Finite Group Databasebeta

← #26272917

Subgroups — #26272917

Order 12032.

1104 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689680C211yesmaximal, characteristic, complemented
2C2×#15689478C212yesmaximal, complemented
3#20251689C211yesmaximal, characteristic
4#20244530C212yesmaximal, complemented
5#20244525C212yesmaximal, complemented
6#20244353C212yesmaximal, complemented
7#20243708C212yesmaximal
8#20243698C212yesmaximal, complemented
9C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
10#15689680—28no—
11C2×#13094024C2212yes—
12C2×#13094016C2212yes—
13C2×#13094012C2211yescharacteristic
14C2×#13094003—22no—
15C2×#13094003C2211yescharacteristic
16C2×#13093998C2211yescharacteristic
17C2×C4×Dic94—22no—
18C2×#13093983C2212yes—
19#15689478—28no—
20C2×#13093949C2214yes—
21C2×#13093946C2214yes—
22#15689029C2211yescharacteristic
23#15689025C2211yescharacteristic
24#15689014—22no—
25#15689002—22no—
26#15688989C2211yescharacteristic
27#15688886C2214yes—
28#15688886C2214yes—
29C22×C42×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2212yes—
31C2×C4×C8×C47C2212yes—
32C47×#336C2212yes—
33C22×Dic94—22no—
34C22×Dic94C2311yescharacteristic
35C22×D188C2311yescharacteristic
36C22×C22⋊D47—21no—
37#13094024—28no—
38#13094016—24no—
39#13094016D418yescomplemented
40#13094012—24no—
41#13094003—216no—
42#13094003—24no—
43#13093998—24no—
44C4×Dic94—216no—
45#13093983—28no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47C2311yescharacteristic
48C2×C4⋊Dic47C2311yescharacteristic
49C2×C4⋊Dic47C2314yes—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—21no—
52C2×C22⋊Dic47—22no—
53C2×C22⋊Dic47—21no—
54C2×(C2×D47)⋊C4—22no—
55C2×(C2×D47)⋊C4—22no—
56C2×(C2×D47)⋊C4—21no—
57C2×C4×Dic47—22no—
58#13093949—28no—
59#13093946—28no—
60C47⋊#95—22no—
61C47⋊#95—22no—
62C23×C4×C47D412yes—
63C23×C4×C47C2311yescharacteristic
64C22×C8×C47C2314yes—
65C2×C42×C47—24no—
66C2×C42×C47D412yes—
67C2×C42×C47C2311yescharacteristic
68C2×C42×C47C2311yescharacteristic
69C22⋊C8×C47—24no—
70C4×C8×C47—24no—
71C24×C47C2×D411yescharacteristic
72C23×D47—21no—
73C22×C4×C47—22no—
74C22×C4×C47—22no—
75C22×C4×C47—24no—
76C22×C4×C47—24no—
77C22×C4×C47—42no—
78C22×C4×C47C2×D412yes—
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47C2×D412yes—
81C22×C4×C47#4114yes—
82C22×C4×C47C2411yescharacteristic
83C2×C22⋊D47—44no—
84C2×C22⋊D47—42no—
85C22×Dic47—24no—
86C22×Dic47—21no—
87C22×Dic47—21no—
88C22×Dic47—21no—
89C2×D188—22no—
90C2×D188—22no—
91C2×D188—22no—
92C2×Dic94—28no—
93C2×Dic94—22no—
94C2×Dic94—22no—
95C2×Dic94—22no—
96C2×Dic94—44no—
97C2×Dic94—44no—
98C2×C8×C47—24no—
99C2×C8×C47—24no—
100C2×C8×C47—24no—
101C42×C47—24no—
102C42×C47—22no—
103C42×C47C2×D414yes—
104C22⋊Dic47—28no—
105C22⋊Dic47—42no—
106(C2×D47)⋊C4—44no—
107(C2×D47)⋊C4—42no—
108(C2×D47)⋊C4—44no—
109C4⋊Dic47—28no—
110C4⋊Dic47—24no—
111C4⋊Dic47—22no—
112C4⋊Dic47—22no—
113C4⋊Dic47C2×D418yes—
114Dic47⋊C4—216no—
115Dic47⋊C4—42no—
116C4×Dic47—28no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—22no—
120C23×C47—22no—
121C23×C47#12412yes—
122C23×C47C22×D411yescharacteristic
123C22×D47—41no—
124C22×D47—41no—
125C22×D47—41no—
126C22×D47—42no—
127C22×D47—42no—
128C2×C4×C47—21no—
129C2×C4×C47—22no—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—28no—
135C2×C4×C47—48no—
136C2×C4×C47#12014yes—
137C2×C4×C47#12412yes—
138C2×C4×C47#13514yes—
139C2×C4×C47C22×D412yes—
140C2×C4×C47C2×#4112yes—
141C2×C4×C472−1+412yes—
142C22⋊D47—84no—
143C2×Dic47—28no—
144C2×Dic47—44no—
145C2×Dic47—44no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—42no—
152C2×Dic47—42no—
153D188—44no—
154Dic94—416no—
155Dic94—44no—
156C8×C47—44no—
157#25906—471nomaximal, Sylow
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—22no—
161C22×C47—42no—
162C22×C47—42no—
163C22×C47C2×#12011yescharacteristic
164C22×C47C2×#12411yescharacteristic
165C22×C47#53611yescharacteristic
166C22×C47C2×#13512yes—
167C22×C47#57512yes—
168C2×D47—81no—
169C2×D47—81no—
170C2×D47—81no—
171C2×D47—82no—
172C2×D47—82no—
173C4×C47—22no—
174C4×C47—24no—
175C4×C47—24no—
176C4×C47#54814yes—
177Dic47—48no—
178Dic47—81no—
179Dic47—81no—
180Dic47—81no—
181C2×#533—471no—
182C2×#488—472no—
183#2850—471no—
184#2024—472no—
185#2023—472no—
186#1991—472no—
187#1875—472no—
188#1873—472no—
189C4×C22⋊C8D4711yescharacteristic, complemented
190C2×C47—42no—
191C2×C47#243611yescharacteristic
192C2×C47#300212yes—
193C2×C47#313111yescharacteristic
194C2×C47#314011yescharacteristic
195C2×C47#323312yes—
196D47—161no—
197#533—948no—
198C2×C4⋊Q8—472no—
199C2×#125—472no—
200C2×#124—471no—
201C2×C22⋊Q8—471no—
202C2×C22⋊Q8—942no—
203C2×#121—471no—
204C2×C4×Q8—942no—
205C2×#117—472no—
206C22×C42C2×D4711yescharacteristic
207#488—948no—
208C2×#103—474no—
209C2×#102—474no—
210C2×C22⋊C8C2×D4712yes—
211C2×C4×C8C2×D4712yes—
212#391—471no—
213#390—471no—
214#388—942no—
215#386—942no—
216#382—471no—
217#340—474no—
218#340—474no—
219#336C2×D4712yes—
220C47#2590611yescharacteristic, complemented, Sylow
221C22×Q8—471no—
222C22×Q8—942no—
223C22×D4—471no—
224C22×D4—941no—
225C23×C4D18812yes—
226C23×C4C22×D4711yescharacteristic
227C22×C8C22×D4714yes—
228C4⋊Q8—948no—
229#125—478no—
230#125—944no—
231#124—944no—
232C22⋊Q8—9416no—
233C22⋊Q8—944no—
234#121—944no—
235C4×Q8—9416no—
236#117—948no—
237C2×C4⋊C4—474no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—471no—
240C2×C4⋊C4—944no—
241C2×C4⋊C4—942no—
242C2×C4⋊C4—941no—
243C2×C22⋊C4—942no—
244C2×C22⋊C4—941no—
245C2×C22⋊C4—941no—
246C2×C22⋊C4—942no—
247C2×C22⋊C4—942no—
248C2×C42—24no—
249C2×C42—942no—
250C2×C42D18812yes—
251C2×C42C22×D4711yescharacteristic
252C2×C42C22×D4711yescharacteristic
253#103—948no—
254#102—948no—
255C22⋊C8—24no—
256C4×C8—24no—
257#95—942no—
258#95—942no—
259C24—941no—
260C24C2×D18811yescharacteristic
261C2×Q8—948no—
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—942no—
265C2×Q8—1884no—
266C2×Q8—1884no—
267C2×D4—942no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—1884no—
271C2×D4—1882no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—42no—
277C22×C4—944no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4C2×D18812yes—
282C22×C4C2×D18811yescharacteristic
283C22×C4C2×D18812yes—
284C22×C4#1062535014yes—
285C22×C4C23×D4711yescharacteristic
286C2×C8—24no—
287C2×C8—24no—
288C2×C8—24no—
289C4⋊C4—478no—
290C4⋊C4—948no—
291C4⋊C4—9416no—
292C4⋊C4—944no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—1882no—
296C22⋊C4—948no—
297C22⋊C4—1882no—
298C22⋊C4—1884no—
299C22⋊C4—1882no—
300C22⋊C4—1884no—
301C42—24no—
302C42—22no—
303C42—948no—
304C42D4×D4714yes—
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—1881no—
310C23—1881no—
311C23—1882no—
312C23—1882no—
313C23—1881no—
314C23#1309401212yes—
315C23C22×D18811yescharacteristic
316Q8—18816no—
317Q8—1884no—
318D4—3764no—
319D4—1884no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—28no—
327C2×C4—48no—
328C2×C4—948no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4—1881no—
336C2×C4—1884no—
337C2×C4—1884no—
338C2×C4#1309399414yes—
339C2×C4#1309401212yes—
340C2×C4#1309404614yes—
341C2×C4C2×D4×D4712yes—
342C2×C4C2×#1062535012yes—
343C2×C4#1309407112yes—
344C8—44no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—3761no—
351C22—3761no—
352C22—3761no—
353C22—3762no—
354C22—3762no—
355C22C2×#1309399411yescharacteristic
356C22C2×#1309401211yescharacteristic
357C22#1568969911yescharacteristic
358C22C2×#1309404612yes—
359C22#1568992312yes—
360C4—22no—
361C4—24no—
362C4—24no—
363C4—3761no—
364C4—3761no—
365C4—3761no—
366C4—1888no—
367C4#1568978214yes—
368C2—42no—
369C2—7521no—
370C2#2024704611yescharacteristic
371C2#2025261012yes—
372C2#2025371111yescharacteristic
373C2#2025377511yescharacteristic
374C2#2025456912yes—
subgroupG/H
centerC23C22×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×C22⋊C8×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC4×C22⋊C8D47
hypocenterC47#25906
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#15689680C2semidirect
2. C2×#15689478C2semidirect
4. #20244530C2semidirect
5. #20244525C2semidirect
6. #20244353C2semidirect
8. #20243698C2semidirect
9. C4×C22⋊C8×C47C2semidirect
39. #13094016D4semidirect
189. C4×C22⋊C8D47semidirect
220. C47#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#156896802
C2×#156894782
#202516892
#202445302
#202445252
#202443532
#202437082
#202436982
C4×C22⋊C8×C472
#2590647