Finite Group Databasebeta

← #26116470

Subgroups — #26116470

Order 12032.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243368C211yesmaximal, characteristic
2#20241615C211yesmaximal, characteristic
3#20241266C212yesmaximal
4#20241266C212yesmaximal
5C47×#2851C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7C2×C22⋊(C47⋊C8)C2212yes—
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—
25C4⋊(C47⋊C8)—42no—
26C22⋊(C47⋊C8)—24no—
27C47⋊#95—22no—
28C47⋊#95—42no—
29C47⋊#95—42no—
30C47⋊#95Q814yes—
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—21no—
59C22×C4×C47—21no—
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×C47—41no—
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×Q812yes—
77C22×C4×C47#4112yes—
78C22×Dic47—24no—
79C22×Dic47—42no—
80C22×Dic47—42no—
81C22×Dic47—42no—
82C22×Dic47—42no—
83C22×Dic47—42no—
84C22×Dic47—42no—
85C4⋊C4×C47—42no—
86C4⋊C4×C47—42no—
87C4⋊C4×C47—42no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—42no—
93C22⋊C4×C47—42no—
94C22⋊C4×C47—41no—
95C22⋊C4×C47—41no—
96C42×C47—22no—
97C42×C47—22no—
98C42×C47—41no—
99C42×C47—41no—
100C2×C47⋊C8—42no—
101C2×C47⋊C8—42no—
102C2×C47⋊C8—42no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47C2×C22⋊C411yescharacteristic
108C23×C47C22⋊Q812yes—
109C23×C47#13512yes—
110C23×C47AGL(1,ℤ/8)11yescharacteristic
111C23×C47#13711yescharacteristic
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—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—44no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
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—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47#9912yes—
145C2×C4×C47C4×Q812yes—
146C2×C4×C47#12411yescharacteristic
147C2×C4×C47C4⋊Q811yescharacteristic
148C2×Dic47—44no—
149C2×Dic47—44no—
150C2×Dic47—44no—
151C2×Dic47—82no—
152C2×Dic47—82no—
153C2×Dic47—82no—
154C2×Dic47—82no—
155C47⋊C8—82no—
156#9913—471nomaximal, Sylow
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47#39111yescharacteristic
166C22×C47C2×#9911yescharacteristic
167C22×C47#41011yescharacteristic
168C22×C47#41611yescharacteristic
169C22×C47#41711yescharacteristic
170C22×C47#42111yescharacteristic
171C22×C47#42111yescharacteristic
172C22×C47#47812yes—
173C22×C47#47912yes—
174C4×C47—21no—
175C4×C47—22no—
176C4×C47—21no—
177C4×C47—22no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—81no—
182C4×C47—81no—
183C4×C47—81no—
184C4×C47—81no—
185Dic47—84no—
186#2851D4711yescharacteristic
187#1797—471no—
188#1434—471no—
189#1294—472no—
190#1294—472no—
191C2×C47—22no—
192C2×C47—22no—
193C2×C47#151211yescharacteristic
194C2×C47#151311yescharacteristic
195C2×C47#151611yescharacteristic
196C2×C47#152111yescharacteristic
197C2×C47#198911yescharacteristic
198C2×C47#199511yescharacteristic
199C2×C47#199611yescharacteristic
200C2×#125Dic4711yescharacteristic, complemented
201C22×C42C2×D4711yescharacteristic
202C2×C4⋊C8—941no—
203C2×C22⋊C8—472no—
204#389Dic4711yescharacteristic, complemented
205#389Dic4711yescharacteristic, complemented
206#387—21no—
207#387—21no—
208#385—21no—
209#385—21no—
210#382Dic4711yescharacteristic, complemented
211#380C2×D4711yescharacteristic
212#380C2×D4711yescharacteristic
213C2×#95—472no—
214C2×#95—941no—
215C2×#95—941no—
216#336—941no—
217C47#991311yescharacteristic, complemented, Sylow
218C23×C4—942no—
219C23×C4C22⋊D4711yescharacteristic
220C23×C4C22⋊D4711yescharacteristic
221C23×C4C22×D4711yescharacteristic
222C22×C8—942no—
223#125—42no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×Dic4711yescharacteristic
229C2×C4⋊C4C2×Dic4711yescharacteristic
230C2×C4⋊C4C2×Dic4711yescharacteristic
231C2×C4⋊C4C2×Dic4711yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C42—42no—
235C2×C42C2×Dic4711yescharacteristic
236C2×C42C2×Dic4711yescharacteristic
237C2×C42C22⋊D4711yescharacteristic
238C2×C42C22⋊D4711yescharacteristic
239C4⋊C8—1882no—
240C22⋊C8—944no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—474no—
248#95—942no—
249#95—1882no—
250#95—1882no—
251C24C2×C22⋊D4711yescharacteristic
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—944no—
266C22×C4—1882no—
267C22×C4—1882no—
268C22×C4—1882no—
269C22×C4—1882no—
270C22×C4—1882no—
271C22×C4—1882no—
272C22×C4C22⋊Dic4711yescharacteristic
273C22×C4C22⋊Dic4711yescharacteristic
274C22×C4C22⋊Dic4711yescharacteristic
275C22×C4C22⋊Dic4711yescharacteristic
276C22×C4Q8×D4712yes—
277C22×C4#1062535412yes—
278C22×C4C22×Dic4711yescharacteristic
279C22×C4C2×C22⋊D4711yescharacteristic
280C2×C8—1882no—
281C2×C8—1882no—
282C2×C8—1882no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊Dic4711yescharacteristic
303C23#1309400012yes—
304C23#1309404412yes—
305C23#1309404911yescharacteristic
306C23#1309405411yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—3762no—
340C2×C4—3762no—
341C2×C4—3762no—
342C2×C4—3762no—
343C2×C4—1884no—
344C2×C4—1884no—
345C2×C4—1884no—
346C2×C4#1309393912yes—
347C2×C4Q8×Dic4712yes—
348C2×C4#1309401311yescharacteristic
349C2×C4#1309402211yescharacteristic
350C8—3762no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22#1568903011yescharacteristic
360C22C2×#1309393911yescharacteristic
361C22#1568909711yescharacteristic
362C22#1568911911yescharacteristic
363C22#1568912411yescharacteristic
364C22#1568914011yescharacteristic
365C22#1568914011yescharacteristic
366C22#1568942012yes—
367C22#1568942712yes—
368C4—22no—
369C4—21no—
370C4—22no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—3764no—
380C2—22no—
381C2—22no—
382C2#2024192611yescharacteristic
383C2#2024193111yescharacteristic
384C2#2024194411yescharacteristic
385C2#2024196511yescharacteristic
386C2#2024434611yescharacteristic
387C2#2024437011yescharacteristic
388C2#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#9913
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
200. C2×#125Dic47semidirect
204. #389Dic47semidirect
205. #389Dic47semidirect
210. #382Dic47semidirect
217. C47#9913semidirect

Maximal subgroups

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

subgroupindex
#202433682
#202416152
#202412662
C47×#28512
#991347