Finite Group Databasebeta

← #26225545

Subgroups — #26225545

Order 12032.

1334 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic
2#20245989C212yesmaximal, complemented
3#20244222C218yesmaximal, complemented
4#20243306C211yesmaximal, characteristic, complemented
5#20243305C212yesmaximal, complemented
6C47×#1782C211yesmaximal, characteristic, complemented
7C22×#10625350C2211yescharacteristic
8#15689701—24no—
9#15689701—24no—
10C2×#13094003C412yescomplemented
11C2×#13094000C412yescomplemented
12C2×#13093998C412yescomplemented
13C2×#13093996C2214yes—
14C2×#13093995C412yescomplemented
15C22×C4⋊Dic47C2211yescharacteristic
16C2×#13093939C2214yes—
17C2×#13093938C2218yes—
18#15689008—24no—
19#15689006—24no—
20#15688986C2212yes—
21#15688981C2214yes—
22C22⋊C4×Dic47C2214yes—
23C22×#41×C47C2211yescharacteristic
24C2×#99×C47C2214yes—
25C47×#381C2212yes—
26C2×#10625350—22no—
27C2×#10625350—22no—
28C2×#10625350—44no—
29C22×Dic94C2×C411yescharacteristic
30C22×D188C2×C411yescharacteristic
31C22×C22⋊D47C2×C414yes—
32C22×C22⋊D47C2312yes—
33C23×Dic47C2312yes—
34C22×C4×D47C2×C412yes—
35#13094003—24no—
36#13094003—24no—
37#13094000—28no—
38#13093998—24no—
39#13093998—24no—
40#13093996—28no—
41#13093996—28no—
42#13093995—28no—
43C2×C4⋊Dic47C2×C412yes—
44C2×C4⋊Dic47C2×C412yes—
45C2×C4⋊Dic47D414yes—
46C2×C4⋊Dic47D414yes—
47C2×Dic47⋊C4—24no—
48C2×Dic47⋊C4C2×C414yes—
49C2×C22⋊Dic47C2×C414yes—
50C2×C22⋊Dic47C2314yes—
51C2×(C2×D47)⋊C4C2×C414yes—
52C2×C4×Dic47—24no—
53#13093939—44no—
54#13093938—48no—
55C47⋊#95—22no—
56C47⋊#95—22no—
57C47⋊#95—24no—
58C47⋊#95—24no—
59C2×#41×C47—22no—
60C2×#41×C47—22no—
61C2×#41×C47—44no—
62C22×Q8×C47C2×C411yescharacteristic
63C22×D4×C47C2×C411yescharacteristic
64C22×D4×C47C2312yes—
65C23×C4×C47C2×C412yes—
66C23×C4×C47C2311yescharacteristic
67C2×C22⋊C4×C47C2314yes—
68#99×C47—44no—
69#95×C47—22no—
70#95×C47—22no—
71C24×C47C22×C412yes—
72C24×C47C2411yescharacteristic
73C23×D47C22×C412yes—
74#41×C47—48no—
75#41×C47—48no—
76C2×Q8×C47—22no—
77C2×Q8×C47—42no—
78C2×D4×C47—24no—
79C2×D4×C47—24no—
80C2×D4×C47—24no—
81C2×D4×C47—22no—
82C2×D4×C47—42no—
83C22×C4×C47—24no—
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—24no—
87C22×C4×C47—42no—
88C22×C4×C47—42no—
89C22×C4×C47C22×C412yes—
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C22×C411yescharacteristic
92C22×C4×C47C2×D412yes—
93C22×C4×C47C2×D412yes—
94C2×C22⋊D47—24no—
95C2×C22⋊D47—28no—
96C2×C22⋊D47—28no—
97C2×C22⋊D47—84no—
98C22×Dic47—24no—
99C22×Dic47—82no—
100C22×Dic47C22×C412yes—
101C22×Dic47C22×C414yes—
102C22×Dic47C2×D414yes—
103C22×Dic47C2×D414yes—
104#10625350—48no—
105#10625350—48no—
106C2×D188—21no—
107C2×D188—21no—
108C2×D188—42no—
109C2×C4×D47—24no—
110C2×C4×D47—44no—
111C2×Dic94—21no—
112C2×Dic94—21no—
113C2×Dic94—42no—
114C22⋊C4×C47—28no—
115C22⋊Dic47—28no—
116C22⋊Dic47—28no—
117(C2×D47)⋊C4—28no—
118C4⋊Dic47C22⋊C418yes—
119C4⋊Dic47C22⋊C414yes—
120C4⋊Dic47C22⋊C414yes—
121Dic47⋊C4—28no—
122Dic47⋊C4—84no—
123C4×Dic47—84no—
124C23×C47—22no—
125C23×C47—22no—
126C23×C47—22no—
127C23×C47—41no—
128C23×C47—41no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47C23×C411yescharacteristic
132C23×C47C22×D412yes—
133C23×C47H(5,𝔽2)14yes—
134C22×D47—22no—
135C22×D47—24no—
136C22×D47—42no—
137C22×D47—42no—
138Q8×C47—44no—
139D4×C47—44no—
140D4×C47—48no—
141C2×C4×C47—22no—
142C2×C4×C47—22no—
143C2×C4×C47—24no—
144C2×C4×C47—24no—
145C2×C4×C47—22no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—44no—
149C2×C4×C47—44no—
150C2×C4×C47—44no—
151C2×C4×C47—44no—
152C2×C4×C47—44no—
153C2×C4×C47C2×C22⋊C411yescharacteristic
154C2×C4×C47C2×C22⋊C411yescharacteristic
155C2×C4×C47C2×C22⋊C412yes—
156C22⋊D47—48no—
157C22⋊D47—88no—
158C2×Dic47—22no—
159C2×Dic47—24no—
160C2×Dic47—44no—
161C2×Dic47—44no—
162C2×Dic47—44no—
163C2×Dic47—44no—
164C2×Dic47—44no—
165C2×Dic47—44no—
166C2×Dic47C2×C22⋊C418yes—
167D188—42no—
168D188—42no—
169C4×D47—48no—
170Dic94—42no—
171Dic94—42no—
172#21796—471nomaximal, Sylow
173C22×C47—22no—
174C22×C47—21no—
175C22×C47—22no—
176C22×C47—21no—
177C22×C47—44no—
178C22×C47—42no—
179C22×C47—42no—
180C22×C47—42no—
181C22×C47—82no—
182C22×C47—82no—
183C22×C47C22×C22⋊C411yescharacteristic
184C22×C47#51812yes—
185C22×C47#53514yes—
186C2×D47—42no—
187C2×D47—42no—
188C2×D47—42no—
189C2×D47—84no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—22no—
193C4×C47—42no—
194C4×C47—84no—
195Dic47—28no—
196Dic47—42no—
197Dic47—84no—
198C2×#537—471no—
199#2313—472no—
200#1964—478no—
201#1782—472no—
202#1782—471no—
203#1782D4711yescharacteristic, complemented
204C2×C47—24no—
205C2×C47—22no—
206C2×C47—82no—
207C2×C47#230911yescharacteristic
208C2×C47#288311yescharacteristic
209C2×C47#288411yescharacteristic
210D47—82no—
211C22×#41—471no—
212C22×#41C2×D4711yescharacteristic
213#537—944no—
214#537—944no—
215C2×C22⋊Q8—472no—
216C2×C22⋊Q8—472no—
217C2×#121—472no—
218C2×#121—474no—
219C2×#121—472no—
220C22×C4⋊C4—471no—
221C2×#99—474no—
222C2×#99—478no—
223C2×#99C2×D4714yes—
224#387—944no—
225#387—944no—
226#381—472no—
227#381C2×D4712yes—
228#380—474no—
229C4×C22⋊C4—474no—
230C47#2179611yescharacteristic, complemented, Sylow
231C2×#41—22no—
232C2×#41—22no—
233C2×#41—44no—
234C2×#41—942no—
235C2×#41—942no—
236C2×#41—1884no—
237C22×Q8—471no—
238C22×Q8C4×D4711yescharacteristic
239C22×D4—472no—
240C22×D4—474no—
241C22×D4—471no—
242C22×D4C4×D4711yescharacteristic
243C22×D4C22×D4712yes—
244C23×C4—472no—
245C23×C4—472no—
246C23×C4C4×D4712yes—
247C23×C4C22×D4711yescharacteristic
248C22⋊Q8—944no—
249C22⋊Q8—944no—
250C22⋊Q8—948no—
251#121—944no—
252#121—944no—
253#121—948no—
254#121—948no—
255#121—948no—
256C2×C4⋊C4—472no—
257C2×C4⋊C4—472no—
258C2×C4⋊C4—474no—
259C2×C4⋊C4—474no—
260C2×C4⋊C4—474no—
261C2×C4⋊C4—944no—
262C2×C22⋊C4—474no—
263C2×C22⋊C4—474no—
264C2×C22⋊C4—474no—
265C2×C22⋊C4C22×D4714yes—
266C2×C42—944no—
267#99—44no—
268#99—1888no—
269#99—1884no—
270#95—22no—
271#95—22no—
272#95—944no—
273#95—944no—
274#95—942no—
275#95—942no—
276C24—472no—
277C24C2×C4×D4712yes—
278C24C23×D4711yescharacteristic
279#41—48no—
280#41—48no—
281#41—1888no—
282#41—1888no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—941no—
286C2×Q8—941no—
287C2×Q8—1882no—
288C2×D4—24no—
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—948no—
294C2×D4—944no—
295C2×D4—948no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—3764no—
299C2×D4—1882no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—474no—
307C22×C4—474no—
308C22×C4—474no—
309C22×C4—472no—
310C22×C4—944no—
311C22×C4—944no—
312C22×C4—3762no—
313C22×C4—1884no—
314C22×C4C2×C4×D4712yes—
315C22×C4C2×C4×D4711yescharacteristic
316C22×C4C2×C4×D4711yescharacteristic
317C22×C4D4×D4712yes—
318C22×C4D4×D4712yes—
319C4⋊C4—474no—
320C4⋊C4—474no—
321C4⋊C4—478no—
322C4⋊C4—948no—
323C4⋊C4—3764no—
324C22⋊C4—28no—
325C22⋊C4—948no—
326C22⋊C4—948no—
327C22⋊C4—948no—
328C42—3764no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—42no—
336C23—944no—
337C23—942no—
338C23—1882no—
339C23—1882no—
340C23C22×C4×D4711yescharacteristic
341C23C2×D4×D4712yes—
342C23#1309406914yes—
343Q8—44no—
344Q8—1882no—
345Q8—1882no—
346D4—44no—
347D4—48no—
348D4—3768no—
349D4—1882no—
350D4—1882no—
351D4—1888no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—478no—
365C2×C4—942no—
366C2×C4—944no—
367C2×C4—1888no—
368C2×C4—1884no—
369C2×C4—1884no—
370C2×C4—1884no—
371C2×C4—1884no—
372C2×C4—1884no—
373C2×C4—1884no—
374C2×C4C22⋊C4×D4711yescharacteristic
375C2×C4C22⋊C4×D4711yescharacteristic
376C2×C4C22⋊C4×D4712yes—
377C22—22no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—82no—
386C22—82no—
387C22—3764no—
388C22—1882no—
389C22—1882no—
390C22—1882no—
391C22C2×C22⋊C4×D4711yescharacteristic
392C22#1568959612yes—
393C22#1568968814yes—
394C4—21no—
395C4—21no—
396C4—22no—
397C4—42no—
398C4—84no—
399C4—948no—
400C4—3764no—
401C4—1882no—
402C2—24no—
403C2—22no—
404C2—82no—
405C2—3762no—
406C2#2024596911yescharacteristic
407C2#2025184711yescharacteristic
408C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1782C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689701C2
cosocleC24×C47C24
hypercenter#1782D47
hypocenterC47#21796
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #20245989C2semidirect
3. #20244222C2semidirect
4. #20243306C2semidirect
5. #20243305C2semidirect
6. C47×#1782C2semidirect
10. C2×#13094003C4semidirect
11. C2×#13094000C4semidirect
12. C2×#13093998C4semidirect
14. C2×#13093995C4semidirect
203. #1782D47semidirect
230. C47#21796semidirect

Maximal subgroups

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

subgroupindex
C2×#156897012
#202459892
#202442222
#202433062
#202433052
C47×#17822
#2179647