Finite Group Databasebeta

← #26119007

Subgroups — #26119007

Order 12032.

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

normal subgroups only

This group has 504 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
1#20254536C211yesmaximal, characteristic
2#20254529C211yesmaximal, characteristic
3#20251766C211yesmaximal, characteristic
4#20242074C211yesmaximal, characteristic
5#20242061C211yesmaximal, characteristic
6#20241221C211yesmaximal, characteristic
7C47×#1994C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×#13094024C2211yescharacteristic
10#15689526—21no—
11#15689519—21no—
12#15689473—21no—
13#15689473—21no—
14#15689456—22no—
15#15689451—22no—
16#15689418—22no—
17#15689408—22no—
18#15689176C2211yescharacteristic
19#15689176C2211yescharacteristic
20#15689029—22no—
21#15689029—22no—
22#15688989—22no—
23#15688870—22no—
24#15688868—22no—
25C47×#533C2211yescharacteristic
26C47×#423C2211yescharacteristic
27C43×C47C2211yescharacteristic
28C47×#339—22no—
29C22×Dic94—21no—
30C22×Dic94—21no—
31#13094024—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024—21no—
38#13094024—21no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47D412yes—
42C2×C4⋊Dic47D412yes—
43#13093957—24no—
44#13093955—24no—
45C4⋊(C47⋊C8)D412yes—
46C4⋊(C47⋊C8)D412yes—
47#13093948—24no—
48#13093948—24no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C4×C47⋊C8—21no—
52C4×C47⋊C8—21no—
53C47⋊#95—28no—
54C2×M16×C47—21no—
55C4⋊Q8×C47D411yescharacteristic
56C4⋊Q8×C47D411yescharacteristic
57#125×C47—21no—
58C22⋊Q8×C47—21no—
59C22⋊Q8×C47—21no—
60C4×Q8×C47—21no—
61C4×Q8×C47—21no—
62#117×C47—21no—
63C2×C42×C47—21no—
64C2×C42×C47—21no—
65C2×C42×C47D412yes—
66C2×C42×C47C2311yescharacteristic
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C22×C4×C47—22no—
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—22no—
76C22×Dic47—22no—
77C2×Dic94—44no—
78C2×Dic94—41no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—42no—
83C2×Dic94—42no—
84M16×C47—42no—
85C2×C8×C47—41no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C22⋊C4×C47—41no—
93C42×C47—24no—
94C42×C47—22no—
95C42×C47—22no—
96C42×C47—42no—
97C42×C47—41no—
98C42×C47C2×D411yescharacteristic
99C42×C47C2×D411yescharacteristic
100C42×C47C2×D411yescharacteristic
101C42×C47#4111yescharacteristic
102C4⋊Dic47—22no—
103C4⋊Dic47—22no—
104C4⋊Dic47—22no—
105C4⋊Dic47—22no—
106C4⋊Dic47—41no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—41no—
110C2×C47⋊C8—22no—
111C2×C47⋊C8—22no—
112C23×C47#12011yescharacteristic
113Q8×C47—42no—
114Q8×C47—42no—
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47—24no—
118C2×C4×C47—42no—
119C2×C4×C47—42no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47#12011yescharacteristic
123C2×C4×C47#12011yescharacteristic
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12111yescharacteristic
127C2×C4×C47#12711yescharacteristic
128C2×C4×C47#13512yes—
129C2×C4×C47#13712yes—
130C2×Dic47—44no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133C2×Dic47—44no—
134Dic94—82no—
135Dic94—82no—
136Dic94—82no—
137Dic94—81no—
138Dic94—81no—
139C8×C47—81no—
140C47⋊C8—42no—
141C47⋊C8—42no—
142#10296—471nomaximal, Sylow
143C22×C47—21no—
144C22×C47—21no—
145C22×C47#39211yescharacteristic
146C22×C47#45212yes—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—44no—
150C4×C47—81no—
151C4×C47—81no—
152C4×C47#45412yes—
153C4×C47#45612yes—
154C4×C47#46412yes—
155C4×C47#49511yescharacteristic
156C4×C47#49711yescharacteristic
157Dic47—82no—
158Dic47—82no—
159#3230—471no—
160#3229—471no—
161#2862—471no—
162#1994D4711yescharacteristic
163#1549—471no—
164#1546—471no—
165#1276—471no—
166C2×C47—22no—
167C2×C47#200311yescharacteristic
168C2×C47#200511yescharacteristic
169C2×C47#201511yescharacteristic
170#533C2×D4711yescharacteristic
171C2×C4⋊Q8—471no—
172C2×C4⋊Q8—471no—
173#500—941no—
174#498—941no—
175#487—941no—
176#487—941no—
177#484—942no—
178#483—942no—
179#477—942no—
180#475—942no—
181#431—471no—
182#431—471no—
183#423C2×D4711yescharacteristic
184#391—942no—
185#391—942no—
186#382—942no—
187C43C2×D4711yescharacteristic
188#339—22no—
189#332—942no—
190#332—942no—
191C47#1029611yescharacteristic, complemented, Sylow
192C22×Q8—941no—
193C22×Q8—941no—
194C2×M16—21no—
195C4⋊Q8—941no—
196C4⋊Q8—941no—
197C4⋊Q8—941no—
198C4⋊Q8—941no—
199C4⋊Q8—941no—
200C4⋊Q8—941no—
201C4⋊Q8—941no—
202C4⋊Q8—941no—
203C4⋊Q8D18811yescharacteristic
204C4⋊Q8D18811yescharacteristic
205#125—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210#117—21no—
211C2×C4⋊C4—472no—
212C2×C4⋊C4—472no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42C22⋊D4712yes—
218C2×C42C22×D4711yescharacteristic
219#107—944no—
220#106—944no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—472no—
224C4⋊C8—472no—
225#103—944no—
226#103—944no—
227C22⋊C8—941no—
228C22⋊C8—941no—
229C4×C8—941no—
230C4×C8—941no—
231#95—948no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—1884no—
235C2×Q8—1881no—
236C2×Q8—1881no—
237C2×Q8—1881no—
238C2×Q8—1881no—
239C2×Q8—1882no—
240C2×Q8—1882no—
241C22×C4—22no—
242C22×C4—942no—
243C22×C4—942no—
244C22×C4D4×D4711yescharacteristic
245C22×C4D4×D4711yescharacteristic
246C22×C4C2×C22⋊D4711yescharacteristic
247M16—42no—
248C2×C8—41no—
249C2×C8—942no—
250C2×C8—942no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—942no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C22⋊C4—41no—
266C42—24no—
267C42—22no—
268C42—22no—
269C42—42no—
270C42—41no—
271C42C2×D18811yescharacteristic
272C42#1062535011yescharacteristic
273C42D4×D4711yescharacteristic
274C42D4×D4711yescharacteristic
275C23#1309399211yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—3762no—
279Q8—3761no—
280Q8—3761no—
281Q8—3762no—
282Q8—3762no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—1884no—
291C2×C4—1884no—
292C2×C4—1882no—
293C2×C4—1882no—
294C2×C4#1309399411yescharacteristic
295C2×C4#1309399411yescharacteristic
296C2×C4#1309399711yescharacteristic
297C2×C4#1309399711yescharacteristic
298C2×C4#1309399811yescharacteristic
299C2×C4#1309402011yescharacteristic
300C2×C4#1309404412yes—
301C2×C4#1309405512yes—
302C8—81no—
303C8—1882no—
304C8—1882no—
305C22—21no—
306C22—21no—
307C22#1568903211yescharacteristic
308C22#1568928312yes—
309C4—21no—
310C4—21no—
311C4—44no—
312C4—81no—
313C4—81no—
314C4—3762no—
315C4—3762no—
316C4#1568929712yes—
317C4#1568930712yes—
318C4#1568934512yes—
319C4#1568950511yescharacteristic
320C4#1568951511yescharacteristic
321C2—22no—
322C2#2024440911yescharacteristic
323C2#2024442311yescharacteristic
324C2#2024448111yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1994D47
hypocenterC47#10296
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
191. C47#10296semidirect

Maximal subgroups

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

subgroupindex
#202545362
#202545292
#202517662
#202420742
#202420612
#202412212
C47×#19942
#1029647