Finite Group Databasebeta

← #26120213

Subgroups — #26120213

Order 12032.

372 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 81 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#20254333C211yesmaximal, characteristic
2#20244231C211yesmaximal, characteristic
3#20242179C211yesmaximal, characteristic
4#20242070C211yesmaximal, characteristic
5#20241809C211yesmaximal, characteristic
6#20241277C211yesmaximal, characteristic
7C47×#1561C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9#15689502—21no—
10#15689475—21no—
11#15689333—21no—
12#15689333—21no—
13#15689278—22no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16C2×#13093942—22no—
17C4×#10625329C2211yescharacteristic
18#15688875—21no—
19#15688873—21no—
20#15688871—22no—
21Q8⋊(C47⋊C8)—22no—
22C47×#533C2211yescharacteristic
23C47×#423C2211yescharacteristic
24C47×#423C2211yescharacteristic
25C47×#332—21no—
26C47×#332—21no—
27C22×Dic94D412yes—
28C2×#10625337—22no—
29C2×#10625337—22no—
30C2×#10625329—21no—
31#13094024—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C4⋊(C47⋊C8)D411yescharacteristic
38C4⋊(C47⋊C8)D411yescharacteristic
39C4⋊(C47⋊C8)D412yes—
40#13093947—22no—
41#13093947—22no—
42#13093942—44no—
43C22⋊(C47⋊C8)—21no—
44C22⋊(C47⋊C8)—21no—
45#13093935—21no—
46C4×C47⋊C8—21no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8—21no—
49C2×M16×C47—21no—
50C2×M16×C47—21no—
51C4⋊Q8×C47D411yescharacteristic
52C4⋊Q8×C47D411yescharacteristic
53#125×C47—21no—
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58#117×C47—21no—
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C2×Q8×C47—21no—
65C2×Q8×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47#4111yescharacteristic
68C22×C4×C47#4111yescharacteristic
69C22×Dic47—22no—
70C2×Dic94—22no—
71C2×Dic94—22no—
72C2×Dic94—42no—
73C2×Dic94—42no—
74M16×C47—42no—
75M16×C47—81no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C22⋊C4×C47—41no—
85C42×C47—41no—
86C42×C47C2×D411yescharacteristic
87C42×C47C2×D411yescharacteristic
88C42×C47C2×D411yescharacteristic
89C42×C47#4111yescharacteristic
90#10625337—82no—
91#10625337—82no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94C4⋊Dic47—41no—
95C4⋊Dic47—41no—
96#10625329—22no—
97#10625329—41no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8—41no—
102C23×C47#12311yescharacteristic
103Q8×C47—41no—
104Q8×C47—41no—
105Q8×C47—41no—
106Q8×C47—41no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—22no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47#12111yescharacteristic
117C2×C4×C47#12111yescharacteristic
118C2×C4×C47#12311yescharacteristic
119C2×C4×C47#12411yescharacteristic
120C2×Dic47—44no—
121C2×Dic47—42no—
122Dic94—42no—
123Dic94—42no—
124Dic94—82no—
125C8×C47—81no—
126C8×C47—81no—
127C47⋊C8—42no—
128C47⋊C8—41no—
129C47⋊C8—41no—
130C47⋊C8—42no—
131#10493—471nomaximal, Sylow
132C22×C47—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47#39411yescharacteristic
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—81no—
140C4×C47—81no—
141C4×C47#45311yescharacteristic
142C4×C47#45511yescharacteristic
143C4×C47#47111yescharacteristic
144C4×C47#47311yescharacteristic
145C4×C47#47312yes—
146Dic47—82no—
147#3209—471no—
148#1966—471no—
149#1574—471no—
150#1561D4711yescharacteristic
151#1548—471no—
152#1485—471no—
153#1299—471no—
154C2×C47—41no—
155C2×C47#203711yescharacteristic
156C2×C47#204711yescharacteristic
157C2×C47#205211yescharacteristic
158#533C2×D4711yescharacteristic
159C2×C4⋊Q8—471no—
160#494—941no—
161#487—941no—
162#462—941no—
163#462—941no—
164#451—942no—
165#431—471no—
166#431—471no—
167#423C2×D4711yescharacteristic
168#423C2×D4711yescharacteristic
169C2×#101—942no—
170C4×M16—471no—
171#335—941no—
172#334—941no—
173#333—942no—
174#332—21no—
175#332—21no—
176Q8⋊C8—942no—
177C47#1049311yescharacteristic, complemented, Sylow
178C22×Q8—472no—
179C2×Q16—942no—
180C2×Q16—942no—
181C2×M16—21no—
182C2×M16—21no—
183C2×M16—941no—
184C4⋊Q8—941no—
185C4⋊Q8—941no—
186C4⋊Q8—941no—
187C4⋊Q8—941no—
188C4⋊Q8C22⋊D4711yescharacteristic
189C4⋊Q8C22⋊D4711yescharacteristic
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—941no—
197C2×C4⋊C4—941no—
198C2×C42C22×D4711yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—472no—
204C4⋊C8—471no—
205C4⋊C8—471no—
206#103—942no—
207#103—942no—
208#101—1884no—
209C22⋊C8—941no—
210C22⋊C8—941no—
211#97—941no—
212C4×C8—941no—
213C4×C8—941no—
214C4×C8—941no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—942no—
218C2×Q8—942no—
219C2×Q8—1882no—
220C2×Q8—1882no—
221C22×C4—942no—
222C22×C4#1062535011yescharacteristic
223C22×C4D4×D4711yescharacteristic
224C22×C4#1062535211yescharacteristic
225Q16—3762no—
226Q16—3762no—
227M16—42no—
228M16—81no—
229M16—942no—
230M16—1881no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—941no—
234C2×C8—941no—
235C2×C8—942no—
236C2×C8—1881no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—1881no—
244C4⋊C4—1881no—
245C4⋊C4—1881no—
246C4⋊C4—1881no—
247C22⋊C4—41no—
248C42—41no—
249C42#1062535011yescharacteristic
250C42D4×D4711yescharacteristic
251C42D4×D4711yescharacteristic
252C42C2×C22⋊D4711yescharacteristic
253C23#1309400611yescharacteristic
254Q8—41no—
255Q8—41no—
256Q8—41no—
257Q8—41no—
258Q8—3762no—
259Q8—1882no—
260Q8—1882no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—1884no—
269C2×C4—1882no—
270C2×C4#1309399211yescharacteristic
271C2×C4#1309399611yescharacteristic
272C2×C4#1309399711yescharacteristic
273C2×C4#1309399711yescharacteristic
274C2×C4#1309400711yescharacteristic
275C2×C4#1309401011yescharacteristic
276C8—81no—
277C8—81no—
278C8—1882no—
279C8—1881no—
280C8—1881no—
281C8—1882no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1568903811yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—3762no—
292C4#1568928911yescharacteristic
293C4#1568929911yescharacteristic
294C4#1568938411yescharacteristic
295C4#1568939611yescharacteristic
296C4#1568939712yes—
297C2—41no—
298C2#2024459611yescharacteristic
299C2#2024465411yescharacteristic
300C2#2024468511yescharacteristic
subgroupG/H
centerC22#15689038
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1561C2
socleC22×C47#394
prime radicalC23×C47#123
hypercenter#1561D47
hypocenterC47#10493
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
177. C47#10493semidirect

Maximal subgroups

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

subgroupindex
#202543332
#202442312
#202421792
#202420702
#202418092
#202412772
C47×#15612
#1049347