Finite Group Databasebeta

← #26132574

Subgroups — #26132574

Order 12032.

426 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689160C211yesmaximal, 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×#13093982—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689160—22no—
12#15689160C414yescomplemented
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15C2×#13093955—21no—
16#15688980—21no—
17(C2×D47)⋊C16—22no—
18#15688885—21no—
19C22×C16×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C22×C4×D47D411yescharacteristic
23C22×C47⋊C8D411yescharacteristic
24C2×C8×D47—21no—
25C2×C8×D47—21no—
26C2×C8×D47—21no—
27C2×C8×D47—21no—
28C2×C8×D47C2×C412yes—
29C2×C8×D47D412yes—
30#13093982—24no—
31#13093982—42no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34C2×(C2×D47)⋊C4—41no—
35C2×(C2×D47)⋊C4—41no—
36C2×C4×Dic47—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#13093955—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×D47C22⋊C412yes—
68C2×C4×D47SD1612yes—
69C2×C8×C47C22×C411yescharacteristic
70C2×C8×C47C2×D411yescharacteristic
71C2×C8×C47#4111yescharacteristic
72C2×C8×C47#4111yescharacteristic
73C2×C8×C47#4111yescharacteristic
74C2×C8×C47#4111yescharacteristic
75C4⋊C4×C47—22no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79(C2×D47)⋊C4—44no—
80(C2×D47)⋊C4—82no—
81C4⋊Dic47—22no—
82C4⋊Dic47—41no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C4×Dic47—44no—
86C2×C47⋊C8—21no—
87C2×C47⋊C8—21no—
88C2×C47⋊C8C22⋊C412yes—
89C8×D47—22no—
90C8×D47—22no—
91C8×D47—22no—
92C8×D47—22no—
93C16×C47—41no—
94C47⋊C16—41no—
95C23×C47C2×D811yescharacteristic
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47#10212yes—
103C2×C4×C47—42no—
104C2×C4×C47—81no—
105C2×C4×C47—81no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47—81no—
109C2×C4×C47C2×C22⋊C411yescharacteristic
110C2×C4×C47#12311yescharacteristic
111C2×C4×C47#12311yescharacteristic
112C2×C4×C47C2×SD1611yescharacteristic
113C2×C4×C47#13711yescharacteristic
114C2×C4×C47#13711yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—42no—
118C2×Dic47—81no—
119C2×Dic47—81no—
120C2×Dic47—81no—
121C2×Dic47—81no—
122C2×Dic47—81no—
123C2×Dic47#10212yes—
124C4×D47—22no—
125C4×D47—22no—
126C4×D47—22no—
127C4×D47—22no—
128C8×C47#11711yescharacteristic
129C8×C47#11711yescharacteristic
130C8×C47#12311yescharacteristic
131C8×C47#12311yescharacteristic
132C47⋊C8—22no—
133#12868—471nomaximal, Sylow
134C22×C47C2×#10211yescharacteristic
135C22×C47#48011yescharacteristic
136C22×C47#48011yescharacteristic
137C22×C47#50811yescharacteristic
138C22×C47#50811yescharacteristic
139C22×C47#50911yescharacteristic
140C22×C47#51011yescharacteristic
141C2×D47—22no—
142C2×D47—22no—
143C2×D47—22no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C4×C47—82no—
149C4×C47—161no—
150C4×C47#38111yescharacteristic
151C4×C47#41911yescharacteristic
152C4×C47#48311yescharacteristic
153C4×C47#48311yescharacteristic
154Dic47—22no—
155Dic47—82no—
156Dic47—161no—
157C2×#427—471no—
158C2×C22⋊C16—471no—
159#1808—471no—
160#1380—471no—
161#1380—471no—
162#1380—471no—
163#1380D4711yescharacteristic, complemented
164C2×C47#182311yescharacteristic
165C2×C47#213811yescharacteristic
166C2×C47#213911yescharacteristic
167C2×C47#223411yescharacteristic
168C2×C47#223411yescharacteristic
169C2×C47#223711yescharacteristic
170C2×C47#223711yescharacteristic
171D47—42no—
172C23×C8—471no—
173C2×#117—941no—
174C22×C16—471no—
175C22×C16C2×D4711yescharacteristic
176#427—474no—
177#427—942no—
178C2×#107—471no—
179C2×#107—471no—
180C2×#107C2×D4711yescharacteristic
181C2×#107C2×D4711yescharacteristic
182C2×#106—941no—
183#380—941no—
184C22⋊C16—942no—
185#340—941no—
186C47#1286811yescharacteristic, complemented, Sylow
187C23×C4—471no—
188C22×C8—471no—
189C22×C8—472no—
190C22×C8—472no—
191C22×C8—941no—
192C22×C8—941no—
193C22×C8—941no—
194C22×C8—941no—
195C22×C8C22×D4711yescharacteristic
196#117—944no—
197#117—1882no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—941no—
201C2×C4⋊C4—941no—
202C2×C22⋊C4—1881no—
203C2×C22⋊C4—1881no—
204C2×C42—1881no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16—941no—
209C2×C16—941no—
210C2×C16—941no—
211#107—21no—
212#107—21no—
213#107—21no—
214#107—472no—
215#107—941no—
216#107—941no—
217#107—941no—
218#107C4×D4712yes—
219#106—944no—
220#95—1881no—
221C24—471no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—471no—
225C22×C4—472no—
226C22×C4—472no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4—1881no—
232C22×C4—1881no—
233C22×C4D4×D4711yescharacteristic
234C2×C8—472no—
235C2×C8—941no—
236C2×C8—941no—
237C2×C8—942no—
238C2×C8—942no—
239C2×C8—942no—
240C2×C8—942no—
241C2×C8C2×C4×D4711yescharacteristic
242C2×C8#1062535011yescharacteristic
243C2×C8#1062535011yescharacteristic
244C2×C8D4×D4711yescharacteristic
245C2×C8#1062535211yescharacteristic
246C2×C8#1062535411yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—942no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C22⋊C4—3762no—
256C22⋊C4—1884no—
257C42—1884no—
258C16—41no—
259C16—1881no—
260C23—472no—
261C23—941no—
262C23—941no—
263C23—941no—
264C23—941no—
265C23—941no—
266C23—941no—
267C23D8×D4711yescharacteristic
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—472no—
275C2×C4—941no—
276C2×C4—941no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—942no—
280C2×C4—942no—
281C2×C4—3761no—
282C2×C4—3761no—
283C2×C4—3761no—
284C2×C4—3761no—
285C2×C4—3761no—
286C2×C4—1882no—
287C2×C4C22⋊C4×D4711yescharacteristic
288C2×C4#1309400611yescharacteristic
289C2×C4#1309400911yescharacteristic
290C2×C4SD16×D4711yescharacteristic
291C2×C4#1309405311yescharacteristic
292C2×C4#1309405611yescharacteristic
293C8—942no—
294C8#1309398111yescharacteristic
295C8#1309398211yescharacteristic
296C8#1309400611yescharacteristic
297C8#1309400911yescharacteristic
298C22—942no—
299C22—942no—
300C22—942no—
301C22—1881no—
302C22—1881no—
303C22—1881no—
304C22—1881no—
305C22#102×D4711yescharacteristic
306C22#1568943511yescharacteristic
307C22#1568943811yescharacteristic
308C22#1568955411yescharacteristic
309C22#1568955611yescharacteristic
310C22#1568955711yescharacteristic
311C22#1568956211yescharacteristic
312C4—82no—
313C4—161no—
314C4—942no—
315C4—3762no—
316C4—7521no—
317C4#1568898511yescharacteristic
318C4#1568913011yescharacteristic
319C4#1568945211yescharacteristic
320C4#1568945511yescharacteristic
321C2—1882no—
322C2#2024347311yescharacteristic
323C2#2024509411yescharacteristic
324C2#2024509711yescharacteristic
325C2#2024557811yescharacteristic
326C2#2024558211yescharacteristic
327C2#2024559511yescharacteristic
328C2#2024559911yescharacteristic
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#12868
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
12. #15689160C4semidirect
163. #1380D47semidirect
186. C47#12868semidirect

Maximal subgroups

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

subgroupindex
C2×#156891602
C2×(C2×D47)⋊C162
#202434142
#202414802
#202414792
C47×#13802
#1286847