Finite Group Databasebeta

← #26104963

Subgroups — #26104963

Order 12032.

450 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243456C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic
3#20241211C212yesmaximal, complemented
4#20241211C212yesmaximal, complemented
5C47×#2851C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7C2×C22⋊(C47⋊C8)—21no—
8C2×C22⋊(C47⋊C8)—21no—
9#15688878—21no—
10#15688878C2212yes—
11#15688878C2212yes—
12C2×#125×C47C411yescharacteristic
13C22×C42×C47C2211yescharacteristic
14C47×#389C2211yescharacteristic
15C47×#389C2211yescharacteristic
16C47×#387—21no—
17C47×#387—21no—
18C47×#385—21no—
19C47×#385—21no—
20C47×#382C411yescharacteristic
21C47×#380C411yescharacteristic
22C47×#380C411yescharacteristic
23C22×C47⋊C8—22no—
24C22×C47⋊C8—22no—
25C4⋊(C47⋊C8)—42no—
26C22⋊(C47⋊C8)—42no—
27C22⋊(C47⋊C8)—42no—
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47D411yescharacteristic
30C23×C4×C47D411yescharacteristic
31#125×C47—42no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—21no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47C2×C411yescharacteristic
37C2×C4⋊C4×C47C2×C411yescharacteristic
38C2×C4⋊C4×C47C2×C411yescharacteristic
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C22⋊C4×C47—21no—
41C2×C22⋊C4×C47—21no—
42C2×C42×C47—42no—
43C2×C42×C47C2×C411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C2×C42×C47D411yescharacteristic
46C2×C42×C47C2311yescharacteristic
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×C47C22⋊C411yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
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×C47—41no—
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C4⋊C4×C47—22no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—42no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—42no—
80C4⋊C4×C47—42no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C22⋊C4×C47—42no—
84C22⋊C4×C47—42no—
85C42×C47—22no—
86C42×C47—22no—
87C42×C47—41no—
88C42×C47—41no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C2×C47⋊C8—42no—
94C2×C47⋊C8—42no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47#10112yes—
102C23×C47C2×C22⋊C411yescharacteristic
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
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—44no—
118C2×C4×C47—44no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
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#9912yes—
134C2×C4×C47#13112yes—
135C2×C4×C47#13512yes—
136C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C47#13711yescharacteristic
138C47⋊C8—82no—
139C47⋊C8—82no—
140#7731—471nomaximal, Sylow
141C22×C47—22no—
142C22×C47—22no—
143C22×C47—22no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47#40811yescharacteristic
149C22×C47C2×#9911yescharacteristic
150C22×C47C2×#10111yescharacteristic
151C22×C47#41611yescharacteristic
152C22×C47#41711yescharacteristic
153C22×C47#42111yescharacteristic
154C22×C47#42111yescharacteristic
155C4×C47—22no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—81no—
163C4×C47—81no—
164C4×C47—81no—
165C4×C47—81no—
166#2851D4711yescharacteristic
167#1817—471no—
168#1797—471no—
169#1271—472no—
170#1271—472no—
171C2×C47—42no—
172C2×C47#147211yescharacteristic
173C2×C47#148211yescharacteristic
174C2×C47#149511yescharacteristic
175C2×C47#151311yescharacteristic
176C2×C47#151611yescharacteristic
177C2×C47#153411yescharacteristic
178C2×C47#155211yescharacteristic
179C2×#125Dic4711yescharacteristic
180C22×C42C2×D4711yescharacteristic
181C2×C4⋊C8—941no—
182C2×C22⋊C8—941no—
183C2×C22⋊C8—941no—
184#389C2×D4711yescharacteristic
185#389C2×D4711yescharacteristic
186#387—21no—
187#387—21no—
188#385—21no—
189#385—21no—
190#382Dic4711yescharacteristic
191#380Dic4711yescharacteristic
192#380Dic4711yescharacteristic
193#336—472no—
194#336—472no—
195#336—941no—
196C47#773111yescharacteristic, complemented, Sylow
197C23×C4C2×Dic4711yescharacteristic
198C23×C4C22⋊D4711yescharacteristic
199C23×C4C22⋊D4711yescharacteristic
200C22×C8—942no—
201C22×C8—942no—
202#125—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic4711yescharacteristic
208C2×C4⋊C4C2×Dic4711yescharacteristic
209C2×C4⋊C4C2×Dic4711yescharacteristic
210C2×C4⋊C4C2×Dic4711yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—42no—
214C2×C42C2×Dic4711yescharacteristic
215C2×C42C22⋊D4711yescharacteristic
216C2×C42C22⋊D4711yescharacteristic
217C2×C42C22×D4711yescharacteristic
218C4⋊C8—1882no—
219C22⋊C8—1882no—
220C22⋊C8—1882no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C24C22⋊Dic4711yescharacteristic
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C22⋊Dic4711yescharacteristic
243C22×C4C22⋊Dic4711yescharacteristic
244C22×C4C22⋊Dic4711yescharacteristic
245C22×C4C22×Dic4711yescharacteristic
246C22×C4C2×C22⋊D4711yescharacteristic
247C22×C4C2×C22⋊D4711yescharacteristic
248C2×C8—1882no—
249C2×C8—1882no—
250C2×C8—1882no—
251C2×C8—1882no—
252C2×C8—1882no—
253C2×C8—1882no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#1309394312yes—
276C23C2×C22⋊Dic4711yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#1309393912yes—
308C2×C4#1309403112yes—
309C2×C4#1309404412yes—
310C2×C4#1309404911yescharacteristic
311C2×C4#1309405411yescharacteristic
312C8—3762no—
313C8—3762no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#1568909011yescharacteristic
322C22C2×#1309393911yescharacteristic
323C22C2×#1309394311yescharacteristic
324C22#1568911911yescharacteristic
325C22#1568912411yescharacteristic
326C22#1568914011yescharacteristic
327C22#1568914011yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—42no—
340C2#2024175211yescharacteristic
341C2#2024179611yescharacteristic
342C2#2024185311yescharacteristic
343C2#2024193111yescharacteristic
344C2#2024194411yescharacteristic
345C2#2024201511yescharacteristic
346C2#2024208811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2851C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2851D47
hypocenterC47#7731
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
3. #20241211C2semidirect
4. #20241211C2semidirect
196. C47#7731semidirect

Maximal subgroups

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

subgroupindex
#202434562
#202433682
#202412112
C47×#28512
#773147