Finite Group Databasebeta

← #26109660

Subgroups — #26109660

Order 12032.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243456C211yesmaximal, characteristic
2#20241615C211yesmaximal, characteristic
3#20241266C212yesmaximal
4#20241266C212yesmaximal
5C47×#2283C211yesmaximal, characteristic
6C2×C22⋊(C47⋊C8)C2212yes—
7C2×C47⋊#95—21no—
8C2×C47⋊#95—21no—
9C2×C47⋊#95C2212yes—
10#15688878—21no—
11#15688878—21no—
12C22×C42×C47C2211yescharacteristic
13C47×#383—21no—
14C47×#382C411yescharacteristic, complemented
15C47×#382C411yescharacteristic, complemented
16C47×#381—21no—
17C47×#380C2211yescharacteristic
18C47×#380C2211yescharacteristic
19C4×C4⋊C4×C47C411yescharacteristic, complemented
20C4×C4⋊C4×C47C411yescharacteristic, complemented
21C4×C22⋊C4×C47—21no—
22C47×#376—21no—
23C23×Dic47—22no—
24C22×C47⋊C8—22no—
25C22⋊(C47⋊C8)—24no—
26C47⋊#95—24no—
27C47⋊#95—24no—
28C47⋊#95—42no—
29C23×C4×C47D411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C23×C4×C47C2311yescharacteristic
32C2×C4⋊C4×C47C2×C411yescharacteristic
33C2×C4⋊C4×C47C2×C411yescharacteristic
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C4⋊C4×C47C2×C411yescharacteristic
36C2×C22⋊C4×C47—21no—
37C2×C22⋊C4×C47—21no—
38C2×C42×C47—24no—
39C2×C42×C47—21no—
40C2×C42×C47—21no—
41C2×C42×C47C2×C411yescharacteristic
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45#95×C47—21no—
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53C24×C47C2×D411yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—22no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47#4114yes—
74C22×Dic47—24no—
75C22×Dic47—42no—
76C22×Dic47—42no—
77C22×Dic47—42no—
78C22×Dic47—42no—
79C22×Dic47—42no—
80C22×Dic47—42no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C22⋊C4×C47—42no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C42×C47—22no—
89C42×C47—22no—
90C42×C47—22no—
91C42×C47—22no—
92C42×C47—42no—
93C42×C47—42no—
94C2×C47⋊C8—42no—
95C2×C47⋊C8—42no—
96C2×C47⋊C8—42no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47C2×C22⋊C411yescharacteristic
102C23×C47#12312yes—
103C23×C47#13512yes—
104C23×C47AGL(1,ℤ/8)11yescharacteristic
105C23×C47#13711yescharacteristic
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
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—44no—
122C2×C4×C47—44no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
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#10412yes—
138C2×C4×C47#11712yes—
139C2×C4×C47#12312yes—
140C2×Dic47—44no—
141C2×Dic47—44no—
142C2×Dic47—44no—
143C2×Dic47—82no—
144C2×Dic47—82no—
145C2×Dic47—82no—
146C2×Dic47—82no—
147C47⋊C8—82no—
148#8714—471nomaximal, Sylow
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—22no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—22no—
157C22×C47#38111yescharacteristic
158C22×C47#41011yescharacteristic
159C22×C47#41011yescharacteristic
160C22×C47#41611yescharacteristic
161C22×C47#41711yescharacteristic
162C22×C47C2×#10411yescharacteristic
163C22×C47#42111yescharacteristic
164C22×C47#48212yes—
165C22×C47#48512yes—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—81no—
173C4×C47—81no—
174C4×C47—81no—
175C4×C47—81no—
176Dic47—84no—
177#2283D4711yescharacteristic
178#1817—471no—
179#1434—471no—
180#1294—472no—
181#1294—472no—
182C2×C47—22no—
183C2×C47—22no—
184C2×C47#150011yescharacteristic
185C2×C47#150911yescharacteristic
186C2×C47#151211yescharacteristic
187C2×C47#152111yescharacteristic
188C2×C47#182011yescharacteristic
189C2×C47#182511yescharacteristic
190C2×C47#182611yescharacteristic
191C22×C42C2×D4711yescharacteristic
192C2×C22⋊C8—472no—
193#383—21no—
194#382Dic4711yescharacteristic, complemented
195#382Dic4711yescharacteristic, complemented
196#381—21no—
197#380C2×D4711yescharacteristic
198#380C2×D4711yescharacteristic
199C4×C4⋊C4Dic4711yescharacteristic, complemented
200C4×C4⋊C4Dic4711yescharacteristic, complemented
201C4×C22⋊C4—21no—
202#376—21no—
203C2×#95—472no—
204C2×#95—941no—
205C2×#95—941no—
206#336—941no—
207#336—941no—
208C47#871411yescharacteristic, complemented, Sylow
209C23×C4—942no—
210C23×C4C22⋊D4711yescharacteristic
211C23×C4C22⋊D4711yescharacteristic
212C23×C4C22×D4711yescharacteristic
213C22×C8—942no—
214C2×C4⋊C4C2×Dic4711yescharacteristic
215C2×C4⋊C4C2×Dic4711yescharacteristic
216C2×C4⋊C4C2×Dic4711yescharacteristic
217C2×C4⋊C4C2×Dic4711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—24no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C2×Dic4711yescharacteristic
224C2×C42C2×Dic4711yescharacteristic
225C2×C42C22⋊D4711yescharacteristic
226C2×C42C22⋊D4711yescharacteristic
227C22⋊C8—944no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—944no—
237#95—944no—
238#95—1882no—
239C24C2×C22⋊D4711yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—944no—
254C22×C4—1882no—
255C22×C4—1882no—
256C22×C4—1882no—
257C22×C4—1882no—
258C22×C4—1882no—
259C22×C4—1882no—
260C22×C4C22⋊Dic4711yescharacteristic
261C22×C4C22⋊Dic4711yescharacteristic
262C22×C4C22⋊Dic4711yescharacteristic
263C22×C4C22⋊Dic4711yescharacteristic
264C22×C4#1062535014yes—
265C22×C4C22×Dic4711yescharacteristic
266C22×C4C2×C22⋊D4711yescharacteristic
267C2×C8—1882no—
268C2×C8—1882no—
269C2×C8—1882no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C22⋊Dic4711yescharacteristic
288C23#1309400712yes—
289C23#1309404412yes—
290C23#1309404911yescharacteristic
291C23#1309405411yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—3762no—
324C2×C4—3762no—
325C2×C4—3762no—
326C2×C4—3762no—
327C2×C4—1884no—
328C2×C4—1884no—
329C2×C4—1884no—
330C2×C4#1309395112yes—
331C2×C4#1309398312yes—
332C2×C4#1309400712yes—
333C8—3762no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22#1568898611yescharacteristic
343C22#1568909711yescharacteristic
344C22#1568909711yescharacteristic
345C22#1568911911yescharacteristic
346C22#1568912411yescharacteristic
347C22C2×#1309395111yescharacteristic
348C22#1568914011yescharacteristic
349C22#1568944712yes—
350C22#1568946412yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—3764no—
362C2—22no—
363C2—22no—
364C2#2024187411yescharacteristic
365C2#2024191311yescharacteristic
366C2#2024192611yescharacteristic
367C2#2024196511yescharacteristic
368C2#2024346511yescharacteristic
369C2#2024348311yescharacteristic
370C2#2024348711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2283C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#2283D47
hypocenterC47#8714
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
14. C47×#382C4semidirect
15. C47×#382C4semidirect
19. C4×C4⋊C4×C47C4semidirect
20. C4×C4⋊C4×C47C4semidirect
194. #382Dic47semidirect
195. #382Dic47semidirect
199. C4×C4⋊C4Dic47semidirect
200. C4×C4⋊C4Dic47semidirect
208. C47#8714semidirect

Maximal subgroups

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

subgroupindex
#202434562
#202416152
#202412662
C47×#22832
#871447