Finite Group Databasebeta

← #26370945

Subgroups — #26370945

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094046C211yesmaximal, characteristic
2#20245537C212yesmaximal, complemented
3#20245532C212yesmaximal, complemented
4#20245527C212yesmaximal, complemented
5#20245522C212yesmaximal, complemented
6#20245174C212yesmaximal, complemented
7#20245144C211yesmaximal, characteristic, complemented
8#20245098C212yesmaximal
9C2×C47×#500C211yesmaximal, characteristic, complemented
10C2×#13094046C2211yescharacteristic
11C4×#10625350—21no—
12C2×#13093964C2212yes—
13C4×Dic188C2211yescharacteristic
14C4×Dic188C2211yescharacteristic
15C4×#10625325—21no—
16C4×#10625325—21no—
17C4×D376C2211yescharacteristic
18C4×D376C2211yescharacteristic
19#15689161C2211yescharacteristic
20#15689120—21no—
21#15688950C2214yes—
22#15688948C2214yes—
23C4⋊(C47⋊C16)C2212yes—
24C4⋊(C47⋊C16)C2212yes—
25#15688926C2214yes—
26#15688923C2214yes—
27C2×C4⋊Q8×C47—21no—
28C47×#500—21no—
29C47×#500—21no—
30C47×#500C2212yes—
31C47×#500C2212yes—
32C2×#107×C47—21no—
33C2×#107×C47C2212yes—
34C2×C4×C8×C47C2211yescharacteristic
35C2×#10625350—21no—
36#13094046—22no—
37#13094046Q814yescomplemented
38C2×Dic188C2311yescharacteristic
39C2×#10625325—21no—
40C2×D376C2311yescharacteristic
41C4×Dic94—21no—
42C4×Dic94—21no—
43C4×D188—21no—
44C4×D188—21no—
45C4×C22⋊D47—41no—
46C4×C22⋊D47—41no—
47#13093983—21no—
48#13093981—41no—
49C42×D47—41no—
50#13093964—24no—
51C2×C47⋊C16C2314yes—
52#13093958C2311yescharacteristic
53#13093958C2311yescharacteristic
54#13093956—21no—
55#13093949—21no—
56#13093949—21no—
57#13093946—21no—
58#13093946—21no—
59C22×Q8×C47—41no—
60C22×C8×C47D411yescharacteristic
61C22×C8×C47C2311yescharacteristic
62C4⋊Q8×C47—22no—
63C4⋊Q8×C47—22no—
64C4⋊Q8×C47—41no—
65C4⋊Q8×C47—41no—
66C2×C4⋊C4×C47—22no—
67C2×C4⋊C4×C47—41no—
68C2×C42×C47D411yescharacteristic
69#107×C47—22no—
70#107×C47—22no—
71#107×C47—22no—
72#107×C47C2314yes—
73C4×C8×C47D411yescharacteristic
74C4×C8×C47D411yescharacteristic
75C4×C8×C47C2311yescharacteristic
76C4×C8×C47C2311yescharacteristic
77C2×Q8×C47—42no—
78C2×Q8×C47—42no—
79C2×Q8×C47—84no—
80C22×C4×C47—42no—
81C22×C4×C47D811yescharacteristic
82C22×C4×C47D811yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C2×C22⋊D47—41no—
85#10625350—24no—
86#10625350—42no—
87C2×D188—21no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×Dic94—21no—
92C2×C8×C47—22no—
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×Q812yes—
97C2×C8×C47#4112yes—
98C2×C8×C47C2411yescharacteristic
99C4⋊C4×C47—24no—
100C4⋊C4×C47—42no—
101C4⋊C4×C47—42no—
102C4⋊C4×C47—42no—
103C42×C47D811yescharacteristic
104C42×C47D811yescharacteristic
105C42×C47C2×D411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C22⋊Dic47—41no—
108(C2×D47)⋊C4—41no—
109(C2×D47)⋊C4—41no—
110C4⋊Dic47—21no—
111C4⋊Dic47—21no—
112Dic47⋊C4—41no—
113Dic47⋊C4—41no—
114C4×Dic47—41no—
115C4×Dic47—41no—
116C4×Dic47—41no—
117Dic188—21no—
118Dic188C2×Q812yescomplemented
119D376—21no—
120D376C2×Q812yescomplemented
121#10625325—24no—
122C47⋊C16—24no—
123C23×C47C2×D811yescharacteristic
124C22×D47—41no—
125Q8×C47—84no—
126Q8×C47—84no—
127C2×C4×C47—22no—
128C2×C4×C47—22no—
129C2×C4×C47—44no—
130C2×C4×C47—84no—
131C2×C4×C47C22⋊Q812yes—
132C2×C4×C47C2×D811yescharacteristic
133C2×C4×C47C2×D811yescharacteristic
134C2×C4×C47C2×D811yescharacteristic
135C2×C4×C47C2×D811yescharacteristic
136C2×C4×C47C2×D811yescharacteristic
137C2×C4×C47#13712yes—
138C2×C4×C47C22×D411yescharacteristic
139C22⋊D47—44no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143D188—22no—
144D188—41no—
145C4×D47—44no—
146C4×D47—82no—
147C4×D47—82no—
148Dic94—22no—
149Dic94—41no—
150C8×C47—21no—
151C8×C47—21no—
152C8×C47C22⋊Q812yes—
153C8×C47C22×Q811yescharacteristic
154C8×C47C2×#4111yescharacteristic
155#33629—471nomaximal, Sylow
156C22×C47—21no—
157C22×C47—21no—
158C22×C47#47412yes—
159C22×C47C22×D811yescharacteristic
160C2×D47—42no—
161C2×D47—81no—
162C2×D47—81no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—84no—
166C4×C47#47412yes—
167C4×C47#50912yes—
168C4×C47#51012yes—
169C4×C47C2×C22⋊Q811yescharacteristic
170C4×C47C2×#13711yescharacteristic
171Dic47—42no—
172Dic47—81no—
173Dic47—81no—
174C2×#500D4711yescharacteristic, complemented
175C4×#135—471no—
176#2227—472no—
177#2226—472no—
178#2225—472no—
179#2224—472no—
180#2159—472no—
181#2150—471no—
182#2139—472no—
183C2×C47—22no—
184C2×C47C2×#47411yescharacteristic
185C2×C47C2×#50911yescharacteristic
186C2×C47C2×#51011yescharacteristic
187D47—82no—
188C2×#135—471no—
189C2×C4⋊Q8—21no—
190C4×#41—941no—
191C2×M32—472no—
192#500—21no—
193#500—21no—
194#500C2×D4712yes—
195#500C2×D4712yes—
196C4×Q16—471no—
197C4×Q16—471no—
198C4×SD16—941no—
199C4×SD16—941no—
200C4×D8—471no—
201C4×D8—471no—
202#427—471no—
203C2×#107—21no—
204C2×#107C2×D4712yes—
205#416—941no—
206C2×C4×C8C2×D4711yescharacteristic
207#367—474no—
208#366—474no—
209C4⋊C16—472no—
210C4⋊C16—472no—
211#358—474no—
212#357—474no—
213C47#3362911yescharacteristic, complemented, Sylow
214C2×#41—941no—
215C22×Q8—41no—
216#135—474no—
217#135—942no—
218C2×Q16—471no—
219C2×SD16—941no—
220C2×D8—471no—
221C22×C8C22⋊D4711yescharacteristic
222C22×C8C22×D4711yescharacteristic
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—41no—
226C4⋊Q8—41no—
227C4×Q8—941no—
228C4×Q8—941no—
229C4×D4—941no—
230C4×D4—941no—
231C4×D4—1881no—
232C4×D4—1881no—
233#117—941no—
234#117—1881no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—41no—
237C2×C42—1881no—
238C2×C42C22⋊D4711yescharacteristic
239M32—944no—
240C2×C16—474no—
241#107—22no—
242#107—22no—
243#107—22no—
244#107—471no—
245#107—471no—
246#107C22×D4714yes—
247#106—941no—
248#103—941no—
249#103—941no—
250#102—941no—
251#102—941no—
252C4×C8C22⋊D4711yescharacteristic
253C4×C8C22⋊D4711yescharacteristic
254C4×C8C22×D4711yescharacteristic
255C4×C8C22×D4711yescharacteristic
256#41—944no—
257#41—1882no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—84no—
261C2×Q8—941no—
262C2×D4—941no—
263C2×D4—1881no—
264C22×C4—42no—
265C22×C4—1881no—
266C22×C4—1881no—
267C22×C4—1881no—
268C22×C4#1062533411yescharacteristic
269C22×C4#1062533411yescharacteristic
270C22×C4C2×C22⋊D4711yescharacteristic
271Q16—472no—
272Q16—941no—
273SD16—944no—
274D8—472no—
275D8—941no—
276C2×C8—22no—
277C2×C8Q8×D4712yes—
278C2×C8#1062535412yes—
279C2×C8C2×C22⋊D4711yescharacteristic
280C2×C8C2×C22⋊D4711yescharacteristic
281C2×C8C2×C22⋊D4711yescharacteristic
282C2×C8C23×D4711yescharacteristic
283C4⋊C4—24no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—1881no—
290C4⋊C4—1881no—
291C22⋊C4—1881no—
292C22⋊C4—1881no—
293C22⋊C4—1881no—
294C42—1881no—
295C42—1881no—
296C42—1881no—
297C42#1062533411yescharacteristic
298C42#1062533411yescharacteristic
299C42C2×C22⋊D4711yescharacteristic
300C42C2×C22⋊D4711yescharacteristic
301C16—944no—
302C23—1881no—
303C23C2×#1062533411yescharacteristic
304Q8—84no—
305Q8—84no—
306Q8—942no—
307Q8—1881no—
308D4—942no—
309D4—1884no—
310D4—1881no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—44no—
314C2×C4—84no—
315C2×C4—3762no—
316C2×C4—3762no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1884no—
321C2×C4#1309400012yes—
322C2×C4C2×#1062533411yescharacteristic
323C2×C4C2×#1062533411yescharacteristic
324C2×C4C2×#1062533411yescharacteristic
325C2×C4C2×#1062533411yescharacteristic
326C2×C4C2×#1062533411yescharacteristic
327C2×C4#1309405512yes—
328C2×C4C22×C22⋊D4711yescharacteristic
329C8—21no—
330C8—21no—
331C8#1309400012yes—
332C8C2×Q8×D4711yescharacteristic
333C8C2×#1062535411yescharacteristic
334C22—21no—
335C22—21no—
336C22—3761no—
337C22—3761no—
338C22—1882no—
339C22#1568940012yes—
340C22C22×#1062533411yescharacteristic
341C4—21no—
342C4—21no—
343C4—84no—
344C4—3761no—
345C4—3761no—
346C4—1882no—
347C4#1568940012yes—
348C4#1568955912yes—
349C4#1568956412yes—
350C4C2×#1309400011yescharacteristic
351C4C2×#1309405511yescharacteristic
352C2—22no—
353C2—3762no—
354C2C2×#1568940011yescharacteristic
355C2C2×#1568955911yescharacteristic
356C2C2×#1568956411yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#500C2
socleC22×C47C22×D8
prime radicalC2×#13094046C22
hypercenterC2×#500D47
hypocenterC47#33629
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #20245537C2semidirect
3. #20245532C2semidirect
4. #20245527C2semidirect
5. #20245522C2semidirect
6. #20245174C2semidirect
7. #20245144C2semidirect
9. C2×C47×#500C2semidirect
37. #13094046Q8semidirect
118. Dic188C2×Q8semidirect
120. D376C2×Q8semidirect
174. C2×#500D47semidirect
213. C47#33629semidirect

Maximal subgroups

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

subgroupindex
C4×#130940462
#202455372
#202455322
#202455272
#202455222
#202451742
#202451442
#202450982
C2×C47×#5002
#3362947