Group #19151980 — subgroups

Subgroups — #19151980

Order 5696.

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×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13083559	C₂	1	1	yes	maximal, characteristic
5	#15668000	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
7	#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
9	C₂×D₃₅₆	C₂²	1	1	yes	characteristic
10	#13083564	—	2	2	no	—
11	#13083562	—	2	2	no	—
12	#13083561	—	2	2	no	—
13	#13083559	—	2	2	no	—
14	C₂×#10623494	C₂²	1	1	yes	characteristic
15	C₂×#10623494	C₂²	1	1	yes	characteristic
16	#13083551	—	2	2	no	—
17	C₂×Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²⋊C₄×C₈₉	—	2	2	no	—
20	C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈₉	—	2	1	no	—
22	C₂²×D₈₉	—	2	1	no	—
23	Q₈×C₈₉	—	2	1	no	—
24	Q₈×C₈₉	—	2	1	no	—
25	D₄×C₈₉	—	2	1	no	—
26	D₄×C₈₉	—	2	1	no	—
27	C₂×C₄×C₈₉	—	2	1	no	—
28	C₂×C₄×C₈₉	D₄	1	2	yes	—
29	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₈₉	—	2	1	no	—
31	D₃₅₆	—	2	1	no	—
32	D₃₅₆	—	2	1	no	—
33	Dic₁₇₈	—	2	1	no	—
34	Dic₁₇₈	—	2	1	no	—
35	#10623494	D₄	1	2	yes	—
36	#10623494	D₄	1	2	yes	—
37	C₂²×C₈₉	—	4	1	no	—
38	C₂²×C₈₉	—	4	2	no	—
39	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
40	C₂×D₈₉	—	4	1	no	—
41	C₂×D₈₉	—	4	2	no	—
42	C₄×C₈₉	—	2	2	no	—
43	C₄×C₈₉	—	4	1	no	—
44	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
45	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
46	Dic₈₉	—	4	1	no	—
47	C₂×C₈₉	—	8	1	no	—
48	C₂×C₈₉	#127	1	1	yes	characteristic
49	C₂×C₈₉	#135	1	2	yes	—
50	D₈₉	—	8	1	no	—
51	C₈₉	#495	1	1	yes	characteristic, complemented, Sylow
52	#495	—	89	1	no	maximal, Sylow
53	C₂×Q₁₆	—	89	1	no	—
54	C₂×SD₁₆	—	89	1	no	—
55	C₂×SD₁₆	—	89	1	no	—
56	C₂×D₈	—	89	1	no	—
57	#124	—	89	1	no	—
58	#124	D₈₉	1	1	yes	characteristic, complemented
59	C₄×C₈	—	89	1	no	—
60	C₂×Q₈	—	89	1	no	—
61	C₂×Q₈	C₂×D₈₉	1	1	yes	characteristic
62	C₂×D₄	—	89	1	no	—
63	C₂×D₄	C₂×D₈₉	1	1	yes	characteristic
64	Q₁₆	—	178	2	no	—
65	SD₁₆	—	178	2	no	—
66	SD₁₆	—	178	2	no	—
67	D₈	—	178	2	no	—
68	C₂×C₈	—	89	1	no	—
69	C₂×C₈	—	89	1	no	—
70	C₂²⋊C₄	—	2	2	no	—
71	C₂²⋊C₄	—	178	2	no	—
72	C₄²	C₂×D₈₉	1	1	yes	characteristic
73	C₂³	—	2	1	no	—
74	C₂³	—	178	1	no	—
75	Q₈	—	2	1	no	—
76	Q₈	—	2	1	no	—
77	Q₈	—	178	1	no	—
78	Q₈	—	178	1	no	—
79	D₄	—	2	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	178	1	no	—
82	D₄	—	178	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	178	1	no	—
85	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
86	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
87	C₈	—	89	2	no	—
88	C₈	—	89	2	no	—
89	C₂²	—	4	1	no	—
90	C₂²	—	4	2	no	—
91	C₂²	—	356	1	no	—
92	C₂²	—	356	2	no	—
93	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	4	1	no	—
96	C₄	—	356	1	no	—
97	C₄	D₄×D₈₉	1	1	yes	characteristic
98	C₄	D₄×D₈₉	1	1	yes	characteristic
99	C₂	—	8	1	no	—
100	C₂	—	712	1	no	—
101	C₂	#15668008	1	1	yes	characteristic
102	C₂	#15668032	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13083564

C₂

yes

maximal, characteristic, complemented

C₂×#13083562

C₂

yes

maximal, characteristic, complemented

C₂×#13083561

C₂

yes

maximal, characteristic, complemented

C₂×#13083559

C₂

yes

maximal, characteristic

#15668000

C₂

yes

maximal, characteristic, complemented

C₄×#10623494

C₂

yes

maximal, characteristic, complemented

#124×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₈

C₂²

yes

characteristic

C₂×D₃₅₆

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#10623494

C₂²

yes

characteristic

#13083551

—

C₂×Q₈×C₈₉

C₂²

yes

characteristic

C₂×D₄×C₈₉

C₂²

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂²

yes

characteristic

C₂³×C₈₉

—

C₂²×D₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₄

yes

—

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

—

Dic₁₇₈

—

Dic₁₇₈

—

#10623494

D₄

yes

—

#10623494

D₄

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

C₂×D₄

yes

characteristic

C₄×C₈₉

C₂×D₄

yes

characteristic

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#127

yes

characteristic

C₂×C₈₉

#135

yes

—

D₈₉

—

C₈₉

#495

yes

characteristic, complemented, Sylow

#495

—

maximal, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

#124

D₈₉

yes

characteristic, complemented

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

C₂×D₈₉

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂×D₈₉

yes

characteristic

Q₁₆

—

178

—

SD₁₆

—

178

—

SD₁₆

—

178

—

D₈

—

178

—

C₂×C₈

—

C₂×C₈

—

C₂²⋊C₄

—

C₂²⋊C₄

—

178

—

C₄²

C₂×D₈₉

yes

characteristic

C₂³

—

C₂³

—

178

—

Q₈

—

Q₈

—

Q₈

—

178

—

Q₈

—

178

—

D₄

—

D₄

—

D₄

—

178

—

D₄

—

178

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

C₂²⋊D₈₉

yes

—

C₂×C₄

C₂²×D₈₉

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

C₂×C₂²⋊D₈₉

yes

characteristic

C₄

—

C₄

—

C₄

—

356

—

C₄

D₄×D₈₉

yes

characteristic

C₄

D₄×D₈₉

yes

characteristic

C₂

—

100

C₂

—

712

—

101

C₂

#15668008

yes

characteristic

102

C₂

#15668032

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#124×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#124	D₈₉
hypocenter	C₈₉	#495
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

subgroup

G/H

center

C₂²

C₂×C₂²⋊D₈₉

commutator

C₂×C₄×C₈₉

C₂³

Frattini

C₂×C₄

C₂²×D₈₉

Fitting

#124×C₈₉

C₂

socle

C₂²×C₈₉

C₂×D₄

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #124

N	H ≅ G/N	type
1. C₂×#13083564	C₂	semidirect
2. C₂×#13083562	C₂	semidirect
3. C₂×#13083561	C₂	semidirect
5. #15668000	C₂	semidirect
6. C₄×#10623494	C₂	semidirect
7. #124×C₈₉	C₂	semidirect
51. C₈₉	#495	semidirect
58. #124	D₈₉	semidirect

H ≅ G/N

type

1. C₂×#13083564

C₂

semidirect

2. C₂×#13083562

C₂

semidirect

3. C₂×#13083561

C₂

semidirect

5. #15668000

C₂

semidirect

6. C₄×#10623494

C₂

semidirect

7. #124×C₈₉

C₂

semidirect

51. C₈₉

#495

semidirect

58. #124

D₈₉

semidirect

Subgroups — #19151980

Conjugacy classes of subgroups

Complements