Finite Group Databasebeta

← #34067613

Subgroups — #34067613

Order 19328.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#23752725C211yesmaximal, characteristic
2#23752174C211yesmaximal, characteristic, complemented
3#95×D151C211yesmaximal, characteristic, complemented
4#23751949C211yesmaximal, characteristic, complemented
5#23751947C211yesmaximal, characteristic, complemented
6#23751945C211yesmaximal, characteristic, complemented
7#328×C151C211yesmaximal, characteristic, complemented
8C2×#14559005C411yescharacteristic, complemented
9C22×C4×D151—21no—
10C22×C4×D151C2211yescharacteristic
11C2×#14558987—21no—
12#18012724—21no—
13#18012715C411yescharacteristic, complemented
14#18012714C411yescharacteristic, complemented
15#18012713C2211yescharacteristic
16#18012709—21no—
17#18012701—21no—
18(C22⋊D151)⋊C4—21no—
19#18012697C411yescharacteristic, complemented
20C22⋊(C151⋊C8)C2211yescharacteristic
21(C2×D151)⋊C8—21no—
22C151⋊#95—21no—
23C151⋊#95C2211yescharacteristic
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28#14559005—42no—
29C2×D604—21no—
30C2×D604—21no—
31C2×D604C2×C411yescharacteristic, complemented
32C2×C22⋊D151—21no—
33C22×Dic151—21no—
34C22×Dic151D411yescharacteristic
35C2×C4×D151—24no—
36C2×C4×D151—21no—
37C2×C4×D151—42no—
38C2×C4×D151—42no—
39C2×C4×D151—42no—
40C2×C4×D151C2×C411yescharacteristic
41C2×C4×D151C2×C411yescharacteristic
42C2×C4×D151D411yescharacteristic
43C2×C4×D151D411yescharacteristic
44#14558987—42no—
45C2×C151⋊C8—21no—
46C4⋊Dic151C2×C411yescharacteristic, complemented
47Dic151⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52C4×Dic151—21no—
53C2×Q8×C151C2×C411yescharacteristic, complemented
54C22×C4×C151—21no—
55C22×C4×C151C2311yescharacteristic
56C2×C8×C151—21no—
57C4⋊C4×C151—21no—
58C4⋊C4×C151C2×C411yescharacteristic, complemented
59C22⋊C4×C151—21no—
60C22×D151—21no—
61C22×D151—21no—
62C22×D151—22no—
63C22×D151—22no—
64C22×D151—21no—
65C22×D151C22⋊C411yescharacteristic
66C22×D151C22⋊C411yescharacteristic
67D604—41no—
68D604—42no—
69D604—42no—
70C22⋊D151—41no—
71C22⋊D151—41no—
72C2×Dic151—22no—
73C2×Dic151—21no—
74C2×Dic151—41no—
75C2×Dic151—41no—
76C2×Dic151—41no—
77C2×Dic151C22⋊C411yescharacteristic
78C2×Dic151C22⋊C411yescharacteristic
79C4×D151—22no—
80C4×D151—22no—
81C4×D151—41no—
82C4×D151—41no—
83C4×D151—42no—
84C4×D151—48no—
85C151⋊C8—41no—
86C23×C151C2×D411yescharacteristic
87Q8×C151—41no—
88C2×C4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—41no—
92C2×C4×C151—41no—
93C2×C4×C151—41no—
94C2×C4×C151C22×C411yescharacteristic
95C2×C4×C151C2×D411yescharacteristic
96C8×C151—41no—
97C22×C151—21no—
98C22×C151—21no—
99C22×C151C2×C22⋊C411yescharacteristic
100C22×C151AGL(1,ℤ/8)11yescharacteristic
101C22×C151#13711yescharacteristic
102C2×D151—24no—
103C2×D151—24no—
104C2×D151—21no—
105C2×D151—21no—
106C2×D151—21no—
107C2×D151—21no—
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—41no—
111C2×D151#9912yes—
112C2×D151#10412yes—
113C4×C151—21no—
114C4×C151—21no—
115C4×C151—42no—
116C4×C151—41no—
117C4×C151—41no—
118Dic151—21no—
119Dic151—21no—
120Dic151—42no—
121Dic151—41no—
122C2×C151—21no—
123C2×C151—21no—
124C2×C151C2×#9911yescharacteristic
125C2×C151#41711yescharacteristic
126C2×C151C2×#10411yescharacteristic
127D151—22no—
128D151—22no—
129D151—81no—
130C151#150411yescharacteristic, complemented, Sylow
131#1504—1511nomaximal, Sylow
132#525—1511no—
133#407—1511no—
134C2×#95—1511no—
135#328—1511no—
136#328D15111yescharacteristic, complemented
137#327—1511no—
138#327—1511no—
139C2×#41—1511no—
140C23×C4—3021no—
141C23×C4—1511no—
142C2×M16—3021no—
143#123—3021no—
144C22⋊Q8—1511no—
145C22⋊Q8C2×D15111yescharacteristic
146#121—1511no—
147#121—1511no—
148#120—3021no—
149C4×D4—3021no—
150C4×D4—3021no—
151#117—1511no—
152C22⋊C8—3021no—
153C22⋊C8—1511no—
154C22⋊C8C2×D15111yescharacteristic
155#95—3021no—
156#95—1511no—
157#95C2×D15111yescharacteristic
158C24—1511no—
159#41—6042no—
160C2×Q8C4×D15111yescharacteristic, complemented
161C2×D4—3021no—
162C2×D4—3021no—
163C2×D4—3021no—
164C2×D4—1511no—
165C22×C4—21no—
166C22×C4—3024no—
167C22×C4—3021no—
168C22×C4—3021no—
169C22×C4—6042no—
170C22×C4—6042no—
171C22×C4—6042no—
172C22×C4—1511no—
173C22×C4—1511no—
174C22×C4—1511no—
175C22×C4—1511no—
176C22×C4—1511no—
177C22×C4C22×D15111yescharacteristic
178M16—6042no—
179C2×C8—21no—
180C2×C8—3021no—
181C4⋊C4—21no—
182C4⋊C4—3021no—
183C4⋊C4—1511no—
184C4⋊C4C4×D15111yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—3021no—
187C22⋊C4—3021no—
188C22⋊C4—3021no—
189C22⋊C4—3021no—
190C42—3021no—
191C23—3022no—
192C23—3022no—
193C23—3021no—
194C23—3021no—
195C23—3021no—
196C23—1511no—
197C23—1511no—
198C23D4×D15111yescharacteristic
199Q8—41no—
200D4—6041no—
201D4—6042no—
202D4—6042no—
203D4—6041no—
204D4—6041no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3022no—
212C2×C4—3022no—
213C2×C4—3022no—
214C2×C4—3021no—
215C2×C4—6041no—
216C2×C4—6041no—
217C2×C4—6042no—
218C2×C4—6048no—
219C2×C4—6041no—
220C2×C4—6041no—
221C2×C4—6041no—
222C2×C4—1511no—
223C2×C4—1511no—
224C2×C4C2×C4×D15111yescharacteristic
225C2×C4D4×D15111yescharacteristic
226C8—41no—
227C8—6041no—
228C22—21no—
229C22—21no—
230C22—3024no—
231C22—3024no—
232C22—3021no—
233C22—3021no—
234C22—3021no—
235C22—3021no—
236C22—6041no—
237C22—6041no—
238C22—6041no—
239C22—1512no—
240C22—1512no—
241C22C22⋊C4×D15111yescharacteristic
242C22#1801276611yescharacteristic
243C22#1801277111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3021no—
250C4—3021no—
251C4—6042no—
252C4—6041no—
253C2—21no—
254C2—21no—
255C2—3022no—
256C2—3022no—
257C2—12081no—
258C2#99×D15111yescharacteristic
259C2#2375221211yescharacteristic
260C2#104×D15111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752725C2
cosocleC22×C4×C151C23
hypercenter#328D151
hypocenterC151#1504
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23752174C2semidirect
3. #95×D151C2semidirect
4. #23751949C2semidirect
5. #23751947C2semidirect
6. #23751945C2semidirect
7. #328×C151C2semidirect
8. C2×#14559005C4semidirect
13. #18012715C4semidirect
14. #18012714C4semidirect
19. #18012697C4semidirect
31. C2×D604C2×C4semidirect
46. C4⋊Dic151C2×C4semidirect
53. C2×Q8×C151C2×C4semidirect
58. C4⋊C4×C151C2×C4semidirect
130. C151#1504semidirect
136. #328D151semidirect
160. C2×Q8C4×D151semidirect
184. C4⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#237521742
#95×D1512
#237519492
#237519472
#237519452
#328×C1512
#1504151