Finite Group Databasebeta

← #26121006

Subgroups — #26121006

Order 12032.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244324C211yesmaximal, characteristic
2#20243390C211yesmaximal, characteristic
3#20243390C211yesmaximal, characteristic
4#20241271C211yesmaximal, characteristic
5#20241271C211yesmaximal, characteristic
6#20241223C211yesmaximal, characteristic
7C47×#1844C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×#13093947—21no—
13C2×#13093947—21no—
14#15688885—21no—
15#15688885—21no—
16#15688877—21no—
17#15688877—21no—
18C2×#106×C47—21no—
19C2×#106×C47—21no—
20C2×C4×C8×C47C2211yescharacteristic
21C47×#384C2211yescharacteristic
22C47×#384C2211yescharacteristic
23C22×Dic94D411yescharacteristic
24C22×C47⋊C8—21no—
25C22×C47⋊C8—21no—
26C22×C47⋊C8—21no—
27C4×Dic94—21no—
28C4×Dic94—21no—
29C4×Dic94—21no—
30C4×Dic94—21no—
31C2×C4⋊Dic47D411yescharacteristic
32C2×Dic47⋊C4—21no—
33C2×C4×Dic47—21no—
34C4⋊(C47⋊C8)—21no—
35C4⋊(C47⋊C8)—21no—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40#13093947—42no—
41#13093947—42no—
42C22×C8×C47D411yescharacteristic
43C22×C8×C47D411yescharacteristic
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47—21no—
46C2×C4⋊C4×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C42×C47C2311yescharacteristic
51#106×C47—42no—
52#106×C47—42no—
53C4×C8×C47—21no—
54C4×C8×C47—21no—
55C22×C4×C47—41no—
56C22×C4×C47—41no—
57C22×C4×C47C2×D411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×C4×C47#4111yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C2×Dic94—21no—
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94SD1612yes—
68C2×C8×C47—21no—
69C2×C8×C47—21no—
70C2×C8×C47—21no—
71C2×C8×C47—21no—
72C2×C8×C47SD1612yes—
73C2×C8×C47Q1612yes—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—81no—
83C4⋊C4×C47—81no—
84C42×C47#4111yescharacteristic
85C42×C47#4111yescharacteristic
86C42×C47#4111yescharacteristic
87C42×C47#4111yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90Dic47⋊C4—41no—
91Dic47⋊C4—41no—
92C4×Dic47—41no—
93C4×Dic47—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C23×C47#12111yescharacteristic
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47—81no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47#12311yescharacteristic
113C2×C4×C47#12311yescharacteristic
114C2×C4×C47#12311yescharacteristic
115C2×C4×C47#12411yescharacteristic
116C2×C4×C47#12611yescharacteristic
117C2×C4×C47#12611yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47C2×SD1611yescharacteristic
120C2×C4×C47C2×Q1611yescharacteristic
121C2×C4×C47#13511yescharacteristic
122C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×C4×C47#13711yescharacteristic
126C2×Dic47—22no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132Dic94—22no—
133Dic94—22no—
134Dic94—41no—
135Dic94—41no—
136C8×C47—22no—
137C8×C47—22no—
138C47⋊C8—81no—
139C47⋊C8—81no—
140C47⋊C8—81no—
141#10620—471nomaximal, Sylow
142C22×C47#39711yescharacteristic
143C22×C47#46011yescharacteristic
144C22×C47#46211yescharacteristic
145C22×C47#46511yescharacteristic
146C22×C47#46811yescharacteristic
147C22×C47#47111yescharacteristic
148C22×C47#47111yescharacteristic
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—161no—
152C4×C47—161no—
153C4×C47#48111yescharacteristic
154C4×C47#48211yescharacteristic
155C4×C47#48311yescharacteristic
156C4×C47#48311yescharacteristic
157C4×C47#48411yescharacteristic
158C4×C47#48511yescharacteristic
159C4×C47#48711yescharacteristic
160C4×C47#48911yescharacteristic
161Dic47—42no—
162Dic47—81no—
163#1984—471no—
164#1844D4711yescharacteristic
165#1803—471no—
166#1803—471no—
167#1296—471no—
168#1296—471no—
169#1277—471no—
170C2×C47#166611yescharacteristic
171C2×C47#167211yescharacteristic
172C2×C47#168611yescharacteristic
173C2×C47#169211yescharacteristic
174C2×C47#207211yescharacteristic
175C2×C47#207711yescharacteristic
176C2×C47#207911yescharacteristic
177C2×C4×Q8—471no—
178C2×#106—21no—
179C2×#106—21no—
180C2×C4⋊C8—471no—
181C2×C4⋊C8—471no—
182C2×C4⋊C8—471no—
183C2×#103—941no—
184C2×#103—941no—
185C2×C4×C8C2×D4711yescharacteristic
186#384C2×D4711yescharacteristic
187#384C2×D4711yescharacteristic
188#340—941no—
189#340—941no—
190#336—941no—
191#336—941no—
192C47#1062011yescharacteristic, complemented, Sylow
193C22×Q8—471no—
194C22×C8—941no—
195C22×C8—941no—
196C22×C8—941no—
197C22×C8C22⋊D4711yescharacteristic
198C22×C8C22⋊D4711yescharacteristic
199C4×Q8—941no—
200C4×Q8—941no—
201C4×Q8—941no—
202C4×Q8—941no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—941no—
211C2×C42—941no—
212C2×C42C22×D4711yescharacteristic
213#106—42no—
214#106—42no—
215C4⋊C8—941no—
216C4⋊C8—941no—
217C4⋊C8—941no—
218C4⋊C8—941no—
219C4⋊C8—941no—
220C4⋊C8—941no—
221#103—1882no—
222#103—1882no—
223C4×C8—21no—
224C4×C8—21no—
225C2×Q8—472no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8—941no—
230C2×Q8—941no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4D4×D4711yescharacteristic
236C22×C4#1062535211yescharacteristic
237C22×C4C2×C22⋊D4711yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—1881no—
243C2×C8—1881no—
244C2×C8—1881no—
245C2×C8—1881no—
246C2×C8—1881no—
247C2×C8—1881no—
248C2×C8—1881no—
249C2×C8—1881no—
250C2×C8—1881no—
251C2×C8#1062533512yes—
252C2×C8#1062533712yes—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—1881no—
266C4⋊C4—1881no—
267C42—1881no—
268C42—1881no—
269C42#1062535011yescharacteristic
270C42#1062535011yescharacteristic
271C42#1062535411yescharacteristic
272C42#1062535411yescharacteristic
273C23#1309399511yescharacteristic
274Q8—942no—
275Q8—942no—
276Q8—1881no—
277Q8—1881no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—942no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4#1309400711yescharacteristic
293C2×C4#1309400911yescharacteristic
294C2×C4#1309400911yescharacteristic
295C2×C4#1309401311yescharacteristic
296C2×C4#1309401911yescharacteristic
297C2×C4#1309401911yescharacteristic
298C2×C4SD16×D4711yescharacteristic
299C2×C4C2×#1062533511yescharacteristic
300C2×C4C2×#1062533711yescharacteristic
301C2×C4#1309404511yescharacteristic
302C2×C4#1309405011yescharacteristic
303C2×C4#1309405111yescharacteristic
304C2×C4#1309405311yescharacteristic
305C2×C4#1309405511yescharacteristic
306C8—22no—
307C8—22no—
308C8—3761no—
309C8—3761no—
310C8—3761no—
311C22#1568904911yescharacteristic
312C22#1568932011yescharacteristic
313C22#1568933011yescharacteristic
314C22#1568934911yescharacteristic
315C22#1568936611yescharacteristic
316C22#1568938311yescharacteristic
317C22#1568938311yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—161no—
322C4—3761no—
323C4—1882no—
324C4#1568944311yescharacteristic
325C4#1568944911yescharacteristic
326C4#1568945311yescharacteristic
327C4#1568945511yescharacteristic
328C4#1568945811yescharacteristic
329C4#1568946711yescharacteristic
330C4#1568947511yescharacteristic
331C4#1568948511yescharacteristic
332C2#2024273311yescharacteristic
333C2#2024276711yescharacteristic
334C2#2024285711yescharacteristic
335C2#2024289111yescharacteristic
336C2#2024479711yescharacteristic
337C2#2024482211yescharacteristic
338C2#2024483411yescharacteristic
subgroupG/H
centerC23#13093995
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1844C2
socle, prime radicalC23×C47#121
hypercenter#1844D47
hypocenterC47#10620
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
192. C47#10620semidirect

Maximal subgroups

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

subgroupindex
#202443242
#202433902
#202412712
#202412232
C47×#18442
#1062047