Finite Group Databasebeta

← #34079056

Subgroups — #34079056

Order 19328.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#18012715C211yesmaximal, characteristic
2#117×D151C211yesmaximal, characteristic
3#23752552C212yesmaximal, complemented
4#23752551C212yesmaximal, complemented
5#23752546C212yesmaximal, complemented
6#23752541C212yesmaximal, complemented
7#23752255C211yesmaximal, characteristic, complemented
8#23752254C211yesmaximal, characteristic, complemented
9#23752221C211yesmaximal, characteristic, complemented
10#23752175C211yesmaximal, characteristic
11#419×C151C211yesmaximal, characteristic, complemented
12C22×C4×D151C2211yescharacteristic
13C2×#14558988C2211yescharacteristic
14#18012715—21no—
15#18012715—21no—
16#18012715C2212yes—
17#18012715C2212yes—
18#18012698C2211yescharacteristic
19#18012697C2211yescharacteristic
20#18012697C2211yescharacteristic
21#18012696—21no—
22#18012695—21no—
23C2×C4⋊Dic151C2211yescharacteristic
24C2×Dic151⋊C4—21no—
25C4⋊C4×D151C2211yescharacteristic
26C4⋊C4×D151C2211yescharacteristic
27C2×(C2×D151)⋊C4—21no—
28C22⋊C4×D151—21no—
29C42×D151—21no—
30#18012673C2212yescomplemented
31#18012672C2212yescomplemented
32#18012671C2212yescomplemented
33#18012670C2212yescomplemented
34#18012663C2212yescomplemented
35#18012663C2212yescomplemented
36(C2×D151)⋊C8C2212yes—
37(C2×D151)⋊C8C2212yes—
38C22×Q8×C151C2211yescharacteristic
39C2×M16×C151C2211yescharacteristic
40#117×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42#103×C151C2212yescomplemented
43C23×D151D411yescharacteristic
44C22×Dic151—21no—
45C22×Dic151D411yescharacteristic
46C2×C4×D151—21no—
47C2×C4×D151—21no—
48C2×C4×D151—22no—
49C2×C4×D151—22no—
50C2×C4×D151D411yescharacteristic
51C2×C4×D151D411yescharacteristic
52C2×C4×D151C2311yescharacteristic
53C2×C4×D151C2311yescharacteristic
54#14558988—22no—
55C2×C151⋊C8C2312yes—
56C4⋊Dic151—21no—
57C4⋊Dic151C2312yes—
58C4⋊Dic151C2311yescharacteristic
59C4⋊Dic151C2311yescharacteristic
60Dic151⋊C4—21no—
61Dic151⋊C4—21no—
62Dic151⋊C4—22no—
63Dic151⋊C4—22no—
64C22⋊Dic151—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69C4×Dic151—21no—
70C4×Dic151—21no—
71C4×Dic151—21no—
72C2×Q8×C151—21no—
73C2×Q8×C151—22no—
74C2×Q8×C151—22no—
75C2×Q8×C151C2312yes—
76C22×C4×C151—21no—
77C22×C4×C151C2311yescharacteristic
78M16×C151—22no—
79C2×C8×C151C2312yes—
80C4⋊C4×C151C2311yescharacteristic
81C4⋊C4×C151C2311yescharacteristic
82C22⋊C4×C151—21no—
83C42×C151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—41no—
87C22×D151C2×D411yescharacteristic
88C22×D151C2×D411yescharacteristic
89C2×Dic151—22no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151—22no—
93C2×Dic151—42no—
94C2×Dic151C2×D411yescharacteristic
95C2×Dic151C2×D411yescharacteristic
96C4×D151—22no—
97C4×D151—22no—
98C4×D151—21no—
99C4×D151—21no—
100C4×D151—21no—
101C4×D151—21no—
102C4×D151—42no—
103C4×D151—42no—
104C151⋊C8—22no—
105C23×C151C2×D411yescharacteristic
106Q8×C151—22no—
107Q8×C151—22no—
108Q8×C151—42no—
109C2×C4×C151—22no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—42no—
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151#4112yes—
115C2×C4×C151#4112yes—
116C2×C4×C151C2411yescharacteristic
117C8×C151—22no—
118C22×C151—21no—
119C22×C151—21no—
120C22×C151#12312yes—
121C22×C151C22×D411yescharacteristic
122C2×D151—21no—
123C2×D151—21no—
124C2×D151—21no—
125C2×D151—21no—
126C2×D151—21no—
127C2×D151—44no—
128C2×D151#13712yes—
129C4×C151—42no—
130C4×C151—41no—
131C4×C151—41no—
132C4×C151#12312yes—
133C4×C151C2×#4111yescharacteristic
134C4×C151C2×#4111yescharacteristic
135Dic151—21no—
136Dic151—21no—
137Dic151—41no—
138Dic151—41no—
139Dic151—42no—
140C2×C151—22no—
141C2×C151C2×#12311yescharacteristic
142C2×C151C2×#13711yescharacteristic
143C2×C151#57511yescharacteristic
144D151—22no—
145D151—41no—
146C151#309511yescharacteristic, complemented, Sylow
147#3095—1511nomaximal, Sylow
148C2×C22⋊Q8—1511no—
149C2×#117—1511no—
150#485—1512no—
151#485—1512no—
152#484—1512no—
153#483—1512no—
154#428—1511no—
155#428—1511no—
156#419—1511no—
157#419D15111yescharacteristic, complemented
158#407—1511no—
159C22×Q8C2×D15111yescharacteristic
160C23×C4—1511no—
161C2×M16—1511no—
162C2×M16C2×D15111yescharacteristic
163C22⋊Q8—3021no—
164C22⋊Q8—3021no—
165C22⋊Q8—1512no—
166C22⋊Q8—1512no—
167#117—3021no—
168#117—3021no—
169#117—1511no—
170#117—1511no—
171#117—1511no—
172#117C2×D15111yescharacteristic
173C2×C4⋊C4—3021no—
174C2×C4⋊C4—1511no—
175C2×C4⋊C4—1511no—
176C2×C4⋊C4—1511no—
177C2×C22⋊C4—3021no—
178C2×C22⋊C4—3021no—
179C2×C42—3021no—
180#107—1512no—
181#107—1512no—
182#106—1512no—
183#106—1512no—
184#103—1512no—
185#103—1512no—
186#103C2×D15112yescomplemented
187#103C2×D15112yescomplemented
188C22⋊C8—1512no—
189C22⋊C8—1512no—
190C24—1511no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8C22×D15112yes—
195C22×C4—21no—
196C22×C4—3021no—
197C22×C4—3021no—
198C22×C4—3022no—
199C22×C4—3022no—
200C22×C4—3021no—
201C22×C4—1511no—
202C22×C4—1511no—
203C22×C4—1511no—
204C22×C4—1511no—
205C22×C4—1511no—
206C22×C4C22×D15111yescharacteristic
207M16—22no—
208M16—3022no—
209C2×C8—1512no—
210C2×C8C22×D15112yes—
211C4⋊C4—3022no—
212C4⋊C4—3022no—
213C4⋊C4—3021no—
214C4⋊C4—3021no—
215C4⋊C4—3021no—
216C4⋊C4—1511no—
217C4⋊C4—1511no—
218C4⋊C4—1512no—
219C4⋊C4C22×D15111yescharacteristic
220C4⋊C4C22×D15111yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—3021no—
223C22⋊C4—3021no—
224C22⋊C4—3022no—
225C22⋊C4—3022no—
226C22⋊C4—3021no—
227C42—21no—
228C42—3021no—
229C42—3021no—
230C42—3021no—
231C23—3022no—
232C23—3022no—
233C23—6041no—
234C23—1511no—
235C23—1511no—
236C23D4×D15111yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—3022no—
245C2×C4—3022no—
246C2×C4—3022no—
247C2×C4—3021no—
248C2×C4—3021no—
249C2×C4—3021no—
250C2×C4—3021no—
251C2×C4—3021no—
252C2×C4—3021no—
253C2×C4—3022no—
254C2×C4—6042no—
255C2×C4—6042no—
256C2×C4—6042no—
257C2×C4—1511no—
258C2×C4—1511no—
259C2×C4D4×D15111yescharacteristic
260C2×C4#1455900312yes—
261C2×C4#1455900412yes—
262C2×C4C23×D15111yescharacteristic
263C8—22no—
264C8—3022no—
265C22—21no—
266C22—21no—
267C22—3021no—
268C22—3021no—
269C22—3021no—
270C22—3021no—
271C22—3021no—
272C22—6044no—
273C22—1512no—
274C22#1801272112yes—
275C22C2×D4×D15111yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—3021no—
280C4—3021no—
281C4—6041no—
282C4—6041no—
283C4—6042no—
284C4#1801272112yes—
285C4C2×#1455900311yescharacteristic
286C4C2×#1455900411yescharacteristic
287C2—22no—
288C2—3022no—
289C2—6041no—
290C2C2×#1801272111yescharacteristic
291C2#137×D15111yescharacteristic
292C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#419×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#419D151
hypocenterC151#3095
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #23752552C2semidirect
4. #23752551C2semidirect
5. #23752546C2semidirect
6. #23752541C2semidirect
7. #23752255C2semidirect
8. #23752254C2semidirect
9. #23752221C2semidirect
11. #419×C151C2semidirect
30. #18012673C22semidirect
31. #18012672C22semidirect
32. #18012671C22semidirect
33. #18012670C22semidirect
34. #18012663C22semidirect
35. #18012663C22semidirect
41. #103×C151C22semidirect
42. #103×C151C22semidirect
146. C151#3095semidirect
157. #419D151semidirect
186. #103C2×D151semidirect
187. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127152
#117×D1512
#237525522
#237525512
#237525462
#237525412
#237522552
#237522542
#237522212
#237521752
#419×C1512
#3095151