Finite Group Databasebeta

← #34080321

Subgroups — #34080321

Order 19328.

322 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752765C211yesmaximal, characteristic
2#23752764C211yesmaximal, characteristic
3#23752620C211yesmaximal, characteristic, complemented
4#23752619C211yesmaximal, characteristic, complemented
5#23752579C211yesmaximal, characteristic, complemented
6#23752579C211yesmaximal, characteristic, complemented
7#23752554C211yesmaximal, characteristic
8#23752553C211yesmaximal, characteristic
9#23752550C211yesmaximal, characteristic
10#23752506C211yesmaximal, characteristic, complemented
11#23752505C211yesmaximal, characteristic, complemented
12#23752496C211yesmaximal, characteristic, complemented
13#23752495C211yesmaximal, characteristic, complemented
14#23752266C211yesmaximal, characteristic
15#485×C151C211yesmaximal, characteristic
16#18012738C2211yescharacteristic
17#18012738C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012737C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012729—21no—
23#18012718C2211yescharacteristic
24#18012716—21no—
25#18012716—21no—
26#18012716—21no—
27Q8×Dic151C2211yescharacteristic
28C4×Dic302—21no—
29C4×Dic302—21no—
30#18012704—21no—
31#18012704C2211yescharacteristic
32#18012698C2211yescharacteristic
33#18012695—21no—
34C2×C4×Dic151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012671C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C22×Dic151D411yescharacteristic
64C22×Dic151D411yescharacteristic
65C2×C151⋊C8C2311yescharacteristic
66C2×C151⋊C8C2311yescharacteristic
67C4⋊Dic151—21no—
68C4⋊Dic151—21no—
69C4⋊Dic151—21no—
70C4⋊Dic151C2311yescharacteristic
71C4⋊Dic151C2311yescharacteristic
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⋊C4—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C4×Dic151—21no—
85C4×Dic151—21no—
86C4×Dic151—21no—
87C4×Dic151D411yescharacteristic
88C4×Dic151D411yescharacteristic
89C4×Dic151C2311yescharacteristic
90C4×Dic151C2311yescharacteristic
91C2×Q8×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C4⋊C4×C151—21no—
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C42×C151—21no—
102Dic302—21no—
103Dic302—21no—
104Dic302—42no—
105Dic302—42no—
106Dic302—42no—
107C2×Dic151—22no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—41no—
113C2×Dic151C2×D411yescharacteristic
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C151⋊C8—21no—
118C151⋊C8—21no—
119C23×C151C2×D411yescharacteristic
120Q8×C151—21no—
121Q8×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151C2×D411yescharacteristic
129C2×C4×C151C2411yescharacteristic
130C8×C151—21no—
131C8×C151—21no—
132C22×C151—21no—
133C22×C151—21no—
134C22×C151—21no—
135C22×C151C22×D411yescharacteristic
136C4×C151—21no—
137C4×C151—41no—
138C4×C151—41no—
139C4×C151—41no—
140C4×C151—41no—
141C4×C1512−1+411yescharacteristic
142C4×C1512−1+411yescharacteristic
143Dic151—21no—
144Dic151—21no—
145Dic151—21no—
146Dic151—41no—
147Dic151—41no—
148Dic151—41no—
149Dic151—41no—
150Dic151#13712yes—
151C2×C151—41no—
152C2×C151#53611yescharacteristic
153C2×C151C2×#13711yescharacteristic
154C2×C151#57511yescharacteristic
155C151#323711yescharacteristic, complemented, Sylow
156#3237—1511nomaximal, Sylow
157#533—1511no—
158#533—1511no—
159#501—1511no—
160#501—1511no—
161#491—1511no—
162#491—1511no—
163#485—1511no—
164#485—1511no—
165#485—1511no—
166#485D15111yescharacteristic
167#477—1511no—
168#477—1511no—
169#475—1511no—
170#475—1511no—
171#432—1511no—
172C4⋊Q8—1511no—
173C4⋊Q8—1511no—
174C4⋊Q8—1511no—
175C4⋊Q8—1511no—
176#125—3021no—
177#125—1511no—
178#125—1511no—
179C22⋊Q8—3021no—
180C22⋊Q8—3021no—
181C22⋊Q8—3021no—
182C22⋊Q8—1511no—
183C22⋊Q8C2×D15111yescharacteristic
184C4×Q8—3021no—
185C4×Q8—3021no—
186C4×Q8—3021no—
187C4×Q8—1511no—
188C4×Q8—1511no—
189#117—3021no—
190#117—1511no—
191#117C2×D15111yescharacteristic
192C2×C42—1511no—
193#107—1511no—
194#107—1511no—
195#107—1511no—
196#107C2×D15111yescharacteristic
197#106—1511no—
198#106—1511no—
199#106—1511no—
200#106C2×D15111yescharacteristic
201C4⋊C8—1511no—
202C4⋊C8—1511no—
203#103—1511no—
204#103—1511no—
205#103—1511no—
206#103—1511no—
207#103—1511no—
208#103—1511no—
209#103C2×D15111yescharacteristic
210#103C2×D15111yescharacteristic
211C22⋊C8—1511no—
212C22⋊C8C2×D15111yescharacteristic
213#97—1511no—
214#97—1511no—
215C2×Q8—3021no—
216C2×Q8—3021no—
217C2×Q8—3021no—
218C2×Q8—1511no—
219C2×Q8C22×D15111yescharacteristic
220C22×C4—1511no—
221C22×C4—1511no—
222C22×C4C22×D15111yescharacteristic
223C2×C8—1511no—
224C2×C8—1511no—
225C2×C8C22×D15111yescharacteristic
226C2×C8C22×D15111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—3021no—
229C4⋊C4—3021no—
230C4⋊C4—3021no—
231C4⋊C4—3021no—
232C4⋊C4—3021no—
233C4⋊C4—3021no—
234C4⋊C4—3021no—
235C4⋊C4—3021no—
236C4⋊C4—3021no—
237C4⋊C4—3021no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—1511no—
241C4⋊C4—1511no—
242C4⋊C4—1511no—
243C4⋊C4C22×D15111yescharacteristic
244C4⋊C4C22×D15111yescharacteristic
245C4⋊C4C22×D15111yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—3021no—
249C22⋊C4—3021no—
250C42—21no—
251C42—3021no—
252C42—3021no—
253C42—3021no—
254C42—1511no—
255C42—1511no—
256C42—1511no—
257C42—1511no—
258C23D4×D15111yescharacteristic
259Q8—21no—
260Q8—21no—
261Q8—3021no—
262Q8—3021no—
263Q8—6042no—
264Q8—6042no—
265Q8—6042no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
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—6041no—
278C2×C4—1511no—
279C2×C4—1511no—
280C2×C4—1511no—
281C2×C4—1511no—
282C2×C4D4×D15111yescharacteristic
283C2×C4C23×D15111yescharacteristic
284C8—21no—
285C8—21no—
286C8—3021no—
287C8—3021no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22C2×D4×D15111yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—3021no—
298C4—3021no—
299C4—3021no—
300C4—6041no—
301C4—6041no—
302C4—6041no—
303C4—6041no—
304C4—1512no—
305C4#1801278611yescharacteristic
306C4#1801278611yescharacteristic
307C2—41no—
308C2#2375278411yescharacteristic
309C2#137×D15111yescharacteristic
310C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenter#485D151
hypocenterC151#3237
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23752620C2semidirect
4. #23752619C2semidirect
5. #23752579C2semidirect
6. #23752579C2semidirect
10. #23752506C2semidirect
11. #23752505C2semidirect
12. #23752496C2semidirect
13. #23752495C2semidirect
155. C151#3237semidirect

Maximal subgroups

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

subgroupindex
#237527652
#237527642
#237526202
#237526192
#237525792
#237525542
#237525532
#237525502
#237525062
#237525052
#237524962
#237524952
#237522662
#485×C1512
#3237151