Finite Group Databasebeta

← #26132565

Subgroups — #26132565

Order 12032.

470 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C211yesmaximal, characteristic
2C2×(C2×D47)⋊C16C211yesmaximal, characteristic
3#20243414C211yesmaximal, characteristic
4#20241480C211yesmaximal, characteristic, complemented
5#20241479C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×C4⋊C4×D47—21no—
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093958C2211yescharacteristic
12C2×#13093958C2211yescharacteristic
13C2×#13093957—21no—
14#107×D47—22no—
15#107×D47C414yescomplemented
16#15688980—21no—
17(C2×D47)⋊C16—22no—
18#15688885—21no—
19C22×C16×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C22×C4×D47—41no—
23C22×C4×D47D411yescharacteristic
24C22×C47⋊C8D411yescharacteristic
25C2×C8×D47—21no—
26C2×C8×D47—21no—
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C8×D47C2×C412yes—
30C2×C8×D47D412yes—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×Dic47⋊C4—41no—
34C4⋊C4×D47—24no—
35C4⋊C4×D47—42no—
36C2×(C2×D47)⋊C4—41no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40#13093958—21no—
41#13093958—21no—
42#13093958—21no—
43#13093958C2×C412yes—
44#13093957—24no—
45C47⋊#95—41no—
46C22×C8×C47C2311yescharacteristic
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C16×C47—21no—
50C2×C16×C47—21no—
51C2×C16×C47—21no—
52#107×C47—21no—
53#107×C47—21no—
54#107×C47—21no—
55#107×C47C2×C412yes—
56C23×D47D811yescharacteristic
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47C2×D411yescharacteristic
60C22×Dic47—41no—
61C22×Dic47—41no—
62C22×Dic47D811yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—44no—
68C2×C4×D47—82no—
69C2×C4×D47—82no—
70C2×C4×D47C22⋊C412yes—
71C2×C4×D47SD1612yes—
72C2×C8×C47C22×C411yescharacteristic
73C2×C8×C47C2×D411yescharacteristic
74C2×C8×C47#4111yescharacteristic
75C2×C8×C47#4111yescharacteristic
76C2×C8×C47#4111yescharacteristic
77C2×C8×C47#4111yescharacteristic
78C4⋊C4×C47—22no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82(C2×D47)⋊C4—82no—
83C4⋊Dic47—22no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87Dic47⋊C4—44no—
88C2×C47⋊C8—21no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8C22⋊C412yes—
91C8×D47—22no—
92C8×D47—22no—
93C8×D47—22no—
94C8×D47—22no—
95C16×C47—41no—
96C47⋊C16—41no—
97C23×C47C2×D811yescharacteristic
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47#10212yes—
103C22×D47D1612yes—
104C22×D47SD3212yes—
105C2×C4×C47—42no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47—81no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47C2×C22⋊C411yescharacteristic
112C2×C4×C47#12311yescharacteristic
113C2×C4×C47#12311yescharacteristic
114C2×C4×C47C2×SD1611yescharacteristic
115C2×C4×C47#13711yescharacteristic
116C2×C4×C47#13711yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—42no—
120C2×Dic47—81no—
121C2×Dic47—81no—
122C2×Dic47—81no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47#10212yes—
126C4×D47—22no—
127C4×D47—22no—
128C4×D47—22no—
129C4×D47—22no—
130C4×D47—88no—
131C8×C47#11711yescharacteristic
132C8×C47#11711yescharacteristic
133C8×C47#12311yescharacteristic
134C8×C47#12311yescharacteristic
135C47⋊C8—22no—
136#12866—471nomaximal, Sylow
137C22×C47C2×#10211yescharacteristic
138C22×C47#48011yescharacteristic
139C22×C47#48011yescharacteristic
140C22×C47C2×D1611yescharacteristic
141C22×C47C2×SD3211yescharacteristic
142C22×C47#51011yescharacteristic
143C22×C47#51011yescharacteristic
144C2×D47—22no—
145C2×D47—22no—
146C2×D47—22no—
147C2×D47—22no—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47#35714yes—
151C4×C47—82no—
152C4×C47—161no—
153C4×C47#38111yescharacteristic
154C4×C47#41911yescharacteristic
155C4×C47#48311yescharacteristic
156C4×C47#48311yescharacteristic
157Dic47—22no—
158Dic47—82no—
159Dic47—161no—
160C22×#107—471no—
161C2×C22⋊C16—471no—
162#1808—471no—
163#1380—471no—
164#1380—471no—
165#1380—471no—
166#1380D4711yescharacteristic, complemented
167C2×C47#182311yescharacteristic
168C2×C47C2×#35711yescharacteristic
169C2×C47#214111yescharacteristic
170C2×C47#223211yescharacteristic
171C2×C47#223211yescharacteristic
172C2×C47#223511yescharacteristic
173C2×C47#223511yescharacteristic
174D47—24no—
175C23×C8—471no—
176C22×C4⋊C4—941no—
177C22×C16—471no—
178C22×C16C2×D4711yescharacteristic
179C2×#107—471no—
180C2×#107—474no—
181C2×#107—471no—
182C2×#107—942no—
183C2×#107—941no—
184C2×#107C2×D4711yescharacteristic
185C2×#107C2×D4711yescharacteristic
186#380—941no—
187C22⋊C16—942no—
188#340—941no—
189C47#1286611yescharacteristic, complemented, Sylow
190C23×C4—471no—
191C23×C4—1881no—
192C22×C8—471no—
193C22×C8—472no—
194C22×C8—472no—
195C22×C8—941no—
196C22×C8—941no—
197C22×C8—941no—
198C22×C8—941no—
199C22×C8C22×D4711yescharacteristic
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—944no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—1882no—
206C2×C4⋊C4—1881no—
207C2×C22⋊C4—1881no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—941no—
212C2×C16—941no—
213C2×C16—941no—
214#107—21no—
215#107—21no—
216#107—21no—
217#107—472no—
218#107—944no—
219#107—941no—
220#107—941no—
221#107—941no—
222#107C4×D4712yes—
223#95—1881no—
224C24—471no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—471no—
228C22×C4—472no—
229C22×C4—472no—
230C22×C4—941no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4—941no—
234C22×C4—3762no—
235C22×C4—3762no—
236C22×C4—1884no—
237C22×C4—1881no—
238C22×C4—1881no—
239C22×C4D4×D4711yescharacteristic
240C2×C8—472no—
241C2×C8—941no—
242C2×C8—941no—
243C2×C8—942no—
244C2×C8—942no—
245C2×C8—942no—
246C2×C8—942no—
247C2×C8C2×C4×D4711yescharacteristic
248C2×C8#1062535011yescharacteristic
249C2×C8#1062535011yescharacteristic
250C2×C8D4×D4711yescharacteristic
251C2×C8#1062535211yescharacteristic
252C2×C8#1062535411yescharacteristic
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—942no—
258C4⋊C4—1884no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C22⋊C4—3762no—
263C16—41no—
264C16—1881no—
265C23—472no—
266C23—472no—
267C23—472no—
268C23—941no—
269C23—941no—
270C23—941no—
271C23—941no—
272C23D8×D4711yescharacteristic
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—472no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—942no—
283C2×C4—942no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—3768no—
287C2×C4—3761no—
288C2×C4—3761no—
289C2×C4—3761no—
290C2×C4—3761no—
291C2×C4—3761no—
292C2×C4—1882no—
293C2×C4C22⋊C4×D4711yescharacteristic
294C2×C4#1309400611yescharacteristic
295C2×C4#1309400911yescharacteristic
296C2×C4SD16×D4711yescharacteristic
297C2×C4#1309405311yescharacteristic
298C2×C4#1309405611yescharacteristic
299C8—942no—
300C8#1309398111yescharacteristic
301C8#1309398211yescharacteristic
302C8#1309400611yescharacteristic
303C8#1309400911yescharacteristic
304C22—474no—
305C22—942no—
306C22—942no—
307C22—942no—
308C22—942no—
309C22—942no—
310C22—942no—
311C22#102×D4711yescharacteristic
312C22#1568943511yescharacteristic
313C22#1568943811yescharacteristic
314C22D16×D4711yescharacteristic
315C22SD32×D4711yescharacteristic
316C22#1568956211yescharacteristic
317C22#1568956511yescharacteristic
318C4—82no—
319C4—161no—
320C4—942no—
321C4—3762no—
322C4—7521no—
323C4#1568898511yescharacteristic
324C4#1568913011yescharacteristic
325C4#1568945211yescharacteristic
326C4#1568945511yescharacteristic
327C2—944no—
328C2#2024347311yescharacteristic
329C2#357×D4711yescharacteristic
330C2#2024510611yescharacteristic
331C2#2024556711yescharacteristic
332C2#2024557011yescharacteristic
333C2#2024558411yescharacteristic
334C2#2024558711yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12866
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
4. #20241480C2semidirect
5. #20241479C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
15. #107×D47C4semidirect
166. #1380D47semidirect
189. C47#12866semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
C2×(C2×D47)⋊C162
#202434142
#202414802
#202414792
C47×#13802
#1286647