Finite Group Databasebeta

← #26126931

Subgroups — #26126931

Order 12032.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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
2C4×#13093943C211yesmaximal, characteristic
3#20241419C214yesmaximal
4C47×#1467C211yesmaximal, characteristic
5C2×#13094024C411yescharacteristic
6C2×#13093943—21no—
7C4×#10625329—21no—
8#15689043C412yes—
9#15689043C2212yes—
10#15689030—21no—
11#15689021—21no—
12#15689021—21no—
13#15688992—21no—
14C4×C4⋊Dic47C411yescharacteristic
15#15688892C2212yes—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#432—21no—
18C47×#324—21no—
19C47×#324C2212yes—
20C22×Dic94C2×C412yes—
21C2×#10625329—22no—
22#13094024—41no—
23#13094024—41no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47—21no—
27C2×Dic47⋊C4—22no—
28C2×Dic47⋊C4—22no—
29C2×C4×Dic47—21no—
30#13093943—24no—
31#13093935—41no—
32C4×C47⋊C8—41no—
33C47⋊#95—22no—
34C47⋊#95—22no—
35C47⋊#95C2×C412yes—
36C22×Q8×C47D411yescharacteristic
37C4×Q8×C47—41no—
38C4×Q8×C47—41no—
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C4⋊C4×C47C2311yescharacteristic
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C4⋊C8×C47—41no—
46C22⋊C8×C47—22no—
47#97×C47—41no—
48C2×Q8×C47—22no—
49C2×Q8×C47—22no—
50C2×Q8×C47—41no—
51C22×C4×C47C22⋊C411yescharacteristic
52C22×C4×C47C22⋊C411yescharacteristic
53C22×C4×C47C22⋊C411yescharacteristic
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22×C411yescharacteristic
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47C2×D411yescharacteristic
58C22×Dic47—22no—
59C22×Dic47—22no—
60C2×Dic94—42no—
61C2×Dic94—82no—
62C2×C8×C47—42no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—41no—
65C4⋊C4×C47—41no—
66C42×C47—21no—
67C42×C47—21no—
68C42×C47—21no—
69C42×C47—21no—
70C42×C47—21no—
71C42×C47—21no—
72C4⋊Dic47—24no—
73C4⋊Dic47—42no—
74C4⋊Dic47—41no—
75C4⋊Dic47—41no—
76Dic47⋊C4—82no—
77Dic47⋊C4—82no—
78C4×Dic47—42no—
79#10625329—24no—
80#10625329—42no—
81C2×C47⋊C8—42no—
82C23×C47C2×C22⋊C411yescharacteristic
83Q8×C47—44no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
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—41no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47#9911yescharacteristic
99C2×C4×C47#9911yescharacteristic
100C2×C4×C47#10412yes—
101C2×C4×C47#13712yes—
102C2×Dic47—24no—
103C2×Dic47—42no—
104C2×Dic47—42no—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108Dic94—84no—
109C8×C47—82no—
110C47⋊C8—44no—
111#11795—471nomaximal, Sylow
112C22×C47—21no—
113C22×C47—21no—
114C22×C47C2×#9911yescharacteristic
115C22×C47#41911yescharacteristic
116C22×C47C2×#10411yescharacteristic
117C4×C47—21no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—41no—
121C4×C47—41no—
122C4×C47—41no—
123C4×C47—41no—
124C4×C47#35612yes—
125Dic47—44no—
126Dic47—82no—
127#2567—471no—
128C4×#101—471no—
129#1467D4711yescharacteristic
130#1354—474no—
131C2×C47—21no—
132C2×C47—21no—
133C2×C47#150811yescharacteristic
134C2×C47#212211yescharacteristic
135C2×C47C2×#35611yescharacteristic
136C2×C4⋊Q8—471no—
137C2×C4×Q8C2×D4711yescharacteristic
138#432—21no—
139C2×#101—941no—
140C4×M16—941no—
141#395—472no—
142#395—472no—
143#391—941no—
144#389—941no—
145#389—941no—
146#384—941no—
147C4×C4⋊C4—471no—
148#343—472no—
149#324—21no—
150#324C2×D4712yes—
151C47#1179511yescharacteristic, complemented, Sylow
152C22×Q8—472no—
153C22×Q8D18811yescharacteristic
154C2×M16—942no—
155C4⋊Q8—1881no—
156C4⋊Q8—1881no—
157C4×Q8—41no—
158C4×Q8—41no—
159C2×C4⋊C4—941no—
160C2×C4⋊C4—942no—
161C2×C4⋊C4—942no—
162C2×C4⋊C4—941no—
163C2×C4⋊C4—941no—
164C2×C4⋊C4C4×D4711yescharacteristic
165C2×C4⋊C4C22⋊D4711yescharacteristic
166C2×C4⋊C4C22×D4711yescharacteristic
167C2×C42—941no—
168C2×C42C4×D4711yescharacteristic
169C2×C42D18811yescharacteristic
170C2×C42C22⋊D4711yescharacteristic
171C4⋊C8—41no—
172#101—944no—
173C22⋊C8—22no—
174#97—41no—
175#97—1881no—
176C4×C8—1881no—
177#95—472no—
178#95—942no—
179#95—942no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—3762no—
184C2×Q8—1882no—
185C22×C4—942no—
186C22×C4—942no—
187C22×C4(C2×D47)⋊C411yescharacteristic
188C22×C4(C2×D47)⋊C411yescharacteristic
189C22×C4(C2×D47)⋊C411yescharacteristic
190C22×C4(C2×D47)⋊C411yescharacteristic
191C22×C4C2×C4×D4711yescharacteristic
192C22×C4C2×D18811yescharacteristic
193C22×C4C2×C22⋊D4711yescharacteristic
194M16—944no—
195M16—1882no—
196C2×C8—42no—
197C2×C8—1882no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—944no—
202C4⋊C4—3762no—
203C4⋊C4—3762no—
204C4⋊C4—1882no—
205C4⋊C4—1881no—
206C4⋊C4—1881no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—1882no—
214C23C2×(C2×D47)⋊C411yescharacteristic
215Q8—44no—
216Q8—3764no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—944no—
232C2×C4—1882no—
233C2×C4—1882no—
234C2×C4—1882no—
235C2×C4—1882no—
236C2×C4—1882no—
237C2×C4#1309393811yescharacteristic
238C2×C4#1309393811yescharacteristic
239C2×C4#1309395012yes—
240C2×C4#1309405712yes—
241C8—82no—
242C8—1884no—
243C22—21no—
244C22—21no—
245C22C2×#1309393811yescharacteristic
246C22#1568913311yescharacteristic
247C22C2×#1309395011yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—3762no—
256C4—1884no—
257C4#1568892112yes—
258C2—21no—
259C2—21no—
260C2#2024190911yescharacteristic
261C2#2024503711yescharacteristic
262C2C2×#1568892111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1467C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1467D47
hypocenterC47#11795
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
151. C47#11795semidirect

Maximal subgroups

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

subgroupindex
#202485932
C4×#130939432
#202414192
C47×#14672
#1179547