Finite Group Databasebeta

← #26119270

Subgroups — #26119270

Order 12032.

640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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#20243322C212yesmaximal
2#20241658C211yesmaximal, characteristic
3#20241266C212yesmaximal
4#20241231C211yesmaximal, characteristic
5C47×#2646C211yesmaximal, characteristic
6C23×Dic94C2211yescharacteristic
7C2×#13093947—22no—
8C2×#13093947—22no—
9C2×C22⋊(C47⋊C8)C2212yes—
10C2×C47⋊#95—22no—
11C2×C47⋊#95C2211yescharacteristic
12C47×#400—22no—
13C47×#398—22no—
14C47×#385—22no—
15C47×#380C2212yes—
16C2×#95×C47C2211yescharacteristic
17C22×Dic94—22no—
18C22×Dic94—22no—
19C22×Dic94—21no—
20C22×Dic94—44no—
21C22×Dic94Q812yes—
22C23×Dic47—21no—
23C23×Dic47—21no—
24C22×C47⋊C8—22no—
25#13093947—44no—
26#13093947—44no—
27C22⋊(C47⋊C8)—22no—
28C22⋊(C47⋊C8)—22no—
29C47⋊#95—22no—
30C47⋊#95—44no—
31C23×C4×C47D412yes—
32C23×C4×C47C2311yescharacteristic
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47D412yes—
36C2×C4⋊C4×C47D412yes—
37C2×C22⋊C4×C47—22no—
38#95×C47—22no—
39#95×C47—22no—
40#95×C47—22no—
41#95×C47—22no—
42C24×C47C2×D411yescharacteristic
43C22×C4×C47—22no—
44C22×C4×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47—42no—
49C22×C4×C47—42no—
50C22×C4×C47—42no—
51C22×C4×C47C2×D412yes—
52C22×C4×C47C2×Q811yescharacteristic
53C22×C4×C47#4112yes—
54C22×C4×C47#4111yescharacteristic
55C22×Dic47—24no—
56C22×Dic47—22no—
57C22×Dic47—22no—
58C22×Dic47—42no—
59C22×Dic47—41no—
60C22×Dic47—41no—
61C22×Dic47—42no—
62C22×Dic47—41no—
63C22×Dic47—41no—
64C22×Dic47—42no—
65C2×Dic94—24no—
66C2×Dic94—24no—
67C2×Dic94—24no—
68C2×Dic94—44no—
69C2×Dic94—48no—
70C2×Dic94—44no—
71C2×Dic94—42no—
72C2×Dic94—42no—
73C2×Dic94—42no—
74C4⋊C4×C47—42no—
75C4⋊C4×C47—42no—
76C4⋊C4×C47—82no—
77C4⋊C4×C47—82no—
78C22⋊C4×C47—42no—
79C22⋊C4×C47—42no—
80C2×C47⋊C8—42no—
81C2×C47⋊C8—42no—
82C2×C47⋊C8—42no—
83C23×C47—21no—
84C23×C47—21no—
85C23×C47—22no—
86C23×C47#12011yescharacteristic
87C23×C47C22⋊Q811yescharacteristic
88C23×C47#12411yescharacteristic
89C23×C47#13512yes—
90C23×C47#13712yes—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—41no—
94C2×C4×C47—41no—
95C2×C4×C47—42no—
96C2×C4×C47—44no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—82no—
107C2×C4×C47C22⋊Q812yes—
108C2×C4×C47#12412yes—
109C2×Dic47—24no—
110C2×Dic47—42no—
111C2×Dic47—44no—
112C2×Dic47—42no—
113C2×Dic47—44no—
114C2×Dic47—44no—
115C2×Dic47—42no—
116C2×Dic47—82no—
117C2×Dic47—81no—
118C2×Dic47—81no—
119Dic94—28no—
120Dic94—44no—
121Dic94—44no—
122Dic94—44no—
123C47⋊C8—82no—
124#10345—471nomaximal, Sylow
125C22×C47—22no—
126C22×C47—22no—
127C22×C47—22no—
128C22×C47—22no—
129C22×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—21no—
133C22×C47#39311yescharacteristic
134C22×C47#45212yes—
135C22×C47#45511yescharacteristic
136C22×C47#45611yescharacteristic
137C22×C47B(4,𝔽2)12yes—
138C22×C47#47912yes—
139C22×C47#48811yescharacteristic
140C22×C47#49111yescharacteristic
141C4×C47—22no—
142C4×C47—22no—
143C4×C47—82no—
144C4×C47—82no—
145C4×C47—82no—
146Dic47—44no—
147Dic47—82no—
148#2646D4711yescharacteristic
149#1787—472no—
150#1446—471no—
151#1294—472no—
152#1280—471no—
153C2×C47—21no—
154C2×C47—22no—
155C2×C47—21no—
156C2×C47#160312yes—
157C2×C47#160612yes—
158C2×C47#202611yescharacteristic
159C2×C47#202811yescharacteristic
160C2×C47#202911yescharacteristic
161C23×Q8—471no—
162C2×#103—942no—
163C2×#103—942no—
164C2×C22⋊C8—472no—
165#400—22no—
166#398—22no—
167#385—22no—
168#380C2×D4712yes—
169C2×#95—471no—
170C2×#95—942no—
171C2×#95C2×D4711yescharacteristic
172C47#1034511yescharacteristic, complemented, Sylow
173C22×Q8—472no—
174C22×Q8—941no—
175C22×Q8—942no—
176C22×Q8—942no—
177C22×Q8—1884no—
178C23×C4—941no—
179C23×C4—941no—
180C23×C4C22⋊D4712yes—
181C23×C4C22×D4711yescharacteristic
182C22×C8—942no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C22⋊D4712yes—
186C2×C4⋊C4C22⋊D4712yes—
187C2×C22⋊C4—22no—
188#103—1884no—
189#103—1884no—
190C22⋊C8—942no—
191C22⋊C8—942no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—942no—
197#95—1884no—
198C24C2×C22⋊D4711yescharacteristic
199C2×Q8—944no—
200C2×Q8—944no—
201C2×Q8—944no—
202C2×Q8—1882no—
203C2×Q8—1882no—
204C2×Q8—1884no—
205C2×Q8—1884no—
206C2×Q8—1888no—
207C2×Q8—1882no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—944no—
217C22×C4—942no—
218C22×C4—942no—
219C22×C4—1882no—
220C22×C4—1881no—
221C22×C4—1881no—
222C22×C4—1882no—
223C22×C4—1882no—
224C22×C4—1881no—
225C22×C4—1881no—
226C22×C4Q8×D4711yescharacteristic
227C22×C4#1062535412yes—
228C22×C4#1062535411yescharacteristic
229C22×C4C2×C22⋊D4712yes—
230C2×C8—1882no—
231C2×C8—1882no—
232C2×C8—1882no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1309399311yescharacteristic
243C23#1309400011yescharacteristic
244C23#1309401311yescharacteristic
245C23#1309404412yes—
246C23#1309405412yes—
247Q8—948no—
248Q8—1884no—
249Q8—1884no—
250Q8—1884no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—944no—
268C2×C4—3761no—
269C2×C4—3762no—
270C2×C4—3761no—
271C2×C4—1882no—
272C2×C4—1884no—
273C2×C4—1882no—
274C2×C4—1884no—
275C2×C4—1882no—
276C2×C4—1884no—
277C2×C4#1309400012yes—
278C2×C4#1309401312yes—
279C8—3762no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22#1568903411yescharacteristic
289C22#1568928512yes—
290C22#1568930111yescharacteristic
291C22#1568930611yescharacteristic
292C22#1568931012yes—
293C22#1568942712yes—
294C22#1568948011yescharacteristic
295C22#1568949311yescharacteristic
296C4—22no—
297C4—22no—
298C4—82no—
299C4—82no—
300C4—82no—
301C4—3762no—
302C4—1884no—
303C2—21no—
304C2—21no—
305C2—22no—
306C2#2024235112yes—
307C2#2024236812yes—
308C2#2024453611yescharacteristic
309C2#2024454611yescharacteristic
310C2#2024455111yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#2646C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenter#2646D47
hypocenterC47#10345
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
172. C47#10345semidirect

Maximal subgroups

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

subgroupindex
#202433222
#202416582
#202412662
#202412312
C47×#26462
#1034547