Finite Group Databasebeta

← #26113962

Subgroups — #26113962

Order 12032.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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#20248373C211yesmaximal, characteristic
2#20242113C212yesmaximal
3#20241732C211yesmaximal, characteristic
4#20241245C212yesmaximal
5C47×#2983C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13094022C412yes—
8#15689180C2212yes—
9#15689053—21no—
10#15689053—21no—
11#15689028C412yes—
12#15689021—21no—
13#15689021—21no—
14C4×C4⋊Dic47C2211yescharacteristic
15#15688871—24no—
16#15688849—21no—
17#15688849—21no—
18C2×C4×Q8×C47C2211yescharacteristic
19C47×#446—24no—
20C47×#432—21no—
21C47×#432C2212yes—
22C47×#431—21no—
23C22×Dic94C2×C412yes—
24#13094024—22no—
25#13094024—22no—
26#13094022—44no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×Dic47⋊C4—22no—
31C2×Dic47⋊C4—22no—
32C2×C4×Dic47C2×C412yes—
33C4⋊(C47⋊C8)—22no—
34C22⋊(C47⋊C8)—22no—
35#13093935—22no—
36C47⋊#95—22no—
37C47⋊#95—22no—
38C47⋊#95—21no—
39C22×Q8×C47C2×C411yescharacteristic
40C4×Q8×C47—22no—
41C4×Q8×C47—22no—
42C2×C4⋊C4×C47C2×C411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C42×C47D411yescharacteristic
46C2×C42×C47D411yescharacteristic
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—22no—
49C4⋊C8×C47—22no—
50C4⋊C8×C47D414yes—
51C22⋊C8×C47—22no—
52#97×C47—22no—
53#97×C47—22no—
54C4×C8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—22no—
57C2×Q8×C47—41no—
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×Dic47—22no—
66C22×Dic47—22no—
67C2×Dic94—24no—
68C2×Dic94—42no—
69C2×Dic94—42no—
70C2×C8×C47—24no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—21no—
77C42×C47—21no—
78C42×C47C2×D412yes—
79C42×C47#4112yes—
80C4⋊Dic47—24no—
81C4⋊Dic47—41no—
82C4⋊Dic47—42no—
83C4⋊Dic47—41no—
84Dic47⋊C4—44no—
85Dic47⋊C4—44no—
86C4×Dic47—42no—
87C2×C47⋊C8—42no—
88C23×C47C2×C22⋊C411yescharacteristic
89Q8×C47—44no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47#10012yes—
104C2×C4×C47C4×D412yes—
105C2×C4×C47#12011yescharacteristic
106C2×C4×C47#12112yes—
107C2×C4×C47#12311yescharacteristic
108C2×Dic47—24no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112C2×Dic47—42no—
113C2×Dic47—42no—
114Dic94—84no—
115C8×C47—44no—
116C47⋊C8—82no—
117#9452—471nomaximal, Sylow
118C22×C47—21no—
119C22×C47—21no—
120C22×C47#38611yescharacteristic
121C22×C47C2×#10011yescharacteristic
122C22×C47#41311yescharacteristic
123C4×C47—21no—
124C4×C47—22no—
125C4×C47—22no—
126C4×C47—22no—
127C4×C47—41no—
128C4×C47—41no—
129C4×C47—41no—
130C4×C47#45612yes—
131Dic47—44no—
132Dic47—82no—
133#2983D4711yescharacteristic
134#2546—471no—
135#1558—472no—
136#1467—471no—
137#1285—472no—
138C2×C47—21no—
139C2×C47—21no—
140C2×C47#188611yescharacteristic
141C2×C47#190011yescharacteristic
142C2×C47#190911yescharacteristic
143C2×C4⋊Q8—472no—
144C2×C4⋊Q8—471no—
145C2×C4×Q8C2×D4711yescharacteristic
146#446—24no—
147#432—21no—
148#432—472no—
149#432C2×D4712yes—
150#431—21no—
151#398—941no—
152#398—941no—
153#391—472no—
154#389—941no—
155#389—941no—
156C4×C4⋊C4—471no—
157#333—944no—
158#324—941no—
159#324—941no—
160C47#945211yescharacteristic, complemented, Sylow
161C22×Q8—472no—
162C22×Q8C4×D4711yescharacteristic
163C4⋊Q8—942no—
164C4⋊Q8—942no—
165C4⋊Q8—1884no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—941no—
169C2×C4⋊C4—942no—
170C2×C4⋊C4—942no—
171C2×C4⋊C4—941no—
172C2×C4⋊C4—941no—
173C2×C4⋊C4C4×D4711yescharacteristic
174C2×C4⋊C4D18811yescharacteristic
175C2×C4⋊C4D18811yescharacteristic
176C2×C42—472no—
177C2×C42C22⋊D4711yescharacteristic
178C2×C42C22⋊D4711yescharacteristic
179C2×C42C22×D4711yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—942no—
183C4⋊C8C22⋊D4714yes—
184C22⋊C8—22no—
185C22⋊C8—942no—
186#97—22no—
187#97—22no—
188#97—942no—
189C4×C8—22no—
190#95—942no—
191#95—942no—
192#95—941no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—944no—
197C2×Q8—1882no—
198C2×Q8—1882no—
199C22×C4—942no—
200C22×C4—942no—
201C22×C4(C2×D47)⋊C411yescharacteristic
202C22×C4(C2×D47)⋊C411yescharacteristic
203C22×C4(C2×D47)⋊C411yescharacteristic
204C22×C4(C2×D47)⋊C411yescharacteristic
205C22×C4C2×C4×D4711yescharacteristic
206C22×C4C2×D18811yescharacteristic
207C22×C4C2×C22⋊D4711yescharacteristic
208C2×C8—24no—
209C2×C8—1882no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—944no—
214C4⋊C4—1884no—
215C4⋊C4—1884no—
216C4⋊C4—1881no—
217C4⋊C4—1882no—
218C4⋊C4—1881no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—1882no—
224C42#1062535012yes—
225C42C2×C22⋊D4712yes—
226C23C2×(C2×D47)⋊C411yescharacteristic
227Q8—44no—
228Q8—3764no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—944no—
243C2×C4—1882no—
244C2×C4—1882no—
245C2×C4—1882no—
246C2×C4—1882no—
247C2×C4—1882no—
248C2×C4#1309394012yes—
249C2×C4C4×C22⋊D4712yes—
250C2×C4#1309399311yescharacteristic
251C2×C4#1309399812yes—
252C2×C4#1309400711yescharacteristic
253C8—44no—
254C8—3762no—
255C22—21no—
256C22—21no—
257C22#1568900211yescharacteristic
258C22C2×#1309394011yescharacteristic
259C22#1568910511yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—3762no—
268C4—1884no—
269C4#1568930612yes—
270C2—21no—
271C2—21no—
272C2#2024378111yescharacteristic
273C2#2024385111yescharacteristic
274C2#2024391011yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2983C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2983D47
hypocenterC47#9452
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
160. C47#9452semidirect

Maximal subgroups

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

subgroupindex
#202483732
#202421132
#202417322
#202412452
C47×#29832
#945247