Finite Group Databasebeta

← #26125947

Subgroups — #26125947

Order 12032.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#20241732C211yesmaximal, characteristic
2#20241712C211yesmaximal, characteristic
3#20241334C214yesmaximal
4C47×#2567C211yesmaximal, characteristic
5#15689180—21no—
6#15689176—21no—
7#15688849—21no—
8#15688849—21no—
9#15688849C2212yes—
10#15688849C2212yes—
11C2×C4⋊Q8×C47C411yescharacteristic
12C2×C4×Q8×C47C2211yescharacteristic
13C47×#395—21no—
14C47×#395—21no—
15C47×#391C412yes—
16C47×#389—21no—
17C47×#389—21no—
18C47×#384C2212yes—
19C4×C4⋊C4×C47C411yescharacteristic
20C4⋊(C47⋊C8)—41no—
21C4⋊(C47⋊C8)—41no—
22C22⋊(C47⋊C8)—22no—
23C22⋊(C47⋊C8)—22no—
24#13093935—41no—
25C4×C47⋊C8—41no—
26C22×Q8×C47—21no—
27C22×Q8×C47C2×C411yescharacteristic
28C4⋊Q8×C47—41no—
29C4⋊Q8×C47—41no—
30C4×Q8×C47—41no—
31C4×Q8×C47—41no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—21no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47—22no—
36C2×C4⋊C4×C47C2×C412yes—
37C2×C4⋊C4×C47D411yescharacteristic
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C4⋊C4×C47C2311yescharacteristic
40C2×C42×C47C2×C412yes—
41C2×C42×C47C2×C411yescharacteristic
42C2×C42×C47D411yescharacteristic
43C2×C42×C47D411yescharacteristic
44#95×C47—21no—
45#95×C47—22no—
46#95×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47—41no—
50C2×Q8×C47—42no—
51C2×Q8×C47—82no—
52C22×C4×C47—22no—
53C22×C4×C47—22no—
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
61C4⋊C4×C47—24no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—41no—
65C4⋊C4×C47—42no—
66C4⋊C4×C47—41no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—82no—
69C4⋊C4×C47—82no—
70C42×C47—21no—
71C42×C47—21no—
72C42×C47—21no—
73C42×C47—21no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—24no—
77C2×C47⋊C8—42no—
78C2×C47⋊C8—42no—
79C23×C47C2×C22⋊C411yescharacteristic
80Q8×C47—44no—
81Q8×C47—84no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—24no—
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—42no—
95C2×C4×C47—42no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47#9911yescharacteristic
103C2×C4×C47#9911yescharacteristic
104C2×C4×C47#10112yes—
105C2×C4×C47#13112yes—
106C47⋊C8—82no—
107C47⋊C8—82no—
108#11574—471nomaximal, Sylow
109C22×C47—21no—
110C22×C47—21no—
111C22×C47#40811yescharacteristic
112C22×C47C2×#9911yescharacteristic
113C22×C47C2×#10111yescharacteristic
114C4×C47—21no—
115C4×C47—22no—
116C4×C47—22no—
117C4×C47—44no—
118C4×C47—41no—
119C4×C47—41no—
120C4×C47—41no—
121C4×C47—41no—
122C4×C47—82no—
123C4×C47#35612yes—
124#2567D4711yescharacteristic
125#1467—471no—
126#1461—471no—
127#1325—474no—
128C2×C47—21no—
129C2×C47—21no—
130C2×C47#147211yescharacteristic
131C2×C47#212811yescharacteristic
132C2×C47C2×#35611yescharacteristic
133C2×C4⋊Q8Dic4711yescharacteristic
134C2×C4×Q8C2×D4711yescharacteristic
135#432—941no—
136#431—941no—
137#395—21no—
138#395—21no—
139#391Dic4712yes—
140#389—21no—
141#389—21no—
142#384C2×D4712yes—
143C4×C4⋊C4Dic4711yescharacteristic
144#324—472no—
145#324—472no—
146#324—941no—
147#324—941no—
148C47#1157411yescharacteristic, complemented, Sylow
149C22×Q8—21no—
150C22×Q8C2×Dic4711yescharacteristic
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×Dic4712yes—
160C2×C4⋊C4C22⋊D4711yescharacteristic
161C2×C4⋊C4C22⋊D4711yescharacteristic
162C2×C4⋊C4C22×D4711yescharacteristic
163C2×C42C2×Dic4712yes—
164C2×C42C2×Dic4711yescharacteristic
165C2×C42C22⋊D4711yescharacteristic
166C2×C42C22⋊D4711yescharacteristic
167C4⋊C8—1881no—
168C4⋊C8—1881no—
169C22⋊C8—942no—
170C22⋊C8—942no—
171#97—1881no—
172C4×C8—1881no—
173#95—21no—
174#95—22no—
175#95—22no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—41no—
179C2×Q8—42no—
180C2×Q8—82no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C22⋊Dic4711yescharacteristic
184C22×C4C22⋊Dic4711yescharacteristic
185C22×C4C22⋊Dic4711yescharacteristic
186C22×C4C22⋊Dic4711yescharacteristic
187C22×C4C22×Dic4711yescharacteristic
188C22×C4C2×C22⋊D4711yescharacteristic
189C22×C4C2×C22⋊D4711yescharacteristic
190C2×C8—1882no—
191C2×C8—1882no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—24no—
208C23C2×C22⋊Dic4711yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#1309393911yescharacteristic
232C2×C4#1309393911yescharacteristic
233C2×C4#1309394312yes—
234C2×C4#1309403112yes—
235C8—3762no—
236C8—3762no—
237C22—21no—
238C22—21no—
239C22#1568909011yescharacteristic
240C22C2×#1309393911yescharacteristic
241C22C2×#1309394311yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#1568892212yes—
252C2—21no—
253C2—21no—
254C2#2024175211yescharacteristic
255C2#2024506011yescharacteristic
256C2C2×#1568892211yescharacteristic
subgroupG/H
centerC22C2×#13093939
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2567C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#2567D47
hypocenterC47#11574
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
148. C47#11574semidirect

Maximal subgroups

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

subgroupindex
#202417322
#202417122
#202413342
C47×#25672
#1157447