Finite Group Databasebeta

← #34080407

Subgroups — #34080407

Order 19328.

320 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#23752842C211yesmaximal, characteristic, complemented
2#23752827C211yesmaximal, characteristic
3#23752620C211yesmaximal, characteristic, complemented
4#23752609C211yesmaximal, characteristic, complemented
5#23752570C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752555C211yesmaximal, characteristic, complemented
8#23752544C211yesmaximal, characteristic, complemented
9#23752535C211yesmaximal, characteristic
10#23752529C211yesmaximal, characteristic
11#23752516C211yesmaximal, characteristic, complemented
12#23752502C211yesmaximal, characteristic, complemented
13#23752498C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#478×C151C211yesmaximal, characteristic, complemented
16#18012739C2211yescharacteristic
17#18012738—21no—
18#18012738C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012732—21no—
21#18012730C2211yescharacteristic
22#18012729—21no—
23#18012726C2211yescharacteristic
24#18012725—21no—
25#18012722—21no—
26#18012719—21no—
27#18012719C2211yescharacteristic
28#18012718—21no—
29#18012717—21no—
30#18012710C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35#18012672C2211yescharacteristic
36#18012671C2211yescharacteristic
37#18012671C2211yescharacteristic
38#18012670C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C4×D151—21no—
65C2×C4×D151C2311yescharacteristic
66C2×C151⋊C8C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C4⋊Dic151—21no—
69C4⋊Dic151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151C2311yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74Dic151⋊C4—21no—
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4D411yescharacteristic
80Dic151⋊C4D411yescharacteristic
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4D411yescharacteristic
87(C2×D151)⋊C4D411yescharacteristic
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C2×D4×C151C2311yescharacteristic
92C22×C4×C151—21no—
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C42×C151C2311yescharacteristic
102C22×D151C2×D411yescharacteristic
103Dic302—21no—
104Dic302—21no—
105Dic302—81no—
106Dic302—81no—
107Dic302—81no—
108C22⋊D151—81no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151C2×D411yescharacteristic
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C4×D151—21no—
117C4×D151—21no—
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C23×C151—21no—
122D4×C151—21no—
123D4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—81no—
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—21no—
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×C151#57711yescharacteristic
157C2×C151#57711yescharacteristic
158D151—41no—
159C151#324411yescharacteristic, complemented, Sylow
160#3244—1511nomaximal, Sylow
161#544—1511no—
162#542—1511no—
163#501—1511no—
164#498—1511no—
165#489—1511no—
166#488—1511no—
167#485—1511no—
168#483—1511no—
169#482—1511no—
170#481—1511no—
171#479—1511no—
172#478D15111yescharacteristic, complemented
173#476—1511no—
174#475—1511no—
175#433—1511no—
176C4⋊Q8—3021no—
177C4⋊Q8—1511no—
178C4⋊Q8—1511no—
179C4⋊Q8—1511no—
180#126—3021no—
181#125—3021no—
182#125—1511no—
183#125C2×D15111yescharacteristic
184#124—3021no—
185#124—1511no—
186#123—3021no—
187C22⋊Q8—3021no—
188C22⋊Q8—3021no—
189C22⋊Q8—3021no—
190C22⋊Q8—1511no—
191#121—1511no—
192C4×Q8—1511no—
193C4×D4C2×D15111yescharacteristic
194#117—1511no—
195#117—1511no—
196C2×C4⋊C4—1511no—
197#107—1511no—
198#107C2×D15111yescharacteristic
199#106—1511no—
200#106—1511no—
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#103—1511no—
210#103—1511no—
211#102—1511no—
212#102—1511no—
213#102C2×D15111yescharacteristic
214#102C2×D15111yescharacteristic
215C22⋊C8—1511no—
216C22⋊C8—1511no—
217#97—1511no—
218C4×C8—1511no—
219C2×Q8—3021no—
220C2×Q8—3021no—
221C2×Q8—3021no—
222C2×Q8—1511no—
223C2×D4—3021no—
224C2×D4C22×D15111yescharacteristic
225C22×C4—21no—
226C22×C4—3021no—
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—1511no—
243C4⋊C4—1511no—
244C4⋊C4—1511no—
245C4⋊C4—1511no—
246C4⋊C4—1511no—
247C4⋊C4C22×D15111yescharacteristic
248C4⋊C4C22×D15111yescharacteristic
249C4⋊C4C22×D15111yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—3021no—
252C22⋊C4—3021no—
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C22⋊C4—1511no—
257C22⋊C4—1511no—
258C42—3021no—
259C42—3021no—
260C42—1511no—
261C42C22×D15111yescharacteristic
262C23—21no—
263C23—1511no—
264Q8—3021no—
265Q8—3021no—
266Q8—12081no—
267Q8—12081no—
268Q8—12081no—
269D4—21no—
270D4—21no—
271D4—12081no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—81no—
276C2×C4—3021no—
277C2×C4—3021no—
278C2×C4—3021no—
279C2×C4—3021no—
280C2×C4—3021no—
281C2×C4—3021no—
282C2×C4—1511no—
283C2×C4—1511no—
284C2×C4—1511no—
285C2×C4—12081no—
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—3021no—
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#1801278711yescharacteristic
314C2—81no—
315C2—6041no—
316C2#2375278511yescharacteristic
317C2#2375301911yescharacteristic
318C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
prime radical#18012710C22
hypercenter#478D151
hypocenterC151#3244
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23752842C2semidirect
3. #23752620C2semidirect
4. #23752609C2semidirect
5. #23752570C2semidirect
6. #23752565C2semidirect
7. #23752555C2semidirect
8. #23752544C2semidirect
11. #23752516C2semidirect
12. #23752502C2semidirect
13. #23752498C2semidirect
14. #23752272C2semidirect
15. #478×C151C2semidirect
159. C151#3244semidirect
172. #478D151semidirect

Maximal subgroups

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

subgroupindex
#237528422
#237528272
#237526202
#237526092
#237525702
#237525652
#237525552
#237525442
#237525352
#237525292
#237525162
#237525022
#237524982
#237522722
#478×C1512
#3244151