Finite Group Databasebeta

← #26116353

Subgroups — #26116353

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic
2#20241615C211yesmaximal, characteristic
3#20241266C212yesmaximal
4#20241266C212yesmaximal
5C47×#2851C211yesmaximal, characteristic
6C2×C22⋊(C47⋊C8)C2212yes—
7C2×C4×C47⋊C8—21no—
8C2×C47⋊#95—21no—
9C2×C47⋊#95—21no—
10C2×C47⋊#95C2212yes—
11#15688878—21no—
12C2×#125×C47C411yescharacteristic, complemented
13C22×C42×C47C2211yescharacteristic
14C47×#389C411yescharacteristic, complemented
15C47×#389C411yescharacteristic, complemented
16C47×#387—21no—
17C47×#387—21no—
18C47×#385—21no—
19C47×#385—21no—
20C47×#382C411yescharacteristic, complemented
21C47×#380C2211yescharacteristic
22C47×#380C2211yescharacteristic
23C23×Dic47—22no—
24C22×C47⋊C8—22no—
25C22⋊(C47⋊C8)—22no—
26C22⋊(C47⋊C8)Q814yes—
27C4×C47⋊C8—42no—
28C47⋊#95—24no—
29C47⋊#95—24no—
30C47⋊#95—42no—
31C23×C4×C47D411yescharacteristic
32C23×C4×C47D411yescharacteristic
33C23×C4×C47C2311yescharacteristic
34#125×C47—42no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47C2×C411yescharacteristic
41C2×C4⋊C4×C47C2×C411yescharacteristic
42C2×C4⋊C4×C47C2×C411yescharacteristic
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C42×C47—42no—
46C2×C42×C47C2×C411yescharacteristic
47C2×C42×C47C2×C411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47D411yescharacteristic
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56C24×C47C2×D411yescharacteristic
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×Q812yes—
76C22×C4×C47#4112yes—
77C22×Dic47—24no—
78C22×Dic47—42no—
79C22×Dic47—42no—
80C22×Dic47—42no—
81C22×Dic47—42no—
82C22×Dic47—42no—
83C22×Dic47—42no—
84C4⋊C4×C47—42no—
85C4⋊C4×C47—42no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—42no—
91C4⋊C4×C47—42no—
92C22⋊C4×C47—42no—
93C22⋊C4×C47—42no—
94C42×C47—22no—
95C42×C47—22no—
96C42×C47—41no—
97C42×C47—41no—
98C2×C47⋊C8—24no—
99C2×C47⋊C8—42no—
100C2×C47⋊C8—42no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47C2×C22⋊C411yescharacteristic
106C23×C47#12411yescharacteristic
107C23×C47C4⋊Q811yescharacteristic
108C23×C47#13512yes—
109C23×C47#13512yes—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47—44no—
127C2×C4×C47—44no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47#9912yes—
141C2×C4×C47#10412yes—
142C2×C4×C47C4×Q812yes—
143C2×C4×C47C22⋊Q812yes—
144C2×Dic47—44no—
145C2×Dic47—44no—
146C2×Dic47—44no—
147C2×Dic47—82no—
148C2×Dic47—82no—
149C2×Dic47—82no—
150C2×Dic47—82no—
151C47⋊C8—44no—
152#9886—471nomaximal, Sylow
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—22no—
161C22×C47#39111yescharacteristic
162C22×C47C2×#9911yescharacteristic
163C22×C47#41011yescharacteristic
164C22×C47#41611yescharacteristic
165C22×C47#41611yescharacteristic
166C22×C47C2×#10411yescharacteristic
167C22×C47#42111yescharacteristic
168C22×C47#48812yes—
169C22×C47#49912yes—
170C4×C47—22no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—22no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—81no—
177C4×C47—81no—
178C4×C47—81no—
179C4×C47—81no—
180Dic47—84no—
181#2851D4711yescharacteristic
182C4×C22⋊C8—471no—
183#1434—471no—
184#1294—472no—
185#1294—472no—
186C2×C47—22no—
187C2×C47—22no—
188C2×C47#150011yescharacteristic
189C2×C47#150111yescharacteristic
190C2×C47#151611yescharacteristic
191C2×C47#152111yescharacteristic
192C2×C47#198611yescharacteristic
193C2×C47#199111yescharacteristic
194C2×C47#199611yescharacteristic
195C2×#125Dic4711yescharacteristic, complemented
196C22×C42C2×D4711yescharacteristic
197C2×C22⋊C8—472no—
198C2×C4×C8—941no—
199#389Dic4711yescharacteristic, complemented
200#389Dic4711yescharacteristic, complemented
201#387—21no—
202#387—21no—
203#385—21no—
204#385—21no—
205#382Dic4711yescharacteristic, complemented
206#380C2×D4711yescharacteristic
207#380C2×D4711yescharacteristic
208C2×#95—472no—
209C2×#95—941no—
210C2×#95—941no—
211#336—941no—
212C47#988611yescharacteristic, complemented, Sylow
213C23×C4—942no—
214C23×C4C22⋊D4711yescharacteristic
215C23×C4C22⋊D4711yescharacteristic
216C23×C4C22×D4711yescharacteristic
217C22×C8—942no—
218#125—42no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×Dic4711yescharacteristic
224C2×C4⋊C4C2×Dic4711yescharacteristic
225C2×C4⋊C4C2×Dic4711yescharacteristic
226C2×C4⋊C4C2×Dic4711yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42—42no—
230C2×C42C2×Dic4711yescharacteristic
231C2×C42C2×Dic4711yescharacteristic
232C2×C42C22⋊D4711yescharacteristic
233C2×C42C22⋊D4711yescharacteristic
234C22⋊C8—474no—
235C22⋊C8—942no—
236C4×C8—1882no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—944no—
244#95—944no—
245#95—1882no—
246C24C2×C22⋊D4711yescharacteristic
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—944no—
260C22×C4—1882no—
261C22×C4—1882no—
262C22×C4—1882no—
263C22×C4—1882no—
264C22×C4—1882no—
265C22×C4—1882no—
266C22×C4C22⋊Dic4711yescharacteristic
267C22×C4C22⋊Dic4711yescharacteristic
268C22×C4C22⋊Dic4711yescharacteristic
269C22×C4C22⋊Dic4711yescharacteristic
270C22×C4Q8×D4712yes—
271C22×C4#1062535412yes—
272C22×C4C22×Dic4711yescharacteristic
273C22×C4C2×C22⋊D4711yescharacteristic
274C2×C8—944no—
275C2×C8—1882no—
276C2×C8—1882no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C42—22no—
288C42—22no—
289C42—41no—
290C42—41no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C2×C22⋊Dic4711yescharacteristic
296C23#1309401311yescharacteristic
297C23#1309402211yescharacteristic
298C23#1309404412yes—
299C23#1309404412yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—3762no—
331C2×C4—3762no—
332C2×C4—3762no—
333C2×C4—3762no—
334C2×C4—1884no—
335C2×C4—1884no—
336C2×C4—1884no—
337C2×C4#1309393912yes—
338C2×C4#1309395112yes—
339C2×C4Q8×Dic4712yes—
340C2×C4#1309400012yes—
341C8—1884no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—22no—
350C22#1568903011yescharacteristic
351C22C2×#1309393911yescharacteristic
352C22#1568909711yescharacteristic
353C22#1568911911yescharacteristic
354C22#1568911911yescharacteristic
355C22C2×#1309395111yescharacteristic
356C22#1568914011yescharacteristic
357C22#1568948012yes—
358C22#1568952212yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—3764no—
370C2—22no—
371C2—22no—
372C2#2024187411yescharacteristic
373C2#2024187911yescharacteristic
374C2#2024194411yescharacteristic
375C2#2024196511yescharacteristic
376C2#2024433311yescharacteristic
377C2#2024435411yescharacteristic
378C2#2024437411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2851C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#2851D47
hypocenterC47#9886
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
12. C2×#125×C47C4semidirect
14. C47×#389C4semidirect
15. C47×#389C4semidirect
20. C47×#382C4semidirect
195. C2×#125Dic47semidirect
199. #389Dic47semidirect
200. #389Dic47semidirect
205. #382Dic47semidirect
212. C47#9886semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C47⋊C8)2
#202416152
#202412662
C47×#28512
#988647