Finite Group Databasebeta

← #26113972

Subgroups — #26113972

Order 12032.

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

normal subgroups only

This group has 448 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#20248593C211yesmaximal, characteristic
2#20242104C212yesmaximal
3#20241732C211yesmaximal, characteristic
4#20241245C212yesmaximal
5C47×#2983C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689180C2212yes—
8#15689043—21no—
9#15689043—21no—
10#15689030C412yes—
11#15689021—21no—
12#15689021—21no—
13#15688992C412yes—
14C4×C4⋊Dic47C2211yescharacteristic
15#15688868—24no—
16#15688849—21no—
17#15688849—21no—
18C2×C4×Q8×C47C2211yescharacteristic
19C47×#446—24no—
20C47×#432—21no—
21C47×#432C2212yes—
22C47×#431—21no—
23C22×Dic94—21no—
24#13094024—22no—
25#13094024—22no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C412yes—
29C2×Dic47⋊C4—22no—
30C2×Dic47⋊C4—22no—
31C2×C4×Dic47C2×C412yes—
32C4⋊(C47⋊C8)—22no—
33C22⋊(C47⋊C8)—22no—
34#13093935—22no—
35C47⋊#95—22no—
36C47⋊#95—22no—
37C47⋊#95—21no—
38C22×Q8×C47C2×C411yescharacteristic
39C4×Q8×C47—22no—
40C4×Q8×C47—22no—
41C2×C4⋊C4×C47C2×C411yescharacteristic
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C2×C42×C47D411yescharacteristic
46C2×C42×C47C2311yescharacteristic
47C4⋊C8×C47—22no—
48C4⋊C8×C47—22no—
49C4⋊C8×C47D414yes—
50C22⋊C8×C47—22no—
51#97×C47—22no—
52#97×C47—22no—
53C4×C8×C47—22no—
54C2×Q8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22×C411yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×Dic47—22no—
65C22×Dic47—22no—
66C2×Dic94—42no—
67C2×Dic94—82no—
68C2×C8×C47—24no—
69C4⋊C4×C47—22no—
70C4⋊C4×C47—22no—
71C4⋊C4×C47—22no—
72C42×C47—21no—
73C42×C47—21no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47C2×D412yes—
77C42×C47#4112yes—
78C4⋊Dic47—24no—
79C4⋊Dic47—24no—
80C4⋊Dic47—41no—
81C4⋊Dic47—41no—
82Dic47⋊C4—82no—
83Dic47⋊C4—82no—
84C4×Dic47—42no—
85C2×C47⋊C8—42no—
86C23×C47C2×C22⋊C411yescharacteristic
87Q8×C47—44no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47#10112yes—
102C2×C4×C47C4×D412yes—
103C2×C4×C47#12011yescharacteristic
104C2×C4×C47#12112yes—
105C2×C4×C47#12311yescharacteristic
106C2×Dic47—24no—
107C2×Dic47—42no—
108C2×Dic47—42no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112Dic94—84no—
113C8×C47—44no—
114C47⋊C8—82no—
115#9454—471nomaximal, Sylow
116C22×C47—21no—
117C22×C47—21no—
118C22×C47#38611yescharacteristic
119C22×C47C2×#10111yescharacteristic
120C22×C47#41311yescharacteristic
121C4×C47—21no—
122C4×C47—22no—
123C4×C47—22no—
124C4×C47—22no—
125C4×C47—41no—
126C4×C47—41no—
127C4×C47—41no—
128C4×C47#45612yes—
129Dic47—44no—
130Dic47—82no—
131#2983D4711yescharacteristic
132#2567—471no—
133#1556—472no—
134#1467—471no—
135#1285—472no—
136C2×C47—21no—
137C2×C47—21no—
138C2×C47#188611yescharacteristic
139C2×C47#190111yescharacteristic
140C2×C47#191011yescharacteristic
141C2×C4⋊Q8—471no—
142C2×C4×Q8C2×D4711yescharacteristic
143#446—24no—
144#432—21no—
145#432—472no—
146#432C2×D4712yes—
147#431—21no—
148#395—941no—
149#395—941no—
150#391—472no—
151#389—941no—
152#389—941no—
153#384—472no—
154C4×C4⋊C4—471no—
155#332—944no—
156#324—941no—
157#324—941no—
158C47#945411yescharacteristic, complemented, Sylow
159C22×Q8—941no—
160C22×Q8C4×D4711yescharacteristic
161C4⋊Q8—942no—
162C4⋊Q8—942no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—472no—
166C2×C4⋊C4—941no—
167C2×C4⋊C4—942no—
168C2×C4⋊C4—942no—
169C2×C4⋊C4—941no—
170C2×C4⋊C4C4×D4711yescharacteristic
171C2×C4⋊C4D18811yescharacteristic
172C2×C4⋊C4D18811yescharacteristic
173C2×C42—472no—
174C2×C42C22⋊D4711yescharacteristic
175C2×C42C22⋊D4711yescharacteristic
176C2×C42C22×D4711yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—942no—
180C4⋊C8C22⋊D4714yes—
181C22⋊C8—22no—
182C22⋊C8—942no—
183#97—22no—
184#97—22no—
185#97—942no—
186C4×C8—22no—
187#95—942no—
188#95—942no—
189#95—941no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—3762no—
194C2×Q8—1882no—
195C22×C4—942no—
196C22×C4—942no—
197C22×C4(C2×D47)⋊C411yescharacteristic
198C22×C4(C2×D47)⋊C411yescharacteristic
199C22×C4(C2×D47)⋊C411yescharacteristic
200C22×C4(C2×D47)⋊C411yescharacteristic
201C22×C4C2×C4×D4711yescharacteristic
202C22×C4C2×D18811yescharacteristic
203C22×C4C2×C22⋊D4711yescharacteristic
204C2×C8—24no—
205C2×C8—1882no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—944no—
210C4⋊C4—944no—
211C4⋊C4—3762no—
212C4⋊C4—3762no—
213C4⋊C4—1881no—
214C4⋊C4—1881no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—1882no—
220C42#1062535012yes—
221C42C2×C22⋊D4712yes—
222C23C2×(C2×D47)⋊C411yescharacteristic
223Q8—44no—
224Q8—3764no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—944no—
239C2×C4—1882no—
240C2×C4—1882no—
241C2×C4—1882no—
242C2×C4—1882no—
243C2×C4—1882no—
244C2×C4#1309394212yes—
245C2×C4C4×C22⋊D4712yes—
246C2×C4#1309399311yescharacteristic
247C2×C4#1309399812yes—
248C2×C4#1309400711yescharacteristic
249C8—44no—
250C8—3762no—
251C22—21no—
252C22—21no—
253C22#1568900211yescharacteristic
254C22C2×#1309394211yescharacteristic
255C22#1568910511yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—3762no—
264C4—1884no—
265C4#1568930612yes—
266C2—21no—
267C2—21no—
268C2#2024378111yescharacteristic
269C2#2024385611yescharacteristic
270C2#2024391511yescharacteristic
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#9454
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
158. C47#9454semidirect

Maximal subgroups

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

subgroupindex
#202485932
#202421042
#202417322
#202412452
C47×#29832
#945447