Finite Group Databasebeta

← #34080282

Subgroups — #34080282

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#23752749C211yesmaximal, characteristic
2#125×D151C211yesmaximal, characteristic, complemented
3#23752613C211yesmaximal, characteristic, complemented
4#23752612C211yesmaximal, characteristic, complemented
5#23752568C211yesmaximal, characteristic, complemented
6#23752568C211yesmaximal, characteristic, complemented
7#23752546C211yesmaximal, characteristic, complemented
8#23752541C211yesmaximal, characteristic, complemented
9#23752532C211yesmaximal, characteristic
10#23752527C211yesmaximal, characteristic
11#23752519C211yesmaximal, characteristic, complemented
12#23752513C211yesmaximal, characteristic, complemented
13#23752509C211yesmaximal, characteristic, complemented
14#23752264C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16#18012734—21no—
17#18012731C2211yescharacteristic
18#18012730C2211yescharacteristic
19#18012730C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012729—21no—
22#18012729—21no—
23#18012728C2211yescharacteristic
24#18012724—21no—
25#18012715C2211yescharacteristic
26#18012714C2211yescharacteristic
27C4×D604—21no—
28C4×D604C2211yescharacteristic
29#18012696—21no—
30C4⋊C4×D151—21no—
31C4⋊C4×D151—21no—
32C4⋊C4×D151C2211yescharacteristic
33C4⋊C4×D151C2211yescharacteristic
34C42×D151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012671C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊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×D604—21no—
60C2×D604C2311yescharacteristic
61C2×C4×D151—21no—
62C2×C4×D151—21no—
63C2×C4×D151—21no—
64C2×C4×D151D411yescharacteristic
65C2×C4×D151D411yescharacteristic
66C2×C4×D151C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C4⋊Dic151—21no—
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⋊C4—21no—
82Dic151⋊C4—21no—
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×Dic151D411yescharacteristic
89C4×Dic151D411yescharacteristic
90C4×Dic151C2311yescharacteristic
91C2×Q8×C151C2311yescharacteristic
92C2×C8×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C42×C151—21no—
101C42×C151C2311yescharacteristic
102C22×D151—21no—
103C22×D151C2×D411yescharacteristic
104D604—21no—
105D604—21no—
106D604—42no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151C2×D411yescharacteristic
111C2×Dic151C2×D411yescharacteristic
112C2×Dic151C2×D411yescharacteristic
113C4×D151—22no—
114C4×D151—21no—
115C4×D151—21no—
116C4×D151—41no—
117C4×D151—42no—
118C4×D151—42no—
119C4×D151—42no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122Q8×C151—21no—
123Q8×C151—21no—
124C2×C4×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×C151C22×D411yescharacteristic
134C2×D151—21no—
135C2×D151—21no—
136C2×D151—41no—
137C2×D151—41no—
138C2×D151—41no—
139C2×D151#13512yes—
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151—41no—
146C4×C1512−1+411yescharacteristic
147C4×C1512−1+411yescharacteristic
148Dic151—21no—
149Dic151—21no—
150Dic151—21no—
151Dic151—41no—
152Dic151—41no—
153Dic151—41no—
154C2×C151#53611yescharacteristic
155C2×C151C2×#13511yescharacteristic
156C2×C151#57511yescharacteristic
157D151—22no—
158D151—81no—
159C151#323211yescharacteristic, complemented, Sylow
160#3232—1511nomaximal, Sylow
161#529—1511no—
162C2×#125—1511no—
163#499—1511no—
164#499—1511no—
165#488—1511no—
166#488—1511no—
167#484—1511no—
168#483—1511no—
169#481—1511no—
170#480—1511no—
171#479—1511no—
172#479D15111yescharacteristic, complemented
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#124—1511no—
185#123—3021no—
186C22⋊Q8—1511no—
187#121—1511no—
188C4×Q8C2×D15111yescharacteristic
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#107C2×D15111yescharacteristic
201#106—1511no—
202#106—1511no—
203#106—1511no—
204#106C2×D15111yescharacteristic
205C4⋊C8—1511no—
206C4⋊C8C2×D15111yescharacteristic
207#103—1511no—
208#103—1511no—
209#103C2×D15111yescharacteristic
210#103C2×D15111yescharacteristic
211#102—1511no—
212#102—1511no—
213#102—1511no—
214#102—1511no—
215C22⋊C8—1511no—
216C22⋊C8—1511no—
217C4×C8—1511no—
218C4×C8—1511no—
219C2×Q8C22×D15111yescharacteristic
220C2×D4—3021no—
221C2×D4—1511no—
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—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—3021no—
245C4⋊C4—3021no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4—1511no—
249C4⋊C4C22×D15111yescharacteristic
250C4⋊C4C22×D15111yescharacteristic
251C4⋊C4C22×D15111yescharacteristic
252C22⋊C4—3021no—
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C22⋊C4—3021no—
257C42—21no—
258C42—1511no—
259C42—1511no—
260C42—1511no—
261C42C22×D15111yescharacteristic
262C23—3021no—
263C23—1511no—
264Q8—21no—
265Q8—21no—
266D4—3021no—
267D4—3021no—
268D4—6042no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—3022no—
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—3021no—
294C22—3021no—
295C22—6041no—
296C22—6041no—
297C22—6041no—
298C22—1512no—
299C22C2×D4×D15111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—3021no—
307C4—3021no—
308C4—3021no—
309C4—6041no—
310C4—6041no—
311C4—6041no—
312C4#1801278611yescharacteristic
313C4#1801278711yescharacteristic
314C2—3022no—
315C2—12081no—
316C2#2375278511yescharacteristic
317C2#135×D15111yescharacteristic
318C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#479D151
hypocenterC151#3232
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
2. #125×D151C2semidirect
3. #23752613C2semidirect
4. #23752612C2semidirect
5. #23752568C2semidirect
6. #23752568C2semidirect
7. #23752546C2semidirect
8. #23752541C2semidirect
11. #23752519C2semidirect
12. #23752513C2semidirect
13. #23752509C2semidirect
14. #23752264C2semidirect
15. #479×C151C2semidirect
159. C151#3232semidirect
172. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
#125×D1512
#237526132
#237526122
#237525682
#237525462
#237525412
#237525322
#237525272
#237525192
#237525132
#237525092
#237522642
#479×C1512
#3232151