Finite Group Databasebeta

← #26114053

Subgroups — #26114053

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252412C211yesmaximal, characteristic
2#20243474C212yesmaximal, complemented
3#20243376C211yesmaximal, characteristic
4#20241255C212yesmaximal, complemented
5C47×#2486C211yesmaximal, characteristic
6D4×C47⋊C8—24no—
7#15689176—21no—
8C2×#13093939—21no—
9C2×C22⋊(C47⋊C8)—21no—
10C2×C22⋊(C47⋊C8)C2212yes—
11#15688983C2212yes—
12#15688890—21no—
13#15688885—24no—
14C2×#123×C47—21no—
15C2×C4×D4×C47C2211yescharacteristic
16C22×C4⋊C4×C47C2211yescharacteristic
17C47×#398C412yescomplemented
18C47×#397C412yescomplemented
19C47×#389—21no—
20C47×#381—21no—
21C47×#380—21no—
22C47×#380C2211yescharacteristic
23C22×C47⋊C8—22no—
24C22×C47⋊C8D414yes—
25C2×C4⋊Dic47—22no—
26C2×C22⋊Dic47—22no—
27C4⋊(C47⋊C8)—22no—
28#13093939—42no—
29C22⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—22no—
31C22⋊(C47⋊C8)—22no—
32C4×C47⋊C8—22no—
33C47⋊#95—22no—
34C22×D4×C47D411yescharacteristic
35C23×C4×C47—21no—
36C23×C4×C47D411yescharacteristic
37C23×C4×C47C2311yescharacteristic
38#123×C47—42no—
39#123×C47—42no—
40C4×D4×C47—22no—
41C4×D4×C47—22no—
42C2×C4⋊C4×C47—22no—
43C2×C4⋊C4×C47—22no—
44C2×C4⋊C4×C47—22no—
45C2×C4⋊C4×C47—21no—
46C2×C4⋊C4×C47—21no—
47C2×C4⋊C4×C47C2×C412yes—
48C2×C4⋊C4×C47C2×C411yescharacteristic
49C2×C22⋊C4×C47—22no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47C2×C411yescharacteristic
52C2×C22⋊C4×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54#95×C47—22no—
55#95×C47—22no—
56#95×C47C2×C412yes—
57C24×C47C22⋊C411yescharacteristic
58C24×C47C2×D411yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47D812yes—
62C2×D4×C47SD1612yes—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—42no—
68C22×C4×C47—42no—
69C22×C4×C47—42no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—42no—
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22×C411yescharacteristic
77C22×C4×C47C2×D412yes—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47#4112yes—
80C22×Dic47—42no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—24no—
83C4⋊C4×C47—42no—
84C4⋊C4×C47—44no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47—22no—
89C22⋊C4×C47—44no—
90C22⋊C4×C47—41no—
91C22⋊C4×C47—41no—
92C42×C47—21no—
93C42×C47—21no—
94C22⋊Dic47—42no—
95C22⋊Dic47—42no—
96C4⋊Dic47—44no—
97C2×C47⋊C8—24no—
98C2×C47⋊C8—44no—
99C2×C47⋊C8—82no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—41no—
103C23×C47—41no—
104C23×C47—41no—
105C23×C47—41no—
106C23×C47#10212yes—
107C23×C47C2×C22⋊C411yescharacteristic
108C23×C47#12112yes—
109C23×C47C2×D811yescharacteristic
110C23×C47C2×SD1611yescharacteristic
111C23×C47#13512yes—
112D4×C47—24no—
113D4×C47—24no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—24no—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—41no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—81no—
132C2×C4×C47—82no—
133C2×C4×C47—82no—
134C2×C4×C47#10212yes—
135C2×C4×C47C4×D412yes—
136C2×C4×C47#12011yescharacteristic
137C2×C4×C47#12311yescharacteristic
138C2×Dic47—82no—
139C2×Dic47—82no—
140C2×Dic47—82no—
141C47⋊C8—44no—
142#9470—471nomaximal, Sylow
143C22×C47—22no—
144C22×C47—21no—
145C22×C47—22no—
146C22×C47—21no—
147C22×C47—22no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—42no—
151C22×C47—42no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—81no—
155C22×C47#38611yescharacteristic
156C22×C47C2×#10211yescharacteristic
157C22×C47#41611yescharacteristic
158C22×C47#46512yes—
159C22×C47#46612yes—
160C4×C47—21no—
161C4×C47—22no—
162C4×C47—22no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—82no—
166C4×C47—82no—
167C4×C47#45812yes—
168Dic47—162no—
169#2972—471no—
170#2486D4711yescharacteristic
171#1823—472no—
172#1799—471no—
173#1289—472no—
174C2×C47—22no—
175C2×C47—21no—
176C2×C47—21no—
177C2×C47—22no—
178C2×C47—42no—
179C2×C47#189011yescharacteristic
180C2×C47#189311yescharacteristic
181C2×C47#190911yescharacteristic
182C2×#123—21no—
183C2×C4×D4C2×D4711yescharacteristic
184C22×C4⋊C4C2×D4711yescharacteristic
185C8×D4—944no—
186#431—941no—
187C2×#99—941no—
188C2×C22⋊C8—472no—
189C2×C22⋊C8—941no—
190#398Dic4712yescomplemented
191#397Dic4712yescomplemented
192#389—21no—
193#381—21no—
194#380—21no—
195#380—472no—
196#380C2×D4711yescharacteristic
197#342—941no—
198#340—944no—
199C47#947011yescharacteristic, complemented, Sylow
200C22×D4C22⋊D4711yescharacteristic
201C23×C4—21no—
202C23×C4C22⋊D4711yescharacteristic
203C23×C4C22×D4711yescharacteristic
204C22×C8—474no—
205C22×C8—942no—
206#123—42no—
207#123—42no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—942no—
216C2×C4⋊C4C2×Dic4712yes—
217C2×C4⋊C4C2×Dic4711yescharacteristic
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—942no—
221C2×C22⋊C4C2×Dic4711yescharacteristic
222C2×C22⋊C4C22⋊D4711yescharacteristic
223C2×C42C22⋊D4711yescharacteristic
224C4⋊C8—942no—
225#99—1882no—
226C22⋊C8—942no—
227C22⋊C8—942no—
228C22⋊C8—942no—
229C4×C8—942no—
230#95—22no—
231#95—22no—
232#95—942no—
233#95C2×Dic4712yes—
234C24C22⋊Dic4711yescharacteristic
235C24C2×C22⋊D4711yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4#1062533412yes—
239C2×D4#1062533512yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—1882no—
251C22×C4C22⋊Dic4711yescharacteristic
252C22×C4C22⋊Dic4711yescharacteristic
253C22×C4C22⋊Dic4711yescharacteristic
254C22×C4D4×D4712yes—
255C22×C4#1062535212yes—
256C22×C4C22×Dic4711yescharacteristic
257C22×C4C2×C22⋊D4711yescharacteristic
258C2×C8—944no—
259C2×C8—3762no—
260C2×C8—1884no—
261C4⋊C4—22no—
262C4⋊C4—24no—
263C4⋊C4—42no—
264C4⋊C4—44no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—1884no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—44no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—1882no—
274C22⋊C4—1882no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#1309394512yes—
284C23C2×C22⋊Dic4711yescharacteristic
285C23#1309399612yes—
286C23C2×#1062533411yescharacteristic
287C23C2×#1062533511yescharacteristic
288C23#1309404412yes—
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—3762no—
312C2×C4—3762no—
313C2×C4—3762no—
314C2×C4#1309394512yes—
315C2×C4D4×Dic4712yes—
316C2×C4#1309399211yescharacteristic
317C2×C4#1309400511yescharacteristic
318C8—1884no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1568900311yescharacteristic
332C22C2×#1309394511yescharacteristic
333C22#1568911911yescharacteristic
334C22#1568935012yes—
335C22#1568935712yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—7522no—
344C4#1568931212yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#2024380211yescharacteristic
351C2#2024381711yescharacteristic
352C2#2024391111yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2486C2
socleC22×C47#386
prime radicalC22×D4×C47D4
cosocleC23×C4×C47C23
hypercenter#2486D47
hypocenterC47#9470
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #20243474C2semidirect
4. #20241255C2semidirect
17. C47×#398C4semidirect
18. C47×#397C4semidirect
190. #398Dic47semidirect
191. #397Dic47semidirect
199. C47#9470semidirect

Maximal subgroups

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

subgroupindex
#202524122
#202434742
#202433762
#202412552
C47×#24862
#947047