Finite Group Databasebeta

← #26114402

Subgroups — #26114402

Order 12032.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244106C211yesmaximal, characteristic
2C4×#13093955C211yesmaximal, characteristic
3#20241229C211yesmaximal, characteristic
4#20241227C211yesmaximal, characteristic
5#20241222C211yesmaximal, characteristic
6C47⋊#1273C211yesmaximal, characteristic
7C8×C4⋊C4×C47C211yesmaximal, characteristic
8C2×#13093955C411yescharacteristic
9C2×#13093955C411yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—21no—
12C2×C4×C47⋊C8C2211yescharacteristic
13C2×C4×C47⋊C8C2211yescharacteristic
14C4×C4⋊Dic47C2211yescharacteristic
15#15688885C411yescharacteristic
16#15688885C411yescharacteristic
17#15688877—21no—
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×C4×C8×C47—21no—
20C2×C4×C8×C47C2211yescharacteristic
21C4×C4⋊C4×C47C2211yescharacteristic
22C47×#336—21no—
23C22×C47⋊C8—21no—
24C22×C47⋊C8—21no—
25C22×C47⋊C8C2×C411yescharacteristic
26C22×C47⋊C8C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×C4×Dic47—21no—
30#13093955—22no—
31#13093955C814yescomplemented
32C4⋊(C47⋊C8)—21no—
33C4⋊(C47⋊C8)—21no—
34Dic47⋊C8—42no—
35C4×C47⋊C8—21no—
36C4×C47⋊C8—21no—
37C4×C47⋊C8—21no—
38C4×C47⋊C8—21no—
39C47⋊#95—21no—
40C22×C8×C47—21no—
41C22×C8×C47D411yescharacteristic
42C22×C8×C47D411yescharacteristic
43C2×C4⋊C4×C47C2×C411yescharacteristic
44C2×C4⋊C4×C47C2×C411yescharacteristic
45C2×C42×C47—21no—
46C2×C42×C47C2311yescharacteristic
47C4⋊C8×C47—21no—
48C4⋊C8×C47Q812yes—
49C4×C8×C47—21no—
50C4×C8×C47—21no—
51C4×C8×C47—42no—
52#95×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47C22×C411yescharacteristic
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47#4111yescharacteristic
58C22×Dic47—21no—
59C22×Dic47—21no—
60C2×C8×C47—21no—
61C2×C8×C47—21no—
62C2×C8×C47—22no—
63C2×C8×C47—21no—
64C2×C8×C47—21no—
65C2×C8×C47—21no—
66C2×C8×C47—41no—
67C2×C8×C47—41no—
68C2×C8×C47SD1612yes—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2×C812yes—
72C4⋊C4×C47M1612yes—
73C42×C47—41no—
74C42×C47—41no—
75C42×C47C2×Q811yescharacteristic
76C42×C47#4111yescharacteristic
77C42×C47#4111yescharacteristic
78C42×C47#4111yescharacteristic
79C4⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47C2×C812yes—
83C4×Dic47—41no—
84C4×Dic47—41no—
85C2×C47⋊C8—21no—
86C2×C47⋊C8—21no—
87C2×C47⋊C8—22no—
88C2×C47⋊C8—21no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—41no—
92C2×C47⋊C8—41no—
93C2×C47⋊C8—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8C2×C812yes—
97C23×C47C4×D411yescharacteristic
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47#11711yescharacteristic
107C2×C4×C47C4×Q811yescharacteristic
108C2×C4×C47C22⋊Q811yescharacteristic
109C2×C4×C47#12311yescharacteristic
110C2×C4×C47#12511yescharacteristic
111C2×C4×C47#12611yescharacteristic
112C2×C4×C47C22×C811yescharacteristic
113C2×C4×C47C2×M1611yescharacteristic
114C2×C4×C47#13111yescharacteristic
115C2×C4×C47#13111yescharacteristic
116C2×C4×C47C2×SD1611yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×Dic47—22no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C8×C47—22no—
127C8×C47—42no—
128C8×C47—41no—
129C47⋊C8—22no—
130C47⋊C8—42no—
131C47⋊C8—41no—
132C47⋊C8—81no—
133#9534—471nomaximal, Sylow
134C22×C47#38711yescharacteristic
135C22×C47C8×D411yescharacteristic
136C22×C47#43511yescharacteristic
137C22×C47C4×SD1611yescharacteristic
138C22×C47#44011yescharacteristic
139C22×C47#44311yescharacteristic
140C22×C47#44411yescharacteristic
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—42no—
144C4×C47—42no—
145C4×C47#43111yescharacteristic
146C4×C47#43311yescharacteristic
147C4×C47C8×Q811yescharacteristic
148C4×C47#44611yescharacteristic
149C4×C47#47511yescharacteristic
150C4×C47#47811yescharacteristic
151C4×C47#48111yescharacteristic
152C4×C47#48511yescharacteristic
153Dic47—42no—
154Dic47—81no—
155#1939—471no—
156C4×#106—471no—
157C8×C4⋊C4D4711yescharacteristic
158#1279—471no—
159#1279—471no—
160#1277—471no—
161#1273—471no—
162C2×C47C8×SD1611yescharacteristic
163C2×C47SD16⋊C811yescharacteristic
164C2×C47#158311yescharacteristic
165C2×C47#158511yescharacteristic
166C2×C47#191611yescharacteristic
167C2×C47#191911yescharacteristic
168C2×C47#192211yescharacteristic
169C2×#106—471no—
170C2×#106—471no—
171C2×C4⋊C8—471no—
172C2×C4⋊C8—941no—
173C2×C4⋊C8C2×D4711yescharacteristic
174C2×C4×C8—21no—
175C2×C4×C8—471no—
176C2×C4×C8—471no—
177C2×C4×C8C2×D4711yescharacteristic
178C4×C4⋊C4—471no—
179C4×C4⋊C4C2×D4711yescharacteristic
180#340—471no—
181#340—471no—
182#336—21no—
183#336—941no—
184C47#953411yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—471no—
187C22×C8—471no—
188C22×C8—941no—
189C22×C8—941no—
190C22×C8C22⋊D4711yescharacteristic
191C22×C8C22⋊D4711yescharacteristic
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4C4×D4711yescharacteristic
195C2×C4⋊C4C4×D4711yescharacteristic
196C2×C42—21no—
197C2×C42—941no—
198C2×C42C22×D4711yescharacteristic
199#106—474no—
200#106—942no—
201C4⋊C8—21no—
202C4⋊C8—941no—
203C4⋊C8—941no—
204C4⋊C8—1882no—
205C4⋊C8Dic9412yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—42no—
209C4×C8—941no—
210C4×C8—941no—
211C4×C8—941no—
212C4×C8—941no—
213#95—21no—
214#95—941no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—941no—
218C22×C4—941no—
219C22×C4C2×C4×D4711yescharacteristic
220C22×C4#1062535011yescharacteristic
221C22×C4C2×C22⋊D4711yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—472no—
231C2×C8—941no—
232C2×C8—941no—
233C2×C8—942no—
234C2×C8—941no—
235C2×C8—941no—
236C2×C8—941no—
237C2×C8—1881no—
238C2×C8—1881no—
239C2×C8—1881no—
240C2×C8—1881no—
241C2×C8—1881no—
242C2×C8#1062533612yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—472no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4C8×D4712yes—
250C4⋊C4#1062532412yes—
251C42—41no—
252C42—41no—
253C42—1881no—
254C42—1881no—
255C42C2×Dic9411yescharacteristic
256C42#1062535011yescharacteristic
257C42#1062535011yescharacteristic
258C42#1062535011yescharacteristic
259C23C4×C22⋊D4711yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—942no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4—1881no—
272C2×C4—1881no—
273C2×C4—1881no—
274C2×C4#1309398111yescharacteristic
275C2×C4C4×Dic9411yescharacteristic
276C2×C4#1309400311yescharacteristic
277C2×C4#1309400711yescharacteristic
278C2×C4#1309401611yescharacteristic
279C2×C4#1309401811yescharacteristic
280C2×C4C2×C8×D4711yescharacteristic
281C2×C4C2×#1062532411yescharacteristic
282C2×C4#1309403011yescharacteristic
283C2×C4#1309403011yescharacteristic
284C2×C4C2×#1062533611yescharacteristic
285C2×C4#1309404411yescharacteristic
286C2×C4#1309405011yescharacteristic
287C2×C4#1309405411yescharacteristic
288C8—22no—
289C8—42no—
290C8—41no—
291C8—942no—
292C8—3761no—
293C8—1882no—
294C8—1881no—
295C22#1568900711yescharacteristic
296C22C8×C22⋊D4711yescharacteristic
297C22#1568919411yescharacteristic
298C22C4×#1062533611yescharacteristic
299C22#1568922311yescharacteristic
300C22#1568923811yescharacteristic
301C22#1568924311yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—3761no—
307C4—1882no—
308C4#1568917411yescharacteristic
309C4#1568918211yescharacteristic
310C4C8×Dic9411yescharacteristic
311C4#1568925311yescharacteristic
312C4#1568940811yescharacteristic
313C4#1568942311yescharacteristic
314C4#1568944111yescharacteristic
315C4#1568946411yescharacteristic
316C2C8×#1062533611yescharacteristic
317C2#2024220011yescharacteristic
318C2#2024223111yescharacteristic
319C2#2024224511yescharacteristic
320C2#2024394511yescharacteristic
321C2#2024396611yescharacteristic
322C2#2024398711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC8×C4⋊C4×C47C2
socle, prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenterC8×C4⋊C4D47
hypocenterC47#9534
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. #13093955C8semidirect
184. C47#9534semidirect

Maximal subgroups

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

subgroupindex
#202441062
C4×#130939552
#202412292
#202412272
#202412222
C47⋊#12732
C8×C4⋊C4×C472
#953447