Finite Group Databasebeta

← #26132500

Subgroups — #26132500

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#405×D47C211yesmaximal, characteristic
2#20244998C211yesmaximal, characteristic
3C2×(C2×D47)⋊C16C211yesmaximal, characteristic
4#20241478C211yesmaximal, characteristic, complemented
5#20241477C211yesmaximal, characteristic, complemented
6#20241476C211yesmaximal, characteristic, complemented
7C47×#1379C211yesmaximal, characteristic, complemented
8C2×M16×D47C411yescharacteristic
9C22×C8×D47C2211yescharacteristic
10#117×D47C411yescharacteristic
11C2×#13093964C2211yescharacteristic
12C22×C47⋊C16C2211yescharacteristic
13#15689081C411yescharacteristic
14#15689080—21no—
15#15689079C411yescharacteristic
16#15689078C2211yescharacteristic
17#15689077—21no—
18#97×D47—21no—
19C4×C8×D47—21no—
20(C2×D47)⋊C16—21no—
21(C2×D47)⋊C16—21no—
22(C2×D47)⋊C16—21no—
23(C2×D47)⋊C16—21no—
24C2×M32×C47C2211yescharacteristic
25C22×C16×C47C2211yescharacteristic
26C47×#405C2211yescharacteristic
27C22×C4×D47C2×C411yescharacteristic
28C2×#10625329C2×C411yescharacteristic
29C2×#10625324—21no—
30M16×D47—22no—
31M16×D47—22no—
32C22×C47⋊C8C2×C411yescharacteristic
33C2×C8×D47—21no—
34C2×C8×D47—21no—
35C2×C8×D47—21no—
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47D411yescharacteristic
39C2×C8×D47D411yescharacteristic
40C2×C8×D47D411yescharacteristic
41C2×C8×D47D411yescharacteristic
42#13093983C2×C411yescharacteristic
43#13093982C811yescharacteristic
44#13093982C811yescharacteristic
45#13093981—21no—
46#13093980—21no—
47C4⋊C4×D47C811yescharacteristic
48C4⋊C4×D47C811yescharacteristic
49C22⋊C4×D47—21no—
50C42×D47—21no—
51#13093964—21no—
52#13093964—21no—
53C2×C47⋊C16—21no—
54C2×C47⋊C16—21no—
55C2×C47⋊C16—21no—
56C2×C47⋊C16—21no—
57#13093935—21no—
58#13093934—21no—
59#13093934—21no—
60C4×C47⋊C8—21no—
61C8×Dic47—21no—
62C8×Dic47—21no—
63C2×M16×C47C2×C411yescharacteristic
64C22×C8×C47C2311yescharacteristic
65#117×C47C2×C411yescharacteristic
66M32×C47—21no—
67M32×C47—21no—
68C2×C16×C47—21no—
69C2×C16×C47—21no—
70C2×C16×C47—21no—
71C2×C16×C47—21no—
72#97×C47—21no—
73C4×C8×C47—21no—
74C23×D47M1611yescharacteristic
75C22×C4×C47C22×C411yescharacteristic
76C22×Dic47M1611yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47C22⋊C411yescharacteristic
84C2×C4×D47C22⋊C411yescharacteristic
85C2×C4×D47C2×C811yescharacteristic
86C2×C4×D47C2×C811yescharacteristic
87M16×C47—21no—
88M16×C47M1612yes—
89C2×C8×C47—21no—
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C2×C8×C47#4111yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C4⋊C4×C47C2×C811yescharacteristic
97C4⋊C4×C47C2×C811yescharacteristic
98C22⋊C4×C47—21no—
99C42×C47—21no—
100C22⋊Dic47—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47C2×C811yescharacteristic
104C4⋊Dic47C2×C811yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108C4×Dic47—21no—
109C4×Dic47—21no—
110#10625329—21no—
111#10625329M1612yes—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—21no—
115C2×C47⋊C8C22⋊C411yescharacteristic
116C2×C47⋊C8C22⋊C411yescharacteristic
117#10625324—24no—
118C8×D47—24no—
119C8×D47—21no—
120C8×D47—21no—
121C8×D47—21no—
122C8×D47—21no—
123C8×D47—21no—
124C8×D47—21no—
125C8×D47—21no—
126C8×D47—21no—
127C16×C47—41no—
128C16×C47—41no—
129C47⋊C16—41no—
130C47⋊C16—41no—
131C23×C47C2×M1611yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—22no—
135C22×D47—41no—
136C22×D47C22⋊C811yescharacteristic
137C22×D47C22⋊C811yescharacteristic
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47C2×C22⋊C411yescharacteristic
141C2×C4×C47#11711yescharacteristic
142C2×C4×C47#11711yescharacteristic
143C2×C4×C47C22×C811yescharacteristic
144C2×C4×C47C2×M1611yescharacteristic
145C2×C4×C47C2×M1611yescharacteristic
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47C22⋊C811yescharacteristic
151C2×Dic47C22⋊C811yescharacteristic
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—42no—
161C4×D47—42no—
162C8×C47—22no—
163C8×C47#12311yescharacteristic
164C8×C47#12311yescharacteristic
165C8×C47#12311yescharacteristic
166C8×C47#12311yescharacteristic
167C47⋊C8—21no—
168C47⋊C8—21no—
169C47⋊C8—22no—
170#12848—471nomaximal, Sylow
171C22×C47—21no—
172C22×C47—21no—
173C22×C47C2×C22⋊C811yescharacteristic
174C22×C47#43211yescharacteristic
175C22×C47#43211yescharacteristic
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—42no—
182C2×D47—42no—
183C2×D47#35012yes—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47#38111yescharacteristic
187C4×C47#40711yescharacteristic
188C4×C47#43111yescharacteristic
189C4×C47#43111yescharacteristic
190Dic47—21no—
191Dic47—21no—
192Dic47—41no—
193Dic47—41no—
194C2×#405—471no—
195#2112—471no—
196C2×C22⋊C16—471no—
197#1379—471no—
198#1379—471no—
199#1379—471no—
200#1379D4711yescharacteristic, complemented
201C2×C47—21no—
202C2×C47—21no—
203C2×C47#181711yescharacteristic
204C2×C47C2×#35011yescharacteristic
205C2×C47#211711yescharacteristic
206D47—22no—
207D47—41no—
208C22×M16—471no—
209C23×C8—471no—
210C2×#117—471no—
211C2×M32—471no—
212C2×M32C2×D4711yescharacteristic
213C22×C16—471no—
214C22×C16C2×D4711yescharacteristic
215#405—471no—
216#405—471no—
217#405—471no—
218#405—941no—
219#405—941no—
220#405C2×D4711yescharacteristic
221C2×#97—941no—
222C2×C4×C8—941no—
223C22⋊C16—941no—
224C22⋊C16—941no—
225C22⋊C16—941no—
226C22⋊C16—941no—
227C47#1284811yescharacteristic, complemented, Sylow
228C23×C4—471no—
229C2×M16—471no—
230C2×M16—941no—
231C2×M16—942no—
232C2×M16—942no—
233C2×M16C4×D4711yescharacteristic
234C22×C8—471no—
235C22×C8—471no—
236C22×C8—471no—
237C22×C8—471no—
238C22×C8—471no—
239C22×C8—941no—
240C22×C8—941no—
241C22×C8—941no—
242C22×C8—941no—
243C22×C8—941no—
244C22×C8C22×D4711yescharacteristic
245#117—471no—
246#117—471no—
247#117—471no—
248#117—941no—
249#117—941no—
250#117C4×D4711yescharacteristic
251C2×C4⋊C4—471no—
252C2×C4⋊C4—471no—
253C2×C22⋊C4—941no—
254C2×C42—941no—
255M32—21no—
256M32—21no—
257M32—941no—
258M32—941no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—21no—
263C2×C16—941no—
264C2×C16—941no—
265C2×C16—941no—
266C2×C16—941no—
267#97—21no—
268#97—941no—
269#97—941no—
270#97—941no—
271C4×C8—21no—
272C4×C8—941no—
273C4×C8—941no—
274C4×C8—941no—
275C24—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4C2×C4×D4711yescharacteristic
288M16—21no—
289M16—472no—
290M16—944no—
291M16—941no—
292M16#1062532412yes—
293C2×C8—21no—
294C2×C8—471no—
295C2×C8—471no—
296C2×C8—944no—
297C2×C8—941no—
298C2×C8—941no—
299C2×C8—941no—
300C2×C8—941no—
301C2×C8—941no—
302C2×C8—941no—
303C2×C8—941no—
304C2×C8—941no—
305C2×C8—941no—
306C2×C8—941no—
307C2×C8—941no—
308C2×C8#1062535011yescharacteristic
309C2×C8#1062535011yescharacteristic
310C2×C8D4×D4711yescharacteristic
311C2×C8D4×D4711yescharacteristic
312C2×C8#1062535211yescharacteristic
313C2×C8#1062535411yescharacteristic
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4C8×D4711yescharacteristic
319C4⋊C4C8×D4711yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C42—21no—
325C42—941no—
326C42—941no—
327C42—941no—
328C16—41no—
329C16—41no—
330C16—1881no—
331C16—1881no—
332C23—471no—
333C23—471no—
334C23—942no—
335C23—941no—
336C23—941no—
337C23—1881no—
338C23M16×D4711yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—471no—
342C2×C4—471no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4C22⋊C4×D4711yescharacteristic
358C2×C4#1309398111yescharacteristic
359C2×C4#1309398211yescharacteristic
360C2×C4C2×C8×D4711yescharacteristic
361C2×C4M16×D4711yescharacteristic
362C2×C4C2×#1062532411yescharacteristic
363C8—22no—
364C8—941no—
365C8—941no—
366C8—942no—
367C8#1309400611yescharacteristic
368C8#1309400611yescharacteristic
369C8#1309400911yescharacteristic
370C8#1309400911yescharacteristic
371C22—21no—
372C22—21no—
373C22—472no—
374C22—941no—
375C22—941no—
376C22—941no—
377C22—941no—
378C22—941no—
379C22—1882no—
380C22—1882no—
381C22C22⋊C8×D4711yescharacteristic
382C22#1568917811yescharacteristic
383C22#1568917911yescharacteristic
384C4—41no—
385C4—41no—
386C4—941no—
387C4—941no—
388C4—1881no—
389C4—1881no—
390C4#1568898511yescharacteristic
391C4#1568908511yescharacteristic
392C4#1568917411yescharacteristic
393C4#1568917511yescharacteristic
394C2—21no—
395C2—21no—
396C2—942no—
397C2—1881no—
398C2#2024345511yescharacteristic
399C2#350×D4711yescharacteristic
400C2#2024501411yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1379C2
socleC22×C47C2×C22⋊C8
prime radicalC23×D47M16
cosocleC22×C8×C47C23
hypercenter#1379D47
hypocenterC47#12848
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
4. #20241478C2semidirect
5. #20241477C2semidirect
6. #20241476C2semidirect
7. C47×#1379C2semidirect
200. #1379D47semidirect
227. C47#12848semidirect

Maximal subgroups

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

subgroupindex
#405×D472
#202449982
C2×(C2×D47)⋊C162
#202414782
#202414772
#202414762
C47×#13792
#1284847