Group #20295408 — subgroups

Subgroups — #20295408

Order 6976.

130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13182019	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13182017	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13182016	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13182014	C₂	1	1	yes	maximal, characteristic
5	#16812687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11724784	C₂	1	1	yes	maximal, characteristic, complemented
7	#124×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
9	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
10	#13182019	—	2	2	no	—
11	#13182017	—	2	2	no	—
12	#13182016	—	2	2	no	—
13	#13182014	—	2	2	no	—
14	C₂×#11724784	C₂²	1	1	yes	characteristic
15	C₂×#11724784	C₂²	1	1	yes	characteristic
16	#13182006	—	2	2	no	—
17	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
20	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₉	—	2	1	no	—
22	C₂²×D₁₀₉	—	2	1	no	—
23	Q₈×C₁₀₉	—	2	1	no	—
24	Q₈×C₁₀₉	—	2	1	no	—
25	D₄×C₁₀₉	—	2	1	no	—
26	D₄×C₁₀₉	—	2	1	no	—
27	C₂×C₄×C₁₀₉	—	2	1	no	—
28	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
29	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₁₀₉	—	2	1	no	—
31	D₄₃₆	—	2	1	no	—
32	D₄₃₆	—	2	1	no	—
33	Dic₂₁₈	—	2	1	no	—
34	Dic₂₁₈	—	2	1	no	—
35	#11724784	D₄	1	2	yes	—
36	#11724784	D₄	1	2	yes	—
37	C₂²×C₁₀₉	—	4	1	no	—
38	C₂²×C₁₀₉	—	4	2	no	—
39	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
40	C₂×D₁₀₉	—	4	1	no	—
41	C₂×D₁₀₉	—	4	2	no	—
42	C₄×C₁₀₉	—	2	2	no	—
43	C₄×C₁₀₉	—	4	1	no	—
44	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
45	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
46	Dic₁₀₉	—	4	1	no	—
47	C₂×C₁₀₉	—	8	1	no	—
48	C₂×C₁₀₉	#127	1	1	yes	characteristic
49	C₂×C₁₀₉	#135	1	2	yes	—
50	D₁₀₉	—	8	1	no	—
51	C₁₀₉	#495	1	1	yes	characteristic, complemented, Sylow
52	#495	—	109	1	no	maximal, Sylow
53	C₂×Q₁₆	—	109	1	no	—
54	C₂×SD₁₆	—	109	1	no	—
55	C₂×SD₁₆	—	109	1	no	—
56	C₂×D₈	—	109	1	no	—
57	#124	—	109	1	no	—
58	#124	D₁₀₉	1	1	yes	characteristic, complemented
59	C₄×C₈	—	109	1	no	—
60	C₂×Q₈	—	109	1	no	—
61	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
62	C₂×D₄	—	109	1	no	—
63	C₂×D₄	C₂×D₁₀₉	1	1	yes	characteristic
64	Q₁₆	—	218	2	no	—
65	SD₁₆	—	218	2	no	—
66	SD₁₆	—	218	2	no	—
67	D₈	—	218	2	no	—
68	C₂×C₈	—	109	1	no	—
69	C₂×C₈	—	109	1	no	—
70	C₂²⋊C₄	—	2	2	no	—
71	C₂²⋊C₄	—	218	2	no	—
72	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
73	C₂³	—	2	1	no	—
74	C₂³	—	218	1	no	—
75	Q₈	—	2	1	no	—
76	Q₈	—	2	1	no	—
77	Q₈	—	218	1	no	—
78	Q₈	—	218	1	no	—
79	D₄	—	2	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	218	1	no	—
82	D₄	—	218	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	218	1	no	—
85	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
86	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
87	C₈	—	109	2	no	—
88	C₈	—	109	2	no	—
89	C₂²	—	4	1	no	—
90	C₂²	—	4	2	no	—
91	C₂²	—	436	1	no	—
92	C₂²	—	436	2	no	—
93	C₂²	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	4	1	no	—
96	C₄	—	436	1	no	—
97	C₄	D₄×D₁₀₉	1	1	yes	characteristic
98	C₄	D₄×D₁₀₉	1	1	yes	characteristic
99	C₂	—	8	1	no	—
100	C₂	—	872	1	no	—
101	C₂	#16812695	1	1	yes	characteristic
102	C₂	#16812719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13182019

C₂

yes

maximal, characteristic, complemented

C₂×#13182017

C₂

yes

maximal, characteristic, complemented

C₂×#13182016

C₂

yes

maximal, characteristic, complemented

C₂×#13182014

C₂

yes

maximal, characteristic

#16812687

C₂

yes

maximal, characteristic, complemented

C₄×#11724784

C₂

yes

maximal, characteristic, complemented

#124×C₁₀₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₁₈

C₂²

yes

characteristic

C₂×D₄₃₆

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#11724784

C₂²

yes

characteristic

#13182006

—

C₂×Q₈×C₁₀₉

C₂²

yes

characteristic

C₂×D₄×C₁₀₉

C₂²

yes

characteristic

C₂²⋊C₄×C₁₀₉

—

C₄²×C₁₀₉

C₂²

yes

characteristic

C₂³×C₁₀₉

—

C₂²×D₁₀₉

—

Q₈×C₁₀₉

—

Q₈×C₁₀₉

—

D₄×C₁₀₉

—

D₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

D₄

yes

—

C₂×C₄×C₁₀₉

C₂³

yes

characteristic

C₂×Dic₁₀₉

—

D₄₃₆

—

D₄₃₆

—

Dic₂₁₈

—

Dic₂₁₈

—

#11724784

D₄

yes

—

#11724784

D₄

yes

—

C₂²×C₁₀₉

—

C₂²×C₁₀₉

—

C₂²×C₁₀₉

C₂×D₄

yes

characteristic

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₄×C₁₀₉

C₂×D₄

yes

characteristic

Dic₁₀₉

—

C₂×C₁₀₉

—

C₂×C₁₀₉

#127

yes

characteristic

C₂×C₁₀₉

#135

yes

—

D₁₀₉

—

C₁₀₉

#495

yes

characteristic, complemented, Sylow

#495

—

109

maximal, Sylow

C₂×Q₁₆

—

109

—

C₂×SD₁₆

—

109

—

C₂×SD₁₆

—

109

—

C₂×D₈

—

109

—

#124

—

109

—

#124

D₁₀₉

yes

characteristic, complemented

C₄×C₈

—

109

—

C₂×Q₈

—

109

—

C₂×Q₈

C₂×D₁₀₉

yes

characteristic

C₂×D₄

—

109

—

C₂×D₄

C₂×D₁₀₉

yes

characteristic

Q₁₆

—

218

—

SD₁₆

—

218

—

SD₁₆

—

218

—

D₈

—

218

—

C₂×C₈

—

109

—

C₂×C₈

—

109

—

C₂²⋊C₄

—

C₂²⋊C₄

—

218

—

C₄²

C₂×D₁₀₉

yes

characteristic

C₂³

—

C₂³

—

218

—

Q₈

—

Q₈

—

Q₈

—

218

—

Q₈

—

218

—

D₄

—

D₄

—

D₄

—

218

—

D₄

—

218

—

C₂×C₄

—

C₂×C₄

—

218

—

C₂×C₄

C₂²⋊D₁₀₉

yes

—

C₂×C₄

C₂²×D₁₀₉

yes

characteristic

C₈

—

109

—

C₈

—

109

—

C₂²

—

C₂²

—

C₂²

—

436

—

C₂²

—

436

—

C₂²

C₂×C₂²⋊D₁₀₉

yes

characteristic

C₄

—

C₄

—

C₄

—

436

—

C₄

D₄×D₁₀₉

yes

characteristic

C₄

D₄×D₁₀₉

yes

characteristic

C₂

—

100

C₂

—

872

—

101

C₂

#16812695

yes

characteristic

102

C₂

#16812719

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#124×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	#124	D₁₀₉
hypocenter	C₁₀₉	#495
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

subgroup

G/H

center

C₂²

C₂×C₂²⋊D₁₀₉

commutator

C₂×C₄×C₁₀₉

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₉

Fitting

#124×C₁₀₉

C₂

socle

C₂²×C₁₀₉

C₂×D₄

D₁₀₉

C₁₀₉

G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #124

N	H ≅ G/N	type
1. C₂×#13182019	C₂	semidirect
2. C₂×#13182017	C₂	semidirect
3. C₂×#13182016	C₂	semidirect
5. #16812687	C₂	semidirect
6. C₄×#11724784	C₂	semidirect
7. #124×C₁₀₉	C₂	semidirect
51. C₁₀₉	#495	semidirect
58. #124	D₁₀₉	semidirect

H ≅ G/N

type

1. C₂×#13182019

C₂

semidirect

2. C₂×#13182017

C₂

semidirect

3. C₂×#13182016

C₂

semidirect

5. #16812687

C₂

semidirect

6. C₄×#11724784

C₂

semidirect

7. #124×C₁₀₉

C₂

semidirect

51. C₁₀₉

#495

semidirect

58. #124

D₁₀₉

semidirect

Subgroups — #20295408

Conjugacy classes of subgroups

Complements