Finite Group Databasebeta

← #26127337

Subgroups — #26127337

Order 12032.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#20243384C211yesmaximal, characteristic
3#20241395C214yesmaximal
4C47×#1461C211yesmaximal, characteristic
5C2×#13094024C411yescharacteristic
6C2×#13094022—21no—
7#15689147—21no—
8C2×#13093943—21no—
9#15689053C412yes—
10#15689053C2212yes—
11#15689028—21no—
12#15689021—21no—
13#15689021—21no—
14C4×C4⋊Dic47C411yescharacteristic
15#15688892C2212yes—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#431—21no—
18C47×#324—21no—
19C47×#324C2212yes—
20C22×Dic94—21no—
21C2×#10625329—22no—
22#13094024—41no—
23#13094024—41no—
24#13094022—42no—
25#13094022—42no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C412yes—
29C2×Dic47⋊C4—22no—
30C2×Dic47⋊C4—22no—
31C2×C4×Dic47—21no—
32C4⋊(C47⋊C8)—41no—
33C4⋊(C47⋊C8)—41no—
34#13093943—42no—
35C47⋊#95—22no—
36C47⋊#95—22no—
37C47⋊#95C2×C412yes—
38C22×Q8×C47D411yescharacteristic
39C4×Q8×C47—41no—
40C4×Q8×C47—41no—
41C2×C4⋊C4×C47C2×C411yescharacteristic
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47C2311yescharacteristic
44C2×C42×C47C2×C411yescharacteristic
45C2×C42×C47D411yescharacteristic
46C2×C42×C47D411yescharacteristic
47C4⋊C8×C47—41no—
48C22⋊C8×C47—22no—
49C4×C8×C47—41no—
50C2×Q8×C47—41no—
51C2×Q8×C47—41no—
52C2×Q8×C47D812yes—
53C2×Q8×C47SD1612yes—
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22⋊C411yescharacteristic
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22×C411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×Dic47—22no—
62C22×Dic47—22no—
63C2×Dic94—42no—
64C2×Dic94—42no—
65C2×Dic94—42no—
66C2×C8×C47—42no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—41no—
69C4⋊C4×C47—41no—
70C42×C47—21no—
71C42×C47—21no—
72C42×C47—21no—
73C42×C47—21no—
74C42×C47—21no—
75C42×C47—21no—
76C4⋊Dic47—24no—
77C4⋊Dic47—41no—
78C4⋊Dic47—41no—
79C4⋊Dic47—42no—
80Dic47⋊C4—44no—
81Dic47⋊C4—42no—
82Dic47⋊C4—42no—
83C4×Dic47—42no—
84#10625329—42no—
85#10625329—42no—
86C2×C47⋊C8—42no—
87C23×C47C2×C22⋊C411yescharacteristic
88Q8×C47—42no—
89Q8×C47—42no—
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—22no—
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#9911yescharacteristic
104C2×C4×C47#9911yescharacteristic
105C2×C4×C47#10212yes—
106C2×C4×C47#10212yes—
107C2×C4×C47C2×D811yescharacteristic
108C2×C4×C47C2×SD1611yescharacteristic
109C2×Dic47—24no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112C2×Dic47—42no—
113C2×Dic47—42no—
114C2×Dic47—42no—
115Dic94—84no—
116C8×C47—82no—
117C47⋊C8—82no—
118#11883—471nomaximal, Sylow
119C22×C47—21no—
120C22×C47—21no—
121C22×C47C2×#9911yescharacteristic
122C22×C47C2×#10211yescharacteristic
123C22×C47#42111yescharacteristic
124C4×C47—21no—
125C4×C47—21no—
126C4×C47—22no—
127C4×C47—22no—
128C4×C47—21no—
129C4×C47—41no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47#35612yes—
133Dic47—44no—
134Dic47—82no—
135#2546—471no—
136#1801—471no—
137#1461D4711yescharacteristic
138#1346—474no—
139C2×C47—21no—
140C2×C47—21no—
141C2×C47#151911yescharacteristic
142C2×C47#212311yescharacteristic
143C2×C47C2×#35611yescharacteristic
144C2×C4⋊Q8—471no—
145C2×C4⋊Q8—941no—
146C2×C4×Q8C2×D4711yescharacteristic
147#431—21no—
148#423—941no—
149C2×#101—941no—
150#398—472no—
151#398—472no—
152#391—941no—
153#389—941no—
154#389—941no—
155C4×C4⋊C4—471no—
156#343—472no—
157#324—21no—
158#324C2×D4712yes—
159C47#1188311yescharacteristic, complemented, Sylow
160C22×Q8—941no—
161C22×Q8D18811yescharacteristic
162C2×M16—942no—
163C4⋊Q8—1881no—
164C4⋊Q8—1881no—
165C4⋊Q8—1882no—
166C4⋊Q8—1882no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—941no—
171C2×C4⋊C4—942no—
172C2×C4⋊C4—941no—
173C2×C4⋊C4—942no—
174C2×C4⋊C4C4×D4711yescharacteristic
175C2×C4⋊C4C22⋊D4711yescharacteristic
176C2×C4⋊C4C22×D4711yescharacteristic
177C2×C42—941no—
178C2×C42C4×D4711yescharacteristic
179C2×C42D18811yescharacteristic
180C2×C42C22⋊D4711yescharacteristic
181C4⋊C8—41no—
182C4⋊C8—1881no—
183C4⋊C8—1881no—
184#101—1882no—
185C22⋊C8—22no—
186C4×C8—41no—
187#95—472no—
188#95—942no—
189#95—942no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—1882no—
193C2×Q8—1882no—
194C2×Q8—1882no—
195C2×Q8#1062532512yes—
196C2×Q8D37612yes—
197C22×C4—942no—
198C22×C4—942no—
199C22×C4(C2×D47)⋊C411yescharacteristic
200C22×C4(C2×D47)⋊C411yescharacteristic
201C22×C4(C2×D47)⋊C411yescharacteristic
202C22×C4(C2×D47)⋊C411yescharacteristic
203C22×C4C2×C4×D4711yescharacteristic
204C22×C4C2×D18811yescharacteristic
205C22×C4C2×C22⋊D4711yescharacteristic
206M16—1882no—
207M16—1882no—
208C2×C8—42no—
209C2×C8—1882no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—944no—
214C4⋊C4—1882no—
215C4⋊C4—1881no—
216C4⋊C4—1881no—
217C4⋊C4—1884no—
218C4⋊C4—1882no—
219C4⋊C4—1882no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—1882no—
227C23C2×(C2×D47)⋊C411yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—3764no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—944no—
245C2×C4—1882no—
246C2×C4—1882no—
247C2×C4—1882no—
248C2×C4—1882no—
249C2×C4—1882no—
250C2×C4#1309393811yescharacteristic
251C2×C4#1309393811yescharacteristic
252C2×C4#1309394612yes—
253C2×C4#1309394612yes—
254C2×C4C2×D37611yescharacteristic
255C2×C4C2×#1062532511yescharacteristic
256C8—82no—
257C8—3762no—
258C22—21no—
259C22—21no—
260C22C2×#1309393811yescharacteristic
261C22C2×#1309394611yescharacteristic
262C22#1568913911yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—3762no—
272C4—1884no—
273C4#1568892112yes—
274C2—21no—
275C2—21no—
276C2#2024195711yescharacteristic
277C2#2024504111yescharacteristic
278C2C2×#1568892111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1461C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1461D47
hypocenterC47#11883
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
159. C47#11883semidirect

Maximal subgroups

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

subgroupindex
#202483732
#202433842
#202413952
C47×#14612
#1188347