Finite Group Databasebeta

← #26127346

Subgroups — #26127346

Order 12032.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
2#20243413C211yesmaximal, characteristic, complemented
3#20241400C212yesmaximal, complemented
4#20241397C212yesmaximal, complemented
5C47×#3050C211yesmaximal, characteristic
6C22×C47⋊C16—21no—
7C2×#13093956—21no—
8#15688983—21no—
9C22⋊(C47⋊C16)—21no—
10C22⋊(C47⋊C16)C2212yes—
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—
23C2×C4⋊Dic47—22no—
24C2×C22⋊Dic47—41no—
25C2×C47⋊C16—22no—
26C2×C47⋊C16—42no—
27#13093956—42no—
28C47⋊#95—41no—
29C2×#41×C47—21no—
30C23×C4×C47D411yescharacteristic
31#135×C47—42no—
32C2×Q16×C47C2×C411yescharacteristic
33C2×SD16×C47—21no—
34C2×D8×C47C2×C411yescharacteristic
35C22×C8×C47—42no—
36C22×C8×C47C2×C411yescharacteristic
37C22×C8×C47C2×C411yescharacteristic
38C22×C8×C47D411yescharacteristic
39C22×C8×C47D411yescharacteristic
40C22×C8×C47D411yescharacteristic
41C22×C8×C47C2311yescharacteristic
42#123×C47—41no—
43C22⋊Q8×C47—21no—
44C22⋊Q8×C47—21no—
45#121×C47—21no—
46#121×C47—21no—
47#120×C47—41no—
48C4×D4×C47—41no—
49C4×D4×C47—41no—
50#117×C47—21no—
51#107×C47C2×C411yescharacteristic
52#107×C47C2×C411yescharacteristic
53#106×C47—21no—
54#103×C47—21no—
55#103×C47—21no—
56#102×C47—21no—
57#102×C47—21no—
58C24×C47D811yescharacteristic
59#41×C47—42no—
60#41×C47—42no—
61C2×Q8×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47D811yescharacteristic
72C22×C4×C47SD1611yescharacteristic
73C22×C4×C47SD1611yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—42no—
76Q16×C47—41no—
77SD16×C47—42no—
78D8×C47—41no—
79C2×C8×C47—22no—
80C2×C8×C47—22no—
81C2×C8×C47—22no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C22⋊C411yescharacteristic
86C2×C8×C47C22⋊C411yescharacteristic
87C2×C8×C47C22×C411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C22⋊C4×C47—41no—
94C22⋊C4×C47—41no—
95C22⋊C4×C47—41no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C42×C47—41no—
99C22⋊Dic47—82no—
100C4⋊Dic47—42no—
101C4⋊Dic47—42no—
102C47⋊C16—42no—
103C23×C47—22no—
104C23×C47—22no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47#10211yescharacteristic
108C23×C47#10211yescharacteristic
109C23×C47C2×D811yescharacteristic
110Q8×C47—41no—
111Q8×C47—41no—
112D4×C47—41no—
113D4×C47—41no—
114D4×C47—82no—
115D4×C47—82no—
116D4×C47—82no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—82no—
130C2×C4×C47#10211yescharacteristic
131C2×C4×C47#10211yescharacteristic
132C2×C4×C47C2×C22⋊C411yescharacteristic
133C2×C4×C47C2×SD1611yescharacteristic
134C2×Dic47—82no—
135C2×Dic47—82no—
136C2×Dic47—82no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47#9912yes—
141#11885—471nomaximal, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—44no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47—81no—
153C22×C47#36012yes—
154C22×C47C2×#10211yescharacteristic
155C22×C47#50812yes—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—81no—
160C4×C47—81no—
161C4×C47—81no—
162C4×C47C2×#9911yescharacteristic
163C4×C47#42111yescharacteristic
164Dic47—162no—
165#3050D4711yescharacteristic
166C2×C22⋊C16—471no—
167#1807—471no—
168#1348—472no—
169#1347—472no—
170C2×C47—22no—
171C2×C47—22no—
172C2×C47—41no—
173C2×C47—161no—
174C2×C47#151911yescharacteristic
175C2×C47#213811yescharacteristic
176C2×C47C2×#36011yescharacteristic
177C2×#135Dic4711yescharacteristic, complemented
178C23×C8C2×D4711yescharacteristic
179#525—21no—
180C22×C16—941no—
181#467Dic4711yescharacteristic, complemented
182#467C2×D4711yescharacteristic
183#466Dic4711yescharacteristic, complemented
184#466C2×D4711yescharacteristic
185#465—21no—
186#465—21no—
187#427Dic4711yescharacteristic, complemented
188C2×#106—941no—
189#416—21no—
190#380—941no—
191C22⋊C16—472no—
192C22⋊C16—941no—
193#340—472no—
194C47#1188511yescharacteristic, complemented, Sylow
195C2×#41—21no—
196C23×C4C22⋊D4711yescharacteristic
197#135—42no—
198C2×Q16C2×Dic4711yescharacteristic
199C2×SD16—21no—
200C2×D8C2×Dic4711yescharacteristic
201C22×C8—42no—
202C22×C8C2×Dic4711yescharacteristic
203C22×C8C2×Dic4711yescharacteristic
204C22×C8C22⋊D4711yescharacteristic
205C22×C8C22⋊D4711yescharacteristic
206C22×C8C22⋊D4711yescharacteristic
207C22×C8C22×D4711yescharacteristic
208#123—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213#120—41no—
214C4×D4—41no—
215C4×D4—41no—
216#117—21no—
217C2×C4⋊C4—942no—
218C2×C22⋊C4—1881no—
219C2×C16—942no—
220C2×C16—1882no—
221#107C2×Dic4711yescharacteristic
222#107C2×Dic4711yescharacteristic
223#106—21no—
224#106—1882no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#95—1881no—
230C24#1062533411yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—1882no—
242C22×C4#1062533411yescharacteristic
243C22×C4#1062533511yescharacteristic
244C22×C4#1062533511yescharacteristic
245C22×C4C22⋊Dic4711yescharacteristic
246C22×C4C22⋊Dic4711yescharacteristic
247C22×C4C2×C22⋊D4711yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊Dic4711yescharacteristic
258C2×C8C22⋊Dic4711yescharacteristic
259C2×C8C22×Dic4711yescharacteristic
260C2×C8C2×C22⋊D4711yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1882no—
266C4⋊C4—1882no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—3762no—
273C42—41no—
274C16—1882no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#1309394511yescharacteristic
280C23#1309394511yescharacteristic
281C23C2×#1062533411yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—3762no—
303C2×C4—3762no—
304C2×C4—3762no—
305C2×C4#1309394511yescharacteristic
306C2×C4#1309394511yescharacteristic
307C2×C4C2×C22⋊Dic4711yescharacteristic
308C2×C4C2×#1062533511yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#1309393912yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1568893312yes—
325C22C2×#1309394511yescharacteristic
326C22#1568955312yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—7522no—
334C4C2×#1309393911yescharacteristic
335C4#1568914011yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2#2024195611yescharacteristic
341C2#2024509511yescharacteristic
342C2C2×#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#11885
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. C2×C22⋊(C47⋊C16)C2semidirect
2. #20243413C2semidirect
3. #20241400C2semidirect
4. #20241397C2semidirect
12. C2×#135×C47C4semidirect
15. C47×#467C4semidirect
17. C47×#466C4semidirect
21. C47×#427C4semidirect
177. C2×#135Dic47semidirect
181. #467Dic47semidirect
183. #466Dic47semidirect
187. #427Dic47semidirect
194. C47#11885semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C47⋊C16)2
#202434132
#202414002
#202413972
C47×#30502
#1188547