Finite Group Databasebeta

← #34079033

Subgroups — #34079033

Order 19328.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#23752723C211yesmaximal, characteristic
2#23752547C212yesmaximal, complemented
3#23752542C212yesmaximal, complemented
4#23752530C212yesmaximal, complemented
5#23752525C212yesmaximal, complemented
6#23752252C212yesmaximal, complemented
7#23752211C212yesmaximal, complemented
8#23752176C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C2×#14558988C2212yes—
12#18012722—21no—
13#18012718C2211yescharacteristic
14#18012718C2211yescharacteristic
15#18012713C2211yescharacteristic
16#18012713C2211yescharacteristic
17#18012708—21no—
18C4×C22⋊D151—21no—
19C4×C22⋊D151—21no—
20#18012698C2211yescharacteristic
21#18012672C2214yescomplemented
22#18012670C2214yescomplemented
23#18012662C2214yescomplemented
24#18012659C2214yescomplemented
25C22⋊(C151⋊C8)C2212yes—
26C22⋊(C151⋊C8)C2212yes—
27C23×C4×C151—21no—
28C23×C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151C2212yes—
33C2×C4⋊C4×C151C2212yes—
34C2×C4⋊C4×C151C2212yes—
35#14559004—24no—
36C2×Dic302C2311yescharacteristic
37C2×D604C2311yescharacteristic
38C2×C22⋊D151—21no—
39C2×C22⋊D151—21no—
40C2×C22⋊D151—21no—
41C2×C4×D151—21no—
42#14558988—24no—
43C2×C151⋊C8C2314yes—
44C4⋊Dic151C2311yescharacteristic
45C4⋊Dic151C2311yescharacteristic
46Dic151⋊C4—21no—
47Dic151⋊C4—21no—
48C22⋊Dic151—21no—
49C22⋊Dic151—21no—
50C22⋊Dic151—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53C4×Dic151—21no—
54C24×C151D411yescharacteristic
55C22×C4×C151—24no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—44no—
60C22×C4×C151D411yescharacteristic
61C22×C4×C151D411yescharacteristic
62C22×C4×C151D411yescharacteristic
63C22×C4×C151C2311yescharacteristic
64C22×C4×C151C2311yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—22no—
67C4⋊C4×C151—22no—
68C4⋊C4×C151—22no—
69C4⋊C4×C151C2314yes—
70C22×D151—21no—
71Dic302—22no—
72D604—22no—
73C22⋊D151—42no—
74C22⋊D151—42no—
75C22⋊D151—42no—
76C2×Dic151—21no—
77C2×Dic151—21no—
78C2×Dic151—21no—
79C4×D151—42no—
80C151⋊C8—24no—
81C23×C151—22no—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151C2×D411yescharacteristic
85C23×C151C2×D411yescharacteristic
86C23×C151C2×D411yescharacteristic
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—24no—
93C2×C4×C151—44no—
94C2×C4×C151—44no—
95C2×C4×C151—44no—
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151#4114yes—
100C2×C4×C151C2411yescharacteristic
101C22×C151—28no—
102C22×C151—21no—
103C22×C151—21no—
104C22×C151—21no—
105C22×C151—21no—
106C22×C151—21no—
107C22×C151—21no—
108C22×C151#12312yes—
109C22×C151AGL(1,ℤ/8)12yes—
110C22×C151#13712yes—
111C22×C151C22×D411yescharacteristic
112C2×D151—41no—
113C2×D151—41no—
114C2×D151—41no—
115C4×C151—21no—
116C4×C151—21no—
117C4×C151—44no—
118C4×C151#12312yes—
119C4×C151C2×#4112yes—
120Dic151—41no—
121Dic151—41no—
122Dic151—41no—
123C2×C151—22no—
124C2×C151—22no—
125C2×C151—22no—
126C2×C151C2×#12311yescharacteristic
127C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C151C2×#13711yescharacteristic
129D151—81no—
130C151#309211yescharacteristic, complemented, Sylow
131#3092—1511nomaximal, Sylow
132#525—1511no—
133C22×C4⋊C4D15111yescharacteristic, complemented
134#484—1512no—
135#483—1512no—
136#481—1512no—
137#480—1512no—
138#428—1512no—
139#417—1512no—
140#407—1511no—
141C2×#41—1511no—
142C23×C4—21no—
143C23×C4C2×D15111yescharacteristic
144C2×M16—1512no—
145#123—3021no—
146C22⋊Q8—1511no—
147C22⋊Q8—1511no—
148#121—1511no—
149#121—1511no—
150#120—3021no—
151C4×D4—3021no—
152C4×D4—3021no—
153#117—1511no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D15112yes—
158C2×C4⋊C4C2×D15112yes—
159C2×C4⋊C4C2×D15112yes—
160#107—1514no—
161#106—1514no—
162#103—1514no—
163#102—1514no—
164C22⋊C8—1512no—
165C22⋊C8—1512no—
166C24C22⋊D15111yescharacteristic
167#41—3024no—
168C2×Q8—1511no—
169C2×D4—3021no—
170C2×D4—3021no—
171C2×D4—3021no—
172C2×D4—1511no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—3021no—
179C22×C4C22⋊D15111yescharacteristic
180C22×C4C22⋊D15111yescharacteristic
181C22×C4C22⋊D15111yescharacteristic
182C22×C4C22×D15111yescharacteristic
183C22×C4C22×D15111yescharacteristic
184C22×C4C22×D15111yescharacteristic
185M16—3024no—
186C2×C8—1514no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—3021no—
191C4⋊C4—3021no—
192C4⋊C4—1511no—
193C4⋊C4—1511no—
194C4⋊C4C22×D15114yes—
195C22⋊C4—3021no—
196C22⋊C4—3021no—
197C22⋊C4—3021no—
198C22⋊C4—3021no—
199C22⋊C4—3021no—
200C42—3021no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—3021no—
205C23C2×C22⋊D15111yescharacteristic
206C23C2×C22⋊D15111yescharacteristic
207C23C2×C22⋊D15111yescharacteristic
208Q8—3022no—
209D4—3022no—
210D4—6042no—
211D4—6042no—
212D4—6042no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—3021no—
223C2×C4—3021no—
224C2×C4—3021no—
225C2×C4—6042no—
226C2×C4C2×C22⋊D15111yescharacteristic
227C2×C4C2×C22⋊D15111yescharacteristic
228C2×C4C2×C22⋊D15111yescharacteristic
229C2×C4#1455900414yes—
230C2×C4C23×D15111yescharacteristic
231C8—3024no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—6041no—
240C22—6041no—
241C22—6041no—
242C22#1801272212yes—
243C22#1801276512yes—
244C22#1801277012yes—
245C22C22×C22⋊D15111yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—6041no—
250C4—6041no—
251C4—6041no—
252C4#1801272212yes—
253C4C2×#1455900412yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—12081no—
258C2C2×#1801272211yescharacteristic
259C2C2×#1801276511yescharacteristic
260C2C2×#1801277011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×C4⋊C4×C151C2
socleC22×C151C22×D4
prime radical#23752723C2
hypercenterC22×C4⋊C4D151
hypocenterC151#3092
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23752547C2semidirect
3. #23752542C2semidirect
4. #23752530C2semidirect
5. #23752525C2semidirect
6. #23752252C2semidirect
7. #23752211C2semidirect
8. #23752176C2semidirect
9. C22×C4⋊C4×C151C2semidirect
21. #18012672C22semidirect
22. #18012670C22semidirect
23. #18012662C22semidirect
24. #18012659C22semidirect
130. C151#3092semidirect
133. C22×C4⋊C4D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
#237525472
#237525422
#237525302
#237525252
#237522522
#237522112
#237521762
C22×C4⋊C4×C1512
#3092151