Finite Group Databasebeta

← #26120745

Subgroups — #26120745

Order 12032.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248627C211yesmaximal, characteristic
2#20244151C211yesmaximal, characteristic
3#20244147C211yesmaximal, characteristic
4#20243516C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic
6#20241228C211yesmaximal, characteristic
7C47×#1279C211yesmaximal, characteristic
8C2×#13093958—21no—
9C2×#13093955—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11#15689065—22no—
12#15689021—21no—
13#15689019—21no—
14#15688993C2211yescharacteristic
15#15688993C2211yescharacteristic
16#15688989—21no—
17#15688988—21no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688886—22no—
20#15688886—21no—
21#15688885—21no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4×C8×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C22×C47⋊C8—21no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4⋊Dic47D411yescharacteristic
33C2×C4⋊Dic47D412yes—
34C2×Dic47⋊C4—22no—
35C2×C4×Dic47—21no—
36#13093958—42no—
37#13093955—42no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)Q812yes—
40C47⋊#95—22no—
41C47⋊#95—22no—
42C47⋊#95—22no—
43C47⋊#95—21no—
44C22×C8×C47—21no—
45C22×C8×C47—21no—
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C42×C47—21no—
49C2×C42×C47C2311yescharacteristic
50C4⋊C8×C47—21no—
51C4⋊C8×C47Q812yes—
52C4×C8×C47—21no—
53C4×C8×C47Q812yes—
54#95×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C2×D411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—22no—
63C22×Dic47—41no—
64C2×C8×C47—22no—
65C2×C8×C47—22no—
66C2×C8×C47—41no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C42×C47—41no—
75C42×C47—41no—
76C42×C47C2×Q811yescharacteristic
77C42×C47C2×Q811yescharacteristic
78C42×C47C2×Q811yescharacteristic
79C42×C47#4111yescharacteristic
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C4⋊Dic47—42no—
89C4⋊Dic47—42no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94Dic47⋊C4—82no—
95C4×Dic47—41no—
96C4×Dic47—41no—
97C2×C47⋊C8—22no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C23×C47#12011yescharacteristic
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47C22⋊Q811yescharacteristic
110C2×C4×C47C22⋊Q811yescharacteristic
111C2×C4×C47C22⋊Q811yescharacteristic
112C2×C4×C47C4⋊Q811yescharacteristic
113C2×C4×C47C4⋊Q811yescharacteristic
114C2×C4×C47C4⋊Q811yescharacteristic
115C2×C4×C47#13511yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×C4×C47#13711yescharacteristic
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—42no—
127C2×Dic47—41no—
128C2×Dic47—42no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—42no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C8×C47—42no—
136C8×C47—42no—
137C47⋊C8—42no—
138#10578—471nomaximal, Sylow
139C22×C47#39511yescharacteristic
140C22×C47#44911yescharacteristic
141C22×C47#44911yescharacteristic
142C22×C47#45211yescharacteristic
143C22×C47#45211yescharacteristic
144C22×C47#45411yescharacteristic
145C22×C47#45511yescharacteristic
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—81no—
149C4×C47—81no—
150C4×C47#47811yescharacteristic
151C4×C47#47811yescharacteristic
152C4×C47#47911yescharacteristic
153C4×C47#47911yescharacteristic
154C4×C47#49911yescharacteristic
155C4×C47#49911yescharacteristic
156C4×C47#50111yescharacteristic
157C4×C47#50111yescharacteristic
158Dic47—81no—
159Dic47—82no—
160Dic47—81no—
161Dic47—161no—
162#2571—471no—
163#1948—471no—
164#1947—471no—
165#1834—471no—
166#1296—471no—
167#1279—471no—
168#1279D4711yescharacteristic
169C2×C47#162811yescharacteristic
170C2×C47#163811yescharacteristic
171C2×C47#164011yescharacteristic
172C2×C47#164611yescharacteristic
173C2×C47#205911yescharacteristic
174C2×C47#205911yescharacteristic
175C2×C47#206111yescharacteristic
176C2×#107—941no—
177C2×#106—941no—
178C2×C4⋊C8—471no—
179C2×C4⋊C8C2×D4711yescharacteristic
180C2×C4×C8C2×D4711yescharacteristic
181#400—942no—
182#389—941no—
183#389—941no—
184#384—471no—
185#384—471no—
186#382—941no—
187#382—941no—
188C4×C4⋊C4—471no—
189C4×C4⋊C4C2×D4711yescharacteristic
190#340—942no—
191#340—941no—
192#340—941no—
193C47#1057811yescharacteristic, complemented, Sylow
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—941no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—472no—
200C2×C4⋊C4—942no—
201C2×C4⋊C4—941no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4D18811yescharacteristic
207C2×C4⋊C4D18811yescharacteristic
208C2×C42—21no—
209C2×C42—941no—
210C2×C42C22×D4711yescharacteristic
211#107—1882no—
212#106—1882no—
213C4⋊C8—21no—
214C4⋊C8—472no—
215C4⋊C8—941no—
216C4⋊C8Dic9412yes—
217C4×C8—21no—
218C4×C8Dic9412yes—
219#95—21no—
220#95—942no—
221#95—942no—
222#95—942no—
223#95—941no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4—942no—
229C22×C4—1881no—
230C22×C4C2×D18811yescharacteristic
231C22×C4D4×D4711yescharacteristic
232C22×C4D4×D4711yescharacteristic
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—942no—
240C2×C8—1881no—
241C2×C8—1881no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—3762no—
251C4⋊C4—1882no—
252C4⋊C4—1882no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C42—41no—
262C42—41no—
263C42—1881no—
264C42—1881no—
265C42C2×Dic9411yescharacteristic
266C42C2×Dic9411yescharacteristic
267C42#1062535211yescharacteristic
268C42Q8×D4711yescharacteristic
269C23#1309399411yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—3761no—
279C2×C4—3761no—
280C2×C4—3761no—
281C2×C4—1881no—
282C2×C4—1881no—
283C2×C4—1881no—
284C2×C4—1882no—
285C2×C4—1881no—
286C2×C4—1882no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1882no—
290C2×C4#1309400111yescharacteristic
291C2×C4#1309400111yescharacteristic
292C2×C4#1309400411yescharacteristic
293C2×C4#1309402311yescharacteristic
294C2×C4#1309402311yescharacteristic
295C2×C4#1309402411yescharacteristic
296C2×C4#1309404311yescharacteristic
297C2×C4#1309404611yescharacteristic
298C2×C4#1309404611yescharacteristic
299C2×C4#1309404711yescharacteristic
300C2×C4#1309405111yescharacteristic
301C2×C4#1309405211yescharacteristic
302C2×C4#1309405311yescharacteristic
303C2×C4#1309405711yescharacteristic
304C8—42no—
305C8—42no—
306C8—1882no—
307C22#1568904411yescharacteristic
308C22#1568927011yescharacteristic
309C22#1568927111yescharacteristic
310C22#1568928611yescharacteristic
311C22#1568928711yescharacteristic
312C22#1568929711yescharacteristic
313C22#1568930211yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—3761no—
319C4—3762no—
320C4—3761no—
321C4—7521no—
322C4#1568942111yescharacteristic
323C4#1568942411yescharacteristic
324C4#1568943111yescharacteristic
325C4#1568943211yescharacteristic
326C4#1568952411yescharacteristic
327C4#1568952511yescharacteristic
328C4#1568953011yescharacteristic
329C4#1568953211yescharacteristic
330C2#2024250111yescharacteristic
331C2#2024256211yescharacteristic
332C2#2024257711yescharacteristic
333C2#2024261811yescharacteristic
334C2#2024472711yescharacteristic
335C2#2024472911yescharacteristic
336C2#2024473711yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socle, prime radicalC23×C47#120
hypercenter#1279D47
hypocenterC47#10578
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
193. C47#10578semidirect

Maximal subgroups

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

subgroupindex
#202486272
#202441512
#202441472
#202435162
#202412722
#202412282
C47×#12792
#1057847