Finite Group Databasebeta

← #26126918

Subgroups — #26126918

Order 12032.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#20248750C211yesmaximal, characteristic
2C4×#13093943C211yesmaximal, characteristic
3#20241419C212yesmaximal
4#20241416C212yesmaximal
5C47×#1467C211yesmaximal, characteristic
6C2×C4×Dic94C411yescharacteristic
7C2×#13093943—21no—
8C4×#10625329—21no—
9#15689062C411yescharacteristic
10#15689062C2211yescharacteristic
11#15689043C411yescharacteristic
12#15689043C2211yescharacteristic
13#15689030—21no—
14#15689019—21no—
15#15689007—21no—
16#15689007—21no—
17#15688989C411yescharacteristic
18#15688892C2212yes—
19C2×C4×Q8×C47C2211yescharacteristic
20C47×#432—21no—
21C47×#324—21no—
22C47×#324C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C2×#10625329—22no—
25C4×Dic94—41no—
26C4×Dic94—41no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×C4×Dic47—21no—
33#13093943—24no—
34#13093935—41no—
35C4×C47⋊C8—41no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95C2×C411yescharacteristic
44C47⋊#95C2×C411yescharacteristic
45C22×Q8×C47D411yescharacteristic
46C4×Q8×C47—41no—
47C4×Q8×C47—41no—
48C2×C4⋊C4×C47C2×C411yescharacteristic
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C4⋊C4×C47C2311yescharacteristic
51C2×C42×C47C2×C411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C4⋊C8×C47—41no—
55C22⋊C8×C47—22no—
56#97×C47—41no—
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—41no—
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C22×C411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C2×Dic94—41no—
72C2×Dic94—42no—
73C2×C8×C47—42no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C42×C47—21no—
78C42×C47—21no—
79C42×C47—21no—
80C42×C47—21no—
81C42×C47—21no—
82C42×C47—21no—
83C4⋊Dic47—42no—
84C4⋊Dic47—41no—
85Dic47⋊C4—42no—
86Dic47⋊C4—42no—
87Dic47⋊C4—41no—
88Dic47⋊C4—41no—
89C4×Dic47—42no—
90#10625329—24no—
91#10625329—42no—
92C2×C47⋊C8—42no—
93C23×C47C2×C22⋊C411yescharacteristic
94Q8×C47—44no—
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—21no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47#9911yescharacteristic
110C2×C4×C47#9911yescharacteristic
111C2×C4×C47#10412yes—
112C2×C4×C47#13712yes—
113C2×Dic47—22no—
114C2×Dic47—41no—
115C2×Dic47—41no—
116C2×Dic47—41no—
117C2×Dic47—41no—
118C2×Dic47—41no—
119C2×Dic47—41no—
120C2×Dic47—42no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124Dic94—42no—
125Dic94—42no—
126C8×C47—82no—
127C47⋊C8—44no—
128#11792—471nomaximal, Sylow
129C22×C47—21no—
130C22×C47—21no—
131C22×C47C2×#9911yescharacteristic
132C22×C47#41911yescharacteristic
133C22×C47C2×#10411yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—22no—
137C4×C47—22no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47—41no—
142Dic47—42no—
143Dic47—81no—
144Dic47—81no—
145Dic47—81no—
146#2581—471no—
147C4×#101—471no—
148#1467D4711yescharacteristic
149#1354—472no—
150#1353—472no—
151C2×C47—21no—
152C2×C47—21no—
153C2×C47#150811yescharacteristic
154C2×C47#212011yescharacteristic
155C2×C47#213311yescharacteristic
156C2×C4×Q8—471no—
157C2×C4×Q8C2×D4711yescharacteristic
158#432—21no—
159C2×#101—941no—
160C4×M16—941no—
161#400—471no—
162#400—471no—
163#395—471no—
164#395—471no—
165#391—941no—
166#389—941no—
167#387—941no—
168#387—941no—
169#382—471no—
170#343—472no—
171#324—21no—
172#324C2×D4712yes—
173C47#1179211yescharacteristic, complemented, Sylow
174C22×Q8—471no—
175C22×Q8D18811yescharacteristic
176C2×M16—942no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—1881no—
180C4×Q8—1881no—
181C2×C4⋊C4—471no—
182C2×C4⋊C4—941no—
183C2×C4⋊C4—941no—
184C2×C4⋊C4—941no—
185C2×C4⋊C4—941no—
186C2×C4⋊C4C4×D4711yescharacteristic
187C2×C4⋊C4C22⋊D4711yescharacteristic
188C2×C4⋊C4C22×D4711yescharacteristic
189C2×C42—941no—
190C2×C42C4×D4711yescharacteristic
191C2×C42D18811yescharacteristic
192C2×C42C22⋊D4711yescharacteristic
193C4⋊C8—41no—
194#101—944no—
195C22⋊C8—22no—
196#97—41no—
197#97—1881no—
198C4×C8—1881no—
199#95—471no—
200#95—471no—
201#95—941no—
202#95—941no—
203#95—941no—
204#95—941no—
205#95—941no—
206#95—941no—
207#95—941no—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—1881no—
212C2×Q8—1882no—
213C22×C4—941no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4(C2×D47)⋊C411yescharacteristic
218C22×C4(C2×D47)⋊C411yescharacteristic
219C22×C4(C2×D47)⋊C411yescharacteristic
220C22×C4(C2×D47)⋊C411yescharacteristic
221C22×C4C2×C4×D4711yescharacteristic
222C22×C4C2×D18811yescharacteristic
223C22×C4C2×C22⋊D4711yescharacteristic
224M16—944no—
225M16—1882no—
226C2×C8—42no—
227C2×C8—1882no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—1881no—
232C4⋊C4—1882no—
233C4⋊C4—1882no—
234C4⋊C4—1881no—
235C4⋊C4—1881no—
236C4⋊C4—1882no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—1882no—
244C23C2×(C2×D47)⋊C411yescharacteristic
245Q8—44no—
246Q8—1882no—
247Q8—1882no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—942no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4—1882no—
268C2×C4—1881no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4—1881no—
272C2×C4—1881no—
273C2×C4#1309393811yescharacteristic
274C2×C4#1309393811yescharacteristic
275C2×C4#1309395012yes—
276C2×C4#1309405712yes—
277C8—82no—
278C8—1884no—
279C22—21no—
280C22—21no—
281C22C2×#1309393811yescharacteristic
282C22#1568913311yescharacteristic
283C22C2×#1309395011yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—3761no—
293C4—3761no—
294C4—3761no—
295C4—1882no—
296C2—21no—
297C2—21no—
298C2#2024190911yescharacteristic
299C2#2024502711yescharacteristic
300C2#2024507511yescharacteristic
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#11792
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
173. C47#11792semidirect

Maximal subgroups

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

subgroupindex
#202487502
C4×#130939432
#202414192
#202414162
C47×#14672
#1179247