Finite Group Databasebeta

← #26110946

Subgroups — #26110946

Order 12032.

510 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 119 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#20252473C211yesmaximal, characteristic
2C4×#13094022C211yesmaximal, characteristic
3#20241784C212yesmaximal
4#20241220C212yesmaximal
5C47×#1461C211yesmaximal, characteristic
6C2×#13094022C411yescharacteristic
7C2×C4×Dic94C2211yescharacteristic
8#15689254—24no—
9#15689180—22no—
10#15689176C2212yes—
11#15689030C411yescharacteristic
12#15689028C411yescharacteristic
13#15689018—22no—
14#15688992C411yescharacteristic
15C4×Dic47⋊C4—22no—
16C42×Dic47C2211yescharacteristic
17#15688855—24no—
18C2×C4×Q8×C47C2211yescharacteristic
19C47×#431C2212yes—
20C47×#324—22no—
21C22×Dic94C2×C411yescharacteristic
22#13094022—22no—
23#13094022—22no—
24C4×Dic94—22no—
25C4×Dic94—22no—
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×Dic47⋊C4—22no—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4—21no—
30C2×C4×Dic47—21no—
31C2×C4×Dic47—21no—
32C2×C4×Dic47—21no—
33C2×C4×Dic47C2×C411yescharacteristic
34C2×C4×Dic47C2×C411yescharacteristic
35C4⋊(C47⋊C8)—24no—
36C4⋊(C47⋊C8)D414yes—
37C22⋊(C47⋊C8)—22no—
38#13093935—24no—
39C4×C47⋊C8—22no—
40C47⋊#95—22no—
41C47⋊#95—22no—
42C22×Q8×C47C2×C411yescharacteristic
43C4×Q8×C47—22no—
44C4×Q8×C47—22no—
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47D412yes—
47C2×C42×C47D412yes—
48C2×C42×C47C2311yescharacteristic
49C4⋊C8×C47—22no—
50C22⋊C8×C47—22no—
51C4×C8×C47—22no—
52C2×Q8×C47—22no—
53C2×Q8×C47—21no—
54C2×Q8×C47—21no—
55C2×Q8×C47—22no—
56C22×C4×C47C22⋊C412yes—
57C22×C4×C47C22⋊C412yes—
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×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—21no—
68C2×Dic94M1612yes—
69C2×C8×C47—42no—
70C4⋊C4×C47—22no—
71C4⋊C4×C47—24no—
72C42×C47—22no—
73C42×C47—22no—
74C42×C47C2×D412yes—
75C42×C47#4112yes—
76C4⋊Dic47—22no—
77Dic47⋊C4—28no—
78Dic47⋊C4—44no—
79Dic47⋊C4—42no—
80C4×Dic47—24no—
81C4×Dic47—21no—
82C4×Dic47—22no—
83C4×Dic47—42no—
84C4×Dic47—41no—
85C4×Dic47—41no—
86C4×Dic47M1612yes—
87C2×C47⋊C8—24no—
88C23×C47C2×C22⋊C411yescharacteristic
89Q8×C47—42no—
90Q8×C47—42no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—41no—
97C2×C4×C47—42no—
98C2×C4×C47C4×D412yes—
99C2×C4×C47#12011yescharacteristic
100C2×C4×C47#12112yes—
101C2×C4×C47#12311yescharacteristic
102C2×C4×C47C2×M1611yescharacteristic
103C2×C4×C47C2×M1611yescharacteristic
104C2×C4×C47#13112yes—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—41no—
111C2×Dic47—41no—
112C2×Dic47—41no—
113C2×Dic47—41no—
114C2×Dic47—42no—
115C2×Dic47—41no—
116Dic94—24no—
117Dic94—42no—
118C8×C47—82no—
119C47⋊C8—44no—
120#8962—471nomaximal, Sylow
121C22×C47—21no—
122C22×C47—21no—
123C22×C47#38611yescharacteristic
124C22×C47#40711yescharacteristic
125C22×C47#40811yescharacteristic
126C4×C47—22no—
127C4×C47—21no—
128C4×C47—42no—
129C4×C47—42no—
130C4×C47#43512yes—
131C4×C47#43612yes—
132C4×C47#45612yes—
133Dic47—24no—
134Dic47—42no—
135Dic47—42no—
136Dic47—81no—
137#2983—471no—
138C4×C4⋊Q8—471no—
139#1479—472no—
140#1461D4711yescharacteristic
141#1276—472no—
142C2×C47—21no—
143C2×C47—21no—
144C2×C47#187011yescharacteristic
145C2×C47#188411yescharacteristic
146C2×C47#188611yescharacteristic
147C2×C4⋊Q8—471no—
148C2×C4×Q8—471no—
149C2×C4×Q8C2×D4711yescharacteristic
150#446—944no—
151#432—942no—
152#431—472no—
153#431C2×D4712yes—
154#391—471no—
155#391—471no—
156#389—942no—
157#384—471no—
158C4×C4⋊C4—942no—
159C43—471no—
160Q8⋊C8—944no—
161#324—22no—
162C47#896211yescharacteristic, complemented, Sylow
163C22×Q8—471no—
164C22×Q8C4×D4711yescharacteristic
165C4⋊Q8—942no—
166C4⋊Q8—942no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—942no—
170C4×Q8—942no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4—942no—
173C2×C4⋊C4—942no—
174C2×C4⋊C4—941no—
175C2×C4⋊C4C4×D4711yescharacteristic
176C2×C4⋊C4C22⋊D4712yes—
177C2×C42—471no—
178C2×C42—471no—
179C2×C42—941no—
180C2×C42—941no—
181C2×C42—941no—
182C2×C42D18812yes—
183C2×C42C22×D4711yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—474no—
186C4⋊C8—944no—
187C22⋊C8—22no—
188C22⋊C8—942no—
189#97—944no—
190C4×C8—22no—
191C4×C8—942no—
192#95—942no—
193#95—942no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—472no—
199C2×Q8—941no—
200C2×Q8—942no—
201C2×Q8—942no—
202C22×C4—941no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4—941no—
206C22×C4(C2×D47)⋊C412yes—
207C22×C4(C2×D47)⋊C412yes—
208C22×C4C2×C4×D4711yescharacteristic
209C22×C4C2×D18811yescharacteristic
210C22×C4C2×C22⋊D4711yescharacteristic
211C2×C8—42no—
212C2×C8—944no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—948no—
216C4⋊C4—942no—
217C4⋊C4—1884no—
218C4⋊C4—1882no—
219C42—22no—
220C42—22no—
221C42—472no—
222C42—944no—
223C42—941no—
224C42—942no—
225C42—1882no—
226C42—1881no—
227C42—1881no—
228C42D4×D4712yes—
229C42#1062535212yes—
230C23C2×(C2×D47)⋊C411yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—944no—
234Q8—1882no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—1882no—
248C2×C4—1881no—
249C2×C4—1881no—
250C2×C4—1881no—
251C2×C4—1881no—
252C2×C4—1881no—
253C2×C4(C22⋊D47)⋊C412yes—
254C2×C4#1309399411yescharacteristic
255C2×C4#1309399612yes—
256C2×C4#1309400811yescharacteristic
257C2×C4M16×D4711yescharacteristic
258C2×C4M16×D4711yescharacteristic
259C2×C4#1309403012yes—
260C8—82no—
261C8—1884no—
262C22—21no—
263C22—21no—
264C22#1568900011yescharacteristic
265C22#1568908611yescharacteristic
266C22#1568908911yescharacteristic
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—944no—
272C4—3761no—
273C4—1882no—
274C4—1882no—
275C4#1568919712yes—
276C4#1568919812yes—
277C4#1568930812yes—
278C2—21no—
279C2—21no—
280C2#2024368311yescharacteristic
281C2#2024376911yescharacteristic
282C2#2024377911yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1461C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1461D47
hypocenterC47#8962
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
162. C47#8962semidirect

Maximal subgroups

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

subgroupindex
#202524732
C4×#130940222
#202417842
#202412202
C47×#14612
#896247