×C₈

C₂×D₇₁

yes

characteristic

C₂²×C₈

C₂×D₇₁

yes

characteristic

#125

—

#125

—

142

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

142

—

C₂×C₄²

C₂×D₇₁

yes

characteristic

#107

—

#106

—

C₄×C₈

C₂×D₇₁

yes

—

C₂²×C₄

—

142

—

C₂²×C₄

D₂₈₄

yes

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

C₂×C₈

Dic₁₄₂

yes

—

C₂×C₈

Dic₁₄₂

yes

—

C₂×C₈

C₂²×D₇₁

yes

—

C₂×C₈

C₂²×D₇₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

142

—

C₄⋊C₄

—

142

—

C₄²

D₂₈₄

yes

—

C₄²

C₂²×D₇₁

yes

—

C₂³

C₂×D₂₈₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

142

—

C₂×C₄

C₂×D₂₈₄

yes

—

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₂×C₄

C₂×Dic₁₄₂

yes

—

C₂×C₄

C₂×Dic₁₄₂

yes

—

C₂×C₄

C₂³×D₇₁

yes

characteristic

C₈

C₂×Dic₁₄₂

yes

—

C₈

C₂×Dic₁₄₂

yes

—

C₂²

#14556128

yes

—

C₂²

#14556150

yes

—

C₂²

C₂²×D₂₈₄

yes

characteristic

C₄

—

C₄

—

284

—

C₄

#14556128

yes

—

C₄

C₂²×Dic₁₄₂

yes

characteristic

C₄

C₂²×Dic₁₄₂

yes

characteristic

C₂

#17986401

yes

direct product factor

C₂

C₂×#14556128

yes

characteristic

100

C₂

C₂×#14556150

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₁
Fitting	C₂×C₄×C₈×C₇₁	C₂
socle	C₂³×C₇₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₇₁
hypocenter	C₇₁	C₂×#499
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₂₈₄

commutator

C₂×C₄×C₇₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₁

Fitting

C₂×C₄×C₈×C₇₁

C₂

socle

C₂³×C₇₁

C₂×D₄

hypercenter

C₂×C₄×C₈

D₇₁

hypocenter

C₇₁

C₂×#499

LCS

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #17986401	C₂	direct (N × H)
47. C₂×C₇₁	#499	semidirect
51. C₇₁	C₂×#499	semidirect
98. C₂	#17986401	direct (N × H)

H ≅ G/N

type

2. #17986401

C₂

direct (N × H)

47. C₂×C₇₁

#499

semidirect

51. C₇₁

C₂×#499

semidirect

98. C₂

#17986401

direct (N × H)

Subgroups — C₂×#17986401 #22598844

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17986401 #22598844

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17986401 #22598844