Finite Group Databasebeta

← #34080273

Subgroups — #34080273

Order 19328.

334 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752741C211yesmaximal, characteristic
2#125×D151C211yesmaximal, characteristic, complemented
3#23752614C211yesmaximal, characteristic, complemented
4#23752611C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752546C211yesmaximal, characteristic, complemented
7#23752541C211yesmaximal, characteristic, complemented
8#23752529C211yesmaximal, characteristic
9#23752524C211yesmaximal, characteristic
10#23752521C211yesmaximal, characteristic, complemented
11#23752517C211yesmaximal, characteristic, complemented
12#23752514C211yesmaximal, characteristic, complemented
13#23752510C211yesmaximal, characteristic, complemented
14#23752263C211yesmaximal, characteristic, complemented
15#488×C151C211yesmaximal, characteristic, complemented
16#18012732—21no—
17#18012731C2211yescharacteristic
18#18012731C2211yescharacteristic
19#18012730C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012729—21no—
22#18012729—21no—
23#18012721—21no—
24#18012715C2211yescharacteristic
25#18012710C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27D4×Dic151C2211yescharacteristic
28(C22⋊D151)⋊C4—21no—
29#18012695—21no—
30C4⋊C4×D151—21no—
31C4⋊C4×D151—21no—
32C4⋊C4×D151C2211yescharacteristic
33C4⋊C4×D151C2211yescharacteristic
34C42×D151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012673C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
52#125×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59C2×C22⋊D151—21no—
60C22×Dic151—21no—
61C2×C4×D151—21no—
62C2×C4×D151—21no—
63C2×C4×D151D411yescharacteristic
64C2×C4×D151D411yescharacteristic
65C2×C4×D151C2311yescharacteristic
66C2×C151⋊C8C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C4⋊Dic151—21no—
69C4⋊Dic151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151C2311yescharacteristic
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⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87C4×Dic151—21no—
88C4×Dic151D411yescharacteristic
89C4×Dic151D411yescharacteristic
90C4×Dic151C2311yescharacteristic
91C2×Q8×C151C2311yescharacteristic
92C2×D4×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C42×C151C2311yescharacteristic
102C22×D151C2×D411yescharacteristic
103C22⋊D151—42no—
104C2×Dic151—21no—
105C2×Dic151—21no—
106C2×Dic151—21no—
107C2×Dic151—21no—
108C2×Dic151—42no—
109C2×Dic151C2×D411yescharacteristic
110C2×Dic151C2×D411yescharacteristic
111C2×Dic151C2×D411yescharacteristic
112C4×D151—22no—
113C4×D151—21no—
114C4×D151—21no—
115C4×D151—41no—
116C4×D151—42no—
117C4×D151—42no—
118C151⋊C8—21no—
119C151⋊C8—21no—
120C23×C151—21no—
121Q8×C151—21no—
122Q8×C151—21no—
123D4×C151—21no—
124D4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151C2×D411yescharacteristic
129C2×C4×C151C2×D411yescharacteristic
130C2×C4×C151C2411yescharacteristic
131C8×C151—21no—
132C8×C151—21no—
133C22×C151—41no—
134C22×C151—41no—
135C22×C151—41no—
136C22×C151C22×D411yescharacteristic
137C2×D151—21no—
138C2×D151—21no—
139C2×D151#13512yes—
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C1512−1+411yescharacteristic
146C4×C1512−1+411yescharacteristic
147Dic151—21no—
148Dic151—21no—
149Dic151—21no—
150Dic151—41no—
151Dic151—41no—
152Dic151—41no—
153Dic151—41no—
154C2×C151—81no—
155C2×C151#53611yescharacteristic
156C2×C151C2×#13511yescharacteristic
157C2×C151#57511yescharacteristic
158D151—22no—
159C151#323211yescharacteristic, complemented, Sylow
160#3232—1511nomaximal, Sylow
161#529—1511no—
162C2×#125—1511no—
163#499—1511no—
164#499—1511no—
165#488—1511no—
166#488D15111yescharacteristic, complemented
167#484—1511no—
168#483—1511no—
169#481—1511no—
170#480—1511no—
171#479—1511no—
172#479—1511no—
173#478—1511no—
174#478—1511no—
175#431—1511no—
176#126—3021no—
177#125—3021no—
178#125—3021no—
179#125—1511no—
180#125—1511no—
181#125—1511no—
182#125—1511no—
183#125C2×D15111yescharacteristic
184#124C2×D15111yescharacteristic
185#123—3021no—
186C22⋊Q8—1511no—
187#121—1511no—
188C4×Q8—1511no—
189C4×D4—3021no—
190C4×D4—1511no—
191#117—3021no—
192C2×C4⋊C4—3021no—
193C2×C4⋊C4—3021no—
194C2×C4⋊C4—1511no—
195C2×C4⋊C4—1511no—
196C2×C42—1511no—
197#107—1511no—
198#107—1511no—
199#107—1511no—
200#107—1511no—
201#106—1511no—
202#106—1511no—
203#106—1511no—
204#106—1511no—
205C4⋊C8—1511no—
206C4⋊C8—1511no—
207#103—1511no—
208#103—1511no—
209#103C2×D15111yescharacteristic
210#103C2×D15111yescharacteristic
211#102—1511no—
212#102—1511no—
213#102C2×D15111yescharacteristic
214#102C2×D15111yescharacteristic
215C22⋊C8—1511no—
216C22⋊C8—1511no—
217C4×C8—1511no—
218C4×C8C2×D15111yescharacteristic
219C2×Q8C22×D15111yescharacteristic
220C2×D4—3021no—
221C2×D4C22×D15111yescharacteristic
222C22×C4—3021no—
223C22×C4—3021no—
224C22×C4—3021no—
225C22×C4—1511no—
226C22×C4—1511no—
227C22×C4—1511no—
228C2×C8—1511no—
229C2×C8—1511no—
230C2×C8C22×D15111yescharacteristic
231C2×C8C22×D15111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—3021no—
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—3021no—
245C4⋊C4—3021no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4—1511no—
249C4⋊C4—1511no—
250C4⋊C4C22×D15111yescharacteristic
251C4⋊C4C22×D15111yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C22⋊C4—3021no—
257C42—3021no—
258C42—1511no—
259C42—1511no—
260C42—1511no—
261C42C22×D15111yescharacteristic
262C23—21no—
263C23—1511no—
264Q8—21no—
265Q8—21no—
266D4—21no—
267D4—21no—
268D4—6042no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—3022no—
273C2×C4—3021no—
274C2×C4—3021no—
275C2×C4—3021no—
276C2×C4—3021no—
277C2×C4—3021no—
278C2×C4—3021no—
279C2×C4—6041no—
280C2×C4—6042no—
281C2×C4—6042no—
282C2×C4—6042no—
283C2×C4—1511no—
284C2×C4—1511no—
285C2×C4—1511no—
286C2×C4D4×D15111yescharacteristic
287C2×C4D4×D15111yescharacteristic
288C2×C4C23×D15111yescharacteristic
289C8—21no—
290C8—21no—
291C8—3021no—
292C8—3021no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—3021no—
297C22—3021no—
298C22—1512no—
299C22C2×D4×D15111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—3021no—
306C4—3021no—
307C4—3021no—
308C4—6041no—
309C4—6041no—
310C4—6041no—
311C4—6041no—
312C4#1801278611yescharacteristic
313C4#1801278611yescharacteristic
314C2—81no—
315C2—3022no—
316C2#2375278211yescharacteristic
317C2#135×D15111yescharacteristic
318C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#488×C151C2
socleC22×C151C22×D4
prime radical#18012710C22
hypercenter#488D151
hypocenterC151#3232
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D151C2semidirect
3. #23752614C2semidirect
4. #23752611C2semidirect
5. #23752566C2semidirect
6. #23752546C2semidirect
7. #23752541C2semidirect
10. #23752521C2semidirect
11. #23752517C2semidirect
12. #23752514C2semidirect
13. #23752510C2semidirect
14. #23752263C2semidirect
15. #488×C151C2semidirect
159. C151#3232semidirect
166. #488D151semidirect

Maximal subgroups

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

subgroupindex
#237527412
#125×D1512
#237526142
#237526112
#237525662
#237525462
#237525412
#237525292
#237525242
#237525212
#237525172
#237525142
#237525102
#237522632
#488×C1512
#3232151