Finite Group Databasebeta

← #26126511

Subgroups — #26126511

Order 12032.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244999C211yesmaximal, characteristic, complemented
2C2×#15688886C211yesmaximal, characteristic, complemented
3#20241400C212yesmaximal, complemented
4#20241397C212yesmaximal, complemented
5C47×#3050C211yesmaximal, characteristic
6C22×C4⋊Dic47—21no—
7C2×#13093964—21no—
8C22⋊(C47⋊C16)—21no—
9C22⋊(C47⋊C16)C2212yes—
10#15688886—21no—
11#15688886C2212yes—
12C2×#135×C47C411yescharacteristic, complemented
13C23×C8×C47C2211yescharacteristic
14C47×#525—21no—
15C47×#467C411yescharacteristic, complemented
16C47×#467C2211yescharacteristic
17C47×#466C411yescharacteristic, complemented
18C47×#466C2211yescharacteristic
19C47×#465—21no—
20C47×#465—21no—
21C47×#427C411yescharacteristic, complemented
22C47×#416—21no—
23C23×Dic47—41no—
24C2×C4⋊Dic47—24no—
25C2×C4⋊Dic47—22no—
26C2×C4⋊Dic47—42no—
27C2×C4⋊Dic47—41no—
28#13093964—42no—
29C2×C47⋊C16—22no—
30C2×#41×C47—21no—
31C23×C4×C47D411yescharacteristic
32#135×C47—42no—
33C2×Q16×C47C2×C411yescharacteristic, complemented
34C2×SD16×C47—21no—
35C2×D8×C47C2×C411yescharacteristic, complemented
36C22×C8×C47—42no—
37C22×C8×C47C2×C411yescharacteristic
38C22×C8×C47C2×C411yescharacteristic
39C22×C8×C47D411yescharacteristic
40C22×C8×C47D411yescharacteristic
41C22×C8×C47D411yescharacteristic
42C22×C8×C47C2311yescharacteristic
43#123×C47—41no—
44C22⋊Q8×C47—21no—
45C22⋊Q8×C47—21no—
46#121×C47—21no—
47#121×C47—21no—
48#120×C47—41no—
49C4×D4×C47—41no—
50C4×D4×C47—41no—
51#117×C47—21no—
52#107×C47C2×C411yescharacteristic, complemented
53#107×C47C2×C411yescharacteristic, complemented
54#106×C47—21no—
55#103×C47—21no—
56#103×C47—21no—
57#102×C47—21no—
58#102×C47—21no—
59C24×C47D811yescharacteristic
60#41×C47—42no—
61#41×C47—42no—
62C2×Q8×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C2×D4×C47—41no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—41no—
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47D811yescharacteristic
73C22×C4×C47SD1611yescharacteristic
74C22×C4×C47SD1611yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—44no—
77C22×Dic47—42no—
78C22×Dic47—82no—
79C22×Dic47—82no—
80Q16×C47—41no—
81SD16×C47—42no—
82D8×C47—41no—
83C2×C8×C47—22no—
84C2×C8×C47—22no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C2×C8×C47C22⋊C411yescharacteristic
90C2×C8×C47C22⋊C411yescharacteristic
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C42×C47—41no—
103C4⋊Dic47—24no—
104C4⋊Dic47—44no—
105C4⋊Dic47—42no—
106C47⋊C16—42no—
107C23×C47—22no—
108C23×C47—22no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—41no—
112C23×C47#10211yescharacteristic
113C23×C47#10211yescharacteristic
114C23×C47C2×D811yescharacteristic
115Q8×C47—41no—
116Q8×C47—41no—
117D4×C47—41no—
118D4×C47—41no—
119D4×C47—82no—
120D4×C47—82no—
121D4×C47—81no—
122D4×C47—81no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—82no—
134C2×C4×C47#9912yes—
135C2×C4×C47#10211yescharacteristic
136C2×C4×C47#10211yescharacteristic
137C2×C4×C47#10412yes—
138C2×C4×C47C2×C22⋊C411yescharacteristic
139C2×C4×C47C2×SD1611yescharacteristic
140C2×Dic47—44no—
141C2×Dic47—88no—
142C2×Dic47—82no—
143C2×Dic47—82no—
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47—21no—
148#11704—471nomaximal, Sylow
149C22×C47—24no—
150C22×C47—24no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—81no—
158C22×C47—81no—
159C22×C47—81no—
160C22×C47#32712yes—
161C22×C47#36012yes—
162C22×C47C2×#10211yescharacteristic
163C22×C47#50911yescharacteristic
164C22×C47#51011yescharacteristic
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—81no—
168C4×C47—81no—
169C4×C47—81no—
170C4×C47#32712yes—
171C4×C47C2×#9911yescharacteristic
172C4×C47C2×#10411yescharacteristic
173Dic47—84no—
174#3050D4711yescharacteristic
175#2112—471no—
176C2×#340—471no—
177#1348—472no—
178#1347—472no—
179C2×C47—21no—
180C2×C47—22no—
181C2×C47—22no—
182C2×C47—21no—
183C2×C47—161no—
184C2×C47C2×#32711yescharacteristic
185C2×C47#213911yescharacteristic
186C2×C47C2×#36011yescharacteristic
187C2×#135Dic4711yescharacteristic, complemented
188C23×C8C2×D4711yescharacteristic
189#525—21no—
190C22×C4⋊C4—941no—
191C2×M32—941no—
192#467Dic4711yescharacteristic, complemented
193#467C2×D4711yescharacteristic
194#466Dic4711yescharacteristic, complemented
195#466C2×D4711yescharacteristic
196#465—21no—
197#465—21no—
198#427Dic4711yescharacteristic, complemented
199#416—21no—
200C22⋊C16—472no—
201C22⋊C16—941no—
202#340—472no—
203#340—941no—
204C47#1170411yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C23×C4—1881no—
207C23×C4C22⋊D4711yescharacteristic
208#135—42no—
209C2×Q16C2×Dic4711yescharacteristic, complemented
210C2×SD16—21no—
211C2×D8C2×Dic4711yescharacteristic, complemented
212C22×C8—42no—
213C22×C8C2×Dic4711yescharacteristic
214C22×C8C2×Dic4711yescharacteristic
215C22×C8C22⋊D4711yescharacteristic
216C22×C8C22⋊D4711yescharacteristic
217C22×C8C22⋊D4711yescharacteristic
218C22×C8C22×D4711yescharacteristic
219#123—41no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222#121—21no—
223#121—21no—
224#120—41no—
225C4×D4—41no—
226C4×D4—41no—
227#117—21no—
228C2×C4⋊C4—944no—
229C2×C4⋊C4—942no—
230C2×C4⋊C4—1882no—
231C2×C4⋊C4—1881no—
232M32—1882no—
233C2×C16—942no—
234#107C2×Dic4711yescharacteristic, complemented
235#107C2×Dic4711yescharacteristic, complemented
236#106—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C24#1062533411yescharacteristic
242#41—42no—
243#41—42no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—3762no—
253C22×C4—3762no—
254C22×C4—1884no—
255C22×C4—1882no—
256C22×C4#1062533411yescharacteristic
257C22×C4#1062533511yescharacteristic
258C22×C4#1062533511yescharacteristic
259C22×C4C22⋊Dic4711yescharacteristic
260C22×C4C22⋊Dic4711yescharacteristic
261C22×C4C2×C22⋊D4711yescharacteristic
262Q16—41no—
263SD16—42no—
264D8—41no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊Dic4711yescharacteristic
272C2×C8C22⋊Dic4711yescharacteristic
273C2×C8C22×Dic4711yescharacteristic
274C2×C8C2×C22⋊D4711yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—944no—
280C4⋊C4—1882no—
281C4⋊C4—1884no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—41no—
288C16—1882no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—41no—
294C23#1309394511yescharacteristic
295C23#1309394511yescharacteristic
296C23C2×#1062533411yescharacteristic
297Q8—41no—
298Q8—41no—
299D4—41no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—82no—
304D4—82no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—3768no—
317C2×C4—3762no—
318C2×C4—3762no—
319C2×C4—1884no—
320C2×C4#1309393912yes—
321C2×C4#1309394511yescharacteristic
322C2×C4#1309394511yescharacteristic
323C2×C4#1309395112yes—
324C2×C4C2×C22⋊Dic4711yescharacteristic
325C2×C4C2×#1062533511yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1568885712yes—
342C22#1568893312yes—
343C22C2×#1309394511yescharacteristic
344C22#1568955811yescharacteristic
345C22#1568956311yescharacteristic
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—3764no—
352C4#1568885712yes—
353C4C2×#1309393911yescharacteristic
354C4C2×#1309395111yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—161no—
360C2C2×#1568885711yescharacteristic
361C2#2024510011yescharacteristic
362C2C2×#1568893311yescharacteristic
subgroupG/H
centerC22C2×#13093945
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC47×#3050C2
socleC22×C47C2×#102
cosocleC22×C8×C47C23
hypercenter#3050D47
hypocenterC47#11704
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #20244999C2semidirect
2. C2×#15688886C2semidirect
3. #20241400C2semidirect
4. #20241397C2semidirect
12. C2×#135×C47C4semidirect
15. C47×#467C4semidirect
17. C47×#466C4semidirect
21. C47×#427C4semidirect
33. C2×Q16×C47C2×C4semidirect
35. C2×D8×C47C2×C4semidirect
52. #107×C47C2×C4semidirect
53. #107×C47C2×C4semidirect
187. C2×#135Dic47semidirect
192. #467Dic47semidirect
194. #466Dic47semidirect
198. #427Dic47semidirect
204. C47#11704semidirect
209. C2×Q16C2×Dic47semidirect
211. C2×D8C2×Dic47semidirect
234. #107C2×Dic47semidirect
235. #107C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202449992
C2×#156888862
#202414002
#202413972
C47×#30502
#1170447