Finite Group Databasebeta

← #26109894

Subgroups — #26109894

Order 12032.

384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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#20241281C212yesmaximal
4#20241252C212yesmaximal
5C47×#2356C211yesmaximal, characteristic
6#15689180C2212yes—
7C2×#13093943—21no—
8C4×#10625329C2212yes—
9#15688892—21no—
10#15688849—21no—
11#15688849—21no—
12C2×C4×Q8×C47C2211yescharacteristic
13C47×#391—21no—
14C47×#387—21no—
15C47×#387—21no—
16C47×#383C411yescharacteristic
17C47×#383C2211yescharacteristic
18C47×#382C411yescharacteristic
19C4×C4⋊C4×C47—21no—
20C4×C4⋊C4×C47C411yescharacteristic
21C47×#376C411yescharacteristic
22C47×#376C2211yescharacteristic
23C2×#10625329—22no—
24C4⋊(C47⋊C8)—22no—
25#13093943—24no—
26C22⋊(C47⋊C8)—22no—
27#13093935—22no—
28#13093935—22no—
29C4×C47⋊C8—22no—
30C22×Q8×C47D411yescharacteristic
31C4×Q8×C47—22no—
32C4×Q8×C47—22no—
33C2×C4⋊C4×C47—21no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47D411yescharacteristic
36C2×C4⋊C4×C47D411yescharacteristic
37C2×C4⋊C4×C47D411yescharacteristic
38C2×C42×C47—21no—
39C2×C42×C47—21no—
40C2×C42×C47—21no—
41C2×C42×C47C2×C411yescharacteristic
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47C2311yescharacteristic
44#95×C47—21no—
45#95×C47—21no—
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47C2×C411yescharacteristic
52#95×C47C2×C411yescharacteristic
53#95×C47C2×C411yescharacteristic
54#95×C47C2×C411yescharacteristic
55C2×Q8×C47—22no—
56C2×Q8×C47—22no—
57C2×Q8×C47—41no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22×C411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C4⋊C4×C47—22no—
70C4⋊C4×C47—22no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47—42no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—21no—
77C42×C47—21no—
78C42×C47—42no—
79C42×C47—42no—
80C42×C47—42no—
81C42×C47#4112yes—
82C42×C47#4112yes—
83#10625329—24no—
84#10625329—42no—
85C2×C47⋊C8—42no—
86C2×C47⋊C8—42no—
87C23×C47C2×C22⋊C411yescharacteristic
88Q8×C47—44no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47#10412yes—
115C2×C4×C47#11711yescharacteristic
116C2×C4×C47#11711yescharacteristic
117C2×C4×C47#12312yes—
118C2×C4×C47#12312yes—
119C47⋊C8—44no—
120C47⋊C8—82no—
121#8774—471nomaximal, Sylow
122C22×C47—21no—
123C22×C47—21no—
124C22×C47#38111yescharacteristic
125C22×C47C2×#10411yescharacteristic
126C22×C47#42111yescharacteristic
127C4×C47—22no—
128C4×C47—22no—
129C4×C47—22no—
130C4×C47—21no—
131C4×C47—21no—
132C4×C47—42no—
133C4×C47—41no—
134C4×C47—41no—
135C4×C47—41no—
136C4×C47—81no—
137C4×C47—81no—
138C4×C47—81no—
139#2356D4711yescharacteristic
140C4×#101—471no—
141#1467—471no—
142#1300—472no—
143#1288—472no—
144C2×C47—21no—
145C2×C47—21no—
146C2×C47#182611yescharacteristic
147C2×C47#182711yescharacteristic
148C2×C47#183011yescharacteristic
149C2×C4×Q8C2×D4711yescharacteristic
150#432—472no—
151C2×#101—941no—
152C4×M16—472no—
153#391—21no—
154#387—21no—
155#387—21no—
156#383Dic4711yescharacteristic
157#383C2×D4711yescharacteristic
158#382Dic4711yescharacteristic
159C4×C4⋊C4—21no—
160C4×C4⋊C4Dic4711yescharacteristic
161#376Dic4711yescharacteristic
162#376C2×D4711yescharacteristic
163#343—941no—
164#324—941no—
165#324—941no—
166C47#877411yescharacteristic, complemented, Sylow
167C22×Q8C22⋊D4711yescharacteristic
168C2×M16—942no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C22⋊D4711yescharacteristic
174C2×C4⋊C4C22⋊D4711yescharacteristic
175C2×C4⋊C4C22⋊D4711yescharacteristic
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C2×Dic4711yescharacteristic
180C2×C42C2×Dic4711yescharacteristic
181C2×C42C22×D4711yescharacteristic
182C4⋊C8—942no—
183#101—944no—
184C22⋊C8—942no—
185#97—942no—
186#97—942no—
187C4×C8—942no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95C2×Dic4711yescharacteristic
196#95C2×Dic4711yescharacteristic
197#95C2×Dic4711yescharacteristic
198#95C2×Dic4711yescharacteristic
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊Dic4711yescharacteristic
207C22×C4C22⋊Dic4711yescharacteristic
208C22×C4C22⋊Dic4711yescharacteristic
209C22×C4C22⋊Dic4711yescharacteristic
210C22×C4C22×Dic4711yescharacteristic
211C22×C4C2×C22⋊D4711yescharacteristic
212C22×C4C2×C22⋊D4711yescharacteristic
213M16—944no—
214M16—1882no—
215C2×C8—1882no—
216C2×C8—1882no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C42—42no—
228C42—42no—
229C42#1062535012yes—
230C42#1062535012yes—
231C23C2×C22⋊Dic4711yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4#1309395112yes—
259C2×C4#1309398311yescharacteristic
260C2×C4#1309398311yescharacteristic
261C2×C4#1309400712yes—
262C2×C4#1309400712yes—
263C8—3762no—
264C8—1884no—
265C22—21no—
266C22—21no—
267C22#1568898611yescharacteristic
268C22C2×#1309395111yescharacteristic
269C22#1568914011yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—81no—
282C2—21no—
283C2—21no—
284C2#2024348711yescharacteristic
285C2#2024349211yescharacteristic
286C2#2024350211yescharacteristic
subgroupG/H
centerC22#15688986
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2356C2
socleC22×C47#381
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2356D47
hypocenterC47#8774
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
166. C47#8774semidirect

Maximal subgroups

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

subgroupindex
C4×#130939432
#202417322
#202412812
#202412522
C47×#23562
#877447