Group #19151925 — subgroups

Subgroups — #19151925

Order 5696.

106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 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	#15667987	C₂	1	1	yes	maximal, characteristic
2	#15667970	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667943	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667934	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667932	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667924	C₂	1	1	yes	maximal, characteristic, complemented
7	#107×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₅₆	—	2	1	no	—
9	C₂×D₃₅₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₈₉	C₂²	1	1	yes	characteristic
11	C₂×#10623494	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
13	#13083551	—	2	1	no	—
14	#13083551	—	2	1	no	—
15	C₄×Dic₈₉	—	2	1	no	—
16	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈₉	—	2	1	no	—
20	C₂²×D₈₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₈₉	—	2	1	no	—
22	C₂×C₄×C₈₉	—	2	1	no	—
23	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₈₉	—	2	1	no	—
25	C₂×Dic₈₉	D₄	1	1	yes	characteristic
26	D₃₅₆	—	2	1	no	—
27	D₃₅₆	—	2	1	no	—
28	D₃₅₆	—	4	2	no	—
29	C₄×D₈₉	—	2	1	no	—
30	C₄×D₈₉	—	2	1	no	—
31	C₈×C₈₉	—	2	1	no	—
32	#10623494	—	2	1	no	—
33	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
34	C₂×D₈₉	—	2	1	no	—
35	C₂×D₈₉	—	2	1	no	—
36	C₂×D₈₉	—	2	1	no	—
37	C₂×D₈₉	—	4	1	no	—
38	C₂×D₈₉	—	4	1	no	—
39	C₂×D₈₉	—	4	1	no	—
40	C₄×C₈₉	—	4	1	no	—
41	C₄×C₈₉	—	4	1	no	—
42	C₄×C₈₉	#41	1	1	yes	characteristic
43	C₄×C₈₉	#41	1	1	yes	characteristic
44	Dic₈₉	—	2	1	no	—
45	Dic₈₉	—	4	1	no	—
46	C₂×C₈₉	#123	1	1	yes	characteristic
47	C₂×C₈₉	#135	1	1	yes	characteristic
48	C₂×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
49	D₈₉	—	4	1	no	—
50	D₈₉	—	8	1	no	—
51	C₈₉	#482	1	1	yes	characteristic, complemented, Sylow
52	#482	—	89	1	no	maximal, Sylow
53	#121	—	89	1	no	—
54	#117	—	89	1	no	—
55	#107	D₈₉	1	1	yes	characteristic, complemented
56	#106	—	89	1	no	—
57	#102	—	89	1	no	—
58	#102	—	89	1	no	—
59	C₂²⋊C₈	—	89	1	no	—
60	C₂×D₄	—	89	1	no	—
61	C₂×D₄	—	178	1	no	—
62	C₂²×C₄	—	89	1	no	—
63	C₂×C₈	—	89	1	no	—
64	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
65	C₄⋊C₄	—	89	1	no	—
66	C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
67	C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
68	C₂²⋊C₄	—	178	1	no	—
69	C₂²⋊C₄	—	178	1	no	—
70	C₄²	—	178	1	no	—
71	C₂³	—	89	1	no	—
72	C₂³	—	178	1	no	—
73	D₄	—	356	2	no	—
74	D₄	—	178	1	no	—
75	D₄	—	178	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	89	1	no	—
79	C₂×C₄	—	178	1	no	—
80	C₂×C₄	—	178	1	no	—
81	C₂×C₄	—	178	1	no	—
82	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	178	1	no	—
85	C₂²	—	356	1	no	—
86	C₂²	—	356	1	no	—
87	C₂²	—	356	1	no	—
88	C₂²	—	178	1	no	—
89	C₂²	—	178	1	no	—
90	C₂²	—	178	1	no	—
91	C₂²	D₄×D₈₉	1	1	yes	characteristic
92	C₄	—	4	1	no	—
93	C₄	—	4	1	no	—
94	C₄	—	356	1	no	—
95	C₄	—	178	1	no	—
96	C₄	#13083574	1	1	yes	characteristic
97	C₄	#13083575	1	1	yes	characteristic
98	C₂	—	356	1	no	—
99	C₂	—	712	1	no	—
100	C₂	#15667997	1	1	yes	characteristic
101	C₂	#15668035	1	1	yes	characteristic
102	C₂	#15668036	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15667987

C₂

yes

maximal, characteristic

#15667970

C₂

yes

maximal, characteristic, complemented

#15667943

C₂

yes

maximal, characteristic, complemented

#15667934

C₂

yes

maximal, characteristic, complemented

#15667932

C₂

yes

maximal, characteristic, complemented

#15667924

C₂

yes

maximal, characteristic, complemented

#107×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×D₃₅₆

—

C₂×D₃₅₆

C₂²

yes

characteristic

C₂×C₄×D₈₉

C₂²

yes

characteristic

C₂×#10623494

C₂²

yes

characteristic

C₄⋊Dic₈₉

C₂²

yes

characteristic

#13083551

—

#13083551

—

C₄×Dic₈₉

—

C₂×C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₄×C₈₉

C₂²

yes

characteristic

C₄⋊C₄×C₈₉

C₂²

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

D₄

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

D₄

yes

characteristic

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

D₈₉

—

D₈₉

—

C₈₉

#482

yes

characteristic, complemented, Sylow

—

—

—

D₈₉

yes

characteristic, complemented

#106

—

#102

—

#102

—

C₂²⋊C₈

—

C₂×D₄

—

C₂×D₄

—

178

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

C₂×D₈₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×D₈₉

yes

characteristic

C₄⋊C₄

C₂×D₈₉

yes

characteristic

C₂²⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₄²

—

178

—

C₂³

—

C₂³

—

178

—

D₄

—

356

—

D₄

—

178

—

D₄

—

178

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂²×D₈₉

yes

characteristic

C₈

—

C₈

—

178

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

178

—

C₂²

—

178

—

C₂²

—

178

—

C₂²

D₄×D₈₉

yes

characteristic

C₄

—

C₄

—

C₄

—

356

—

C₄

—

178

—

C₄

yes

C₄

yes

C₂

—

356

—

C₂

—

712

—

100

C₂

#15667997

yes

characteristic

101

C₂

#15668035

yes

characteristic

102

C₂

#15668036

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#107×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#107	D₈₉
hypocenter	C₈₉	#482
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×D₈₉

commutator

C₂×C₄×C₈₉

C₂³

Frattini

C₂×C₄

C₂²×D₈₉

Fitting

#107×C₈₉

C₂

socle

C₂²×C₈₉

C₂×D₄

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
2. #15667970	C₂	semidirect
3. #15667943	C₂	semidirect
4. #15667934	C₂	semidirect
5. #15667932	C₂	semidirect
6. #15667924	C₂	semidirect
7. #107×C₈₉	C₂	semidirect
51. C₈₉	#482	semidirect
55. #107	D₈₉	semidirect

H ≅ G/N

type

2. #15667970

C₂

semidirect

3. #15667943

C₂

semidirect

4. #15667934

C₂

semidirect

5. #15667932

C₂

semidirect

6. #15667924

C₂

semidirect

7. #107×C₈₉

C₂

semidirect

51. C₈₉

#482

semidirect

55. #107

D₈₉

semidirect

Subgroups — #19151925

Conjugacy classes of subgroups

Complements