Finite Group Databasebeta

← #26316840

Subgroups — #26316840

Order 12032.

658 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249363C211yesmaximal, characteristic
2#20244783C212yesmaximal
3#20244769C212yesmaximal
4#20244209C211yesmaximal, characteristic
5#20244191C211yesmaximal, characteristic
6#20243656C212yesmaximal
7#20243642C212yesmaximal
8#20243557C211yesmaximal, characteristic
9#20243518C211yesmaximal, characteristic
10#20243245C211yesmaximal, characteristic
11C47×#2327C211yesmaximal, characteristic
12C2×#13093957C2212yes—
13C2×#13093955C2212yes—
14C2×C4⋊(C47⋊C8)C2212yes—
15C2×#13093948C2212yes—
16C2×#13093948C2212yes—
17C2×#13093948C2212yes—
18C2×#13093948C2212yes—
19C2×#13093935C2211yescharacteristic
20C2×C4×C47⋊C8C2211yescharacteristic
21#15689065—22no—
22#15689057—22no—
23#15689021C2212yes—
24#15689021C2212yes—
25#15688993C2211yescharacteristic
26#15688989C2211yescharacteristic
27#15688885C2212yes—
28#15688885C2212yes—
29#15688878C2212yes—
30C2×C4⋊Q8×C47C2211yescharacteristic
31C2×C4×Q8×C47C2211yescharacteristic
32C2×C4×Q8×C47C2211yescharacteristic
33C47×#391C2211yescharacteristic
34C47×#391C2211yescharacteristic
35C47×#387—22no—
36C47×#387—22no—
37C47×#382C2211yescharacteristic
38C47×#376C2211yescharacteristic
39C22×C47⋊C8C2312yes—
40C22×C47⋊C8C2312yes—
41C2×C4⋊Dic47—22no—
42C2×C4⋊Dic47C2312yes—
43C2×C4⋊Dic47C2312yes—
44C2×Dic47⋊C4—22no—
45C2×Dic47⋊C4—22no—
46#13093957—42no—
47#13093955—42no—
48C4⋊(C47⋊C8)—24no—
49#13093948—24no—
50#13093948—24no—
51#13093948—42no—
52#13093948—42no—
53#13093935—22no—
54C4×C47⋊C8—22no—
55C47⋊#95—22no—
56C47⋊#95—22no—
57C47⋊#95—22no—
58C22×Q8×C47C2311yescharacteristic
59C22×Q8×C47C2311yescharacteristic
60C4⋊Q8×C47—22no—
61C4⋊Q8×C47Q814yes—
62C4×Q8×C47—42no—
63C4×Q8×C47—42no—
64C2×C4⋊C4×C47—22no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47C2311yescharacteristic
68C2×C4⋊C4×C47C2311yescharacteristic
69C2×C42×C47—21no—
70C2×C42×C47—21no—
71C2×C42×C47C2311yescharacteristic
72C2×C42×C47C2311yescharacteristic
73C2×C42×C47C2311yescharacteristic
74#95×C47—22no—
75#95×C47—22no—
76#95×C47—22no—
77#95×C47D412yes—
78#95×C47D412yes—
79C2×Q8×C47—21no—
80C2×Q8×C47—21no—
81C2×Q8×C47—22no—
82C2×Q8×C47—22no—
83C2×Q8×C47—22no—
84C2×Q8×C47—22no—
85C2×Q8×C47C2×Q812yes—
86C2×Q8×C47C2×Q812yes—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47C2×D412yes—
94C22×C4×C47C2×D412yes—
95C22×C4×C47C2411yescharacteristic
96C22×Dic47—22no—
97C22×Dic47—22no—
98C4⋊C4×C47—28no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—22no—
101C4⋊C4×C47—42no—
102C4⋊C4×C47—42no—
103C42×C47—22no—
104C42×C47—22no—
105C42×C47—42no—
106C42×C47—42no—
107C42×C47C2×Q812yes—
108C42×C47#4112yes—
109C4⋊Dic47—22no—
110C4⋊Dic47—22no—
111C4⋊Dic47—22no—
112C4⋊Dic47—22no—
113C4⋊Dic47—82no—
114Dic47⋊C4—82no—
115Dic47⋊C4—82no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8#4114yes—
122C23×C47C22×D411yescharacteristic
123Q8×C47—24no—
124Q8×C47—24no—
125Q8×C47—42no—
126Q8×C47—42no—
127C2×C4×C47—22no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—22no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47C22⋊Q814yes—
147C2×C4×C47C22×Q811yescharacteristic
148C2×C4×C47C2×#4112yes—
149C2×C4×C47C2×#4111yescharacteristic
150C2×C4×C47H(5,𝔽2)12yes—
151C2×Dic47—42no—
152C2×Dic47—42no—
153C2×Dic47—42no—
154C2×Dic47—42no—
155C2×Dic47—42no—
156C2×Dic47—42no—
157C47⋊C8—24no—
158C47⋊C8—42no—
159#29205—471nomaximal, Sylow
160C22×C47C2×C22⋊Q811yescharacteristic
161C22×C47#53211yescharacteristic
162C22×C47#53511yescharacteristic
163C22×C47#57712yes—
164C22×C47#57812yes—
165C4×C47—24no—
166C4×C47—42no—
167C4×C47—42no—
168C4×C47—42no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—81no—
172C4×C47—81no—
173C4×C47#55312yes—
174C4×C47#55412yes—
175Dic47—82no—
176Dic47—82no—
177#2647—471no—
178#2327D4711yescharacteristic
179#2068—472no—
180#2066—472no—
181#1960—471no—
182#1956—471no—
183#1865—472no—
184#1863—472no—
185#1847—471no—
186#1835—471no—
187#1768—471no—
188C2×C47#256611yescharacteristic
189C2×C47#308212yes—
190C2×C47#317812yes—
191C2×C47#322111yescharacteristic
192C2×C47#322311yescharacteristic
193C2×C4⋊Q8C2×D4711yescharacteristic
194C2×C4×Q8C2×D4711yescharacteristic
195C2×C4×Q8C2×D4711yescharacteristic
196C2×#107—472no—
197C2×#106—472no—
198C2×C4⋊C8—472no—
199C2×#103—472no—
200C2×#103—472no—
201C2×#103—472no—
202C2×#103—472no—
203C2×#97—471no—
204C2×C4×C8—471no—
205#400—942no—
206#398—942no—
207#391C2×D4711yescharacteristic
208#391C2×D4711yescharacteristic
209#389—472no—
210#389—472no—
211#387—22no—
212#387—22no—
213#384—471no—
214#382—471no—
215#382C2×D4711yescharacteristic
216#376C2×D4711yescharacteristic
217#340—472no—
218#340—472no—
219#336—472no—
220C47#2920511yescharacteristic, complemented, Sylow
221C22×Q8C22×D4711yescharacteristic
222C22×Q8C22×D4711yescharacteristic
223C22×C8—472no—
224C22×C8—472no—
225C4⋊Q8—22no—
226C4⋊Q8Dic9414yes—
227C4×Q8—42no—
228C4×Q8—42no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—472no—
233C2×C4⋊C4—472no—
234C2×C4⋊C4—942no—
235C2×C4⋊C4—942no—
236C2×C4⋊C4—942no—
237C2×C4⋊C4C22×D4711yescharacteristic
238C2×C4⋊C4C22×D4711yescharacteristic
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C22×D4711yescharacteristic
242C2×C42C22×D4711yescharacteristic
243C2×C42C22×D4711yescharacteristic
244#107—1882no—
245#106—1882no—
246C4⋊C8—944no—
247#103—944no—
248#103—944no—
249#103—1882no—
250#103—1882no—
251#97—942no—
252C4×C8—942no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—942no—
257#95—942no—
258#95—942no—
259#95C22⋊D4712yes—
260#95C22⋊D4712yes—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8C2×Dic9412yes—
268C2×Q8C2×Dic9412yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—942no—
274C22×C4—942no—
275C22×C4C2×C22⋊D4712yes—
276C22×C4C2×C22⋊D4711yescharacteristic
277C22×C4C2×C22⋊D4711yescharacteristic
278C22×C4C2×C22⋊D4712yes—
279C22×C4C23×D4711yescharacteristic
280C2×C8—474no—
281C2×C8—942no—
282C2×C8—942no—
283C2×C8—942no—
284C2×C8—942no—
285C2×C8—942no—
286C4⋊C4—28no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—942no—
292C4⋊C4—942no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—3762no—
296C4⋊C4—3762no—
297C4⋊C4—3762no—
298C42—22no—
299C42—22no—
300C42—42no—
301C42—42no—
302C42C2×Dic9412yes—
303C42#1062535012yes—
304C23C22×C22⋊D4711yescharacteristic
305Q8—24no—
306Q8—24no—
307Q8—42no—
308Q8—42no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—1882no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4—1882no—
333C2×C4—1882no—
334C2×C4#1309400314yes—
335C2×C4C22×Dic9411yescharacteristic
336C2×C4#41×D4712yes—
337C2×C4C2×#1062535011yescharacteristic
338C2×C4#1309406912yes—
339C8—944no—
340C8—1882no—
341C22C2×#1309400311yescharacteristic
342C22#1568966911yescharacteristic
343C22#1568969011yescharacteristic
344C22#1568993112yes—
345C22#1568993812yes—
346C4—24no—
347C4—41no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—41no—
352C4—81no—
353C4—81no—
354C4—3762no—
355C4—3762no—
356C4#1568982312yes—
357C4#1568983212yes—
358C2#2024858411yescharacteristic
359C2#2025323012yes—
360C2#2025405812yes—
361C2#2025444911yescharacteristic
362C2#2025447111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2327C2
socle, prime radicalC23×C47C22×D4
hypercenter#2327D47
hypocenterC47#29205
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2327

Complements

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

NH ≅ G/Ntype
220. C47#29205semidirect

Maximal subgroups

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

subgroupindex
#202493632
#202447832
#202447692
#202442092
#202441912
#202436562
#202436422
#202435572
#202435182
#202432452
C47×#23272
#2920547