Finite Group Databasebeta

← #34071686

Subgroups — #34071686

Order 19328.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D151C211yesmaximal, characteristic
2C2×C22⋊C4×D151C212yesmaximal, complemented
3#23752088C218yesmaximal, complemented
4#23752073C212yesmaximal, complemented
5#23752068C211yesmaximal, characteristic, complemented
6#379×C151C211yesmaximal, characteristic, complemented
7C24×D151C2211yescharacteristic
8C22×C22⋊D151—28no—
9C22×C22⋊D151C418yescomplemented
10C22×C22⋊D151C2214yes—
11C23×Dic151C2211yescharacteristic
12C22×C4×D151C2214yescomplemented
13C2×C22⋊Dic151C2212yes—
14C2×C22⋊Dic151C2214yescomplemented
15C2×(C2×D151)⋊C4C2214yescomplemented
16C22⋊C4×D151—28no—
17C151⋊#95C2218yescomplemented
18C25×C151C2211yescharacteristic
19C2×C22⋊C4×C151C2212yes—
20C2×C22⋊C4×C151C2214yescomplemented
21C23×D151—44no—
22C23×D151C2×C414yes—
23C23×D151D418yes—
24C23×D151C2312yes—
25C2×C22⋊D151—232no—
26C2×C22⋊D151—28no—
27C2×C22⋊D151—28no—
28C2×C22⋊D151C2×C4116yescomplemented
29C22×Dic151—24no—
30C22×Dic151C2×C414yescomplemented
31C22×Dic151C2314yes—
32C22×Dic151C2312yes—
33C2×C4×D151—28no—
34C2×C4×D151—48no—
35C22⋊Dic151—24no—
36C22⋊Dic151—44no—
37(C2×D151)⋊C4—28no—
38C24×C151—24no—
39C24×C151—44no—
40C24×C151C2×C414yescomplemented
41C24×C151C2312yes—
42C24×C151C2311yescharacteristic
43C22×C4×C151C2314yes—
44C22⋊C4×C151—24no—
45C22⋊C4×C151—44no—
46C22×D151—28no—
47C22×D151—48no—
48C22×D151—416no—
49C22×D151C22⋊C4116yescomplemented
50C22×D151C22×C414yes—
51C22×D151C2×D414yes—
52C22×D151C2×D414yes—
53C22⋊D151—232no—
54C2×Dic151—28no—
55C2×Dic151—24no—
56C2×Dic151—24no—
57C2×Dic151—28no—
58C2×Dic151C22×C414yes—
59C4×D151—416no—
60C23×C151—24no—
61C23×C151—28no—
62C23×C151—24no—
63C23×C151—24no—
64C23×C151—24no—
65C23×C151—48no—
66C23×C151—416no—
67C23×C151C22×C414yes—
68C23×C151C22×C412yes—
69C23×C151C2×D414yes—
70C23×C151C2411yescharacteristic
71C2×C4×C151—24no—
72C2×C4×C151—28no—
73C22×C151—24no—
74C22×C151—28no—
75C22×C151—24no—
76C22×C151—24no—
77C22×C151—24no—
78C22×C151—416no—
79C22×C151—48no—
80C22×C151C2×C22⋊C414yes—
81C22×C151C23×C411yescharacteristic
82C22×C151C22×D412yes—
83C22×C151H(5,𝔽2)14yes—
84C2×D151—28no—
85C2×D151—28no—
86C2×D151—28no—
87C2×D151—416no—
88C2×D151C2×C22⋊C418yes—
89C4×C151—44no—
90Dic151—24no—
91Dic151—44no—
92C2×C151—24no—
93C2×C151—44no—
94C2×C151C22×C22⋊C411yescharacteristic
95C2×C151#51812yes—
96C2×C151#53414yes—
97D151—28no—
98C151#230811yescharacteristic, complemented, Sylow
99#2308—1511nomaximal, Sylow
100C23×D4—1511no—
101C22×C22⋊C4—1512no—
102#386—1518no—
103#381—1512no—
104#379—1511no—
105#379D15111yescharacteristic, complemented
106C25—1511no—
107C25C2×D15111yescharacteristic
108C22×D4—3028no—
109C22×D4—1518no—
110C22×D4—1514no—
111C23×C4—1511no—
112C23×C4—1514no—
113C2×C22⋊C4—3028no—
114C2×C22⋊C4—1512no—
115C2×C22⋊C4—1514no—
116C2×C22⋊C4—1514no—
117C2×C22⋊C4C2×D15112yes—
118C2×C22⋊C4C2×D15114yescomplemented
119#95—1518no—
120C24—24no—
121C24—44no—
122C24—6044no—
123C24—1512no—
124C24—1514no—
125C24—1518no—
126C24C4×D15114yescomplemented
127C24C22×D15112yes—
128C24C22×D15111yescharacteristic
129C2×D4—30232no—
130C2×D4—3028no—
131C2×D4—3028no—
132C2×D4—15116no—
133C22×C4—3028no—
134C22×C4—3024no—
135C22×C4—6048no—
136C22×C4—1514no—
137C22×C4—1514no—
138C22×C4—1512no—
139C22×C4C22×D15114yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—3028no—
143C22⋊C4—3024no—
144C22⋊C4—6044no—
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—3028no—
153C23—60416no—
154C23—6048no—
155C23—1514no—
156C23—1514no—
157C23—1514no—
158C23—15116no—
159C23C2×C4×D15114yes—
160C23C2×C4×D15112yes—
161C23D4×D15114yes—
162C23C23×D15111yescharacteristic
163D4—30232no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—3028no—
167C2×C4—3024no—
168C2×C4—3024no—
169C2×C4—3028no—
170C2×C4—60416no—
171C2×C4—1514no—
172C22—28no—
173C22—24no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—3028no—
180C22—3028no—
181C22—3028no—
182C22—60416no—
183C22—1518no—
184C22C22⋊C4×D15114yes—
185C22C22×C4×D15111yescharacteristic
186C22C2×D4×D15112yes—
187C22#1801278414yes—
188C4—44no—
189C4—3024no—
190C4—6044no—
191C2—24no—
192C2—44no—
193C2—3028no—
194C2C2×C22⋊C4×D15111yescharacteristic
195C2#2375268512yes—
196C2#2375277214yes—
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#379×C151C2
socle, cosocleC23×C151C24
prime radicalC23×C22⋊D151C2
hypercenter#379D151
hypocenterC151#2308
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #379

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C22⋊C4×D151C2semidirect
3. #23752088C2semidirect
4. #23752073C2semidirect
5. #23752068C2semidirect
6. #379×C151C2semidirect
9. C22×C22⋊D151C4semidirect
12. C22×C4×D151C22semidirect
14. C2×C22⋊Dic151C22semidirect
15. C2×(C2×D151)⋊C4C22semidirect
17. C151⋊#95C22semidirect
20. C2×C22⋊C4×C151C22semidirect
28. C2×C22⋊D151C2×C4semidirect
30. C22×Dic151C2×C4semidirect
40. C24×C151C2×C4semidirect
49. C22×D151C22⋊C4semidirect
98. C151#2308semidirect
105. #379D151semidirect
118. C2×C22⋊C4C2×D151semidirect
126. C24C4×D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C22⋊D1512
C2×C22⋊C4×D1512
#237520882
#237520732
#237520682
#379×C1512
#2308151