Finite Group Databasebeta

← #26109805

Subgroups — #26109805

Order 12032.

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

normal subgroups only

This group has 398 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#20245989C211yesmaximal, characteristic
2#20243466C211yesmaximal, characteristic
3#20243466C211yesmaximal, characteristic
4#20241297C211yesmaximal, characteristic
5#20241297C211yesmaximal, characteristic
6#20241296C211yesmaximal, characteristic
7C47×#1306C211yesmaximal, characteristic
8C22×C4⋊Dic47C2211yescharacteristic
9#15689087C2211yescharacteristic
10#15689087C2211yescharacteristic
11#15689008—22no—
12#15689006—22no—
13#15688986C2211yescharacteristic
14#15688981C412yes—
15C22⋊C4×Dic47C412yes—
16#15688891—22no—
17#15688891—22no—
18C47×#407C2211yescharacteristic
19C47×#407C2211yescharacteristic
20C47×#381C2211yescharacteristic
21C23×Dic47C2×C411yescharacteristic
22C23×Dic47C2×C411yescharacteristic
23C2×#10625329—21no—
24C2×#10625329—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47D412yes—
30C2×C4⋊Dic47D412yes—
31C2×Dic47⋊C4—22no—
32C2×C22⋊Dic47C2×C412yes—
33C2×C4×Dic47—22no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36C22⋊(C47⋊C8)—21no—
37C22⋊(C47⋊C8)—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—22no—
41C47⋊#95—22no—
42C23×C4×C47C2311yescharacteristic
43C2×M16×C47—21no—
44C2×M16×C47—21no—
45C2×C22⋊C4×C47C2×C412yes—
46C22⋊C8×C47—21no—
47C22⋊C8×C47—21no—
48C22⋊C8×C47—21no—
49C22⋊C8×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52C24×C47C22×C411yescharacteristic
53C22×C4×C47—22no—
54C22×C4×C47—42no—
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47#4111yescharacteristic
58C22×C4×C47#4111yescharacteristic
59C22×C4×C47#4111yescharacteristic
60C22×C4×C47#4111yescharacteristic
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—22no—
66C22×Dic47—81no—
67C22×Dic47—81no—
68C22×Dic47C22⋊C412yes—
69C22×Dic47C22⋊C412yes—
70M16×C47—42no—
71M16×C47—42no—
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C22⋊C4×C47—42no—
75C22⋊Dic47—42no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—22no—
79C4⋊Dic47—22no—
80Dic47⋊C4—82no—
81C4×Dic47—82no—
82#10625329—42no—
83#10625329—42no—
84C2×C47⋊C8—41no—
85C2×C47⋊C8—41no—
86C23×C47—22no—
87C23×C47—41no—
88C23×C47—41no—
89C23×C47C2×C22⋊C411yescharacteristic
90C23×C47#11711yescharacteristic
91C23×C47#11711yescharacteristic
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—41no—
95C2×C4×C47—41no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47#12311yescharacteristic
102C2×C4×C47#12311yescharacteristic
103C2×C4×C47#12311yescharacteristic
104C2×C4×C47#12311yescharacteristic
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—42no—
108C2×Dic47—42no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112C2×Dic47—81no—
113C2×Dic47—81no—
114C2×Dic47—81no—
115C2×Dic47—81no—
116C8×C47—81no—
117C8×C47—81no—
118C47⋊C8—81no—
119C47⋊C8—81no—
120#8755—471nomaximal, Sylow
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—44no—
130C22×C47#38111yescharacteristic
131C22×C47#41012yes—
132C4×C47—21no—
133C4×C47—21no—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—82no—
137Dic47—42no—
138Dic47—42no—
139Dic47—82no—
140#2313—471no—
141#1821—471no—
142#1821—471no—
143#1306—471no—
144#1306—471no—
145#1306—471no—
146#1306D4711yescharacteristic
147C2×C47—22no—
148C2×C47—41no—
149C2×C47—41no—
150C2×C47#182011yescharacteristic
151C2×C47#182911yescharacteristic
152C2×C47#183011yescharacteristic
153C22×C4⋊C4—471no—
154#407—471no—
155#407—471no—
156#407C2×D4711yescharacteristic
157#407C2×D4711yescharacteristic
158#387—942no—
159#387—942no—
160#381—471no—
161#381C2×D4711yescharacteristic
162#380—472no—
163C4×C22⋊C4—472no—
164#343—942no—
165#343—942no—
166C47#875511yescharacteristic, complemented, Sylow
167C23×C4—471no—
168C23×C4—471no—
169C23×C4C22×D4711yescharacteristic
170C2×M16—21no—
171C2×M16—21no—
172C2×M16—941no—
173C2×M16—941no—
174C2×C4⋊C4—472no—
175C2×C4⋊C4—472no—
176C2×C4⋊C4—941no—
177C2×C4⋊C4—941no—
178C2×C4⋊C4—941no—
179C2×C4⋊C4—941no—
180C2×C4⋊C4—942no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4C4×D4712yes—
183C2×C42—942no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C22⋊C8—21no—
187C22⋊C8—21no—
188C22⋊C8—941no—
189C22⋊C8—941no—
190C22⋊C8—941no—
191C22⋊C8—941no—
192#95—21no—
193#95—21no—
194#95—942no—
195#95—942no—
196#95—941no—
197#95—941no—
198C24C2×C4×D4711yescharacteristic
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—472no—
202C22×C4—472no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4—941no—
206C22×C4—941no—
207C22×C4—942no—
208C22×C4—3761no—
209C22×C4—3761no—
210C22×C4#1062535011yescharacteristic
211C22×C4#1062535011yescharacteristic
212C22×C4D4×D4711yescharacteristic
213C22×C4D4×D4711yescharacteristic
214C22×C4#1062535211yescharacteristic
215C22×C4#1062535411yescharacteristic
216M16—42no—
217M16—42no—
218M16—1882no—
219M16—1882no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—1881no—
223C2×C8—1881no—
224C4⋊C4—942no—
225C4⋊C4—942no—
226C4⋊C4—942no—
227C4⋊C4—942no—
228C4⋊C4—3762no—
229C22⋊C4—42no—
230C22⋊C4—1882no—
231C42—3762no—
232C23—22no—
233C23—41no—
234C23—41no—
235C23C22⋊C4×D4711yescharacteristic
236C23#1309398111yescharacteristic
237C23#1309398211yescharacteristic
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—3761no—
250C2×C4—3761no—
251C2×C4—3761no—
252C2×C4—3761no—
253C2×C4—1882no—
254C2×C4—1882no—
255C2×C4—1882no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4#1309400611yescharacteristic
259C2×C4#1309400611yescharacteristic
260C2×C4#1309400911yescharacteristic
261C2×C4#1309400911yescharacteristic
262C8—81no—
263C8—81no—
264C8—3761no—
265C8—3761no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22#1568898511yescharacteristic
276C22#1568909512yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—82no—
282C4—3762no—
283C4—1882no—
284C4—1882no—
285C2—22no—
286C2—41no—
287C2—41no—
288C2#2024346411yescharacteristic
289C2#2024349811yescharacteristic
290C2#2024350111yescharacteristic
subgroupG/H
centerC22#15688985
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1306C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1306D47
hypocenterC47#8755
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
166. C47#8755semidirect

Maximal subgroups

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

subgroupindex
#202459892
#202434662
#202412972
#202412962
C47×#13062
#875547