Finite Group Databasebeta

← #26131394

Subgroups — #26131394

Order 12032.

420 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic
2#20244998C211yesmaximal, characteristic
3C2×#15688900C211yesmaximal, characteristic, complemented
4#20243165C211yesmaximal, characteristic
5#20241468C211yesmaximal, characteristic, complemented
6#20241467C211yesmaximal, characteristic, complemented
7C2×C47×#347C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093964C2211yescharacteristic
10C2×#13093964C2211yescharacteristic
11C2×#13093963C412yescomplemented
12M32×D47—22no—
13M32×D47—22no—
14C2×C16×D47C412yescomplemented
15C2×(C2×D47)⋊C8C411yescharacteristic
16C2×#13093934C2211yescharacteristic
17C4×(C2×D47)⋊C4C411yescharacteristic
18(C2×D47)⋊C16C412yescomplemented
19(C2×D47)⋊C16C412yescomplemented
20#15688900—22no—
21#15688878C411yescharacteristic
22#15688877C411yescharacteristic
23C2×M32×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×#97×C47C2211yescharacteristic
26C47×#347—22no—
27C22×C4×D47C2×C411yescharacteristic
28C22×C47⋊C8C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47—21no—
34C2×C8×D47C2×C411yescharacteristic
35C2×C8×D47C2×C411yescharacteristic
36C2×C8×D47C2×C411yescharacteristic
37C2×C8×D47C2×C411yescharacteristic
38C2×(C2×D47)⋊C4—21no—
39C2×C4×Dic47C2×C411yescharacteristic
40#13093964—21no—
41#13093964—21no—
42#13093964—21no—
43#13093964—21no—
44#13093963—24no—
45C2×C47⋊C16C2×C412yes—
46C2×C47⋊C16C2×C412yes—
47C16×D47—24no—
48(C2×D47)⋊C8—21no—
49(C2×D47)⋊C8—21no—
50#13093934—21no—
51#13093934—21no—
52C47⋊#95—21no—
53C22×C8×C47C2×C411yescharacteristic
54C22×C8×C47C2311yescharacteristic
55C2×C42×C47C2×C411yescharacteristic
56M32×C47—21no—
57M32×C47—21no—
58M32×C47D412yes—
59M32×C47D412yes—
60C2×C16×C47C2×C412yes—
61C2×C16×C47C2×C412yes—
62#97×C47—21no—
63#97×C47—21no—
64C23×D47M1611yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C22×C411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47M1611yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C4211yescharacteristic
74C2×C4×D47C4211yescharacteristic
75C2×C4×D47M1611yescharacteristic
76C2×C4×D47M1611yescharacteristic
77C2×C8×C47—21no—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47C22×C411yescharacteristic
81C2×C8×C47C22×C411yescharacteristic
82C2×C8×C47C2×D411yescharacteristic
83C2×C8×C47C2×D411yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C2×C8×C47#4111yescharacteristic
86C42×C47—21no—
87C42×C47—21no—
88(C2×D47)⋊C4—42no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—21no—
93C2×C47⋊C8—21no—
94C2×C47⋊C8—21no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8C4211yescharacteristic
97C2×C47⋊C8C4211yescharacteristic
98C8×D47—21no—
99C8×D47—21no—
100C8×D47—21no—
101C8×D47—21no—
102C8×D47—21no—
103C8×D47—21no—
104C8×D47—21no—
105C8×D47—21no—
106C16×C47—22no—
107C16×C47C22⋊C414yescomplemented
108C47⋊C16—22no—
109C47⋊C16—22no—
110C23×C47C2×M1611yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—22no—
114C22×D47—41no—
115C22×D47#9711yescharacteristic
116C22×D47#9711yescharacteristic
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47C2×C4211yescharacteristic
121C2×C4×C47C4×D411yescharacteristic
122C2×C4×C47C4×D411yescharacteristic
123C2×C4×C47C2×M1611yescharacteristic
124C2×C4×C47#13111yescharacteristic
125C2×C4×C47#13111yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47#9711yescharacteristic
132C2×Dic47#9711yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—21no—
140C4×D47—21no—
141C8×C47—41no—
142C8×C47C2×C22⋊C411yescharacteristic
143C8×C47#11711yescharacteristic
144C8×C47C4×D411yescharacteristic
145C8×C47C4×D411yescharacteristic
146C47⋊C8—21no—
147C47⋊C8—21no—
148C47⋊C8—41no—
149#12616—471nomaximal, Sylow
150C22×C47—21no—
151C22×C47—21no—
152C22×C47C2×#9711yescharacteristic
153C22×C47#43511yescharacteristic
154C22×C47#43511yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—42no—
161C2×D47—42no—
162C2×D47#34712yescomplemented
163C4×C47—81no—
164C4×C47C4×C22⋊C411yescharacteristic
165C4×C47#40511yescharacteristic
166C4×C47#43511yescharacteristic
167C4×C47#43511yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—81no—
171C22×M32—471no—
172#2112—471no—
173C2×#347—471no—
174C2×#347D4711yescharacteristic, complemented
175#1752—471no—
176#1375—471no—
177#1375—471no—
178C2×C47—21no—
179C2×C47—21no—
180C2×C47#175211yescharacteristic
181C2×C47C2×#34711yescharacteristic
182C2×C47#211011yescharacteristic
183D47—22no—
184D47—41no—
185C23×C8—471no—
186C2×M32—471no—
187C2×M32—471no—
188C2×M32—472no—
189C2×M32—942no—
190C2×M32—942no—
191C2×M32C2×D4711yescharacteristic
192C2×M32C2×D4711yescharacteristic
193C22×C16—472no—
194C2×C22⋊C8—471no—
195C2×#97—471no—
196C2×#97C2×D4711yescharacteristic
197C4×C22⋊C4—471no—
198C22⋊C16—472no—
199C22⋊C16—472no—
200#347—22no—
201#347—942no—
202#336—471no—
203#336—471no—
204C47#1261611yescharacteristic, complemented, Sylow
205C23×C4—471no—
206C22×C8—471no—
207C22×C8—471no—
208C22×C8—471no—
209C22×C8—471no—
210C22×C8—471no—
211C22×C8—471no—
212C22×C8—941no—
213C22×C8—941no—
214C22×C8—941no—
215C22×C8—941no—
216C22×C8C4×D4711yescharacteristic
217C22×C8C22×D4711yescharacteristic
218C2×C22⋊C4—941no—
219C2×C42—471no—
220C2×C42C4×D4711yescharacteristic
221M32—21no—
222M32—21no—
223M32—941no—
224M32—941no—
225M32—941no—
226M32—941no—
227M32—944no—
228M32D18812yes—
229M32C22⋊D4712yes—
230C2×C16—472no—
231C2×C16—472no—
232C2×C16—944no—
233C2×C16C4×D4712yes—
234C2×C16C4×D4712yes—
235C22⋊C8—941no—
236C22⋊C8—941no—
237#97—21no—
238#97—21no—
239#97—941no—
240#97—941no—
241#95—941no—
242C24—471no—
243C22×C4—21no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4C2×C4×D4711yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—941no—
264C2×C8—941no—
265C2×C8—941no—
266C2×C8—941no—
267C2×C8—941no—
268C2×C8—941no—
269C2×C8—941no—
270C2×C8—941no—
271C2×C8—941no—
272C2×C8—941no—
273C2×C8C2×C4×D4711yescharacteristic
274C2×C8C2×C4×D4711yescharacteristic
275C2×C8C2×D18811yescharacteristic
276C2×C8#1062535011yescharacteristic
277C2×C8#1062535011yescharacteristic
278C2×C8C2×C22⋊D4711yescharacteristic
279C22⋊C4—1882no—
280C42—21no—
281C42—21no—
282C42—941no—
283C42—941no—
284C16—22no—
285C16—942no—
286C16—942no—
287C16(C2×D47)⋊C414yescomplemented
288C23—471no—
289C23—471no—
290C23—942no—
291C23—941no—
292C23—941no—
293C23—1881no—
294C23M16×D4711yescharacteristic
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—471no—
299C2×C4—471no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4C42×D4711yescharacteristic
314C2×C4C4×C22⋊D4711yescharacteristic
315C2×C4C4×D18811yescharacteristic
316C2×C4M16×D4711yescharacteristic
317C2×C4#1309403211yescharacteristic
318C2×C4#1309403211yescharacteristic
319C8—41no—
320C8—941no—
321C8—941no—
322C8—1881no—
323C8C2×(C2×D47)⋊C411yescharacteristic
324C8#1309398111yescharacteristic
325C8C4×C22⋊D4711yescharacteristic
326C8C4×D18811yescharacteristic
327C22—21no—
328C22—21no—
329C22—472no—
330C22—941no—
331C22—941no—
332C22—941no—
333C22—941no—
334C22—941no—
335C22—1882no—
336C22—1882no—
337C22#97×D4711yescharacteristic
338C22#1568919211yescharacteristic
339C22#1568919611yescharacteristic
340C4—81no—
341C4—941no—
342C4—941no—
343C4—3761no—
344C4C4×(C2×D47)⋊C411yescharacteristic
345C4#1568908011yescharacteristic
346C4#1568919211yescharacteristic
347C4#1568919611yescharacteristic
348C2—21no—
349C2—21no—
350C2—942no—
351C2—1881no—
352C2#2024316511yescharacteristic
353C2#347×D4711yescharacteristic
354C2#2024499111yescharacteristic
subgroupG/H
centerC2×C4C42×D47
commutatorC2×C4×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#347C2
socleC22×C47C2×#97
prime radicalC23×D47M16
cosocleC22×C8×C47C23
hypercenterC2×#347D47
hypocenterC47#12616
LCSG ▷ C2×C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#347

Complements

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

NH ≅ G/Ntype
3. C2×#15688900C2semidirect
5. #20241468C2semidirect
6. #20241467C2semidirect
7. C2×C47×#347C2semidirect
11. C2×#13093963C4semidirect
14. C2×C16×D47C4semidirect
18. (C2×D47)⋊C16C4semidirect
19. (C2×D47)⋊C16C4semidirect
107. C16×C47C22⋊C4semidirect
162. C2×D47#347semidirect
174. C2×#347D47semidirect
204. C47#12616semidirect
287. C16(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
#202449982
C2×#156889002
#202431652
#202414682
#202414672
C2×C47×#3472
#1261647