Finite Group Databasebeta

← #34081718

Subgroups — #34081718

Order 19328.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752933C211yesmaximal, characteristic
2#23752917C211yesmaximal, characteristic
3#23752609C211yesmaximal, characteristic, complemented
4#23752556C211yesmaximal, characteristic, complemented
5#23752554C211yesmaximal, characteristic, complemented
6#23752541C211yesmaximal, characteristic, complemented
7#23752505C211yesmaximal, characteristic, complemented
8#23752496C211yesmaximal, characteristic, complemented
9#23752469C211yesmaximal, characteristic, complemented
10#23752468C211yesmaximal, characteristic, complemented
11#23752304C211yesmaximal, characteristic, complemented
12#23752287C211yesmaximal, characteristic
13#23752252C211yesmaximal, characteristic, complemented
14#23752251C211yesmaximal, characteristic, complemented
15#483×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558988C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012734—21no—
22#18012732—21no—
23#18012729—21no—
24#18012725—21no—
25#18012719C2211yescharacteristic
26#18012718—21no—
27#18012718C2211yescharacteristic
28#18012717—21no—
29#18012715C2211yescharacteristic
30Q8×Dic151C2211yescharacteristic
31#18012704—21no—
32#18012704C2211yescharacteristic
33C4×C22⋊D151—21no—
34C4×C22⋊D151C2211yescharacteristic
35#18012698C2211yescharacteristic
36#18012697C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012670C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012662C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×C22⋊D151D411yescharacteristic
63C2×C4×D151—21no—
64C2×C4×D151C2311yescharacteristic
65#14558994—22no—
66#14558988—22no—
67#14558987—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151D411yescharacteristic
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151C2311yescharacteristic
94C2×Q8×C151C2311yescharacteristic
95C22×C4×C151—21no—
96C22×C4×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22×D151C2×D411yescharacteristic
106Dic302—21no—
107Dic302—21no—
108Dic302—42no—
109Dic302—81no—
110C22⋊D151—22no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C4×D151—21no—
119C4×D151—21no—
120C4×D151—81no—
121C151⋊C8—21no—
122C151⋊C8#4112yes—
123C23×C151C2×D411yescharacteristic
124Q8×C151—21no—
125Q8×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—81no—
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2411yescharacteristic
135C8×C151—21no—
136C8×C151—21no—
137C22×C151—21no—
138C22×C151—21no—
139C22×C151—21no—
140C22×C151C22×D411yescharacteristic
141C2×D151—21no—
142C2×D151—21no—
143C2×D151—21no—
144C4×C151—21no—
145C4×C151—41no—
146C4×C151—41no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151C2×#4111yescharacteristic
150C4×C1512−1+411yescharacteristic
151Dic151—21no—
152Dic151—21no—
153Dic151—41no—
154Dic151—41no—
155Dic151—41no—
156Dic151—41no—
157Dic151#13712yes—
158C2×C151—41no—
159C2×C151#54711yescharacteristic
160C2×C151C2×#13711yescharacteristic
161C2×C151#57711yescharacteristic
162D151—41no—
163C151#335611yescharacteristic, complemented, Sylow
164#3356—1511nomaximal, Sylow
165#556—1511no—
166#554—1511no—
167#498—1511no—
168#485—1511no—
169#485—1511no—
170#483—1511no—
171#483D15111yescharacteristic, complemented
172#477—1511no—
173#475—1511no—
174#470—1511no—
175#470—1511no—
176C4×Q16—1511no—
177#436—1511no—
178#428—1511no—
179#428—1511no—
180C2×Q16—1511no—
181C2×M16—1511no—
182C2×M16—1511no—
183C4⋊Q8—1511no—
184C4⋊Q8—1511no—
185#126—3021no—
186#126—3021no—
187#125—3021no—
188#124—3021no—
189C22⋊Q8—3021no—
190C22⋊Q8—3021no—
191C22⋊Q8—1511no—
192C22⋊Q8—1511no—
193C22⋊Q8—1511no—
194C22⋊Q8C2×D15111yescharacteristic
195C4×Q8—3021no—
196C4×Q8—1511no—
197C4×Q8—1511no—
198C4×D4—3021no—
199C4×D4—1511no—
200#117—1511no—
201#117—1511no—
202C2×C4⋊C4—1511no—
203C2×C4⋊C4C2×D15111yescharacteristic
204#107—1511no—
205#107—1511no—
206#107—1511no—
207#106—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211#106C2×D15111yescharacteristic
212#106C2×D15111yescharacteristic
213C4⋊C8—1511no—
214#103—1511no—
215#103—1511no—
216#103—1511no—
217#103—1511no—
218#103C2×D15111yescharacteristic
219#103C2×D15111yescharacteristic
220C22⋊C8—1511no—
221C22⋊C8C2×D15111yescharacteristic
222C4×C8—1511no—
223C2×Q8—3021no—
224C2×Q8—3021no—
225C2×Q8—1511no—
226C2×Q8C22×D15111yescharacteristic
227C2×D4—1511no—
228C22×C4—21no—
229C22×C4—3021no—
230C22×C4—1511no—
231C22×C4C22×D15111yescharacteristic
232Q16—3022no—
233M16—3022no—
234M16—3022no—
235C2×C8—1511no—
236C2×C8—1511no—
237C2×C8C22×D15111yescharacteristic
238C2×C8C22×D15111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—1511no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4C22×D15111yescharacteristic
254C4⋊C4C22×D15111yescharacteristic
255C4⋊C4C22×D15111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—3021no—
258C22⋊C4—3021no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—1511no—
263C22⋊C4—1511no—
264C42—3021no—
265C42—3021no—
266C42—3021no—
267C42—3021no—
268C42—1511no—
269C23—1511no—
270C23D4×D15111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—3021no—
274Q8—3021no—
275Q8—6042no—
276Q8—12081no—
277D4—3022no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—3021no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—3021no—
291C2×C4—1511no—
292C2×C4—1511no—
293C2×C4—1511no—
294C2×C4—12081no—
295C2×C4D4×D15111yescharacteristic
296C2×C4C23×D15111yescharacteristic
297C8—21no—
298C8—21no—
299C8—3021no—
300C8—1512no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—3021no—
305C22—3021no—
306C22—3021no—
307C22C2×D4×D15111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3021no—
314C4—3021no—
315C4—6041no—
316C4—6041no—
317C4—6041no—
318C4—6041no—
319C4—1512no—
320C4#41×D15111yescharacteristic
321C4#1801278611yescharacteristic
322C2—41no—
323C2—6041no—
324C2#2375286011yescharacteristic
325C2#137×D15111yescharacteristic
326C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#483×C151C2
socleC22×C151C22×D4
prime radicalC2×C22⋊D151D4
hypercenter#483D151
hypocenterC151#3356
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #23752609C2semidirect
4. #23752556C2semidirect
5. #23752554C2semidirect
6. #23752541C2semidirect
7. #23752505C2semidirect
8. #23752496C2semidirect
9. #23752469C2semidirect
10. #23752468C2semidirect
11. #23752304C2semidirect
13. #23752252C2semidirect
14. #23752251C2semidirect
15. #483×C151C2semidirect
163. C151#3356semidirect
171. #483D151semidirect

Maximal subgroups

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

subgroupindex
#237529332
#237529172
#237526092
#237525562
#237525542
#237525412
#237525052
#237524962
#237524692
#237524682
#237523042
#237522872
#237522522
#237522512
#483×C1512
#3356151