Finite Group Databasebeta

← #26109452

Subgroups — #26109452

Order 12032.

432 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
1#20243408C212yesmaximal
2C4×#13093958C211yesmaximal, characteristic, complemented
3#20242144C211yesmaximal, characteristic, complemented
4#20241290C212yesmaximal, complemented
5C47×#2965C211yesmaximal, characteristic
6C2×#13093958—21no—
7#15689147C2212yes—
8C2×#13093951—22no—
9C4×C4⋊Dic47C2212yes—
10#15688886—21no—
11#15688882—22no—
12#15688874—21no—
13#15688874—21no—
14C4×#41×C47C2211yescharacteristic
15C47×#446C411yescharacteristic, complemented
16C47×#446C411yescharacteristic, complemented
17C47×#436C411yescharacteristic, complemented
18C47×#436C411yescharacteristic, complemented
19C47×#435—21no—
20C47×#435—21no—
21C47×#431—21no—
22C47×#431C2211yescharacteristic
23C4×M16×C47—21no—
24C2×C4×C8×C47C2211yescharacteristic
25C2×#10625329—22no—
26C2×C4⋊Dic47—22no—
27C2×C4×Dic47—22no—
28#13093958—24no—
29C4⋊(C47⋊C8)—22no—
30C4⋊(C47⋊C8)—22no—
31#13093951—44no—
32C47⋊#95—22no—
33C2×#41×C47D411yescharacteristic
34C2×M16×C47—21no—
35C2×M16×C47—21no—
36C22×C8×C47D411yescharacteristic
37C22×C8×C47D411yescharacteristic
38C4×Q8×C47C2×C411yescharacteristic
39C4×Q8×C47Q811yescharacteristic
40C4×D4×C47—21no—
41C4×D4×C47—21no—
42C4×D4×C47C2×C411yescharacteristic
43C4×D4×C47Q811yescharacteristic
44#117×C47—21no—
45#117×C47D411yescharacteristic
46C2×C42×C47—21no—
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—21no—
49C4⋊C8×C47—21no—
50C4⋊C8×C47C2×C411yescharacteristic
51C4⋊C8×C47C2×C411yescharacteristic
52C22⋊C8×C47—21no—
53C22⋊C8×C47—21no—
54C22⋊C8×C47—21no—
55#97×C47—21no—
56#97×C47—21no—
57C4×C8×C47—21no—
58C4×C8×C47C2×C411yescharacteristic
59C4×C8×C47C2×C411yescharacteristic
60C4×C8×C47D411yescharacteristic
61C4×C8×C47D411yescharacteristic
62#41×C47—22no—
63#41×C47—22no—
64C2×Q8×C47C4⋊C411yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47C4⋊C411yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47#4111yescharacteristic
73C22×Dic47—42no—
74M16×C47—42no—
75M16×C47—42no—
76C2×C8×C47—22no—
77C2×C8×C47—21no—
78C2×C8×C47—21no—
79C2×C8×C47—41no—
80C2×C8×C47C22⋊C411yescharacteristic
81C2×C8×C47C22⋊C411yescharacteristic
82C2×C8×C47C22⋊C411yescharacteristic
83C2×C8×C47C22⋊C411yescharacteristic
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47C4⋊C411yescharacteristic
87C4⋊C4×C47C4⋊C411yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C42×C47—21no—
92C42×C47—21no—
93C42×C47—21no—
94C42×C47C22×C411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×Q811yescharacteristic
97C42×C47#4111yescharacteristic
98C4⋊Dic47—24no—
99C4⋊Dic47—42no—
100C4×Dic47—42no—
101C4×Dic47—42no—
102#10625329—42no—
103#10625329—42no—
104C2×C47⋊C8—42no—
105C23×C47—21no—
106C23×C47#12111yescharacteristic
107Q8×C47—22no—
108D4×C47—22no—
109D4×C47—41no—
110D4×C47—41no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—41no—
117C2×C4×C47—42no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—42no—
121C2×C4×C47C2×C22⋊C411yescharacteristic
122C2×C4×C47C2×C4⋊C411yescharacteristic
123C2×C4×C47#11711yescharacteristic
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47C22⋊Q811yescharacteristic
126C2×C4×C47C22⋊Q811yescharacteristic
127C2×C4×C47AGL(1,ℤ/8)12yes—
128C2×C4×C47#13712yes—
129C2×Dic47—44no—
130C2×Dic47—82no—
131C2×Dic47—82no—
132C8×C47—21no—
133C8×C47—21no—
134C8×C47—21no—
135C8×C47—41no—
136C8×C47—41no—
137C8×C47#10412yescomplemented
138C47⋊C8—82no—
139#8668—471nomaximal, Sylow
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47#38011yescharacteristic
146C22×C47#46911yescharacteristic
147C22×C47#47011yescharacteristic
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47C2×#10411yescharacteristic
155C4×C47#42111yescharacteristic
156C4×C47#42812yes—
157C4×C47#46812yes—
158Dic47—84no—
159#2965D4711yescharacteristic
160#1806—472no—
161C4×#107—471no—
162#1566—471no—
163#1303—472no—
164C2×C47—21no—
165C2×C47—21no—
166C2×C47—81no—
167C2×C47#180611yescharacteristic
168C2×C47#180911yescharacteristic
169C2×C47#181411yescharacteristic
170C4×#41C2×D4711yescharacteristic
171#446Dic4711yescharacteristic, complemented
172#446Dic4711yescharacteristic, complemented
173#436Dic4711yescharacteristic, complemented
174#436Dic4711yescharacteristic, complemented
175#435—21no—
176#435—21no—
177#431—21no—
178#431C2×D4711yescharacteristic
179C2×#107—941no—
180#423—472no—
181C2×#104—942no—
182C4×M16—21no—
183C2×C4×C8C2×D4711yescharacteristic
184C4×C4⋊C4—472no—
185#340—941no—
186#339—942no—
187#334—941no—
188#334—941no—
189C47#866811yescharacteristic, complemented, Sylow
190C2×#41D18811yescharacteristic
191C2×M16—21no—
192C2×M16—21no—
193C2×M16—942no—
194C22×C8C22⋊D4711yescharacteristic
195C22×C8C22⋊D4711yescharacteristic
196C4×Q8Dic9411yescharacteristic
197C4×Q8C2×Dic4711yescharacteristic
198C4×D4—21no—
199C4×D4—21no—
200C4×D4Dic9411yescharacteristic
201C4×D4C2×Dic4711yescharacteristic
202#117—21no—
203#117D18811yescharacteristic
204C2×C4⋊C4—942no—
205C2×C42—21no—
206C2×C42—942no—
207C2×C42C22×D4711yescharacteristic
208#107—944no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—942no—
212C4⋊C8—942no—
213C4⋊C8C2×Dic4711yescharacteristic
214C4⋊C8C2×Dic4711yescharacteristic
215#104—1884no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219#97—21no—
220#97—21no—
221C4×C8—21no—
222C4×C8C2×Dic4711yescharacteristic
223C4×C8C2×Dic4711yescharacteristic
224C4×C8C22⋊D4711yescharacteristic
225C4×C8C22⋊D4711yescharacteristic
226#95—942no—
227#41—22no—
228#41—22no—
229C2×Q8C4⋊Dic4711yescharacteristic
230C2×D4—21no—
231C2×D4C4⋊Dic4711yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—1882no—
236C22×C4C2×D18811yescharacteristic
237C22×C4#1062535011yescharacteristic
238C22×C4C2×C22⋊D4711yescharacteristic
239M16—42no—
240M16—42no—
241M16—1882no—
242M16—1882no—
243C2×C8—22no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—1882no—
248C2×C8C22⋊Dic4711yescharacteristic
249C2×C8C22⋊Dic4711yescharacteristic
250C2×C8C22⋊Dic4711yescharacteristic
251C2×C8C22⋊Dic4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—944no—
255C4⋊C4—1882no—
256C4⋊C4C4⋊Dic4711yescharacteristic
257C4⋊C4C4⋊Dic4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—1882no—
265C42—1882no—
266C42C2×Dic9411yescharacteristic
267C42#1062535011yescharacteristic
268C42C22×Dic4711yescharacteristic
269C42C2×C22⋊D4711yescharacteristic
270C23—21no—
271C23#1309399811yescharacteristic
272Q8—22no—
273D4—22no—
274D4—41no—
275D4—41no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—3762no—
287C2×C4—3762no—
288C2×C4—1884no—
289C2×C4C2×C22⋊Dic4711yescharacteristic
290C2×C4C2×C4⋊Dic4711yescharacteristic
291C2×C4#1309398311yescharacteristic
292C2×C4#1309399811yescharacteristic
293C2×C4#1309400311yescharacteristic
294C2×C4#1309400311yescharacteristic
295C2×C4#1309405212yes—
296C2×C4#1309405712yes—
297C8—21no—
298C8—21no—
299C8—21no—
300C8—41no—
301C8—41no—
302C8—3762no—
303C8#1309395112yescomplemented
304C22—21no—
305C22—21no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1568898311yescharacteristic
310C22#1568937611yescharacteristic
311C22#1568938111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3764no—
319C4C2×#1309395111yescharacteristic
320C4#1568914011yescharacteristic
321C4#1568916512yes—
322C4#1568936912yes—
323C2—21no—
324C2—21no—
325C2—81no—
326C2#2024340811yescharacteristic
327C2#2024342111yescharacteristic
328C2#2024344211yescharacteristic
subgroupG/H
centerC2×C4#13093998
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2965C2
socleC22×C47#380
prime radicalC2×#41×C47D4
cosocleC2×C42×C47C23
hypercenter#2965D47
hypocenterC47#8668
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. C4×#13093958C2semidirect
3. #20242144C2semidirect
4. #20241290C2semidirect
15. C47×#446C4semidirect
16. C47×#446C4semidirect
17. C47×#436C4semidirect
18. C47×#436C4semidirect
137. C8×C47#104semidirect
171. #446Dic47semidirect
172. #446Dic47semidirect
173. #436Dic47semidirect
174. #436Dic47semidirect
189. C47#8668semidirect
303. C8#13093951semidirect

Maximal subgroups

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

subgroupindex
#202434082
C4×#130939582
#202421442
#202412902
C47×#29652
#866847