Finite Group Databasebeta

← #26119280

Subgroups — #26119280

Order 12032.

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

normal subgroups only

This group has 500 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#20243476C212yesmaximal
2#20241657C211yesmaximal, characteristic
3#20241266C212yesmaximal
4#20241231C211yesmaximal, characteristic
5C47×#2646C211yesmaximal, characteristic
6C22×C4⋊Dic47C2211yescharacteristic
7C2×C22⋊(C47⋊C8)C2212yes—
8C2×C47⋊#95—22no—
9C2×C47⋊#95C2211yescharacteristic
10#15688885—22no—
11#15688885—22no—
12C47×#400—22no—
13C47×#398—22no—
14C47×#385—22no—
15C47×#380C2212yes—
16C2×#95×C47C2211yescharacteristic
17C23×Dic47—21no—
18C23×Dic47—21no—
19C22×C47⋊C8—22no—
20C2×C4⋊Dic47—22no—
21C2×C4⋊Dic47—22no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47Q812yes—
24C22⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)—22no—
26C47⋊#95—22no—
27C47⋊#95—44no—
28C23×C4×C47D412yes—
29C23×C4×C47C2311yescharacteristic
30C2×C4⋊C4×C47—22no—
31C2×C4⋊C4×C47—22no—
32C2×C4⋊C4×C47D412yes—
33C2×C4⋊C4×C47D412yes—
34C2×C22⋊C4×C47—22no—
35#95×C47—22no—
36#95×C47—22no—
37#95×C47—22no—
38#95×C47—22no—
39C24×C47C2×D411yescharacteristic
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47—22no—
45C22×C4×C47—42no—
46C22×C4×C47—42no—
47C22×C4×C47—42no—
48C22×C4×C47C2×D412yes—
49C22×C4×C47C2×Q811yescharacteristic
50C22×C4×C47#4112yes—
51C22×C4×C47#4111yescharacteristic
52C22×Dic47—22no—
53C22×Dic47—22no—
54C22×Dic47—42no—
55C22×Dic47—41no—
56C22×Dic47—42no—
57C22×Dic47—42no—
58C22×Dic47—41no—
59C22×Dic47—41no—
60C22×Dic47—41no—
61C22×Dic47—42no—
62C4⋊C4×C47—42no—
63C4⋊C4×C47—42no—
64C4⋊C4×C47—82no—
65C4⋊C4×C47—82no—
66C22⋊C4×C47—42no—
67C22⋊C4×C47—42no—
68C4⋊Dic47—24no—
69C4⋊Dic47—42no—
70C2×C47⋊C8—42no—
71C2×C47⋊C8—42no—
72C2×C47⋊C8—42no—
73C23×C47—21no—
74C23×C47—21no—
75C23×C47—22no—
76C23×C47#12011yescharacteristic
77C23×C47C22⋊Q811yescharacteristic
78C23×C47#12411yescharacteristic
79C23×C47#13512yes—
80C23×C47#13712yes—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
85C2×C4×C47—42no—
86C2×C4×C47—44no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47—42no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47—42no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—82no—
97C2×C4×C47C22⋊Q812yes—
98C2×C4×C47#12412yes—
99C2×Dic47—44no—
100C2×Dic47—42no—
101C2×Dic47—44no—
102C2×Dic47—42no—
103C2×Dic47—82no—
104C2×Dic47—81no—
105C2×Dic47—82no—
106C2×Dic47—81no—
107C2×Dic47—81no—
108C2×Dic47—81no—
109C47⋊C8—82no—
110#10347—471nomaximal, Sylow
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—22no—
114C22×C47—22no—
115C22×C47—21no—
116C22×C47—21no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47#39311yescharacteristic
120C22×C47#45212yes—
121C22×C47#45311yescharacteristic
122C22×C47#45411yescharacteristic
123C22×C47#45812yes—
124C22×C47#47912yes—
125C22×C47#48811yescharacteristic
126C22×C47#49111yescharacteristic
127C4×C47—22no—
128C4×C47—22no—
129C4×C47—82no—
130C4×C47—82no—
131C4×C47—82no—
132Dic47—82no—
133Dic47—82no—
134#2646D4711yescharacteristic
135#1824—472no—
136#1445—471no—
137#1294—472no—
138#1280—471no—
139C2×C47—21no—
140C2×C47—22no—
141C2×C47—21no—
142C2×C47#161512yes—
143C2×C47#161812yes—
144C2×C47#202611yescharacteristic
145C2×C47#202711yescharacteristic
146C2×C47#203011yescharacteristic
147C22×C4⋊C4—471no—
148C2×C22⋊C8—472no—
149#400—22no—
150#398—22no—
151#385—22no—
152#380C2×D4712yes—
153C2×#95—471no—
154C2×#95—942no—
155C2×#95C2×D4711yescharacteristic
156#340—942no—
157#340—942no—
158C47#1034711yescharacteristic, complemented, Sylow
159C23×C4—941no—
160C23×C4—941no—
161C23×C4C22⋊D4712yes—
162C23×C4C22×D4711yescharacteristic
163C22×C8—942no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—472no—
167C2×C4⋊C4—942no—
168C2×C4⋊C4—942no—
169C2×C4⋊C4—941no—
170C2×C4⋊C4C22⋊D4712yes—
171C2×C4⋊C4C22⋊D4712yes—
172C2×C22⋊C4—22no—
173C22⋊C8—942no—
174C22⋊C8—942no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—942no—
180#95—1884no—
181C24C2×C22⋊D4711yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—942no—
191C22×C4—942no—
192C22×C4—1882no—
193C22×C4—1881no—
194C22×C4—1882no—
195C22×C4—1882no—
196C22×C4—1881no—
197C22×C4—1881no—
198C22×C4—1881no—
199C22×C4—1882no—
200C22×C4Q8×D4711yescharacteristic
201C22×C4#1062535412yes—
202C22×C4#1062535411yescharacteristic
203C22×C4C2×C22⋊D4712yes—
204C2×C8—1882no—
205C2×C8—1882no—
206C2×C8—1882no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—944no—
212C4⋊C4—1882no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1309399311yescharacteristic
219C23#1309400011yescharacteristic
220C23#1309401311yescharacteristic
221C23#1309404412yes—
222C23#1309405412yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—3761no—
240C2×C4—3762no—
241C2×C4—3762no—
242C2×C4—3761no—
243C2×C4—3761no—
244C2×C4—3761no—
245C2×C4—1884no—
246C2×C4—1882no—
247C2×C4—1884no—
248C2×C4—1882no—
249C2×C4#1309400012yes—
250C2×C4#1309401312yes—
251C8—3762no—
252C22—22no—
253C22—22no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—22no—
259C22—22no—
260C22#1568903411yescharacteristic
261C22#1568928512yes—
262C22#1568929111yescharacteristic
263C22#1568929611yescharacteristic
264C22#1568931312yes—
265C22#1568942712yes—
266C22#1568948011yescharacteristic
267C22#1568949311yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—3762no—
274C4—3762no—
275C2—21no—
276C2—21no—
277C2—22no—
278C2#2024241912yes—
279C2#2024243612yes—
280C2#2024453611yescharacteristic
281C2#2024454111yescharacteristic
282C2#2024455411yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#2646C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenter#2646D47
hypocenterC47#10347
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
158. C47#10347semidirect

Maximal subgroups

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

subgroupindex
#202434762
#202416572
#202412662
#202412312
C47×#26462
#1034747