Finite Group Databasebeta

← #34081853

Subgroups — #34081853

Order 19328.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752942C211yesmaximal, characteristic, complemented
2#23752934C211yesmaximal, characteristic
3#23752574C211yesmaximal, characteristic
4#23752573C211yesmaximal, characteristic
5#23752561C211yesmaximal, characteristic, complemented
6#23752501C211yesmaximal, characteristic
7#23752496C211yesmaximal, characteristic, complemented
8#23752437C211yesmaximal, characteristic
9#23752435C211yesmaximal, characteristic
10#23752421C211yesmaximal, characteristic, complemented
11#23752341C211yesmaximal, characteristic, complemented
12#23752318C211yesmaximal, characteristic, complemented
13#23752317C211yesmaximal, characteristic, complemented
14#23752299C211yesmaximal, characteristic
15#475×C151C211yesmaximal, characteristic, complemented
16C2×Dic604C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19#18012738—21no—
20#18012738C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012737—21no—
23#18012737—21no—
24#18012737C2211yescharacteristic
25#18012734—21no—
26#18012733—21no—
27#18012728C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012717—21no—
30C4×Dic302C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32#18012704—21no—
33#18012704C2211yescharacteristic
34#18012704C2211yescharacteristic
35#18012704C2211yescharacteristic
36#18012701C2211yescharacteristic
37#18012696—21no—
38#18012670C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302D411yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C4×D151—21no—
66Dic604—22no—
67#14558994—22no—
68#14558993—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151D411yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73Dic151⋊C4—21no—
74Dic151⋊C4—21no—
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151C2311yescharacteristic
93C4×Dic151C2311yescharacteristic
94C2×Q8×C151—21no—
95C2×Q8×C151C2311yescharacteristic
96C2×C8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C42×C151—21no—
104C42×C151C2311yescharacteristic
105C22×D151—21no—
106Dic302—21no—
107Dic302—22no—
108Dic302—21no—
109Dic302—21no—
110Dic302—81no—
111Dic302—81no—
112Dic302#4112yes—
113D604—21no—
114D604—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—42no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125Q8×C151—21no—
126Q8×C151—21no—
127Q8×C151—81no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2411yescharacteristic
135C8×C151—21no—
136C8×C151—21no—
137C22×C151C22×D411yescharacteristic
138C2×D151—41no—
139C2×D151—41no—
140C2×D151—41no—
141C4×C151—21no—
142C4×C151—21no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151—41no—
146C4×C151—41no—
147C4×C151C2×#4111yescharacteristic
148C4×C1512−1+411yescharacteristic
149Dic151—22no—
150Dic151—21no—
151Dic151—21no—
152Dic151—21no—
153Dic151—41no—
154Dic151—41no—
155Dic151#13712yes—
156C2×C151#54811yescharacteristic
157C2×C151C2×#13711yescharacteristic
158C2×C151#57711yescharacteristic
159D151—81no—
160C151#336911yescharacteristic, complemented, Sylow
161#3369—1511nomaximal, Sylow
162Q82—1511no—
163#556—1511no—
164#489—1511no—
165#489—1511no—
166#487—1511no—
167#476—1511no—
168#475—1511no—
169#475D15111yescharacteristic, complemented
170#464—1511no—
171#464—1511no—
172#462—1511no—
173#446—1511no—
174#441—1511no—
175#441—1511no—
176C4×SD16—1511no—
177C2×Q16—1511no—
178C2×Q16—1511no—
179C2×SD16—1511no—
180C4⋊Q8—3021no—
181C4⋊Q8—3021no—
182C4⋊Q8—3021no—
183C4⋊Q8—1511no—
184C4⋊Q8—1511no—
185C4⋊Q8—1511no—
186C4⋊Q8C2×D15111yescharacteristic
187#126—3021no—
188#126—3021no—
189#124—1511no—
190#124—1511no—
191C22⋊Q8—3021no—
192C4×Q8—3021no—
193C4×Q8—1511no—
194C4×Q8—1511no—
195C4×Q8—1511no—
196C4×Q8—1511no—
197C4×Q8—1511no—
198C4×Q8C2×D15111yescharacteristic
199C4×D4—1511no—
200#117—3021no—
201#106—1511no—
202#106C2×D15111yescharacteristic
203#106C2×D15111yescharacteristic
204C4⋊C8—1511no—
205C4⋊C8—1511no—
206C4⋊C8C2×D15111yescharacteristic
207#103—1511no—
208#103—1511no—
209#103—1511no—
210#103—1511no—
211#103—1511no—
212#103C2×D15111yescharacteristic
213#103C2×D15111yescharacteristic
214#102—1511no—
215#102—1511no—
216#102—1511no—
217#97—1511no—
218#97—1511no—
219C4×C8—1511no—
220C2×Q8—21no—
221C2×Q8—3021no—
222C2×Q8—3021no—
223C2×Q8—1511no—
224C2×Q8—1511no—
225C2×Q8—1511no—
226C2×Q8C22×D15111yescharacteristic
227C2×D4—1511no—
228C22×C4—3021no—
229Q16—3022no—
230Q16—3022no—
231SD16—3022no—
232C2×C8—1511no—
233C2×C8—1511no—
234C2×C8C22×D15111yescharacteristic
235C2×C8C22×D15111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—3021no—
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4—1511no—
249C4⋊C4—1511no—
250C4⋊C4C22×D15111yescharacteristic
251C4⋊C4C22×D15111yescharacteristic
252C4⋊C4C22×D15111yescharacteristic
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C22⋊C4—3021no—
257C22⋊C4—3021no—
258C42—21no—
259C42—3021no—
260C42—3021no—
261C42—3021no—
262C42—3021no—
263C42—1511no—
264C42—1511no—
265C42C22×D15111yescharacteristic
266C23—3021no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—3022no—
271Q8—3021no—
272Q8—3021no—
273Q8—3021no—
274Q8—1512no—
275Q8—12081no—
276Q8—12081no—
277D4—3021no—
278D4—3021no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3021no—
284C2×C4—3021no—
285C2×C4—3021no—
286C2×C4—6042no—
287C2×C4—1511no—
288C2×C4—1511no—
289C2×C4—1511no—
290C2×C4—1511no—
291C2×C4D4×D15111yescharacteristic
292C2×C4D4×D15111yescharacteristic
293C2×C4C23×D15111yescharacteristic
294C8—21no—
295C8—21no—
296C8—3021no—
297C8—3021no—
298C22—6041no—
299C22—6041no—
300C22—6041no—
301C22C2×D4×D15111yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—3021no—
309C4—3021no—
310C4—3021no—
311C4—3022no—
312C4—6041no—
313C4—6041no—
314C4—1512no—
315C4#41×D15111yescharacteristic
316C4#1801278711yescharacteristic
317C2—12081no—
318C2#2375287211yescharacteristic
319C2#137×D15111yescharacteristic
320C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#475×C151C2
socleC22×C151C22×D4
prime radicalC2×D604C23
hypercenter#475D151
hypocenterC151#3369
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #23752942C2semidirect
5. #23752561C2semidirect
7. #23752496C2semidirect
10. #23752421C2semidirect
11. #23752341C2semidirect
12. #23752318C2semidirect
13. #23752317C2semidirect
15. #475×C151C2semidirect
160. C151#3369semidirect
169. #475D151semidirect

Maximal subgroups

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

subgroupindex
#237529422
#237529342
#237525742
#237525732
#237525612
#237525012
#237524962
#237524372
#237524352
#237524212
#237523412
#237523182
#237523172
#237522992
#475×C1512
#3369151