Finite Group Databasebeta

← #26376329

Subgroups — #26376329

Order 12032.

2446 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093983C211yesmaximal, characteristic
2#20246250C218yesmaximal, complemented
3#20246244C218yesmaximal, complemented
4#20246000C212yesmaximal
5#20245989C214yesmaximal, complemented
6#20245779C214yesmaximal, complemented
7C2×#15688986C211yesmaximal, characteristic
8#20245741C212yesmaximal
9C2×C47×#381C211yesmaximal, characteristic
10C2×#13093983C4116yescomplemented
11C2×#13093983C2214yes—
12C2×#13093983C2214yes—
13C22×C4⋊Dic47C2212yes—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C4×Dic47C2212yes—
18#15689008C22116yescomplemented
19#15689006C22116yescomplemented
20#15688996C2218yes—
21#15688995C2218yes—
22#15688990C2218yescomplemented
23#15688987C2218yescomplemented
24#15688986C2212yes—
25#15688986C2214yes—
26#15688986C2212yes—
27#15688981C2218yes—
28#15688974C2218yescomplemented
29C22⋊C4×Dic47C2218yes—
30C22⋊C4×Dic47C2218yes—
31C4×C22⋊Dic47C2218yes—
32#15688968C2218yescomplemented
33C2×C47⋊#95C2214yes—
34C24×C4×C47C2211yescharacteristic
35C22×C22⋊C4×C47C2212yes—
36C47×#381C2212yes—
37C47×#381C2212yes—
38C47×#381C2214yes—
39C2×#95×C47C2214yes—
40C23×Dic47C2314yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43#13093983C2×C4132yescomplemented
44#13093983C2×C4132yescomplemented
45C2×C4⋊Dic47C2×C4116yescomplemented
46C2×C4⋊Dic47C2314yes—
47C2×C4⋊Dic47C2314yes—
48C2×Dic47⋊C4C23116yes—
49C2×C22⋊Dic47—28no—
50C2×C22⋊Dic47C2×C418yes—
51C2×C22⋊Dic47C2×C418yes—
52C2×C22⋊Dic47C2314yes—
53C2×C22⋊Dic47C2314yes—
54C2×C22⋊Dic47C2312yes—
55C2×C22⋊Dic47C2312yes—
56C2×C22⋊Dic47C2312yes—
57C2×C22⋊Dic47C2312yes—
58C2×C4×Dic47C2×C4116yescomplemented
59C2×C4×Dic47C23116yes—
60C2×C4×Dic47C2314yes—
61C2×C4×Dic47C2314yes—
62C47⋊#95C2318yes—
63C47⋊#95C2318yes—
64C47⋊#95C23116yes—
65C47⋊#95C23116yes—
66C25×C47C2311yescharacteristic
67C23×C4×C47—28no—
68C23×C4×C47C2×C418yes—
69C23×C4×C47C2312yes—
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2312yes—
73C23×C4×C47C2314yes—
74C2×C22⋊C4×C47—28no—
75C2×C22⋊C4×C47C2314yes—
76C2×C22⋊C4×C47C2314yes—
77#95×C47C2318yes—
78#95×C47C2318yes—
79C24×C47—44no—
80C24×C47C22×C414yes—
81C24×C47#4118yes—
82C24×C47C2411yescharacteristic
83C24×C47C2411yescharacteristic
84C24×C47C2411yescharacteristic
85C22×C4×C47—232no—
86C22×C4×C47—24no—
87C22×C4×C47—24no—
88C22×C4×C47—28no—
89C22×C4×C47—28no—
90C22×C4×C47—28no—
91C22×C4×C47—48no—
92C22×C4×C47C22×C414yes—
93C22×C4×C47C22×C414yes—
94C22×C4×C47C22×C418yes—
95C22×C4×C47C22×C418yes—
96C22×C4×C47C2418yes—
97C22×C4×C47C2412yes—
98C22×C4×C47C2412yes—
99C22×Dic47—28no—
100C22×Dic47—44no—
101C22×Dic47—44no—
102C22×Dic47—48no—
103C22×Dic47C22×C418yes—
104C22×Dic47C22×C418yes—
105C22×Dic47C2418yes—
106C22×Dic47C2414yes—
107C22×Dic47C2414yes—
108C22⋊C4×C47—28no—
109C22⋊C4×C47—28no—
110C22⋊Dic47—28no—
111C22⋊Dic47—28no—
112C22⋊Dic47C22×C418yes—
113C22⋊Dic47C22×C418yes—
114C22⋊Dic47C22×C418yes—
115C22⋊Dic47C22×C418yes—
116C4⋊Dic47C22×C4116yes—
117C4⋊Dic47C22×C4116yes—
118Dic47⋊C4—416no—
119C4×Dic47—416no—
120C4×Dic47C22×C4116yes—
121C4×Dic47C22×C4116yes—
122C23×C47—24no—
123C23×C47—24no—
124C23×C47—24no—
125C23×C47—48no—
126C23×C47—416no—
127C23×C47#117116yes—
128C23×C47C23×C412yes—
129C23×C47C23×C412yes—
130C23×C47C23×C412yes—
131C23×C47C2×#4114yes—
132C23×C47C2×#4114yes—
133C23×C47C2×#4114yes—
134C23×C47C2511yescharacteristic
135C2×C4×C47—28no—
136C2×C4×C47—28no—
137C2×C4×C47—216no—
138C2×C4×C47—216no—
139C2×C4×C47—24no—
140C2×C4×C47—24no—
141C2×C4×C47—28no—
142C2×C4×C47—216no—
143C2×C4×C47—88no—
144C2×C4×C47C23×C414yes—
145C2×C4×C47C23×C414yes—
146C2×Dic47—28no—
147C2×Dic47—28no—
148C2×Dic47—28no—
149C2×Dic47—216no—
150C2×Dic47—48no—
151C2×Dic47—48no—
152C2×Dic47—88no—
153C2×Dic47C23×C418yes—
154C2×Dic47C23×C418yes—
155#34177—471nomaximal, Sylow
156C22×C47—24no—
157C22×C47—24no—
158C22×C47—24no—
159C22×C47—28no—
160C22×C47—28no—
161C22×C47—28no—
162C22×C47—416no—
163C22×C47C2×#11714yes—
164C22×C47C2×#11714yes—
165C22×C47C2×#11714yes—
166C22×C47C24×C411yescharacteristic
167C22×C47C22×#4112yes—
168C22×C47#58514yes—
169C4×C47—24no—
170C4×C47—24no—
171C4×C47—48no—
172Dic47—28no—
173Dic47—28no—
174Dic47—48no—
175C22×#117—471no—
176#2343—478no—
177#2343—478no—
178#2315—472no—
179#2313—474no—
180#2283—474no—
181C2×#381—471no—
182C2×#381D4711yescharacteristic
183#2273—472no—
184C2×C47—24no—
185C2×C47—24no—
186C2×C47—24no—
187C2×C47C22×#11711yescharacteristic
188C2×C47#342812yes—
189C2×C47#349114yes—
190C24×C4C2×D4711yescharacteristic
191C2×#117—4716no—
192C2×#117—474no—
193C2×#117—474no—
194C22×C4⋊C4—472no—
195C22×C22⋊C4—471no—
196C22×C22⋊C4—471no—
197C22×C22⋊C4—472no—
198C22×C22⋊C4C2×D4712yes—
199C22×C42—472no—
200#387—4716no—
201#387—4716no—
202#385—478no—
203#385—478no—
204#383—478no—
205#382—478no—
206#381—472no—
207#381—474no—
208#381—472no—
209#381C2×D4712yes—
210#381C2×D4714yes—
211#381C2×D4712yes—
212#380—478no—
213C4×C4⋊C4—478no—
214C4×C22⋊C4—478no—
215C4×C22⋊C4—478no—
216C4×C22⋊C4—478no—
217#376—478no—
218C2×#95—474no—
219C2×#95C2×D4714yes—
220C47#3417711yescharacteristic, complemented, Sylow
221C25C22×D4711yescharacteristic
222C23×C4—28no—
223C23×C4—472no—
224C23×C4—472no—
225C23×C4—474no—
226C23×C4C4×D4718yes—
227C23×C4C22×D4711yescharacteristic
228C23×C4C22×D4712yes—
229C23×C4C22×D4712yes—
230C23×C4C22×D4711yescharacteristic
231C23×C4C22×D4714yes—
232#117—4732no—
233#117—4732no—
234C2×C4⋊C4—4716no—
235C2×C4⋊C4—474no—
236C2×C4⋊C4—474no—
237C2×C4⋊C4—4716no—
238C2×C22⋊C4—28no—
239C2×C22⋊C4—478no—
240C2×C22⋊C4—478no—
241C2×C22⋊C4—472no—
242C2×C22⋊C4—472no—
243C2×C22⋊C4—472no—
244C2×C22⋊C4—472no—
245C2×C22⋊C4—474no—
246C2×C22⋊C4—474no—
247C2×C22⋊C4—948no—
248C2×C22⋊C4C22×D4714yes—
249C2×C22⋊C4C22×D4714yes—
250C2×C42—4716no—
251C2×C42—474no—
252C2×C42—474no—
253C2×C42—4716no—
254#95—478no—
255#95—478no—
256#95—4716no—
257#95—4716no—
258#95C22×D4718yes—
259#95C22×D4718yes—
260C24—44no—
261C24C2×C4×D4714yes—
262C24#1062535218yes—
263C24C23×D4711yescharacteristic
264C24C23×D4711yescharacteristic
265C24C23×D4711yescharacteristic
266C22×C4—232no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—48no—
273C22×C4—474no—
274C22×C4—474no—
275C22×C4—478no—
276C22×C4—478no—
277C22×C4—478no—
278C22×C4—948no—
279C22×C4—1888no—
280C22×C4—1884no—
281C22×C4—1884no—
282C22×C4C2×C4×D4714yes—
283C22×C4C2×C4×D4714yes—
284C22×C4C2×C4×D4718yes—
285C22×C4C2×C4×D4718yes—
286C22×C4C23×D4718yes—
287C22×C4C23×D4712yes—
288C22×C4C23×D4712yes—
289C4⋊C4—4716no—
290C4⋊C4—4716no—
291C4⋊C4—18816no—
292C22⋊C4—28no—
293C22⋊C4—28no—
294C22⋊C4—478no—
295C22⋊C4—478no—
296C22⋊C4—478no—
297C22⋊C4—478no—
298C22⋊C4—948no—
299C22⋊C4—948no—
300C42—4716no—
301C42—4716no—
302C42—18816no—
303C23—24no—
304C23—24no—
305C23—24no—
306C23—48no—
307C23—416no—
308C23#13093980116yes—
309C23C22×C4×D4712yes—
310C23C22×C4×D4712yes—
311C23C22×C4×D4712yes—
312C23C2×#1062535214yes—
313C23C2×#1062535214yes—
314C23C2×#1062535214yes—
315C23C24×D4711yescharacteristic
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—216no—
319C2×C4—216no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—28no—
323C2×C4—216no—
324C2×C4—88no—
325C2×C4—478no—
326C2×C4—478no—
327C2×C4—948no—
328C2×C4—948no—
329C2×C4—948no—
330C2×C4—9416no—
331C2×C4—3768no—
332C2×C4—1888no—
333C2×C4—1888no—
334C2×C4C22×C4×D4714yes—
335C2×C4C22×C4×D4714yes—
336C22—28no—
337C22—28no—
338C22—28no—
339C22—24no—
340C22—24no—
341C22—24no—
342C22—416no—
343C22C2×#1309398014yes—
344C22C2×#1309398014yes—
345C22C2×#1309398014yes—
346C22C23×C4×D4711yescharacteristic
347C22C22×#1062535212yes—
348C22#1568995914yes—
349C4—24no—
350C4—24no—
351C4—48no—
352C4—948no—
353C4—948no—
354C4—1888no—
355C2—24no—
356C2—24no—
357C2—24no—
358C2C22×#1309398011yescharacteristic
359C2#2025658912yes—
360C2#2025708414yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×C47×#381C2
socle, cosocleC23×C47C25
prime radicalC25×C47C23
hypercenterC2×#381D47
hypocenterC47#34177
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. #20246250C2semidirect
3. #20246244C2semidirect
5. #20245989C2semidirect
6. #20245779C2semidirect
10. C2×#13093983C4semidirect
18. #15689008C22semidirect
19. #15689006C22semidirect
22. #15688990C22semidirect
23. #15688987C22semidirect
28. #15688974C22semidirect
32. #15688968C22semidirect
43. #13093983C2×C4semidirect
44. #13093983C2×C4semidirect
45. C2×C4⋊Dic47C2×C4semidirect
58. C2×C4×Dic47C2×C4semidirect
220. C47#34177semidirect

Maximal subgroups

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

subgroupindex
C22×#130939832
#202462502
#202462442
#202460002
#202459892
#202457792
C2×#156889862
#202457412
C2×C47×#3812
#3417747