Finite Group Databasebeta

← #26109824

Subgroups — #26109824

Order 12032.

530 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243376C211yesmaximal, characteristic
2#20241706C211yesmaximal, characteristic
3#20241267C212yesmaximal, complemented
4#20241255C212yesmaximal, complemented
5C47×#2349C211yesmaximal, characteristic
6C2×#13093939—21no—
7C2×C22⋊(C47⋊C8)C2212yes—
8#15688983C2212yes—
9#15688890—21no—
10#15688849—21no—
11#15688847—21no—
12C2×C4×D4×C47—21no—
13C2×C4×D4×C47C2211yescharacteristic
14C47×#389—21no—
15C47×#385—21no—
16C47×#385—21no—
17C47×#382C411yescharacteristic, complemented
18C47×#380C411yescharacteristic, complemented
19C47×#380C2211yescharacteristic
20C4×C4⋊C4×C47C411yescharacteristic, complemented
21C2×#95×C47C411yescharacteristic, complemented
22C2×#95×C47C2211yescharacteristic
23C22×C47⋊C8—22no—
24C2×C4⋊Dic47—22no—
25C2×C22⋊Dic47—22no—
26#13093939—42no—
27C22⋊(C47⋊C8)—22no—
28C22⋊(C47⋊C8)—22no—
29C47⋊#95—22no—
30C22×D4×C47D411yescharacteristic
31C23×C4×C47—21no—
32C23×C4×C47—21no—
33C23×C4×C47C2×C411yescharacteristic
34C23×C4×C47C2311yescharacteristic
35C4×D4×C47—22no—
36C4×D4×C47—22no—
37C4×D4×C47—42no—
38C4×D4×C47—42no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47D411yescharacteristic
47C2×C22⋊C4×C47D411yescharacteristic
48C2×C42×C47—21no—
49C2×C42×C47C2×C411yescharacteristic
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47C2×C411yescharacteristic
54#95×C47C2×C411yescharacteristic
55#95×C47C2×C411yescharacteristic
56#95×C47C2×C411yescharacteristic
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—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—42no—
70C22×C4×C47—42no—
71C22×C4×C47—42no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—81no—
75C22×C4×C47—81no—
76C22×C4×C47—81no—
77C22×C4×C47—81no—
78C22×C4×C47C22⋊C411yescharacteristic
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22×C411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47#4112yes—
84C22×C4×C47#4112yes—
85C22×Dic47—42no—
86C4⋊C4×C47—22no—
87C4⋊C4×C47—42no—
88C4⋊C4×C47—42no—
89C4⋊C4×C47—81no—
90C4⋊C4×C47—81no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—42no—
94C22⋊C4×C47—41no—
95C22⋊C4×C47—41no—
96C42×C47—21no—
97C42×C47—21no—
98C42×C47—42no—
99C22⋊Dic47—42no—
100C22⋊Dic47—42no—
101C4⋊Dic47—82no—
102C2×C47⋊C8—42no—
103C2×C47⋊C8—82no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—41no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47—41no—
110C23×C47#10212yes—
111C23×C47C2×C22⋊C411yescharacteristic
112C23×C47#12312yes—
113C23×C47C2×D811yescharacteristic
114C23×C47C2×SD1611yescharacteristic
115C23×C47#13712yes—
116D4×C47—24no—
117D4×C47—24no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47—82no—
143C2×C4×C47—82no—
144C2×C4×C47—84no—
145C2×C4×C47#10212yes—
146C2×C4×C47#11711yescharacteristic
147C2×C4×C47#11711yescharacteristic
148C2×C4×C47#12312yes—
149C2×Dic47—82no—
150C2×Dic47—82no—
151C2×Dic47—82no—
152C47⋊C8—82no—
153#8760—471nomaximal, Sylow
154C22×C47—22no—
155C22×C47—21no—
156C22×C47—22no—
157C22×C47—21no—
158C22×C47—22no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—42no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47#38111yescharacteristic
167C22×C47C2×#10211yescharacteristic
168C22×C47#41911yescharacteristic
169C22×C47#48012yes—
170C22×C47#48312yes—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—42no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—81no—
179C4×C47—81no—
180C4×C47—81no—
181Dic47—162no—
182#2349D4711yescharacteristic
183#1799—471no—
184#1459—471no—
185#1294—472no—
186#1289—472no—
187C2×C47—22no—
188C2×C47—21no—
189C2×C47—21no—
190C2×C47—22no—
191C2×C47—42no—
192C2×C47#182311yescharacteristic
193C2×C47#182711yescharacteristic
194C2×C47#182811yescharacteristic
195C2×C4×D4—21no—
196C2×C4×D4C2×D4711yescharacteristic
197C2×#99—941no—
198C2×C22⋊C8—472no—
199#389—21no—
200#385—21no—
201#385—21no—
202#382Dic4711yescharacteristic, complemented
203#380—472no—
204#380Dic4711yescharacteristic, complemented
205#380C2×D4711yescharacteristic
206C4×C4⋊C4Dic4711yescharacteristic, complemented
207C2×#95Dic4711yescharacteristic, complemented
208C2×#95C2×D4711yescharacteristic
209#342—941no—
210#324—941no—
211#323—941no—
212C47#876011yescharacteristic, complemented, Sylow
213C22×D4C22⋊D4711yescharacteristic
214C23×C4—21no—
215C23×C4—21no—
216C23×C4C2×Dic4711yescharacteristic
217C23×C4C22×D4711yescharacteristic
218C22×C8—942no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—42no—
222C4×D4—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—942no—
228C2×C4⋊C4C22⋊D4711yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—942no—
232C2×C22⋊C4C22⋊D4711yescharacteristic
233C2×C22⋊C4C22⋊D4711yescharacteristic
234C2×C42—21no—
235C2×C42C2×Dic4711yescharacteristic
236#99—1882no—
237C22⋊C8—942no—
238C22⋊C8—942no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—942no—
243#95C2×Dic4711yescharacteristic
244#95C2×Dic4711yescharacteristic
245#95C2×Dic4711yescharacteristic
246#95C2×Dic4711yescharacteristic
247C24C22⋊Dic4711yescharacteristic
248C24C2×C22⋊D4711yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4#1062533412yes—
252C2×D4#1062533512yes—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—1882no—
269C22×C4C22⋊Dic4711yescharacteristic
270C22×C4C22⋊Dic4711yescharacteristic
271C22×C4C22⋊Dic4711yescharacteristic
272C22×C4#1062535012yes—
273C22×C4#1062535012yes—
274C22×C4C22×Dic4711yescharacteristic
275C22×C4C2×C22⋊D4711yescharacteristic
276C2×C8—3762no—
277C2×C8—1882no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C4⋊C4—3762no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—1882no—
290C22⋊C4—1882no—
291C42—21no—
292C42—21no—
293C42—42no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#1309394512yes—
301C23C2×C22⋊Dic4711yescharacteristic
302C23#1309400712yes—
303C23C2×#1062533411yescharacteristic
304C23C2×#1062533511yescharacteristic
305C23#1309405512yes—
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—84no—
335C2×C4—3762no—
336C2×C4—3762no—
337C2×C4—3762no—
338C2×C4#1309394512yes—
339C2×C4#1309398311yescharacteristic
340C2×C4#1309398311yescharacteristic
341C2×C4#1309400712yes—
342C8—3762no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22#1568898611yescharacteristic
356C22C2×#1309394511yescharacteristic
357C22#1568913211yescharacteristic
358C22#1568943612yes—
359C22#1568945312yes—
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—7522no—
371C2—21no—
372C2—22no—
373C2—21no—
374C2—22no—
375C2—42no—
376C2#2024347411yescharacteristic
377C2#2024349211yescharacteristic
378C2#2024349611yescharacteristic
subgroupG/H
centerC22#15688986
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2349C2
socleC22×C47#381
prime radicalC22×D4×C47D4
cosocleC23×C4×C47C23
hypercenter#2349D47
hypocenterC47#8760
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #20241267C2semidirect
4. #20241255C2semidirect
17. C47×#382C4semidirect
18. C47×#380C4semidirect
20. C4×C4⋊C4×C47C4semidirect
21. C2×#95×C47C4semidirect
202. #382Dic47semidirect
204. #380Dic47semidirect
206. C4×C4⋊C4Dic47semidirect
207. C2×#95Dic47semidirect
212. C47#8760semidirect

Maximal subgroups

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

subgroupindex
#202433762
#202417062
#202412672
#202412552
C47×#23492
#876047