Group #19152255 — subgroups

Subgroups — #19152255

Order 5696.

290 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 113 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×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#15667999	C₂	1	3	yes	maximal, complemented
3	#15667991	C₂	1	3	yes	maximal, complemented
4	#15667983	C₂	1	3	yes	maximal, complemented
5	Q₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₂²⋊D₈₉	C₂	1	3	yes	maximal, complemented
7	C₂×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₈	C₂²	1	3	yes	—
9	Q₈×D₈₉	—	2	4	no	—
10	C₂×C₂²⋊D₈₉	C₂²	1	3	yes	—
11	C₂×C₄×D₈₉	C₂²	1	3	yes	—
12	C₄⋊Dic₈₉	C₂²	1	3	yes	—
13	#13083553	C₂²	1	3	yes	—
14	C₂²⋊Dic₈₉	C₂²	1	3	yes	—
15	C₂²⋊Dic₈₉	C₂²	1	6	yes	—
16	#13083551	C₂²	1	1	yes	characteristic
17	C₄×Dic₈₉	C₂²	1	3	yes	—
18	#41×C₈₉	—	2	4	no	—
19	C₂×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₈₉	C₂²	1	3	yes	—
21	C₂²×C₄×C₈₉	C₂²	1	3	yes	—
22	C₂³×C₈₉	C₂³	1	3	yes	—
23	C₂²×D₈₉	C₂³	1	1	yes	characteristic
24	Q₈×C₈₉	D₄	1	4	yes	complemented
25	D₄×C₈₉	—	2	6	no	—
26	C₂×C₄×C₈₉	—	2	6	no	—
27	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×C₈₉	C₂³	1	3	yes	—
29	C₂²⋊D₈₉	—	2	6	no	—
30	C₂×Dic₈₉	C₂³	1	1	yes	characteristic
31	C₂×Dic₈₉	C₂³	1	3	yes	—
32	C₂×Dic₈₉	C₂³	1	3	yes	—
33	C₄×D₈₉	—	2	6	no	—
34	Dic₁₇₈	—	2	6	no	—
35	C₂²×C₈₉	—	2	3	no	—
36	C₂²×C₈₉	—	2	3	no	—
37	C₂²×C₈₉	—	2	3	no	—
38	C₂²×C₈₉	C₂⁴	1	1	yes	characteristic
39	C₂×D₈₉	—	2	1	no	—
40	C₂×D₈₉	—	2	1	no	—
41	C₂×D₈₉	#41	1	2	yes	complemented
42	C₄×C₈₉	—	2	1	no	—
43	C₄×C₈₉	C₂×D₄	1	6	yes	—
44	Dic₈₉	—	2	3	no	—
45	Dic₈₉	—	2	3	no	—
46	Dic₈₉	—	2	1	no	—
47	C₂×C₈₉	—	4	3	no	—
48	C₂×C₈₉	C₂²×D₄	1	1	yes	characteristic
49	C₂×C₈₉	C₂×#41	1	1	yes	characteristic
50	C₂×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
51	D₈₉	—	2	2	no	—
52	C₈₉	#548	1	1	yes	characteristic, complemented, Sylow
53	#548	—	89	1	no	maximal, Sylow
54	C₂×#41	D₈₉	1	1	yes	characteristic, complemented
55	C₂²×Q₈	—	89	1	no	—
56	#124	—	89	3	no	—
57	C₂²⋊Q₈	—	89	3	no	—
58	#121	—	89	3	no	—
59	C₄×Q₈	—	89	1	no	—
60	C₄×D₄	—	89	3	no	—
61	#41	—	2	4	no	—
62	C₂×Q₈	—	89	3	no	—
63	C₂×Q₈	—	178	4	no	—
64	C₂×Q₈	C₂×D₈₉	1	1	yes	characteristic
65	C₂×D₄	—	89	3	no	—
66	C₂×D₄	C₂×D₈₉	1	3	yes	—
67	C₂²×C₄	—	89	3	no	—
68	C₂²×C₄	C₂×D₈₉	1	3	yes	—
69	C₄⋊C₄	—	89	3	no	—
70	C₄⋊C₄	—	89	3	no	—
71	C₂²⋊C₄	—	89	3	no	—
72	C₂²⋊C₄	—	89	6	no	—
73	C₂²⋊C₄	—	89	1	no	—
74	C₄²	—	89	3	no	—
75	C₂³	—	89	1	no	—
76	C₂³	C₂²×D₈₉	1	3	yes	—
77	Q₈	—	178	6	no	—
78	Q₈	C₂²⋊D₈₉	1	4	yes	complemented
79	D₄	—	2	6	no	—
80	D₄	—	178	6	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	89	1	no	—
83	C₂×C₄	—	89	3	no	—
84	C₂×C₄	—	89	3	no	—
85	C₂×C₄	—	178	6	no	—
86	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
87	C₂×C₄	C₂²×D₈₉	1	3	yes	—
88	C₂²	—	2	3	no	—
89	C₂²	—	2	3	no	—
90	C₂²	—	2	3	no	—
91	C₂²	—	89	2	no	—
92	C₂²	—	178	1	no	—
93	C₂²	—	178	1	no	—
94	C₂²	C₂³×D₈₉	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	178	3	no	—
97	C₄	—	178	3	no	—
98	C₄	—	178	1	no	—
99	C₄	C₂×C₂²⋊D₈₉	1	6	yes	—
100	C₂	—	4	3	no	—
101	C₂	—	178	2	no	—
102	C₂	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
103	C₂	#41×D₈₉	1	1	yes	characteristic
104	C₂	#15668059	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×D₈₉

C₂

yes

maximal, characteristic, complemented

#15667999

C₂

yes

maximal, complemented

#15667991

C₂

yes

maximal, complemented

#15667983

C₂

yes

maximal, complemented

Q₈×Dic₈₉

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₈₉

C₂

yes

maximal, complemented

C₂×#41×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₈

C₂²

yes

—

Q₈×D₈₉

—

C₂×C₂²⋊D₈₉

C₂²

yes

—

C₂×C₄×D₈₉

C₂²

yes

—

C₄⋊Dic₈₉

C₂²

yes

—

#13083553

C₂²

yes

—

C₂²⋊Dic₈₉

C₂²

yes

—

C₂²⋊Dic₈₉

C₂²

yes

—

#13083551

C₂²

yes

characteristic

C₄×Dic₈₉

C₂²

yes

—

#41×C₈₉

—

C₂×Q₈×C₈₉

C₂²

yes

characteristic

C₂×D₄×C₈₉

C₂²

yes

—

C₂²×C₄×C₈₉

C₂²

yes

—

C₂³×C₈₉

C₂³

yes

—

C₂²×D₈₉

C₂³

yes

characteristic

Q₈×C₈₉

D₄

yes

complemented

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂×C₄×C₈₉

C₂³

yes

—

C₂²⋊D₈₉

—

C₂×Dic₈₉

C₂³

yes

characteristic

C₂×Dic₈₉

C₂³

yes

—

C₂×Dic₈₉

C₂³

yes

—

C₄×D₈₉

—

Dic₁₇₈

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂⁴

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

#41

yes

complemented

C₄×C₈₉

—

C₄×C₈₉

C₂×D₄

yes

—

Dic₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

C₂²×D₄

yes

characteristic

C₂×C₈₉

C₂×#41

yes

characteristic

C₂×C₈₉

2₋¹⁺⁴

yes

characteristic

D₈₉

—

C₈₉

#548

yes

characteristic, complemented, Sylow

#548

—

maximal, Sylow

C₂×#41

D₈₉

yes

characteristic, complemented

C₂²×Q₈

—

#124

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

178

—

C₂×Q₈

C₂×D₈₉

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂×D₈₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×D₈₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂²×D₈₉

yes

—

Q₈

—

178

—

Q₈

C₂²⋊D₈₉

yes

complemented

D₄

—

D₄

—

178

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

C₂²×D₈₉

yes

characteristic

C₂×C₄

C₂²×D₈₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

178

—

C₂²

—

178

—

C₂²

C₂³×D₈₉

yes

characteristic

C₄

—

C₄

—

178

—

C₄

—

178

—

C₄

—

178

—

C₄

C₂×C₂²⋊D₈₉

yes

—

100

C₂

—

101

C₂

—

178

—

102

C₂

C₂²×C₂²⋊D₈₉

yes

characteristic

103

C₂

#41×D₈₉

yes

characteristic

104

C₂

#15668059

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂⁴
Fitting	C₂×#41×C₈₉	C₂
hypercenter	C₂×#41	D₈₉
hypocenter	C₈₉	#548
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×#41

subgroup

G/H

center, Frattini

C₂²

C₂³×D₈₉

commutator, socle

C₂²×C₈₉

C₂⁴

Fitting

C₂×#41×C₈₉

C₂

hypercenter

C₂×#41

D₈₉

C₈₉

G ▷ C₂²×C₈₉ ▷ C₈₉

C₁ ◁ C₂² ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×Q₈×D₈₉	C₂	semidirect
2. #15667999	C₂	semidirect
3. #15667991	C₂	semidirect
4. #15667983	C₂	semidirect
5. Q₈×Dic₈₉	C₂	semidirect
6. C₄×C₂²⋊D₈₉	C₂	semidirect
7. C₂×#41×C₈₉	C₂	semidirect
24. Q₈×C₈₉	D₄	semidirect
41. C₂×D₈₉	#41	semidirect
52. C₈₉	#548	semidirect
54. C₂×#41	D₈₉	semidirect
78. Q₈	C₂²⋊D₈₉	semidirect

H ≅ G/N

type

1. C₂×Q₈×D₈₉

C₂

semidirect

2. #15667999

C₂

semidirect

3. #15667991

C₂

semidirect

4. #15667983

C₂

semidirect

5. Q₈×Dic₈₉

C₂

semidirect

6. C₄×C₂²⋊D₈₉

C₂

semidirect

7. C₂×#41×C₈₉

C₂

semidirect

24. Q₈×C₈₉

D₄

semidirect

41. C₂×D₈₉

#41

semidirect

52. C₈₉

#548

semidirect

54. C₂×#41

D₈₉

semidirect

78. Q₈

C₂²⋊D₈₉

semidirect

Subgroups — #19152255

Conjugacy classes of subgroups

Complements