Finite Group Databasebeta

← #26116376

Subgroups — #26116376

Order 12032.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251775C211yesmaximal, characteristic
2C4×#13093935C211yesmaximal, characteristic
3#20241270C212yesmaximal
4#20241270C212yesmaximal
5C47×#1767C211yesmaximal, characteristic
6C2×#13093935—21no—
7C2×#13093935C2212yes—
8C2×C4×C47⋊C8—21no—
9#15689021C411yescharacteristic
10#15689021C411yescharacteristic
11#15689021C411yescharacteristic
12#15689021C411yescharacteristic
13#15689007—21no—
14#15689007—21no—
15#15689007—21no—
16#15689007—21no—
17#15688989C2211yescharacteristic
18#15688989C2211yescharacteristic
19C2×C4⋊C8×C47—21no—
20C2×#97×C47C2212yes—
21C43×C47C2211yescharacteristic
22C47×#336—21no—
23C22×C47⋊C8—22no—
24C2×C4⋊Dic47C2×C411yescharacteristic
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32#13093935—24no—
33#13093935—22no—
34#13093935Q814yes—
35C4×C47⋊C8—24no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C22×C8×C47—22no—
45C2×C42×C47C2×C411yescharacteristic
46C2×C42×C47C2×C411yescharacteristic
47C2×C42×C47D411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47C2311yescharacteristic
52C4⋊C8×C47—24no—
53#97×C47—24no—
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22⋊C411yescharacteristic
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22×C411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×C8×C47—24no—
66C2×C8×C47—42no—
67C2×C8×C47—42no—
68C42×C47—22no—
69C42×C47—22no—
70C42×C47—22no—
71C42×C47—41no—
72C42×C47—41no—
73C42×C47—41no—
74C42×C47C2×Q812yes—
75C42×C47#4112yes—
76C4⋊Dic47—41no—
77C4⋊Dic47—41no—
78C4⋊Dic47—41no—
79C4⋊Dic47—41no—
80Dic47⋊C4—42no—
81Dic47⋊C4—42no—
82Dic47⋊C4—42no—
83Dic47⋊C4—42no—
84C2×C47⋊C8—24no—
85C2×C47⋊C8—24no—
86C2×C47⋊C8—24no—
87C23×C47C2×C22⋊C411yescharacteristic
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47#10412yes—
104C2×C4×C47#10412yes—
105C2×C4×C47#10412yes—
106C2×C4×C47C4×Q812yes—
107C2×C4×C47C22⋊Q812yes—
108C2×C4×C47#12411yescharacteristic
109C2×C4×C47C4⋊Q811yescharacteristic
110C2×Dic47—41no—
111C2×Dic47—41no—
112C2×Dic47—41no—
113C2×Dic47—41no—
114C2×Dic47—41no—
115C2×Dic47—41no—
116C2×Dic47—41no—
117C2×Dic47—41no—
118C2×Dic47—41no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C8×C47—44no—
123C47⋊C8—28no—
124#9892—471nomaximal, Sylow
125C22×C47#39111yescharacteristic
126C22×C47#41311yescharacteristic
127C22×C47#41311yescharacteristic
128C22×C47C2×#10411yescharacteristic
129C22×C47C2×#10411yescharacteristic
130C22×C47C2×#10411yescharacteristic
131C22×C47#42111yescharacteristic
132C4×C47—21no—
133C4×C47—21no—
134C4×C47—22no—
135C4×C47—22no—
136C4×C47—22no—
137C4×C47—22no—
138C4×C47—22no—
139C4×C47—41no—
140Dic47—81no—
141Dic47—81no—
142Dic47—81no—
143Dic47—81no—
144#2864—471no—
145#1767D4711yescharacteristic
146C4×#97—471no—
147#1295—472no—
148#1295—472no—
149C2×C47#152411yescharacteristic
150C2×C47#152411yescharacteristic
151C2×C47#152911yescharacteristic
152C2×C47#153211yescharacteristic
153C2×C47#198611yescharacteristic
154C2×C47#199411yescharacteristic
155C2×C47#199811yescharacteristic
156C2×C4⋊C8—21no—
157C2×#97—472no—
158C2×#97—941no—
159C2×#97C2×D4712yes—
160C2×C4×C8—941no—
161#389—471no—
162#389—471no—
163#389—471no—
164#389—471no—
165#387—941no—
166#387—941no—
167#387—941no—
168#387—941no—
169#382—471no—
170#382—471no—
171C43C2×D4711yescharacteristic
172#336—21no—
173C47#989211yescharacteristic, complemented, Sylow
174C22×C8—22no—
175C22×C8—942no—
176C2×C4⋊C4—471no—
177C2×C4⋊C4—471no—
178C2×C4⋊C4—471no—
179C2×C4⋊C4—471no—
180C2×C4⋊C4—941no—
181C2×C4⋊C4—941no—
182C2×C4⋊C4—941no—
183C2×C4⋊C4—941no—
184C2×C42C4×D4711yescharacteristic
185C2×C42C4×D4711yescharacteristic
186C2×C42D18811yescharacteristic
187C2×C42D18811yescharacteristic
188C2×C42C22⋊D4711yescharacteristic
189C2×C42C22⋊D4711yescharacteristic
190C2×C42C22×D4711yescharacteristic
191C4⋊C8—24no—
192#97—24no—
193#97—474no—
194#97—944no—
195#97—942no—
196C4×C8—944no—
197#95—941no—
198#95—941no—
199#95—941no—
200#95—941no—
201#95—941no—
202#95—941no—
203#95—941no—
204#95—941no—
205C22×C4—941no—
206C22×C4—941no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4(C2×D47)⋊C411yescharacteristic
210C22×C4(C2×D47)⋊C411yescharacteristic
211C22×C4(C2×D47)⋊C411yescharacteristic
212C22×C4(C2×D47)⋊C411yescharacteristic
213C22×C4C2×C4×D4711yescharacteristic
214C22×C4C2×D18811yescharacteristic
215C22×C4C2×C22⋊D4711yescharacteristic
216C2×C8—24no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—944no—
220C2×C8—944no—
221C2×C8—944no—
222C4⋊C4—1881no—
223C4⋊C4—1881no—
224C4⋊C4—1881no—
225C4⋊C4—1881no—
226C4⋊C4—1882no—
227C4⋊C4—1882no—
228C4⋊C4—1882no—
229C4⋊C4—1882no—
230C42—22no—
231C42—22no—
232C42—22no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42#1062535212yes—
237C42Q8×D4712yes—
238C23C2×(C2×D47)⋊C411yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—1881no—
255C2×C4—1881no—
256C2×C4—1881no—
257C2×C4—1881no—
258C2×C4—1881no—
259C2×C4—1881no—
260C2×C4—1881no—
261C2×C4—1881no—
262C2×C4—1881no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4#1309395012yes—
267C2×C4#1309395012yes—
268C2×C4#1309395212yes—
269C2×C4#1309398912yes—
270C2×C4#1309400412yes—
271C2×C4#1309401111yescharacteristic
272C2×C4#1309402211yescharacteristic
273C8—44no—
274C8—948no—
275C22#1568902811yescharacteristic
276C22#1568910511yescharacteristic
277C22#1568910511yescharacteristic
278C22C2×#1309395011yescharacteristic
279C22C2×#1309395011yescharacteristic
280C22C2×#1309395211yescharacteristic
281C22#1568914111yescharacteristic
282C4—22no—
283C4—22no—
284C4—22no—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—41no—
290C4—3761no—
291C4—3761no—
292C4—3761no—
293C4—3761no—
294C2#2024197411yescharacteristic
295C2#2024197711yescharacteristic
296C2#2024199611yescharacteristic
297C2#2024200911yescharacteristic
298C2#2024433111yescharacteristic
299C2#2024436411yescharacteristic
300C2#2024438011yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1767C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1767D47
hypocenterC47#9892
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
173. C47#9892semidirect

Maximal subgroups

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

subgroupindex
#202517752
C4×#130939352
#202412702
C47×#17672
#989247