Finite Group Databasebeta

← #26104707

Subgroups — #26104707

Order 12032.

488 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243150C211yesmaximal, characteristic
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic
3#20241214C212yesmaximal, complemented
4#20241211C212yesmaximal, complemented
5C47×#2855C211yesmaximal, characteristic
6C2×C22⋊(C47⋊C8)—21no—
7C2×C22⋊(C47⋊C8)—21no—
8C2×#13093935—21no—
9C2×C4×C47⋊C8—21no—
10#15688878C2212yes—
11#15688878C2212yes—
12C2×C22⋊Q8×C47C411yescharacteristic
13C22×C42×C47C2211yescharacteristic
14C47×#391C411yescharacteristic
15C47×#391C2211yescharacteristic
16C47×#389C411yescharacteristic
17C47×#389C2211yescharacteristic
18C47×#387—21no—
19C47×#387—21no—
20C47×#385—21no—
21C47×#381—21no—
22C47×#380C411yescharacteristic
23C22×C47⋊C8—22no—
24C22×C47⋊C8—22no—
25C22⋊(C47⋊C8)—24no—
26C22⋊(C47⋊C8)—24no—
27#13093935—42no—
28C4×C47⋊C8—42no—
29C22×Q8×C47C2×C411yescharacteristic
30C23×C4×C47C2×C411yescharacteristic
31C23×C4×C47D411yescharacteristic
32C23×C4×C47D411yescharacteristic
33C22⋊Q8×C47—42no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—21no—
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—
53#95×C47—21no—
54C24×C47C22⋊C411yescharacteristic
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C2×Q8×C47—41no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—22no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C4⋊C4×C47—22no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—42no—
81C4⋊C4×C47—42no—
82C4⋊C4×C47—42no—
83C22⋊C4×C47—42no—
84C22⋊C4×C47—42no—
85C42×C47—22no—
86C42×C47—22no—
87C42×C47—41no—
88C42×C47—41no—
89C2×C47⋊C8—24no—
90C2×C47⋊C8—24no—
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#10412yes—
102C23×C47C2×C22⋊C411yescharacteristic
103Q8×C47—82no—
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—44no—
120C2×C4×C47—41no—
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#9912yes—
133C2×C4×C47#10412yes—
134C2×C4×C47#13112yes—
135C2×C4×C47#13512yes—
136C2×C4×C47#13712yes—
137C47⋊C8—44no—
138C47⋊C8—44no—
139#7675—471nomaximal, Sylow
140C22×C47—22no—
141C22×C47—22no—
142C22×C47—22no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47#40811yescharacteristic
148C22×C47C2×#9911yescharacteristic
149C22×C47#41311yescharacteristic
150C22×C47#41611yescharacteristic
151C22×C47#41911yescharacteristic
152C22×C47C2×#10411yescharacteristic
153C22×C47C2×#10411yescharacteristic
154C4×C47—22no—
155C4×C47—22no—
156C4×C47—22no—
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—41no—
160C4×C47—81no—
161C4×C47—81no—
162C4×C47—81no—
163C4×C47—81no—
164#2855D4711yescharacteristic
165#1749—471no—
166C4×C22⋊C8—471no—
167#1272—472no—
168#1271—472no—
169C2×C47—42no—
170C2×C47#146811yescharacteristic
171C2×C47#148511yescharacteristic
172C2×C47#149411yescharacteristic
173C2×C47#150111yescharacteristic
174C2×C47#150811yescharacteristic
175C2×C47#152411yescharacteristic
176C2×C47#155411yescharacteristic
177C2×C22⋊Q8Dic4711yescharacteristic
178C22×C42C2×D4711yescharacteristic
179C2×C22⋊C8—941no—
180C2×C22⋊C8—941no—
181C2×#97—941no—
182C2×C4×C8—941no—
183#391Dic4711yescharacteristic
184#391C2×D4711yescharacteristic
185#389Dic4711yescharacteristic
186#389C2×D4711yescharacteristic
187#387—21no—
188#387—21no—
189#385—21no—
190#381—21no—
191#380Dic4711yescharacteristic
192#336—472no—
193#336—472no—
194C47#767511yescharacteristic, complemented, Sylow
195C22×Q8C2×Dic4711yescharacteristic
196C23×C4C2×Dic4711yescharacteristic
197C23×C4C22⋊D4711yescharacteristic
198C23×C4C22⋊D4711yescharacteristic
199C22×C8—942no—
200C22×C8—942no—
201C22⋊Q8—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic4711yescharacteristic
206C2×C4⋊C4C2×Dic4711yescharacteristic
207C2×C4⋊C4C2×Dic4711yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—42no—
211C2×C42C2×Dic4711yescharacteristic
212C2×C42C22⋊D4711yescharacteristic
213C2×C42C22⋊D4711yescharacteristic
214C2×C42C22×D4711yescharacteristic
215C22⋊C8—944no—
216C22⋊C8—944no—
217#97—1882no—
218C4×C8—1882no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226C24C22⋊Dic4711yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊Dic4711yescharacteristic
244C22×C4C22⋊Dic4711yescharacteristic
245C22×C4C22⋊Dic4711yescharacteristic
246C22×C4C22×Dic4711yescharacteristic
247C22×C4C2×C22⋊D4711yescharacteristic
248C22×C4C2×C22⋊D4711yescharacteristic
249C2×C8—944no—
250C2×C8—944no—
251C2×C8—1882no—
252C2×C8—1882no—
253C2×C8—1882no—
254C2×C8—1882no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—22no—
264C42—22no—
265C42—41no—
266C42—41no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23#1309395112yes—
274C23C2×C22⋊Dic4711yescharacteristic
275Q8—82no—
276C2×C4—21no—
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—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
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#1309393912yes—
305C2×C4#1309395112yes—
306C2×C4#1309403112yes—
307C2×C4#1309404412yes—
308C2×C4#1309405512yes—
309C8—1884no—
310C8—1884no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#1568909011yescharacteristic
319C22C2×#1309393911yescharacteristic
320C22#1568910711yescharacteristic
321C22#1568911911yescharacteristic
322C22#1568913211yescharacteristic
323C22C2×#1309395111yescharacteristic
324C22C2×#1309395111yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—42no—
336C2#2024173611yescharacteristic
337C2#2024180911yescharacteristic
338C2#2024184811yescharacteristic
339C2#2024187911yescharacteristic
340C2#2024190811yescharacteristic
341C2#2024197611yescharacteristic
342C2#2024209811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2855C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2855D47
hypocenterC47#7675
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #20241214C2semidirect
4. #20241211C2semidirect
194. C47#7675semidirect

Maximal subgroups

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

subgroupindex
#202431502
C4×C22⋊(C47⋊C8)2
#202412142
#202412112
C47×#28552
#767547