Finite Group Databasebeta

← #34081762

Subgroups — #34081762

Order 19328.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752934C211yesmaximal, characteristic, complemented
2#23752918C211yesmaximal, characteristic, complemented
3#23752569C211yesmaximal, characteristic, complemented
4#23752568C211yesmaximal, characteristic, complemented
5#23752561C211yesmaximal, characteristic, complemented
6#23752518C211yesmaximal, characteristic, complemented
7#23752501C211yesmaximal, characteristic, complemented
8#23752430C211yesmaximal, characteristic
9#23752428C211yesmaximal, characteristic
10#23752416C211yesmaximal, characteristic, complemented
11#23752336C211yesmaximal, characteristic, complemented
12C4×#14558991C211yesmaximal, characteristic, complemented
13#23752299C211yesmaximal, characteristic, complemented
14#23752294C211yesmaximal, characteristic
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14558993C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012737C2211yescharacteristic
21#18012734—21no—
22#18012733—21no—
23#18012730C2211yescharacteristic
24#18012728C2211yescharacteristic
25#18012727C2211yescharacteristic
26#18012719—21no—
27#18012717—21no—
28#18012717—21no—
29#18012717—21no—
30C4×Dic302C2211yescharacteristic
31#18012704C2211yescharacteristic
32C4×D604C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35#18012701C2211yescharacteristic
36#18012696—21no—
37C4⋊C4×D151—21no—
38#18012670C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012659C2211yescharacteristic
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×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C4×D151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68#14558993—22no—
69#14558991—22no—
70D1208—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151C2311yescharacteristic
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—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—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—
106C22×D151—21no—
107Dic302—22no—
108Dic302—21no—
109Dic302—21no—
110Dic302—81no—
111D604—21no—
112D604—21no—
113D604—21no—
114D604#4112yes—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—42no—
122C4×D151—42no—
123C4×D151—81no—
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127Q8×C151—21no—
128Q8×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2×D411yescharacteristic
135C2×C4×C151C2411yescharacteristic
136C8×C151—21no—
137C8×C151—21no—
138C22×C151C22×D411yescharacteristic
139C2×D151—22no—
140C2×D151—41no—
141C2×D151—41no—
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C4×C151—21no—
146C4×C151—21no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151C2×#4111yescharacteristic
152C4×C1512−1+411yescharacteristic
153Dic151—21no—
154Dic151—21no—
155Dic151—21no—
156Dic151—41no—
157Dic151—41no—
158Dic151#13512yes—
159C2×C151#54811yescharacteristic
160C2×C151C2×#13511yescharacteristic
161C2×C151#57711yescharacteristic
162D151—42no—
163D151—81no—
164C151#336011yescharacteristic, complemented, Sylow
165#3360—1511nomaximal, Sylow
166#556—1511no—
167#554—1511no—
168#488—1511no—
169#488—1511no—
170#487—1511no—
171#479—1511no—
172#479D15111yescharacteristic, complemented
173#476—1511no—
174#463—1511no—
175#463—1511no—
176#461—1511no—
177C8×Q8—1511no—
178C4×SD16—1511no—
179C4×SD16—1511no—
180C4×D8—1511no—
181C2×SD16—1511no—
182C2×SD16—1511no—
183C2×D8—1511no—
184C4⋊Q8—1511no—
185C4⋊Q8—1511no—
186#126—3021no—
187#126—3021no—
188#125—1511no—
189#125C2×D15111yescharacteristic
190#124—1511no—
191#124—1511no—
192C22⋊Q8—3021no—
193C22⋊Q8—3021no—
194C22⋊Q8—3021no—
195C22⋊Q8—3021no—
196C4×Q8—1511no—
197C4×Q8—1511no—
198C4×Q8C2×D15111yescharacteristic
199C4×D4—1511no—
200C4×D4—1511no—
201C4×D4—1511no—
202C4×D4—1511no—
203#117—3021no—
204C2×C4⋊C4—3021no—
205#107C2×D15111yescharacteristic
206#106—1511no—
207#106C2×D15111yescharacteristic
208C4⋊C8—1511no—
209C4⋊C8—1511no—
210C4⋊C8C2×D15111yescharacteristic
211#103—1511no—
212#103—1511no—
213#103—1511no—
214#103—1511no—
215#103C2×D15111yescharacteristic
216#103C2×D15111yescharacteristic
217#102—1511no—
218#102—1511no—
219#102—1511no—
220#102—1511no—
221C4×C8—1511no—
222C4×C8—1511no—
223C4×C8—1511no—
224C2×Q8—3021no—
225C2×Q8—1511no—
226C2×Q8—1511no—
227C2×Q8C22×D15111yescharacteristic
228C2×D4—1511no—
229C2×D4—1511no—
230C22×C4—3021no—
231C22×C4—3021no—
232C22×C4—3021no—
233C22×C4—3021no—
234SD16—3022no—
235SD16—3022no—
236D8—3022no—
237C2×C8—1511no—
238C2×C8—1511no—
239C2×C8C22×D15111yescharacteristic
240C2×C8C22×D15111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4C22×D15111yescharacteristic
255C4⋊C4C22×D15111yescharacteristic
256C4⋊C4C22×D15111yescharacteristic
257C22⋊C4—3021no—
258C22⋊C4—3021no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C42—21no—
266C42—3021no—
267C42—1511no—
268C42—1511no—
269C42C22×D15111yescharacteristic
270C23—3021no—
271C23—3021no—
272Q8—21no—
273Q8—21no—
274Q8—3022no—
275Q8—3021no—
276Q8—3021no—
277Q8—12081no—
278D4—3021no—
279D4—3021no—
280D4—3021no—
281D4—1512no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—6042no—
289C2×C4—6042no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—1511no—
293C2×C4—1511no—
294C2×C4—12081no—
295C2×C4—12081no—
296C2×C4D4×D15111yescharacteristic
297C2×C4D4×D15111yescharacteristic
298C2×C4C23×D15111yescharacteristic
299C8—21no—
300C8—21no—
301C8—3021no—
302C8—3021no—
303C22—3022no—
304C22—6041no—
305C22—6041no—
306C22—6041no—
307C22—6041no—
308C22—6041no—
309C22C2×D4×D15111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3021no—
317C4—3021no—
318C4—3021no—
319C4—6041no—
320C4—6041no—
321C4—1512no—
322C4#41×D15111yescharacteristic
323C4#1801278711yescharacteristic
324C2—6042no—
325C2—12081no—
326C2#2375287211yescharacteristic
327C2#135×D15111yescharacteristic
328C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
prime radicalC2×D1208C22
hypercenter#479D151
hypocenterC151#3360
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. #23752934C2semidirect
2. #23752918C2semidirect
3. #23752569C2semidirect
4. #23752568C2semidirect
5. #23752561C2semidirect
6. #23752518C2semidirect
7. #23752501C2semidirect
10. #23752416C2semidirect
11. #23752336C2semidirect
12. C4×#14558991C2semidirect
13. #23752299C2semidirect
15. #479×C151C2semidirect
164. C151#3360semidirect
172. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237529342
#237529182
#237525692
#237525682
#237525612
#237525182
#237525012
#237524302
#237524282
#237524162
#237523362
C4×#145589912
#237522992
#237522942
#479×C1512
#3360151