Group #19151516 — subgroups

Subgroups — #19151516

Order 5696.

238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 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	C₂²×D₃₅₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#13083553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13083551	C₂	1	2	yes	maximal, complemented
4	C₂×#13083551	C₂	1	2	yes	maximal, complemented
5	#95×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₈₉	C₂²	1	2	yes	—
7	C₂×D₃₅₆	—	2	4	no	—
8	C₂×D₃₅₆	—	2	2	no	—
9	C₂²×Dic₈₉	C₂²	1	1	yes	characteristic
10	C₂²×Dic₈₉	C₂²	1	1	yes	characteristic
11	#13083553	—	2	2	no	—
12	#13083551	—	2	4	no	—
13	#13083551	—	2	4	no	—
14	C₂²×C₄×C₈₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈₉	C₂³	1	1	yes	characteristic
17	C₂²×D₈₉	—	2	2	no	—
18	C₂²×D₈₉	—	2	2	no	—
19	C₂²×D₈₉	—	2	2	no	—
20	C₂²×D₈₉	—	2	2	no	—
21	C₂²×D₈₉	—	2	2	no	—
22	C₂²×D₈₉	—	2	2	no	—
23	C₂²×D₈₉	D₄	1	4	yes	—
24	C₂×C₄×C₈₉	—	2	2	no	—
25	C₂×C₄×C₈₉	—	2	2	no	—
26	C₂×C₄×C₈₉	—	2	2	no	—
27	C₂×C₄×C₈₉	—	2	2	no	—
28	C₂×C₄×C₈₉	D₄	1	2	yes	—
29	C₂×Dic₈₉	—	2	1	no	—
30	C₂×Dic₈₉	—	2	1	no	—
31	C₂×Dic₈₉	—	2	2	no	—
32	C₂×Dic₈₉	—	2	1	no	—
33	C₂×Dic₈₉	D₄	1	2	yes	complemented
34	D₃₅₆	—	2	8	no	—
35	C₂²×C₈₉	C₂×D₄	1	2	yes	—
36	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₈₉	#41	1	1	yes	characteristic
39	C₂²×C₈₉	#41	1	2	yes	—
40	C₂×D₈₉	—	2	4	no	—
41	C₂×D₈₉	—	2	4	no	—
42	C₂×D₈₉	—	2	4	no	—
43	C₂×D₈₉	—	4	2	no	—
44	C₂×D₈₉	—	4	2	no	—
45	C₂×D₈₉	—	4	2	no	—
46	C₂×D₈₉	—	4	2	no	—
47	C₄×C₈₉	—	2	2	no	—
48	C₄×C₈₉	—	4	2	no	—
49	Dic₈₉	—	2	2	no	—
50	Dic₈₉	—	4	1	no	—
51	C₂×C₈₉	#120	1	1	yes	characteristic
52	C₂×C₈₉	#121	1	2	yes	—
53	C₂×C₈₉	#121	1	1	yes	characteristic
54	C₂×C₈₉	#123	1	2	yes	—
55	C₂×C₈₉	#124	1	1	yes	characteristic
56	D₈₉	—	4	4	no	—
57	C₈₉	#394	1	1	yes	characteristic, complemented, Sylow
58	#394	—	89	1	no	maximal, Sylow
59	C₂²×D₄	—	89	1	no	—
60	C₂×C₄⋊C₄	—	89	1	no	—
61	C₂×C₂²⋊C₄	—	89	2	no	—
62	C₂×C₂²⋊C₄	—	89	2	no	—
63	#95	D₈₉	1	1	yes	characteristic, complemented
64	C₂⁴	—	89	2	no	—
65	C₂×D₄	—	178	4	no	—
66	C₂×D₄	—	178	2	no	—
67	C₂²×C₄	—	89	1	no	—
68	C₂²×C₄	—	89	1	no	—
69	C₂²×C₄	C₂×D₈₉	1	2	yes	—
70	C₂²×C₄	C₂×D₈₉	1	1	yes	characteristic
71	C₄⋊C₄	—	178	2	no	—
72	C₂²⋊C₄	—	178	4	no	—
73	C₂²⋊C₄	—	178	4	no	—
74	C₂³	—	89	4	no	—
75	C₂³	—	178	2	no	—
76	C₂³	—	178	2	no	—
77	C₂³	—	178	2	no	—
78	C₂³	—	178	2	no	—
79	C₂³	—	178	2	no	—
80	C₂³	—	178	2	no	—
81	C₂³	C₂²×D₈₉	1	1	yes	characteristic
82	D₄	—	178	8	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	89	2	no	—
88	C₂×C₄	—	178	2	no	—
89	C₂×C₄	—	178	1	no	—
90	C₂×C₄	—	178	1	no	—
91	C₂×C₄	—	178	1	no	—
92	C₂×C₄	D₃₅₆	1	2	yes	—
93	C₂²	—	356	2	no	—
94	C₂²	—	356	2	no	—
95	C₂²	—	356	2	no	—
96	C₂²	—	356	2	no	—
97	C₂²	—	178	4	no	—
98	C₂²	—	178	4	no	—
99	C₂²	—	178	4	no	—
100	C₂²	D₄×D₈₉	1	2	yes	—
101	C₂²	D₄×D₈₉	1	1	yes	characteristic
102	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
103	C₂²	#13083574	1	2	yes	—
104	C₂²	#13083575	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	356	1	no	—
108	C₄	—	178	2	no	—
109	C₂	—	356	4	no	—
110	C₂	#15667982	1	1	yes	characteristic
111	C₂	#15667985	1	2	yes	—
112	C₂	#15667987	1	1	yes	characteristic
113	C₂	#15667997	1	2	yes	—
114	C₂	#15668000	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₅₆

C₂

yes

maximal, characteristic

C₂×#13083553

C₂

yes

maximal, characteristic, complemented

C₂×#13083551

C₂

yes

maximal, complemented

C₂×#13083551

C₂

yes

maximal, complemented

#95×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂³×D₈₉

C₂²

yes

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂²×Dic₈₉

C₂²

yes

characteristic

C₂²×Dic₈₉

C₂²

yes

—

—

—

C₂²×C₄×C₈₉

C₂²

yes

—

C₂²×C₄×C₈₉

C₂²

yes

characteristic

C₂³×C₈₉

C₂³

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

D₄

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₄

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

D₄

yes

complemented

D₃₅₆

—

C₂²×C₈₉

C₂×D₄

yes

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₈₉

C₂×D₄

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

#120

yes

characteristic

C₂×C₈₉

#121

yes

—

C₂×C₈₉

#121

yes

characteristic

C₂×C₈₉

#123

yes

—

C₂×C₈₉

#124

yes

characteristic

D₈₉

—

C₈₉

#394

yes

characteristic, complemented, Sylow

#394

—

maximal, Sylow

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

D₈₉

yes

characteristic, complemented

C₂⁴

—

C₂×D₄

—

178

—

C₂×D₄

—

178

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₈₉

yes

—

C₂²×C₄

C₂×D₈₉

yes

characteristic

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

178

—

C₂³

—

178

—

C₂³

—

178

—

C₂³

—

178

—

C₂³

—

178

—

C₂³

—

178

—

C₂³

C₂²×D₈₉

yes

characteristic

D₄

—

178

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

D₃₅₆

yes

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

178

—

C₂²

—

178

—

C₂²

—

178

—

100

C₂²

D₄×D₈₉

yes

—

101

C₂²

D₄×D₈₉

yes

characteristic

102

C₂²

C₂×D₃₅₆

yes

characteristic

103

C₂²

#13083574

yes

—

104

C₂²

#13083575

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

356

—

108

C₄

—

178

—

109

C₂

—

356

—

110

C₂

#15667982

yes

characteristic

111

C₂

#15667985

yes

—

112

C₂

#15667987

yes

characteristic

113

C₂

#15667997

yes

—

114

C₂

#15668000

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂³
Fitting	#95×C₈₉	C₂
hypercenter	#95	D₈₉
hypocenter	C₈₉	#394
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂³

Fitting

#95×C₈₉

C₂

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
2. C₂×#13083553	C₂	semidirect
3. C₂×#13083551	C₂	semidirect
4. C₂×#13083551	C₂	semidirect
5. #95×C₈₉	C₂	semidirect
33. C₂×Dic₈₉	D₄	semidirect
57. C₈₉	#394	semidirect
63. #95	D₈₉	semidirect

H ≅ G/N

type

2. C₂×#13083553

C₂

semidirect

3. C₂×#13083551

C₂

semidirect

4. C₂×#13083551

C₂

semidirect

5. #95×C₈₉

C₂

semidirect

33. C₂×Dic₈₉

D₄

semidirect

57. C₈₉

#394

semidirect

63. #95

D₈₉

semidirect

Subgroups — #19151516

Conjugacy classes of subgroups

Complements