Finite Group Databasebeta

← #26114093

Subgroups — #26114093

Order 12032.

610 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 115 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#20245745C211yesmaximal, characteristic
2#20243487C212yesmaximal
3#20241718C211yesmaximal, characteristic
4#20241240C212yesmaximal
5C47×#2484C211yesmaximal, characteristic
6C2×#13093983—21no—
7#15689087C2212yes—
8C4⋊C4×Dic47—24no—
9C4×C22⋊Dic47—21no—
10C4×C22⋊Dic47C2212yes—
11#15688882—24no—
12#15688849—22no—
13C2×#117×C47C2211yescharacteristic
14C22×C4⋊C4×C47C2211yescharacteristic
15C47×#400C412yescomplemented
16C47×#398C412yescomplemented
17C47×#387—22no—
18C47×#385—21no—
19C47×#381—21no—
20C47×#381C2211yescharacteristic
21C2×#10625329—22no—
22#13093983—28no—
23C2×C4⋊Dic47—22no—
24C2×C22⋊Dic47—22no—
25C2×C4×Dic47—22no—
26C2×C4×Dic47—22no—
27C2×C4×Dic47D414yes—
28C22⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C23×C4×C47D411yescharacteristic
33C23×C4×C47D411yescharacteristic
34C23×C4×C47C2311yescharacteristic
35#117×C47—22no—
36#117×C47—22no—
37C2×C4⋊C4×C47—22no—
38C2×C4⋊C4×C47—22no—
39C2×C4⋊C4×C47—22no—
40C2×C4⋊C4×C47C2×C411yescharacteristic
41C2×C4⋊C4×C47C2×C411yescharacteristic
42C2×C4⋊C4×C47C2×C412yes—
43C2×C4⋊C4×C47D412yes—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C42×C47—21no—
47#95×C47—22no—
48#95×C47—22no—
49#95×C47—22no—
50#95×C47—21no—
51#95×C47C2×C412yes—
52C24×C47C2×D411yescharacteristic
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—24no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—22no—
61C22×C4×C47—42no—
62C22×C4×C47—42no—
63C22×C4×C47C22⋊C412yes—
64C22×C4×C47C22⋊C412yes—
65C22×C4×C47C22×C411yescharacteristic
66C22×C4×C47C2×D412yes—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47#4112yes—
69C22×Dic47—24no—
70C4⋊C4×C47—24no—
71C4⋊C4×C47—24no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C4⋊C4×C47—44no—
75C22⋊C4×C47—42no—
76C22⋊C4×C47—41no—
77C22⋊C4×C47—41no—
78C42×C47—42no—
79C22⋊Dic47—28no—
80C4⋊Dic47—28no—
81C4×Dic47—28no—
82C4×Dic47—44no—
83C4×Dic47—82no—
84#10625329—44no—
85C2×C47⋊C8—42no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—41no—
89C23×C47C2×C22⋊C411yescharacteristic
90C23×C47#12011yescharacteristic
91C23×C47#12311yescharacteristic
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—24no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—24no—
98C2×C4×C47—22no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—42no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—42no—
110C2×C4×C47—42no—
111C2×C4×C47—81no—
112C2×C4×C47#10414yes—
113C2×C4×C47C4×D412yes—
114C2×C4×C47#12112yes—
115C2×Dic47—28no—
116C2×Dic47—44no—
117C2×Dic47—44no—
118C47⋊C8—82no—
119#9478—471nomaximal, Sylow
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—44no—
128C22×C47#38611yescharacteristic
129C22×C47C2×#10412yes—
130C22×C47#45812yes—
131C4×C47—22no—
132C4×C47—22no—
133C4×C47—24no—
134C4×C47—42no—
135C4×C47—82no—
136C4×C47—81no—
137C4×C47—81no—
138Dic47—48no—
139#2484D4711yescharacteristic
140#2274—471no—
141#1826—472no—
142#1463—471no—
143#1284—472no—
144C2×C47—22no—
145C2×C47—22no—
146C2×C47—41no—
147C2×C47#189011yescharacteristic
148C2×C47#189611yescharacteristic
149C2×C47#191211yescharacteristic
150C2×#117—941no—
151C2×#117C2×D4711yescharacteristic
152C22×C4⋊C4C2×D4711yescharacteristic
153#407—472no—
154#400Dic4712yescomplemented
155#398Dic4712yescomplemented
156#387—22no—
157#385—21no—
158#381—21no—
159#381C2×D4711yescharacteristic
160C4×C4⋊C4—944no—
161C4×C22⋊C4—472no—
162C4×C22⋊C4—941no—
163#339—944no—
164#324—942no—
165C47#947811yescharacteristic, complemented, Sylow
166C23×C4C22⋊D4711yescharacteristic
167C23×C4C22⋊D4711yescharacteristic
168C23×C4C22×D4711yescharacteristic
169C2×M16—942no—
170#117—22no—
171#117—22no—
172#117—948no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—942no—
177C2×C4⋊C4C2×Dic4711yescharacteristic
178C2×C4⋊C4C2×Dic4711yescharacteristic
179C2×C4⋊C4C2×Dic4712yes—
180C2×C4⋊C4C22⋊D4712yes—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—942no—
184C2×C42—21no—
185C2×C42—474no—
186C2×C42—942no—
187C2×C42—942no—
188C22⋊C8—942no—
189C22⋊C8—942no—
190#95—22no—
191#95—22no—
192#95—22no—
193#95—21no—
194#95—942no—
195#95—942no—
196#95C2×Dic4712yes—
197C24C2×C22⋊D4711yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—944no—
209C22×C4C22⋊Dic4712yes—
210C22×C4C22⋊Dic4712yes—
211C22×C4D4×D4712yes—
212C22×C4#1062535212yes—
213C22×C4C22×Dic4711yescharacteristic
214C22×C4C2×C22⋊D4711yescharacteristic
215M16—1884no—
216C2×C8—1882no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—44no—
222C4⋊C4—948no—
223C22⋊C4—42no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—948no—
227C42—42no—
228C42—948no—
229C42—3762no—
230C42—1884no—
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×C22⋊Dic4711yescharacteristic
235C23#1309399211yescharacteristic
236C23#1309400511yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—81no—
257C2×C4—948no—
258C2×C4—1884no—
259C2×C4—1884no—
260C2×C4#1309395114yes—
261C2×C4D4×Dic4712yes—
262C2×C4#1309399612yes—
263C8—3762no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1568900311yescharacteristic
273C22C2×#1309395112yes—
274C22#1568931212yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—42no—
279C4—82no—
280C4—81no—
281C4—81no—
282C4—1888no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#2024380211yescharacteristic
287C2#2024383211yescharacteristic
288C2#2024392611yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2484C2
socleC22×C47#386
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#2484D47
hypocenterC47#9478
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
15. C47×#400C4semidirect
16. C47×#398C4semidirect
154. #400Dic47semidirect
155. #398Dic47semidirect
165. C47#9478semidirect

Maximal subgroups

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

subgroupindex
#202457452
#202434872
#202417182
#202412402
C47×#24842
#947847