Finite Group Databasebeta

← #26126873

Subgroups — #26126873

Order 12032.

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

normal subgroups only

This group has 414 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
1C4×#13093943C211yesmaximal, characteristic
2#20241732C211yesmaximal, characteristic
3#20241394C214yesmaximal
4C47×#2546C211yesmaximal, characteristic
5#15689180—21no—
6C2×#13093943—21no—
7C4×#10625329—21no—
8#15688892C2212yes—
9#15688849—21no—
10#15688849C2212yes—
11C2×C4⋊Q8×C47—21no—
12C2×C4⋊Q8×C47C411yescharacteristic
13C2×C4×Q8×C47C2211yescharacteristic
14C47×#398C412yes—
15C47×#398C2212yes—
16C47×#391—21no—
17C47×#389—21no—
18C47×#389—21no—
19C4×C4⋊C4×C47C411yescharacteristic
20C2×#10625329—22no—
21C4⋊(C47⋊C8)—41no—
22#13093943—24no—
23C22⋊(C47⋊C8)—22no—
24#13093935—41no—
25#13093935—41no—
26C4×C47⋊C8—41no—
27C22×Q8×C47—21no—
28C22×Q8×C47D411yescharacteristic
29C4⋊Q8×C47—41no—
30C4⋊Q8×C47—41no—
31C4⋊Q8×C47—44no—
32C4×Q8×C47—41no—
33C4×Q8×C47—41no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—22no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—22no—
38C2×C4⋊C4×C47C2×C412yes—
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C4⋊C4×C47C2311yescharacteristic
42C2×C42×C47—21no—
43C2×C42×C47C2×C411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C2×C42×C47D411yescharacteristic
46#95×C47—22no—
47#95×C47—22no—
48#95×C47C2×C412yes—
49C2×Q8×C47—22no—
50C2×Q8×C47—22no—
51C2×Q8×C47—41no—
52C2×Q8×C47—42no—
53C2×Q8×C47—42no—
54C2×Q8×C47—42no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
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
64C4⋊C4×C47—24no—
65C4⋊C4×C47—41no—
66C4⋊C4×C47—41no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—44no—
69C4⋊C4×C47—42no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47—41no—
72C4⋊C4×C47—44no—
73C42×C47—21no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—21no—
77C42×C47—21no—
78C42×C47—21no—
79C42×C47—42no—
80#10625329—24no—
81#10625329—42no—
82C2×C47⋊C8—42no—
83C2×C47⋊C8—42no—
84C23×C47C2×C22⋊C411yescharacteristic
85Q8×C47—44no—
86Q8×C47—84no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—24no—
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—42no—
100C2×C4×C47—42no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—42no—
107C2×C4×C47#9911yescharacteristic
108C2×C4×C47#9911yescharacteristic
109C2×C4×C47#10412yes—
110C2×C4×C47AGL(1,ℤ/8)12yes—
111C47⋊C8—44no—
112C47⋊C8—82no—
113#11782—471nomaximal, Sylow
114C22×C47—21no—
115C22×C47—21no—
116C22×C47C2×#9911yescharacteristic
117C22×C47#41811yescharacteristic
118C22×C47C2×#10411yescharacteristic
119C4×C47—21no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—44no—
123C4×C47—41no—
124C4×C47—41no—
125C4×C47—41no—
126C4×C47—41no—
127C4×C47—82no—
128C4×C47#35612yes—
129#2546D4711yescharacteristic
130C4×#101—471no—
131#1467—471no—
132#1346—474no—
133C2×C47—21no—
134C2×C47—21no—
135C2×C47#150711yescharacteristic
136C2×C47#212311yescharacteristic
137C2×C47C2×#35611yescharacteristic
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8Dic4711yescharacteristic
140C2×C4×Q8C2×D4711yescharacteristic
141#432—941no—
142C2×#101—941no—
143C4×M16—941no—
144#398Dic4712yes—
145#398C2×D4712yes—
146#391—21no—
147#389—21no—
148#389—21no—
149C4×C4⋊C4Dic4711yescharacteristic
150#343—472no—
151#324—472no—
152#324—941no—
153C47#1178211yescharacteristic, complemented, Sylow
154C22×Q8—21no—
155C22×Q8C22⋊D4711yescharacteristic
156C2×M16—942no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—44no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic4712yes—
167C2×C4⋊C4C2×Dic4711yescharacteristic
168C2×C4⋊C4C22⋊D4711yescharacteristic
169C2×C4⋊C4C22×D4711yescharacteristic
170C2×C42—21no—
171C2×C42C2×Dic4711yescharacteristic
172C2×C42C22⋊D4711yescharacteristic
173C2×C42C22⋊D4711yescharacteristic
174C4⋊C8—1881no—
175#101—944no—
176C22⋊C8—942no—
177#97—1881no—
178#97—1881no—
179C4×C8—1881no—
180#95—22no—
181#95—22no—
182#95C2×Dic4712yes—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊Dic4711yescharacteristic
192C22×C4C22⋊Dic4711yescharacteristic
193C22×C4C22⋊Dic4711yescharacteristic
194C22×C4C22⋊Dic4711yescharacteristic
195C22×C4C22×Dic4711yescharacteristic
196C22×C4C2×C22⋊D4711yescharacteristic
197C22×C4C2×C22⋊D4711yescharacteristic
198M16—944no—
199M16—1882no—
200C2×C8—1882no—
201C2×C8—1882no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊Dic4711yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#1309393911yescharacteristic
242C2×C4#1309393911yescharacteristic
243C2×C4#1309395112yes—
244C2×C4#1309405012yes—
245C8—3762no—
246C8—1884no—
247C22—21no—
248C22—21no—
249C22C2×#1309393911yescharacteristic
250C22#1568912811yescharacteristic
251C22C2×#1309395111yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#1568892212yes—
262C2—21no—
263C2—21no—
264C2#2024190411yescharacteristic
265C2#2024504211yescharacteristic
266C2C2×#1568892211yescharacteristic
subgroupG/H
centerC22C2×#13093939
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2546C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#2546D47
hypocenterC47#11782
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
153. C47#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#130939432
#202417322
#202413942
C47×#25462
#1178247