Finite Group Databasebeta

← #34081798

Subgroups — #34081798

Order 19328.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752939C211yesmaximal, characteristic, complemented
2#23752934C211yesmaximal, characteristic
3#23752569C211yesmaximal, characteristic
4#23752568C211yesmaximal, characteristic
5#23752561C211yesmaximal, characteristic, complemented
6#23752522C211yesmaximal, characteristic, complemented
7#23752491C211yesmaximal, characteristic
8#23752437C211yesmaximal, characteristic
9#23752435C211yesmaximal, characteristic
10#23752421C211yesmaximal, characteristic, complemented
11#23752336C211yesmaximal, characteristic, complemented
12#23752306C211yesmaximal, characteristic, complemented
13C4×#14558994C211yesmaximal, characteristic, complemented
14#23752299C211yesmaximal, characteristic
15#479×C151C211yesmaximal, characteristic, complemented
16C2×Dic604C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19#18012738—21no—
20#18012738C2211yescharacteristic
21#18012737C2211yescharacteristic
22#18012734—21no—
23#18012733—21no—
24#18012730C2211yescharacteristic
25#18012729—21no—
26#18012729—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#18012672C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C4×C151⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302D411yescharacteristic
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C4×D151—21no—
65Dic604—22no—
66#14558994—22no—
67#14558993—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151—21no—
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×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C2×C8×C151C2311yescharacteristic
97C4⋊C4×C151—21no—
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—42no—
111Dic302#4112yes—
112D604—21no—
113D604—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—42no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124Q8×C151—21no—
125Q8×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151C2×D411yescharacteristic
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2411yescharacteristic
133C8×C151—21no—
134C8×C151—21no—
135C22×C151C22×D411yescharacteristic
136C2×D151—41no—
137C2×D151—41no—
138C2×D151—41no—
139C4×C151—21no—
140C4×C151—21no—
141C4×C151—41no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151C2×#4111yescharacteristic
146C4×C1512−1+411yescharacteristic
147Dic151—22no—
148Dic151—21no—
149Dic151—21no—
150Dic151—21no—
151Dic151—41no—
152Dic151—41no—
153Dic151#13512yes—
154C2×C151#54811yescharacteristic
155C2×C151C2×#13511yescharacteristic
156C2×C151#57811yescharacteristic
157D151—81no—
158C151#336411yescharacteristic, complemented, Sylow
159#3364—1511nomaximal, Sylow
160#557—1511no—
161#556—1511no—
162#488—1511no—
163#488—1511no—
164#487—1511no—
165#479—1511no—
166#479D15111yescharacteristic, complemented
167#474—1511no—
168#464—1511no—
169#464—1511no—
170#462—1511no—
171C8×Q8—1511no—
172C4×Q16—1511no—
173C4×Q16—1511no—
174C4×SD16—1511no—
175C2×Q16—1511no—
176C2×Q16—1511no—
177C2×SD16—1511no—
178C4⋊Q8—3021no—
179C4⋊Q8—1511no—
180C4⋊Q8—1511no—
181#126—3021no—
182#126—3021no—
183#125—3021no—
184#125—3021no—
185#125—1511no—
186#125C2×D15111yescharacteristic
187#124—1511no—
188#124—1511no—
189C22⋊Q8—3021no—
190C4×Q8—3021no—
191C4×Q8—1511no—
192C4×Q8—1511no—
193C4×Q8—1511no—
194C4×Q8—1511no—
195C4×Q8—1511no—
196C4×Q8C2×D15111yescharacteristic
197C4×D4—1511no—
198#117—3021no—
199#107—1511no—
200#107C2×D15111yescharacteristic
201#106C2×D15111yescharacteristic
202C4⋊C8—1511no—
203C4⋊C8—1511no—
204C4⋊C8C2×D15111yescharacteristic
205#103—1511no—
206#103—1511no—
207#103—1511no—
208#103—1511no—
209#103—1511no—
210#103C2×D15111yescharacteristic
211#103C2×D15111yescharacteristic
212#102—1511no—
213#102—1511no—
214#102—1511no—
215C4×C8—1511no—
216C4×C8—1511no—
217C4×C8—1511no—
218C2×Q8—3021no—
219C2×Q8—1511no—
220C2×Q8—1511no—
221C2×Q8—1511no—
222C2×Q8C22×D15111yescharacteristic
223C2×D4—1511no—
224C22×C4—3021no—
225Q16—3022no—
226Q16—3022no—
227SD16—3022no—
228C2×C8—1511no—
229C2×C8—1511no—
230C2×C8C22×D15111yescharacteristic
231C2×C8C22×D15111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—3021no—
236C4⋊C4—3021no—
237C4⋊C4—3021no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—3021no—
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—1511no—
245C4⋊C4—1511no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4C22×D15111yescharacteristic
249C4⋊C4C22×D15111yescharacteristic
250C4⋊C4C22×D15111yescharacteristic
251C22⋊C4—3021no—
252C22⋊C4—3021no—
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C42—21no—
257C42—3021no—
258C42—3021no—
259C42—3021no—
260C42—3021no—
261C42—1511no—
262C42—1511no—
263C42C22×D15111yescharacteristic
264C23—3021no—
265Q8—21no—
266Q8—21no—
267Q8—3022no—
268Q8—3021no—
269Q8—3021no—
270Q8—3021no—
271Q8—6042no—
272Q8—1512no—
273D4—3021no—
274D4—3021no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—3021no—
280C2×C4—3021no—
281C2×C4—3021no—
282C2×C4—6042no—
283C2×C4—1511no—
284C2×C4—1511no—
285C2×C4—1511no—
286C2×C4—1511no—
287C2×C4D4×D15111yescharacteristic
288C2×C4D4×D15111yescharacteristic
289C2×C4C23×D15111yescharacteristic
290C8—21no—
291C8—21no—
292C8—3021no—
293C8—3021no—
294C22—6041no—
295C22—6041no—
296C22—6041no—
297C22C2×D4×D15111yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—3021no—
305C4—3021no—
306C4—3021no—
307C4—3022no—
308C4—6041no—
309C4—6041no—
310C4—1512no—
311C4#41×D15111yescharacteristic
312C4#1801278711yescharacteristic
313C2—12081no—
314C2#2375287211yescharacteristic
315C2#135×D15111yescharacteristic
316C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
prime radicalC2×D604C23
hypercenter#479D151
hypocenterC151#3364
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23752939C2semidirect
5. #23752561C2semidirect
6. #23752522C2semidirect
10. #23752421C2semidirect
11. #23752336C2semidirect
12. #23752306C2semidirect
13. C4×#14558994C2semidirect
15. #479×C151C2semidirect
158. C151#3364semidirect
166. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237529392
#237529342
#237525692
#237525682
#237525612
#237525222
#237524912
#237524372
#237524352
#237524212
#237523362
#237523062
C4×#145589942
#237522992
#479×C1512
#3364151