Finite Group Databasebeta

← #34079906

Subgroups — #34079906

Order 19328.

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

normal subgroups only

This group has 514 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.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D151C212yesmaximal, complemented
2#23752532C212yesmaximal, complemented
3#23752529C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic, complemented
5#23752463C212yesmaximal, complemented
6#23752347C212yesmaximal, complemented
7#23752344C212yesmaximal, complemented
8#23752175C211yesmaximal, characteristic, complemented
9#469×C151C211yesmaximal, characteristic, complemented
10C2×D4×D151—22no—
11C2×D4×D151C2212yescomplemented
12C22×C4×D151C2211yescharacteristic
13C2×D1208C2211yescharacteristic, complemented
14C2×#14558989C2212yescomplemented
15C2×#14558988C2211yescharacteristic, complemented
16#18012714C2212yes—
17#18012713C2212yescomplemented
18#18012712—22no—
19#18012711—22no—
20#18012710C2212yes—
21C4⋊C4×D151C2212yescomplemented
22C22⋊C4×D151—22no—
23#18012671C2211yescharacteristic, complemented
24#18012670C2212yescomplemented
25#18012661C2212yescomplemented
26#18012660C2212yescomplemented
27#18012659C2212yescomplemented
28(C2×D151)⋊C8C2212yescomplemented
29(C2×D151)⋊C8C2212yescomplemented
30C2×D8×C151C2211yescharacteristic, complemented
31C2×M16×C151C2211yescharacteristic, complemented
32#121×C151C2212yescomplemented
33#106×C151C2211yescharacteristic, complemented
34#102×C151C2212yescomplemented
35C23×D151—22no—
36C23×D151D411yescharacteristic
37C2×D604—22no—
38C2×D604C2312yes—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—22no—
42D4×D151—42no—
43D4×D151—42no—
44D4×D151—48no—
45C22×Dic151D411yescharacteristic
46C2×C4×D151—22no—
47C2×C4×D151—41no—
48C2×C4×D151—41no—
49C2×C4×D151D412yes—
50C2×C4×D151C2312yes—
51D1208—41no—
52#14558989—42no—
53#14558988—41no—
54C2×C151⋊C8C2312yes—
55C4⋊Dic151C2312yes—
56Dic151⋊C4—22no—
57C22⋊Dic151—22no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60C2×D4×C151—22no—
61C2×D4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63D8×C151—41no—
64M16×C151—41no—
65C2×C8×C151C2311yescharacteristic
66C2×C8×C151C2311yescharacteristic
67C4⋊C4×C151C2312yes—
68C22⋊C4×C151—22no—
69C22×D151—24no—
70C22×D151—22no—
71C22×D151—41no—
72C22×D151—44no—
73C22×D151—44no—
74C22×D151—44no—
75C22×D151C2×D412yes—
76D604—22no—
77D604—22no—
78D604—44no—
79C22⋊D151—44no—
80C22⋊D151—44no—
81C22⋊D151—44no—
82C2×Dic151—22no—
83C2×Dic151—41no—
84C2×Dic151C2×D412yes—
85C4×D151—22no—
86C4×D151—22no—
87C4×D151—42no—
88C4×D151—44no—
89C151⋊C8—22no—
90C23×C151—22no—
91C23×C151C2×D411yescharacteristic
92D4×C151—22no—
93D4×C151—22no—
94D4×C151—44no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—22no—
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2411yescharacteristic
100C8×C151—21no—
101C8×C151—21no—
102C22×C151—21no—
103C22×C151—22no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151C22×D411yescharacteristic
108C2×D151—22no—
109C2×D151—22no—
110C2×D151—44no—
111C2×D151—42no—
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—88no—
115C2×D151AGL(1,ℤ/8)14yes—
116C4×C151—21no—
117C4×C151—42no—
118C4×C151H(5,𝔽2)11yescharacteristic
119C4×C151H(5,𝔽2)11yescharacteristic
120Dic151—22no—
121Dic151—42no—
122C2×C151—41no—
123C2×C151—82no—
124C2×C151#53411yescharacteristic
125C2×C151C2×AGL(1,ℤ/8)12yes—
126D151—24no—
127D151—82no—
128C151#319211yescharacteristic, complemented, Sylow
129#3192—1511nomaximal, Sylow
130C2×#121—1512no—
131#481—1512no—
132#481—1512no—
133#469—1511no—
134#469—1512no—
135#469D15111yescharacteristic, complemented
136#447—1512no—
137#447—1512no—
138#407—1511no—
139C22×D4—3022no—
140C22×D4—1512no—
141C23×C4—1511no—
142C2×D8—1512no—
143C2×D8—1511no—
144C2×D8C2×D15111yescharacteristic, complemented
145C2×M16—1511no—
146C2×M16C2×D15111yescharacteristic, complemented
147#121—3022no—
148#121—3022no—
149#121—1512no—
150#121—1512no—
151#121—1512no—
152#121C2×D15112yescomplemented
153C2×C4⋊C4—1512no—
154C2×C22⋊C4—3022no—
155#106—1511no—
156#106—1512no—
157#106C2×D15111yescharacteristic, complemented
158#102—1512no—
159#102—1512no—
160#102—1512no—
161#102C2×D15112yescomplemented
162C22⋊C8—1512no—
163C22⋊C8—1512no—
164C24—3022no—
165C24—1511no—
166C2×D4—22no—
167C2×D4—3022no—
168C2×D4—3022no—
169C2×D4—3022no—
170C2×D4—3022no—
171C2×D4—6042no—
172C2×D4—6042no—
173C2×D4—6048no—
174C2×D4—1512no—
175C2×D4C22×D15112yes—
176C22×C4—3022no—
177C22×C4—6041no—
178C22×C4—6041no—
179C22×C4—1512no—
180C22×C4—1511no—
181C22×C4—1512no—
182C22×C4C22×D15111yescharacteristic
183D8—41no—
184D8—6041no—
185D8—6042no—
186M16—41no—
187M16—6041no—
188C2×C8—1512no—
189C2×C8C22×D15111yescharacteristic
190C2×C8C22×D15111yescharacteristic
191C4⋊C4—3022no—
192C4⋊C4—1512no—
193C4⋊C4C22×D15112yes—
194C22⋊C4—22no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C23—22no—
199C23—3024no—
200C23—3022no—
201C23—6041no—
202C23—6044no—
203C23—6044no—
204C23—6044no—
205C23—1512no—
206C23D4×D15111yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—3022no—
211D4—3022no—
212D4—6044no—
213D4—6044no—
214D4—6044no—
215D4—6044no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—3022no—
220C2×C4—3022no—
221C2×C4—3022no—
222C2×C4—6042no—
223C2×C4—6044no—
224C2×C4—6041no—
225C2×C4—1512no—
226C2×C4D4×D15111yescharacteristic
227C2×C4C23×D15111yescharacteristic
228C8—21no—
229C8—21no—
230C8—3022no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—3022no—
237C22—3022no—
238C22—6044no—
239C22—6042no—
240C22—6042no—
241C22—6042no—
242C22—1514no—
243C22—12088no—
244C22C2×D4×D15111yescharacteristic
245C4—21no—
246C4—42no—
247C4—3022no—
248C4—6042no—
249C4#1801278411yescharacteristic
250C4#1801278511yescharacteristic
251C2—41no—
252C2—82no—
253C2—3024no—
254C2—12082no—
255C2#2375277011yescharacteristic
256C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3192
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D151C2semidirect
2. #23752532C2semidirect
3. #23752529C2semidirect
4. #23752465C2semidirect
5. #23752463C2semidirect
6. #23752347C2semidirect
7. #23752344C2semidirect
8. #23752175C2semidirect
9. #469×C151C2semidirect
11. C2×D4×D151C22semidirect
13. C2×D1208C22semidirect
14. C2×#14558989C22semidirect
15. C2×#14558988C22semidirect
17. #18012713C22semidirect
21. C4⋊C4×D151C22semidirect
23. #18012671C22semidirect
24. #18012670C22semidirect
25. #18012661C22semidirect
26. #18012660C22semidirect
27. #18012659C22semidirect
28. (C2×D151)⋊C8C22semidirect
29. (C2×D151)⋊C8C22semidirect
30. C2×D8×C151C22semidirect
31. C2×M16×C151C22semidirect
32. #121×C151C22semidirect
33. #106×C151C22semidirect
34. #102×C151C22semidirect
128. C151#3192semidirect
135. #469D151semidirect
144. C2×D8C2×D151semidirect
146. C2×M16C2×D151semidirect
152. #121C2×D151semidirect
157. #106C2×D151semidirect
161. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#121×D1512
#237525322
#237525292
#237524652
#237524632
#237523472
#237523442
#237521752
#469×C1512
#3192151