Finite Group Databasebeta

← #26103558

Subgroups — #26103558

Order 12032.

518 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 79 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#20243312C211yesmaximal, characteristic
2#20241659C211yesmaximal, characteristic
3C47×#1784C211yesmaximal, characteristic
4C2×#13093943—21no—
5C2×#13093943C412yescomplemented
6#15689087—21no—
7C2×C47⋊#95—21no—
8C2×C47⋊#95—21no—
9C2×C47⋊#95C412yes—
10C23×Q8×C47C2211yescharacteristic
11C2×#101×C47—21no—
12C2×#101×C47C412yescomplemented
13C47×#407—21no—
14C23×Dic47—22no—
15C2×#10625329—22no—
16#13093943—42no—
17#13093943—42no—
18C22⋊(C47⋊C8)—42no—
19C47⋊#95—42no—
20C47⋊#95—42no—
21C47⋊#95—42no—
22C22×Q8×C47—42no—
23C22×Q8×C47—42no—
24C22×Q8×C47—42no—
25C22×Q8×C47C2×C411yescharacteristic
26C22×Q8×C47C2×C411yescharacteristic
27C22×Q8×C47D411yescharacteristic
28C22×Q8×C47Q811yescharacteristic
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C23×C4×C47D411yescharacteristic
32C2×M16×C47—22no—
33#101×C47—42no—
34#101×C47—42no—
35C22⋊C8×C47—42no—
36C24×C47C22⋊C411yescharacteristic
37C2×Q8×C47—22no—
38C2×Q8×C47—22no—
39C2×Q8×C47—22no—
40C2×Q8×C47—22no—
41C2×Q8×C47—41no—
42C2×Q8×C47—41no—
43C2×Q8×C47—41no—
44C2×Q8×C47—41no—
45C2×Q8×C47—41no—
46C2×Q8×C47—41no—
47C2×Q8×C47—41no—
48C2×Q8×C47—41no—
49C2×Q8×C47—416no—
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—22no—
53C22×C4×C47—22no—
54C22×C4×C47—22no—
55C22×C4×C47—41no—
56C22×C4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47C4211yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C4⋊C411yescharacteristic
63C22×C4×C47C4⋊C411yescharacteristic
64C22×C4×C47C4⋊C411yescharacteristic
65C22×Dic47—24no—
66C22×Dic47—42no—
67C22×Dic47—42no—
68C22×Dic47—42no—
69C22×Dic47—42no—
70C22×Dic47—42no—
71C22×Dic47—42no—
72M16×C47—42no—
73M16×C47—42no—
74C2×C8×C47—42no—
75#10625329—42no—
76#10625329—42no—
77C2×C47⋊C8—42no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47#9511yescharacteristic
83C23×C47#9912yes—
84Q8×C47—44no—
85Q8×C47—44no—
86Q8×C47—44no—
87Q8×C47—44no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—44no—
105C2×C4×C47—44no—
106C2×C4×C47—44no—
107C2×C4×C47#9912yes—
108C2×C4×C47#9912yes—
109C2×Dic47—44no—
110C2×Dic47—44no—
111C2×Dic47—44no—
112C2×Dic47—82no—
113C2×Dic47—82no—
114C2×Dic47—82no—
115C2×Dic47—82no—
116C8×C47—82no—
117C47⋊C8—82no—
118#7308—471nomaximal, Sylow
119C22×C47—22no—
120C22×C47—22no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—22no—
126C22×C47—22no—
127C22×C47—22no—
128C22×C47#34211yescharacteristic
129C22×C47#34211yescharacteristic
130C22×C47#34211yescharacteristic
131C22×C47#35512yes—
132C22×C47#35612yes—
133C4×C47—22no—
134C4×C47—22no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47—41no—
139Dic47—84no—
140#1784—471no—
141#1784D4711yescharacteristic
142#1446—471no—
143C2×C47—22no—
144C2×C47—21no—
145C2×C47—21no—
146C2×C47—22no—
147C2×C47#130411yescharacteristic
148C2×C47#139412yes—
149C23×Q8C2×D4711yescharacteristic
150C2×#101—21no—
151C2×#101—472no—
152C2×#101—941no—
153C2×#101Dic4712yescomplemented
154#407—21no—
155#407—941no—
156C2×#95—472no—
157C2×#95—941no—
158C2×#95—941no—
159C47#730811yescharacteristic, complemented, Sylow
160C22×Q8—42no—
161C22×Q8—42no—
162C22×Q8—42no—
163C22×Q8Dic9411yescharacteristic
164C22×Q8C4×D4711yescharacteristic
165C22×Q8C2×Dic4711yescharacteristic
166C22×Q8C22⋊D4711yescharacteristic
167C23×C4—942no—
168C23×C4C4×D4711yescharacteristic
169C23×C4D18811yescharacteristic
170C23×C4C22⋊D4711yescharacteristic
171C2×M16—22no—
172C2×M16—942no—
173#101—42no—
174#101—42no—
175#101—1882no—
176#101—1882no—
177C22⋊C8—42no—
178C22⋊C8—1882no—
179#95—1882no—
180#95—1882no—
181#95—1882no—
182C24(C2×D47)⋊C411yescharacteristic
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—416no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—944no—
206C22×C4—1882no—
207C22×C4—1882no—
208C22×C4—1882no—
209C22×C4—1882no—
210C22×C4—1882no—
211C22×C4—1882no—
212C22×C4C4×Dic4711yescharacteristic
213C22×C4Dic47⋊C411yescharacteristic
214C22×C4Dic47⋊C411yescharacteristic
215C22×C4C4⋊Dic4711yescharacteristic
216C22×C4(C2×D47)⋊C411yescharacteristic
217C22×C4C22⋊Dic4711yescharacteristic
218M16—42no—
219M16—42no—
220M16—1882no—
221M16—1882no—
222C2×C8—42no—
223C2×C8—1882no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23—22no—
228C23C47⋊#9511yescharacteristic
229C23#1309393812yes—
230Q8—44no—
231Q8—44no—
232Q8—44no—
233Q8—44no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—44no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—3762no—
254C2×C4—3762no—
255C2×C4—3762no—
256C2×C4—3762no—
257C2×C4—1884no—
258C2×C4—1884no—
259C2×C4—1884no—
260C2×C4#1309393812yes—
261C2×C4#1309393912yes—
262C8—82no—
263C8—3762no—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—22no—
268C22—21no—
269C22—21no—
270C22—22no—
271C22—22no—
272C22—22no—
273C22#1568888911yescharacteristic
274C22#1568888911yescharacteristic
275C22#1568889011yescharacteristic
276C22#1568891912yes—
277C22#1568892112yes—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—3764no—
285C2—22no—
286C2—21no—
287C2—21no—
288C2—22no—
289C2C47⋊#130411yescharacteristic
290C2#2024151412yes—
subgroupG/H
centerC22#15688889
commutatorC22×C4×C47C42
FrattiniC23×Q8C2×D47
FittingC47×#1784C2
socleC22×C47#342
prime radicalC24×C47C22⋊C4
cosocleC23×Q8×C47C22
hypercenter#1784D47
hypocenterC47#7308
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
5. C2×#13093943C4semidirect
12. C2×#101×C47C4semidirect
153. C2×#101Dic47semidirect
159. C47#7308semidirect

Maximal subgroups

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

subgroupindex
#202433122
#202416592
C47×#17842
#730847