Finite Group Databasebeta

← #26109816

Subgroups — #26109816

Order 12032.

394 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245990C211yesmaximal, characteristic
2#20241717C211yesmaximal, characteristic
3#20241717C211yesmaximal, characteristic
4#20241295C211yesmaximal, characteristic
5#20241294C211yesmaximal, characteristic
6#20241293C211yesmaximal, characteristic
7C47×#1305C211yesmaximal, characteristic
8C22×Dic47⋊C4C2211yescharacteristic
9#15689087C2211yescharacteristic
10#15689087C2211yescharacteristic
11#15689010—22no—
12#15689004—22no—
13#15688984C412yes—
14#15688983C2211yescharacteristic
15C22⋊C4×Dic47C412yes—
16#15688848—22no—
17#15688848—22no—
18C47×#407C2211yescharacteristic
19C47×#407C2211yescharacteristic
20C47×#380C2211yescharacteristic
21C23×Dic47C2×C411yescharacteristic
22C23×Dic47C2×C411yescharacteristic
23C2×#10625329—21no—
24C2×#10625329—21no—
25C2×C4⋊Dic47—21no—
26C2×Dic47⋊C4—21no—
27C2×Dic47⋊C4—21no—
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4D412yes—
31C2×Dic47⋊C4D412yes—
32C2×C22⋊Dic47C2×C412yes—
33C2×C4×Dic47—22no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36C22⋊(C47⋊C8)—21no—
37C22⋊(C47⋊C8)—21no—
38C47⋊#95—21no—
39C47⋊#95—22no—
40C47⋊#95—24no—
41C23×C4×C47C2311yescharacteristic
42C2×M16×C47—21no—
43C2×M16×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C22⋊C4×C47C2×C412yes—
46C22⋊C8×C47—21no—
47C22⋊C8×C47—21no—
48C22⋊C8×C47—21no—
49C22⋊C8×C47—21no—
50#95×C47—21no—
51C24×C47C22×C411yescharacteristic
52C22×C4×C47—22no—
53C22×C4×C47—81no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47#4111yescharacteristic
57C22×C4×C47#4111yescharacteristic
58C22×C4×C47#4111yescharacteristic
59C22×C4×C47#4111yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—22no—
65C22×Dic47—41no—
66C22×Dic47—41no—
67C22×Dic47—81no—
68C22×Dic47C22⋊C412yes—
69C22×Dic47C22⋊C412yes—
70M16×C47—81no—
71M16×C47—81no—
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C4⋊C4×C47—81no—
75C22⋊C4×C47—42no—
76C22⋊Dic47—42no—
77C4⋊Dic47—81no—
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82C4×Dic47—82no—
83#10625329—81no—
84#10625329—81no—
85C2×C47⋊C8—41no—
86C2×C47⋊C8—41no—
87C23×C47—21no—
88C23×C47—21no—
89C23×C47—41no—
90C23×C47—41no—
91C23×C47C2×C22⋊C411yescharacteristic
92C23×C47#11711yescharacteristic
93C23×C47#11711yescharacteristic
94C2×C4×C47—41no—
95C2×C4×C47—41no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47#12311yescharacteristic
104C2×C4×C47#12311yescharacteristic
105C2×C4×C47#12311yescharacteristic
106C2×C4×C47#12311yescharacteristic
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—42no—
112C2×Dic47—42no—
113C2×Dic47—42no—
114C2×Dic47—42no—
115C2×Dic47—42no—
116C2×Dic47—42no—
117C2×Dic47—81no—
118C2×Dic47—81no—
119C8×C47—81no—
120C8×C47—81no—
121C47⋊C8—81no—
122C47⋊C8—81no—
123#8758—471nomaximal, Sylow
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47#38111yescharacteristic
135C22×C47#41311yescharacteristic
136C22×C47#41311yescharacteristic
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—82no—
142Dic47—42no—
143Dic47—42no—
144Dic47—82no—
145#2313—471no—
146#1463—471no—
147#1463—471no—
148#1305—471no—
149#1305—471no—
150#1305—471no—
151#1305D4711yescharacteristic
152C2×C47—21no—
153C2×C47—21no—
154C2×C47—41no—
155C2×C47—41no—
156C2×C47#182211yescharacteristic
157C2×C47#182811yescharacteristic
158C2×C47#183011yescharacteristic
159C22×C4⋊C4—471no—
160#407—471no—
161#407—471no—
162#407C2×D4711yescharacteristic
163#407C2×D4711yescharacteristic
164#387—942no—
165#387—942no—
166#381—472no—
167#380—471no—
168#380C2×D4711yescharacteristic
169C4×C22⋊C4—472no—
170#324—942no—
171#324—942no—
172C47#875811yescharacteristic, complemented, Sylow
173C23×C4—471no—
174C23×C4—471no—
175C23×C4C22×D4711yescharacteristic
176C2×M16—21no—
177C2×M16—21no—
178C2×M16—941no—
179C2×M16—941no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—472no—
182C2×C4⋊C4—472no—
183C2×C4⋊C4—941no—
184C2×C4⋊C4—941no—
185C2×C4⋊C4—941no—
186C2×C4⋊C4—941no—
187C2×C4⋊C4—941no—
188C2×C22⋊C4—472no—
189C2×C22⋊C4C4×D4712yes—
190C2×C42—942no—
191C22⋊C8—21no—
192C22⋊C8—21no—
193C22⋊C8—21no—
194C22⋊C8—21no—
195C22⋊C8—941no—
196C22⋊C8—941no—
197C22⋊C8—941no—
198C22⋊C8—941no—
199#95—21no—
200#95—942no—
201#95—944no—
202#95—941no—
203C24C2×C4×D4711yescharacteristic
204C22×C4—22no—
205C22×C4—81no—
206C22×C4—472no—
207C22×C4—472no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—942no—
213C22×C4—3761no—
214C22×C4—1881no—
215C22×C4—1881no—
216C22×C4#1062535011yescharacteristic
217C22×C4#1062535011yescharacteristic
218C22×C4D4×D4711yescharacteristic
219C22×C4D4×D4711yescharacteristic
220C22×C4#1062535211yescharacteristic
221C22×C4#1062535411yescharacteristic
222M16—81no—
223M16—81no—
224M16—3761no—
225M16—3761no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—1881no—
229C2×C8—1881no—
230C4⋊C4—81no—
231C4⋊C4—942no—
232C4⋊C4—942no—
233C4⋊C4—942no—
234C4⋊C4—942no—
235C4⋊C4—3761no—
236C22⋊C4—42no—
237C22⋊C4—1882no—
238C42—3762no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23C22⋊C4×D4711yescharacteristic
244C23#1309398111yescharacteristic
245C23#1309398211yescharacteristic
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—3761no—
260C2×C4—3761no—
261C2×C4—1882no—
262C2×C4—1882no—
263C2×C4—1882no—
264C2×C4—1882no—
265C2×C4—1882no—
266C2×C4—1882no—
267C2×C4#1309400611yescharacteristic
268C2×C4#1309400611yescharacteristic
269C2×C4#1309400911yescharacteristic
270C2×C4#1309400911yescharacteristic
271C8—81no—
272C8—81no—
273C8—3761no—
274C8—3761no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—42no—
284C22—42no—
285C22#1568898511yescharacteristic
286C22#1568910411yescharacteristic
287C22#1568910611yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—3762no—
294C4—1882no—
295C4—1882no—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2#2024347011yescharacteristic
301C2#2024349511yescharacteristic
302C2#2024350111yescharacteristic
subgroupG/H
centerC22#15688985
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1305C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1305D47
hypocenterC47#8758
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
172. C47#8758semidirect

Maximal subgroups

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

subgroupindex
#202459902
#202417172
#202412952
#202412942
#202412932
C47×#13052
#875847