Finite Group Databasebeta

← #26121041

Subgroups — #26121041

Order 12032.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244324C211yesmaximal, characteristic
2#20243516C211yesmaximal, characteristic
3#20243394C211yesmaximal, characteristic
4#20243394C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic
6#20241272C211yesmaximal, characteristic
7C47×#1277C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×#13093949—21no—
11C2×#13093949—21no—
12#15688993C2211yescharacteristic
13#15688993C2211yescharacteristic
14#15688886—21no—
15#15688886—21no—
16#15688886—21no—
17#15688886—21no—
18#15688877—21no—
19#15688877—21no—
20C2×C4⋊C8×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4×C8×C47C2211yescharacteristic
23C22×Dic94D411yescharacteristic
24C22×C47⋊C8—21no—
25C4×Dic94—21no—
26C4×Dic94—21no—
27C4×Dic94—21no—
28C4×Dic94—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47D411yescharacteristic
36C2×Dic47⋊C4—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40#13093949—42no—
41#13093949—42no—
42C22×C8×C47—21no—
43C22×C8×C47—21no—
44C22×C8×C47D411yescharacteristic
45C22×C8×C47D411yescharacteristic
46C2×C42×C47C2311yescharacteristic
47C4⋊C8×C47—21no—
48C4⋊C8×C47—21no—
49C4⋊C8×C47—21no—
50C4⋊C8×C47—21no—
51C4×C8×C47—21no—
52C4×C8×C47—21no—
53C22×C4×C47C2×D411yescharacteristic
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47#4111yescharacteristic
56C22×Dic47—21no—
57C22×Dic47—21no—
58C22×Dic47—41no—
59C22×Dic47—41no—
60C2×Dic94—21no—
61C2×Dic94—21no—
62C2×Dic94—21no—
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94SD1612yes—
66C2×C8×C47—21no—
67C2×C8×C47—21no—
68C2×C8×C47—21no—
69C2×C8×C47—21no—
70C2×C8×C47—21no—
71C2×C8×C47—21no—
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C42×C47#4111yescharacteristic
79C42×C47#4111yescharacteristic
80C42×C47#4111yescharacteristic
81C42×C47#4111yescharacteristic
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—81no—
93C4⋊Dic47—81no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96C4×Dic47—41no—
97C4×Dic47—41no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C23×C47#12111yescharacteristic
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47#12311yescharacteristic
105C2×C4×C47#12311yescharacteristic
106C2×C4×C47#12311yescharacteristic
107C2×C4×C47#12411yescharacteristic
108C2×C4×C47#12611yescharacteristic
109C2×C4×C47#12611yescharacteristic
110C2×C4×C47C2×SD1611yescharacteristic
111C2×C4×C47#13511yescharacteristic
112C2×C4×C47#13511yescharacteristic
113C2×C4×C47#13511yescharacteristic
114C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C47#13711yescharacteristic
116C2×C4×C47#13711yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×Dic47—22no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—81no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130Dic94—22no—
131Dic94—22no—
132Dic94—41no—
133Dic94—41no—
134C8×C47—41no—
135C8×C47—41no—
136C8×C47—81no—
137C8×C47—81no—
138C47⋊C8—81no—
139#10626—471nomaximal, Sylow
140C22×C47#39711yescharacteristic
141C22×C47#46411yescharacteristic
142C22×C47#46411yescharacteristic
143C22×C47#46511yescharacteristic
144C22×C47#46811yescharacteristic
145C22×C47#47211yescharacteristic
146C22×C47#47311yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47#48111yescharacteristic
150C4×C47#48211yescharacteristic
151C4×C47#48311yescharacteristic
152C4×C47#48511yescharacteristic
153C4×C47#48511yescharacteristic
154C4×C47#48511yescharacteristic
155C4×C47#48811yescharacteristic
156C4×C47#49111yescharacteristic
157Dic47—42no—
158Dic47—81no—
159Dic47—161no—
160Dic47—161no—
161#1984—471no—
162#1834—471no—
163#1803—471no—
164#1803—471no—
165#1296—471no—
166#1296—471no—
167#1277D4711yescharacteristic
168C2×C47#167811yescharacteristic
169C2×C47#168011yescharacteristic
170C2×C47#169811yescharacteristic
171C2×C47#170011yescharacteristic
172C2×C47#207411yescharacteristic
173C2×C47#207711yescharacteristic
174C2×C47#207811yescharacteristic
175C2×C4×Q8—471no—
176C2×C4⋊C8—471no—
177C2×C4⋊C8C2×D4711yescharacteristic
178C2×C4⋊C8C2×D4711yescharacteristic
179C2×#103—941no—
180C2×#103—941no—
181C2×C4×C8C2×D4711yescharacteristic
182#384—471no—
183#384—471no—
184#340—941no—
185#340—941no—
186#340—941no—
187#340—941no—
188#336—941no—
189#336—941no—
190C47#1062611yescharacteristic, complemented, Sylow
191C22×Q8—471no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—941no—
195C22×C8D18811yescharacteristic
196C22×C8D18811yescharacteristic
197C4×Q8—941no—
198C4×Q8—941no—
199C4×Q8—941no—
200C4×Q8—941no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C42—941no—
210C2×C42C22×D4711yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—941no—
216C4⋊C8—941no—
217#103—1882no—
218#103—1882no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—472no—
222C2×Q8—941no—
223C2×Q8—941no—
224C2×Q8—941no—
225C2×Q8—941no—
226C2×Q8—941no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—1881no—
230C22×C4—1881no—
231C22×C4C2×D18811yescharacteristic
232C22×C4D4×D4711yescharacteristic
233C22×C4#1062535411yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—1881no—
247C2×C8—1881no—
248C2×C8—1881no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—3761no—
252C4⋊C4—3761no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C42—1881no—
264C42—1881no—
265C42#1062535011yescharacteristic
266C42#1062535011yescharacteristic
267C42#1062535211yescharacteristic
268C42#1062535211yescharacteristic
269C23#1309399911yescharacteristic
270Q8—942no—
271Q8—942no—
272Q8—1881no—
273Q8—1881no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—942no—
277C2×C4—3761no—
278C2×C4—3761no—
279C2×C4—3761no—
280C2×C4—3761no—
281C2×C4—3761no—
282C2×C4—3761no—
283C2×C4—1881no—
284C2×C4—1881no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4#1309400611yescharacteristic
289C2×C4#1309400611yescharacteristic
290C2×C4#1309400811yescharacteristic
291C2×C4#1309401211yescharacteristic
292C2×C4#1309401911yescharacteristic
293C2×C4#1309401911yescharacteristic
294C2×C4SD16×D4711yescharacteristic
295C2×C4#1309404511yescharacteristic
296C2×C4#1309404611yescharacteristic
297C2×C4#1309404611yescharacteristic
298C2×C4#1309404811yescharacteristic
299C2×C4#1309405611yescharacteristic
300C2×C4#1309405711yescharacteristic
301C2×C4#1309405711yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—3761no—
307C22#1568905011yescharacteristic
308C22#1568934611yescharacteristic
309C22#1568934611yescharacteristic
310C22#1568935311yescharacteristic
311C22#1568937011yescharacteristic
312C22#1568939411yescharacteristic
313C22#1568939911yescharacteristic
314C4—21no—
315C4—21no—
316C4—3761no—
317C4—1882no—
318C4—7521no—
319C4—7521no—
320C4#1568944011yescharacteristic
321C4#1568944611yescharacteristic
322C4#1568945211yescharacteristic
323C4#1568946211yescharacteristic
324C4#1568946511yescharacteristic
325C4#1568946511yescharacteristic
326C4#1568947811yescharacteristic
327C4#1568949211yescharacteristic
328C2#2024280511yescharacteristic
329C2#2024281911yescharacteristic
330C2#2024292911yescharacteristic
331C2#2024294311yescharacteristic
332C2#2024480811yescharacteristic
333C2#2024482311yescharacteristic
334C2#2024483011yescharacteristic
subgroupG/H
centerC23#13093999
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1277C2
socle, prime radicalC23×C47#121
hypercenter#1277D47
hypocenterC47#10626
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
190. C47#10626semidirect

Maximal subgroups

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

subgroupindex
#202443242
#202435162
#202433942
#202412722
C47×#12772
#1062647