Finite Group Databasebeta

← #26133220

Subgroups — #26133220

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689360C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×C8×D47C2211yescharacteristic
10C2×#13093999—21no—
11C2×#13093982—21no—
12C22×C47⋊C16C2211yescharacteristic
13#15689360—22no—
14#15689360C414yescomplemented
15#15689160—22no—
16#15689160—22no—
17C2×#13093958C2211yescharacteristic
18C2×#13093955—21no—
19C2×#13093944—21no—
20#15688925—22no—
21#15688923—22no—
22(C2×D47)⋊C16—22no—
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C22×D188—21no—
27C22×D188—41no—
28C22×C4×D47D411yescharacteristic
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376C2×C412yes—
35C22×C47⋊C8D411yescharacteristic
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47—21no—
39C2×C8×D47—21no—
40C2×C8×D47C2×C412yes—
41C2×C8×D47D412yes—
42#13093999—24no—
43#13093999—42no—
44#13093982—24no—
45#13093982—42no—
46C2×C4⋊Dic47—21no—
47C2×(C2×D47)⋊C4—41no—
48C2×(C2×D47)⋊C4—41no—
49C2×C4×Dic47—41no—
50C2×C47⋊C16—21no—
51C2×C47⋊C16—21no—
52C2×C47⋊C16—21no—
53#13093958—21no—
54#13093958D412yescomplemented
55#13093955—24no—
56#13093944—24no—
57C22×C8×C47C2311yescharacteristic
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63#107×C47—21no—
64#107×C47—21no—
65#107×C47C2×C412yes—
66#107×C47D412yescomplemented
67C23×D47—41no—
68C23×D47D811yescharacteristic
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47C2×D411yescharacteristic
72C22×Dic47—41no—
73C22×Dic47D811yescharacteristic
74C2×D188—22no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—44no—
80C2×D188—41no—
81C2×D188—82no—
82C2×D188—82no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47C22⋊C412yes—
88C2×C4×D47SD1612yes—
89C2×C8×C47C22×C411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C2×C8×C47#4111yescharacteristic
95C4⋊C4×C47—22no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99(C2×D47)⋊C4—44no—
100(C2×D47)⋊C4—44no—
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103C4×Dic47—44no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8C22⋊C412yes—
107D376—22no—
108D376—22no—
109D376—41no—
110D376—41no—
111C8×D47—22no—
112C8×D47—22no—
113C8×D47—22no—
114C8×D47—22no—
115C16×C47—41no—
116C47⋊C16—41no—
117C23×C47C2×D811yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—42no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47—81no—
128C22×D47—81no—
129C22×D47—81no—
130C22×D47—81no—
131C22×D47#10212yes—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47C2×C22⋊C411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12311yescharacteristic
141C2×C4×C47C2×SD1611yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47#13711yescharacteristic
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—42no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149C2×Dic47#10212yes—
150D188—42no—
151D188—42no—
152D188—88no—
153D188—81no—
154D188—81no—
155C4×D47—22no—
156C4×D47—22no—
157C4×D47—22no—
158C4×D47—22no—
159C8×C47C4×D411yescharacteristic
160C8×C47C4×D411yescharacteristic
161C8×C47#12111yescharacteristic
162C8×C47#12111yescharacteristic
163C47⋊C8—22no—
164#12992—471nomaximal, Sylow
165C22×C47C2×#10211yescharacteristic
166C22×C47#44711yescharacteristic
167C22×C47#48011yescharacteristic
168C22×C47#50811yescharacteristic
169C22×C47#50811yescharacteristic
170C22×C47#50911yescharacteristic
171C22×C47#50911yescharacteristic
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—22no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—82no—
182C2×D47—161no—
183C2×D47—161no—
184C2×D47—161no—
185C2×D47—161no—
186C4×C47—82no—
187C4×C47—82no—
188C4×C47#38611yescharacteristic
189C4×C47#41711yescharacteristic
190C4×C47#44811yescharacteristic
191C4×C47#48111yescharacteristic
192Dic47—22no—
193Dic47—82no—
194C2×#466—471no—
195C2×#427—471no—
196C2×#357—471no—
197C2×#357—471no—
198C2×C22⋊C16—471no—
199#1380—471no—
200#1380D4711yescharacteristic, complemented
201C2×C47#187411yescharacteristic
202C2×C47#213811yescharacteristic
203C2×C47#214011yescharacteristic
204C2×C47#218611yescharacteristic
205C2×C47#218611yescharacteristic
206C2×C47#223411yescharacteristic
207C2×C47#223411yescharacteristic
208D47—42no—
209D47—162no—
210C22×D8—471no—
211C23×C8—471no—
212C2×#121—941no—
213C2×#117—941no—
214C22×C16—471no—
215C22×C16C2×D4711yescharacteristic
216#466—474no—
217#466—942no—
218#427—942no—
219#427—942no—
220C2×#107—471no—
221C2×#107C2×D4711yescharacteristic
222C2×#107C2×D4711yescharacteristic
223C2×#106—941no—
224C2×#102—941no—
225#357—942no—
226#357—942no—
227C22⋊C16—942no—
228C47#1299211yescharacteristic, complemented, Sylow
229C22×D4—941no—
230C22×D4—1881no—
231C23×C4—471no—
232C2×D8—472no—
233C2×D8—941no—
234C2×D8—941no—
235C2×D8—941no—
236C2×D8—941no—
237C2×D8—941no—
238C22×C8—471no—
239C22×C8—472no—
240C22×C8—472no—
241C22×C8—941no—
242C22×C8—941no—
243C22×C8—941no—
244C22×C8—941no—
245C22×C8C22×D4711yescharacteristic
246#121—944no—
247#121—1882no—
248#117—944no—
249#117—1882no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—941no—
253C2×C22⋊C4—1881no—
254C2×C22⋊C4—1881no—
255C2×C42—1881no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—941no—
260C2×C16—941no—
261C2×C16—941no—
262#107—21no—
263#107—21no—
264#107—472no—
265#107—941no—
266#107C4×D4712yes—
267#107D18812yescomplemented
268#106—944no—
269#102—944no—
270C24—471no—
271C24—1881no—
272C2×D4—942no—
273C2×D4—3762no—
274C2×D4—3762no—
275C2×D4—1884no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1881no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—471no—
284C22×C4—472no—
285C22×C4—472no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—1881no—
291C22×C4D4×D4711yescharacteristic
292D8—942no—
293D8—942no—
294D8—1881no—
295D8—1881no—
296C2×C8—472no—
297C2×C8—941no—
298C2×C8—941no—
299C2×C8—942no—
300C2×C8—942no—
301C2×C8—942no—
302C2×C8—942no—
303C2×C8C2×C4×D4711yescharacteristic
304C2×C8C2×D18811yescharacteristic
305C2×C8#1062535011yescharacteristic
306C2×C8D4×D4711yescharacteristic
307C2×C8D4×D4711yescharacteristic
308C2×C8#1062535411yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—942no—
314C4⋊C4—1881no—
315C22⋊C4—1884no—
316C22⋊C4—1884no—
317C42—1884no—
318C16—41no—
319C16—1881no—
320C23—472no—
321C23—941no—
322C23—941no—
323C23—941no—
324C23—941no—
325C23—941no—
326C23—941no—
327C23—3761no—
328C23—3761no—
329C23—3761no—
330C23—3761no—
331C23—3761no—
332C23—3761no—
333C23—1882no—
334C23D8×D4711yescharacteristic
335D4—3768no—
336D4—3761no—
337D4—3761no—
338D4—1882no—
339D4—1882no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—472no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—942no—
350C2×C4—942no—
351C2×C4—942no—
352C2×C4—942no—
353C2×C4—3761no—
354C2×C4—3761no—
355C2×C4—1882no—
356C2×C4C22⋊C4×D4711yescharacteristic
357C2×C4#1309399411yescharacteristic
358C2×C4#1309400911yescharacteristic
359C2×C4SD16×D4711yescharacteristic
360C2×C4#1309405111yescharacteristic
361C2×C4#1309405611yescharacteristic
362C8—942no—
363C8#1309398611yescharacteristic
364C8C4×D18811yescharacteristic
365C8#1309399711yescharacteristic
366C8#1309399911yescharacteristic
367C22—942no—
368C22—942no—
369C22—942no—
370C22—3762no—
371C22—3762no—
372C22—3762no—
373C22—1881no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—7521no—
378C22—7521no—
379C22—7521no—
380C22—7521no—
381C22#102×D4711yescharacteristic
382C22#1568925811yescharacteristic
383C22#1568943811yescharacteristic
384C22#1568955411yescharacteristic
385C22#1568955611yescharacteristic
386C22#1568955711yescharacteristic
387C22#1568956011yescharacteristic
388C4—82no—
389C4—82no—
390C4—942no—
391C4—3762no—
392C4#1568900111yescharacteristic
393C4#1568912311yescharacteristic
394C4#1568926311yescharacteristic
395C4#1568944311yescharacteristic
396C2—1882no—
397C2—7522no—
398C2#2024370411yescharacteristic
399C2#2024509411yescharacteristic
400C2#2024510211yescharacteristic
401C2#2024531211yescharacteristic
402C2#2024531411yescharacteristic
403C2#2024558111yescharacteristic
404C2#2024558211yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC2×#15689360C2
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12992
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#15689160C2semidirect
3. C2×#15688925C2semidirect
4. C2×#15688923C2semidirect
5. C2×(C2×D47)⋊C16C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
14. #15689360C4semidirect
54. #13093958D4semidirect
66. #107×C47D4semidirect
200. #1380D47semidirect
228. C47#12992semidirect
267. #107D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156893602
C2×#156891602
C2×#156889252
C2×#156889232
C2×(C2×D47)⋊C162
#202414792
C47×#13802
#1299247