Finite Group Databasebeta

← #26133218

Subgroups — #26133218

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×#15689356C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093995—21no—
10C2×#13093982—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689356—22no—
13#15689356C414yescomplemented
14#15689160—22no—
15#15689160—22no—
16C2×#13093958C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093955—21no—
19C2×#13093945—21no—
20#15688924—22no—
21(C2×D47)⋊C16—22no—
22C22×D8×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#357—22no—
26C22×C22⋊D47—41no—
27C22×C4×D47D411yescharacteristic
28C22×C47⋊C8D411yescharacteristic
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47C2×C412yes—
34C2×C8×D47D412yes—
35#13093995—24no—
36#13093995—42no—
37#13093982—24no—
38#13093982—42no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C22⋊Dic47—41no—
42C2×(C2×D47)⋊C4—41no—
43C2×C4×Dic47—41no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47#13093958—21no—
48#13093958—21no—
49#13093958C2×C412yes—
50#13093958D412yescomplemented
51#13093955—24no—
52#13093945—24no—
53C22×D4×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47—21no—
57C2×D8×C47—21no—
58C2×D8×C47—21no—
59C2×D8×C47C2×C412yes—
60C22×C8×C47C2311yescharacteristic
61C2×C4⋊C4×C47—21no—
62C2×C16×C47—21no—
63C2×C16×C47—21no—
64C2×C16×C47—21no—
65#107×C47—21no—
66#107×C47D412yescomplemented
67C24×C47—41no—
68C23×D47D811yescharacteristic
69C2×D4×C47—22no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C2×D4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47C2×D411yescharacteristic
77C2×C22⋊D47—44no—
78C2×C22⋊D47—82no—
79C2×C22⋊D47—82no—
80C22×Dic47—41no—
81C22×Dic47—41no—
82C22×Dic47D811yescharacteristic
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47C22⋊C412yes—
88C2×C4×D47SD1612yes—
89D8×C47—22no—
90D8×C47—22no—
91D8×C47—41no—
92D8×C47—41no—
93C2×C8×C47C22×C411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C4⋊C4×C47—22no—
100C4⋊C4×C47—41no—
101C22⋊Dic47—44no—
102(C2×D47)⋊C4—44no—
103C4⋊Dic47—22no—
104C4⋊Dic47—22no—
105C4⋊Dic47—41no—
106C4⋊Dic47—41no—
107C4×Dic47—44no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8C22⋊C412yes—
111C8×D47—22no—
112C8×D47—22no—
113C8×D47—22no—
114C8×D47—22no—
115C16×C47—41no—
116C47⋊C16—41no—
117C23×C47—42no—
118C23×C47—81no—
119C23×C47—81no—
120C23×C47—81no—
121C23×C47—81no—
122C23×C47—81no—
123C23×C47—81no—
124C23×C47C2×D811yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47#10212yes—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—81no—
135D4×C47—81no—
136C2×C4×C47—42no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47C2×C22⋊C411yescharacteristic
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12311yescharacteristic
142C2×C4×C47C2×SD1611yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C47#13711yescharacteristic
145C22⋊D47—88no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150C2×Dic47—81no—
151C2×Dic47—81no—
152C2×Dic47—81no—
153C2×Dic47—81no—
154C2×Dic47#10212yes—
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×C47—82no—
166C22×C47—82no—
167C22×C47—82no—
168C22×C47—161no—
169C22×C47—161no—
170C22×C47—161no—
171C22×C47—161no—
172C22×C47C2×#10211yescharacteristic
173C22×C47#44711yescharacteristic
174C22×C47#48011yescharacteristic
175C22×C47#50811yescharacteristic
176C22×C47#50811yescharacteristic
177C22×C47#50911yescharacteristic
178C22×C47#50911yescharacteristic
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C4×C47—82no—
187C4×C47#38611yescharacteristic
188C4×C47#41711yescharacteristic
189C4×C47#44811yescharacteristic
190C4×C47#48111yescharacteristic
191Dic47—22no—
192Dic47—82no—
193Dic47—82no—
194C2×#466—471no—
195C2×#427—471no—
196C2×#357—471no—
197C2×#357D4711yescharacteristic, complemented
198C2×C22⋊C16—471no—
199#1380—471no—
200#1380—471no—
201C2×C47—162no—
202C2×C47#187411yescharacteristic
203C2×C47#213811yescharacteristic
204C2×C47#214011yescharacteristic
205C2×C47#218611yescharacteristic
206C2×C47#218611yescharacteristic
207C2×C47#223411yescharacteristic
208C2×C47#223411yescharacteristic
209D47—42no—
210C22×D8C2×D4711yescharacteristic
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×#107—471no—
222C2×#107C2×D4711yescharacteristic
223C2×#106—941no—
224C2×#102—941no—
225#357—22no—
226#357—942no—
227C22⋊C16—942no—
228C47#1299211yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—1881no—
231C23×C4—471no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8C4×D4712yes—
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—941no—
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—472no—
264#107—472no—
265#107—941no—
266#107—941no—
267#107C22⋊D4712yescomplemented
268#106—944no—
269#102—944no—
270C24—41no—
271C24—471no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—3762no—
279C2×D4—3762no—
280C2×D4—1884no—
281C22×C4—41no—
282C22×C4—471no—
283C22×C4—472no—
284C22×C4—472no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—1881no—
290C22×C4—1881no—
291C22×C4D4×D4711yescharacteristic
292D8—22no—
293D8—22no—
294D8—41no—
295D8—41no—
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×C8#1062535011yescharacteristic
305C2×C8D4×D4711yescharacteristic
306C2×C8D4×D4711yescharacteristic
307C2×C8#1062535211yescharacteristic
308C2×C8C2×C22⋊D4711yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—942no—
312C4⋊C4—942no—
313C4⋊C4—1881no—
314C4⋊C4—1881no—
315C22⋊C4—1884no—
316C22⋊C4—1884no—
317C42—1884no—
318C16—41no—
319C16—1881no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—472no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23—941no—
334C23D8×D4711yescharacteristic
335D4—42no—
336D4—42no—
337D4—81no—
338D4—81no—
339D4—3768no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—472no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—942no—
350C2×C4—3761no—
351C2×C4—3761no—
352C2×C4—3761no—
353C2×C4—3761no—
354C2×C4—1882no—
355C2×C4—1882no—
356C2×C4C22⋊C4×D4711yescharacteristic
357C2×C4#1309399211yescharacteristic
358C2×C4#1309400611yescharacteristic
359C2×C4SD16×D4711yescharacteristic
360C2×C4#1309404811yescharacteristic
361C2×C4#1309405311yescharacteristic
362C8—942no—
363C8(C22⋊D47)⋊C411yescharacteristic
364C8C4×C22⋊D4711yescharacteristic
365C8#1309399511yescharacteristic
366C8#1309399711yescharacteristic
367C22—82no—
368C22—82no—
369C22—82no—
370C22—161no—
371C22—161no—
372C22—161no—
373C22—161no—
374C22—942no—
375C22—942no—
376C22—942no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22#102×D4711yescharacteristic
382C22#1568925511yescharacteristic
383C22#1568943511yescharacteristic
384C22#1568955211yescharacteristic
385C22#1568955411yescharacteristic
386C22#1568955711yescharacteristic
387C22#1568956011yescharacteristic
388C4—82no—
389C4—942no—
390C4—3762no—
391C4—3762no—
392C4#1568899911yescharacteristic
393C4#1568912111yescharacteristic
394C4#1568926011yescharacteristic
395C4#1568944011yescharacteristic
396C2—162no—
397C2—1882no—
398C2#2024370211yescharacteristic
399C2#2024509211yescharacteristic
400C2#2024510211yescharacteristic
401C2#2024530811yescharacteristic
402C2#2024531011yescharacteristic
403C2#2024557711yescharacteristic
404C2#2024557811yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC2×#15689356C2
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#12992
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#15689160C2semidirect
3. C2×#15688924C2semidirect
4. C2×(C2×D47)⋊C16C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C2×C47×#357C2semidirect
13. #15689356C4semidirect
50. #13093958D4semidirect
66. #107×C47D4semidirect
197. C2×#357D47semidirect
228. C47#12992semidirect
267. #107C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156893562
C2×#156891602
C2×#156889242
C2×(C2×D47)⋊C162
#202414802
#202414792
C2×C47×#3572
#1299247