Finite Group Databasebeta

← #26109684

Subgroups — #26109684

Order 12032.

482 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243150C211yesmaximal, characteristic
2#20243150C211yesmaximal, characteristic
3#20241269C212yesmaximal, complemented
4#20241269C212yesmaximal, complemented
5C47×#2283C211yesmaximal, characteristic
6C2×C22⋊(C47⋊C8)—21no—
7C2×C22⋊(C47⋊C8)—21no—
8C2×#13093935C2212yes—
9C2×#13093935C2212yes—
10#15688878—21no—
11#15688878—21no—
12C22×C42×C47C2211yescharacteristic
13C47×#383—21no—
14C47×#382C2211yescharacteristic
15C47×#382C2211yescharacteristic
16C47×#381—21no—
17C47×#380C411yescharacteristic
18C47×#380C411yescharacteristic
19C4×C4⋊C4×C47C411yescharacteristic
20C4×C4⋊C4×C47C411yescharacteristic
21C4×C22⋊C4×C47—21no—
22C47×#376—21no—
23C22×C47⋊C8—22no—
24C22×C47⋊C8—22no—
25C22⋊(C47⋊C8)—24no—
26C22⋊(C47⋊C8)—24no—
27#13093935—24no—
28#13093935—24no—
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C23×C4×C47D411yescharacteristic
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×C47D411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47C2311yescharacteristic
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×C47C22⋊C411yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—41no—
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×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C22⋊C4×C47—42no—
78C22⋊C4×C47—42no—
79C42×C47—22no—
80C42×C47—22no—
81C42×C47—22no—
82C42×C47—42no—
83C42×C47—42no—
84C42×C47#4114yes—
85C2×C47⋊C8—24no—
86C2×C47⋊C8—24no—
87C2×C47⋊C8—42no—
88C2×C47⋊C8—42no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47#10412yes—
98C23×C47C2×C22⋊C411yescharacteristic
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
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—44no—
114C2×C4×C47—44no—
115C2×C4×C47—44no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
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#10412yes—
129C2×C4×C47#11712yes—
130C2×C4×C47#12312yes—
131C2×C4×C47#12312yes—
132C47⋊C8—44no—
133C47⋊C8—44no—
134#8720—471nomaximal, Sylow
135C22×C47—22no—
136C22×C47—22no—
137C22×C47—22no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47#38111yescharacteristic
143C22×C47#41311yescharacteristic
144C22×C47#41311yescharacteristic
145C22×C47C2×#10411yescharacteristic
146C22×C47C2×#10411yescharacteristic
147C22×C47#42111yescharacteristic
148C22×C47#42111yescharacteristic
149C4×C47—22no—
150C4×C47—22no—
151C4×C47—22no—
152C4×C47—22no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—81no—
156C4×C47—81no—
157C4×C47—81no—
158C4×C47—81no—
159#2283D4711yescharacteristic
160#1749—471no—
161#1749—471no—
162#1295—472no—
163#1295—472no—
164C2×C47—42no—
165C2×C47#152411yescharacteristic
166C2×C47#152911yescharacteristic
167C2×C47#153211yescharacteristic
168C2×C47#153511yescharacteristic
169C2×C47#182211yescharacteristic
170C2×C47#182611yescharacteristic
171C2×C47#182611yescharacteristic
172C22×C42C2×D4711yescharacteristic
173C2×C22⋊C8—941no—
174C2×C22⋊C8—941no—
175C2×#97—472no—
176C2×#97—472no—
177#383—21no—
178#382C2×D4711yescharacteristic
179#382C2×D4711yescharacteristic
180#381—21no—
181#380Dic4711yescharacteristic
182#380Dic4711yescharacteristic
183C4×C4⋊C4Dic4711yescharacteristic
184C4×C4⋊C4Dic4711yescharacteristic
185C4×C22⋊C4—21no—
186#376—21no—
187#336—941no—
188#336—941no—
189C47#872011yescharacteristic, complemented, Sylow
190C23×C4C2×Dic4711yescharacteristic
191C23×C4C22⋊D4711yescharacteristic
192C23×C4C22⋊D4711yescharacteristic
193C22×C8—942no—
194C22×C8—942no—
195C2×C4⋊C4C2×Dic4711yescharacteristic
196C2×C4⋊C4C2×Dic4711yescharacteristic
197C2×C4⋊C4C2×Dic4711yescharacteristic
198C2×C4⋊C4C2×Dic4711yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42—24no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42C2×Dic4711yescharacteristic
205C2×C42C22⋊D4711yescharacteristic
206C2×C42C22⋊D4711yescharacteristic
207C2×C42C22×D4711yescharacteristic
208C22⋊C8—944no—
209C22⋊C8—944no—
210#97—944no—
211#97—944no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220C24C22⋊Dic4711yescharacteristic
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C22⋊Dic4711yescharacteristic
235C22×C4C22⋊Dic4711yescharacteristic
236C22×C4C22⋊Dic4711yescharacteristic
237C22×C4C22×Dic4711yescharacteristic
238C22×C4C2×C22⋊D4711yescharacteristic
239C22×C4C2×C22⋊D4711yescharacteristic
240C2×C8—944no—
241C2×C8—944no—
242C2×C8—1882no—
243C2×C8—1882no—
244C2×C8—1882no—
245C2×C8—1882no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—42no—
256C42—42no—
257C42#1062535014yes—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#1309395112yes—
265C23C2×C22⋊Dic4711yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4#1309395112yes—
296C2×C4#1309398312yes—
297C2×C4#1309400712yes—
298C2×C4#1309400712yes—
299C8—1884no—
300C8—1884no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22#1568898611yescharacteristic
309C22#1568910711yescharacteristic
310C22#1568910711yescharacteristic
311C22C2×#1309395111yescharacteristic
312C22C2×#1309395111yescharacteristic
313C22#1568914011yescharacteristic
314C22#1568914011yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—81no—
325C2—42no—
326C2#2024197611yescharacteristic
327C2#2024199511yescharacteristic
328C2#2024200811yescharacteristic
329C2#2024201911yescharacteristic
330C2#2024347111yescharacteristic
331C2#2024348711yescharacteristic
332C2#2024348711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2283C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2283D47
hypocenterC47#8720
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
3. #20241269C2semidirect
4. #20241269C2semidirect
189. C47#8720semidirect

Maximal subgroups

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

subgroupindex
#202431502
#202412692
C47×#22832
#872047