Group #19151523 — subgroups

Subgroups — #19151523

Order 5696.

170 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 59 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×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Dic₈₉	C₂	1	2	yes	maximal
3	#15667919	C₂	1	2	yes	maximal, complemented
4	#15667919	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₉	C₂²	1	2	yes	—
7	C₂²×Dic₈₉	C₂²	1	2	yes	—
8	C₄⋊Dic₈₉	—	2	2	no	—
9	C₂²⋊Dic₈₉	—	2	4	no	—
10	C₂⁴×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₈₉	—	2	2	no	—
14	C₂³×C₈₉	—	2	1	no	—
15	C₂³×C₈₉	—	2	2	no	—
16	C₂³×C₈₉	—	2	2	no	—
17	C₂³×C₈₉	—	2	1	no	—
18	C₂³×C₈₉	D₄	1	2	yes	—
19	C₂³×C₈₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₈₉	—	2	2	no	—
21	C₂×C₄×C₈₉	—	2	1	no	—
22	C₂×C₄×C₈₉	—	2	2	no	—
23	C₂×C₄×C₈₉	D₄	1	2	yes	—
24	C₂×Dic₈₉	—	2	2	no	—
25	C₂×Dic₈₉	—	2	2	no	—
26	C₂×Dic₈₉	—	2	2	no	—
27	C₂×Dic₈₉	—	2	2	no	—
28	C₂×Dic₈₉	—	2	2	no	—
29	C₂×Dic₈₉	—	2	2	no	—
30	C₂²×C₈₉	—	2	2	no	—
31	C₂²×C₈₉	—	2	4	no	—
32	C₂²×C₈₉	—	4	1	no	—
33	C₂²×C₈₉	—	4	1	no	—
34	C₂²×C₈₉	—	4	2	no	—
35	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₈₉	#41	1	1	yes	characteristic
38	C₂²×C₈₉	#41	1	2	yes	—
39	C₂²×C₈₉	#41	1	2	yes	—
40	C₄×C₈₉	—	2	2	no	—
41	C₄×C₈₉	—	4	1	no	—
42	Dic₈₉	—	4	2	no	—
43	Dic₈₉	—	4	2	no	—
44	C₂×C₈₉	—	4	2	no	—
45	C₂×C₈₉	#121	1	1	yes	characteristic
46	C₂×C₈₉	#123	1	1	yes	characteristic
47	C₂×C₈₉	#123	1	2	yes	—
48	C₂×C₈₉	#124	1	1	yes	characteristic
49	C₂×C₈₉	#126	1	2	yes	—
50	C₈₉	#397	1	1	yes	characteristic, complemented, Sylow
51	#397	—	89	1	no	maximal, Sylow
52	C₂×C₄⋊C₄	—	89	1	no	—
53	C₂×C₂²⋊C₄	—	89	2	no	—
54	C₂×C₂²⋊C₄	D₈₉	1	1	yes	characteristic
55	#95	—	89	1	no	—
56	#95	—	89	2	no	—
57	C₂⁴	C₂×D₈₉	1	1	yes	characteristic
58	C₂²×C₄	—	89	2	no	—
59	C₂²×C₄	—	89	2	no	—
60	C₂²×C₄	C₂×D₈₉	1	1	yes	characteristic
61	C₂²×C₄	C₂×D₈₉	1	1	yes	characteristic
62	C₄⋊C₄	—	178	2	no	—
63	C₂²⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	178	4	no	—
65	C₂³	—	2	1	no	—
66	C₂³	—	2	2	no	—
67	C₂³	—	2	2	no	—
68	C₂³	—	2	1	no	—
69	C₂³	D₃₅₆	1	2	yes	—
70	C₂³	C₂²×D₈₉	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	178	2	no	—
75	C₂×C₄	—	178	2	no	—
76	C₂×C₄	—	178	2	no	—
77	C₂×C₄	—	178	2	no	—
78	C₂×C₄	—	178	2	no	—
79	C₂×C₄	—	178	2	no	—
80	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
81	C₂²	—	2	2	no	—
82	C₂²	—	2	4	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	2	no	—
86	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
87	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
88	C₂²	#13083573	1	2	yes	—
89	C₂²	#13083573	1	2	yes	—
90	C₂²	#13083574	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	4	1	no	—
93	C₄	—	356	2	no	—
94	C₄	—	356	2	no	—
95	C₂	—	4	2	no	—
96	C₂	#15667986	1	1	yes	characteristic
97	C₂	#15667993	1	1	yes	characteristic
98	C₂	#15667996	1	2	yes	—
99	C₂	#15667999	1	1	yes	characteristic
100	C₂	#15668005	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₈₉

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊Dic₈₉

C₂

yes

maximal

#15667919

C₂

yes

maximal, complemented

#15667919

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊C₄×C₈₉

C₂

yes

maximal, characteristic

C₂²×Dic₈₉

C₂²

yes

—

C₂²×Dic₈₉

C₂²

yes

—

C₄⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₂⁴×C₈₉

C₂²

yes

characteristic

C₂²×C₄×C₈₉

C₂²

yes

characteristic

C₂²×C₄×C₈₉

C₂²

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

D₄

yes

—

C₂³×C₈₉

C₂³

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₄

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₈₉

C₂×D₄

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₂²×C₈₉

#41

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#124

yes

characteristic

C₂×C₈₉

#126

yes

—

C₈₉

#397

yes

characteristic, complemented, Sylow

#397

—

maximal, Sylow

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

D₈₉

yes

characteristic

#95

—

#95

—

C₂⁴

C₂×D₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₈₉

yes

characteristic

C₂²×C₄

C₂×D₈₉

yes

characteristic

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

D₃₅₆

yes

—

C₂³

C₂²×D₈₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂²⋊D₈₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊D₈₉

yes

characteristic

C₂²

C₂×D₃₅₆

yes

characteristic

C₂²

#13083573

yes

—

C₂²

#13083573

yes

—

C₂²

#13083574

yes

characteristic

C₄

—

C₄

—

C₄

—

356

—

C₄

—

356

—

C₂

—

C₂

yes

C₂

yes

C₂

yes

—

C₂

#15667999

yes

characteristic

100

C₂

#15668005

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂³
Fitting	C₂×C₂²⋊C₄×C₈₉	C₂
hypercenter	C₂×C₂²⋊C₄	D₈₉
hypocenter	C₈₉	#397
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂³

Fitting

C₂×C₂²⋊C₄×C₈₉

C₂

hypercenter

C₂×C₂²⋊C₄

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₈₉	C₂	semidirect
3. #15667919	C₂	semidirect
4. #15667919	C₂	semidirect
50. C₈₉	#397	semidirect

H ≅ G/N

type

1. C₂×C₄⋊Dic₈₉

C₂

semidirect

3. #15667919

C₂

semidirect

4. #15667919

C₂

semidirect

50. C₈₉

#397

semidirect

Subgroups — #19151523

Conjugacy classes of subgroups

Complements