Finite Group Databasebeta

← #26104292

Subgroups — #26104292

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245869C211yesmaximal, characteristic
2#20243455C211yesmaximal, characteristic
3#336×D47C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic, complemented
5#20241211C211yesmaximal, characteristic, complemented
6#20241210C211yesmaximal, characteristic, complemented
7C47×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D47—21no—
9C2×#13093982C411yescharacteristic
10C2×#13093982C411yescharacteristic
11C2×C42×D47C2211yescharacteristic
12C2×(C2×D47)⋊C8—21no—
13#15689022C411yescharacteristic
14#15689021C2211yescharacteristic
15#15689019C411yescharacteristic
16#15688997—21no—
17#15688994—21no—
18C4⋊C4×Dic47—21no—
19#15688974—21no—
20#15688878C2211yescharacteristic
21#15688878C2211yescharacteristic
22#15688877—21no—
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C4×D47C2×C411yescharacteristic
28C22×C4×D47D411yescharacteristic
29C22×C4×D47D411yescharacteristic
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C2×C8×D47—24no—
33C2×C8×D47—42no—
34C2×C8×D47—42no—
35#13093982—22no—
36#13093982—42no—
37#13093982C814yescomplemented
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47C2×C411yescharacteristic
40C2×C4⋊Dic47C2×C411yescharacteristic
41C2×Dic47⋊C4—21no—
42C2×Dic47⋊C4—21no—
43C2×(C2×D47)⋊C4—21no—
44C2×(C2×D47)⋊C4—21no—
45C2×C4×Dic47—21no—
46C2×C4×Dic47—21no—
47C2×C4×Dic47C2×C411yescharacteristic
48C2×C4×Dic47D411yescharacteristic
49C2×C4×Dic47D411yescharacteristic
50C42×D47—42no—
51(C2×D47)⋊C8—42no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C47⋊#95—21no—
55C22×C8×C47—21no—
56C22×C8×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47C2×C411yescharacteristic
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C42×C47C2311yescharacteristic
61#95×C47—21no—
62C23×D47C22⋊C411yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C22×C411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47C22⋊C411yescharacteristic
71C22×Dic47C22⋊C411yescharacteristic
72C22×Dic47C22⋊C411yescharacteristic
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—41no—
83C2×C4×D47C2×C812yes—
84C2×C4×D47M1612yes—
85C2×C8×C47—22no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47C2×C812yescomplemented
96C42×C47—41no—
97(C2×D47)⋊C4—24no—
98(C2×D47)⋊C4—42no—
99C4⋊Dic47—21no—
100C4⋊Dic47—42no—
101C4⋊Dic47—41no—
102C4⋊Dic47C2×C812yescomplemented
103Dic47⋊C4—42no—
104Dic47⋊C4—41no—
105Dic47⋊C4—41no—
106C4×Dic47—24no—
107C4×Dic47—41no—
108C4×Dic47—41no—
109C4×Dic47—41no—
110C4×Dic47—42no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—41no—
113C2×C47⋊C8—41no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C8×D47—48no—
118C23×C47C2×C22⋊C411yescharacteristic
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47C22⋊C812yes—
124C22×D47#9912yes—
125C22×D47#10112yes—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—22no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47C22×C811yescharacteristic
139C2×C4×C47C2×M1611yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47#13711yescharacteristic
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—22no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47C22⋊C812yes—
158C2×Dic47#10412yes—
159C4×D47—24no—
160C4×D47—24no—
161C4×D47—24no—
162C4×D47—24no—
163C4×D47—42no—
164C4×D47—42no—
165C8×C47—42no—
166C8×C47—81no—
167C47⋊C8—42no—
168C47⋊C8—81no—
169#7579—471nomaximal, Sylow
170C22×C47C2×C22⋊C811yescharacteristic
171C22×C47C2×#9911yescharacteristic
172C22×C47C2×#10111yescharacteristic
173C22×C47#41611yescharacteristic
174C22×C47#41711yescharacteristic
175C22×C47C2×#10411yescharacteristic
176C22×C47#42111yescharacteristic
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—22no—
183C2×D47#32414yes—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—21no—
189C4×C47—21no—
190C4×C47—42no—
191C4×C47—81no—
192Dic47—22no—
193Dic47—22no—
194Dic47—42no—
195Dic47—41no—
196Dic47—81no—
197#2296—471no—
198#1817—471no—
199C2×#336—471no—
200#1271—471no—
201#1271—471no—
202#1271—471no—
203#1271D4711yescharacteristic, complemented
204C2×C47C2×#32411yescharacteristic
205C2×C47#147611yescharacteristic
206C2×C47#147711yescharacteristic
207C2×C47#150411yescharacteristic
208C2×C47#151611yescharacteristic
209C2×C47#153111yescharacteristic
210C2×C47#155211yescharacteristic
211D47—24no—
212C23×C8—941no—
213C2×#117—471no—
214C2×#117—471no—
215C22×C42—471no—
216C2×C22⋊C8—941no—
217#389—471no—
218#389—471no—
219#389—471no—
220#389C2×D4711yescharacteristic
221#385—941no—
222#385—941no—
223C4×C4⋊C4—941no—
224C4×C4⋊C4—941no—
225#336—471no—
226#336—471no—
227#336—941no—
228#336—941no—
229#336C2×D4711yescharacteristic
230#336C2×D4711yescharacteristic
231C47#757911yescharacteristic, complemented, Sylow
232C23×C4—471no—
233C23×C4—471no—
234C23×C4—471no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—944no—
238C22×C8—941no—
239C22×C8—941no—
240C22×C8—1882no—
241C22×C8—1882no—
242#117—474no—
243#117—942no—
244#117—1882no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—471no—
248C2×C4⋊C4—941no—
249C2×C4⋊C4—941no—
250C2×C4⋊C4—941no—
251C2×C4⋊C4C4×D4711yescharacteristic
252C2×C4⋊C4C4×D4711yescharacteristic
253C2×C22⋊C4—941no—
254C2×C22⋊C4—941no—
255C2×C42—471no—
256C2×C42—471no—
257C2×C42—471no—
258C2×C42—941no—
259C2×C42—941no—
260C2×C42—1882no—
261C2×C42C22×D4711yescharacteristic
262C22⋊C8—1882no—
263#95—21no—
264#95—941no—
265#95—941no—
266#95—941no—
267C24—471no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—472no—
273C22×C4—472no—
274C22×C4—471no—
275C22×C4—942no—
276C22×C4—942no—
277C22×C4—942no—
278C22×C4—942no—
279C22×C4—942no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4—1881no—
287C22×C4C2×C4×D4711yescharacteristic
288C22×C4D4×D4711yescharacteristic
289C22×C4D4×D4711yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—942no—
297C2×C8—1888no—
298C2×C8—1881no—
299C2×C8—1881no—
300C2×C8—1881no—
301C2×C8—1881no—
302C2×C8—1881no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—472no—
308C4⋊C4—941no—
309C4⋊C4—1881no—
310C4⋊C4—1882no—
311C4⋊C4—1882no—
312C4⋊C4—1881no—
313C4⋊C4—1881no—
314C4⋊C4C8×D4712yescomplemented
315C22⋊C4—944no—
316C22⋊C4—1882no—
317C42—41no—
318C42—944no—
319C42—1881no—
320C42—1881no—
321C42—1881no—
322C42—1882no—
323C23—472no—
324C23—472no—
325C23—472no—
326C23—941no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23C22⋊C4×D4711yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—472no—
344C2×C4—472no—
345C2×C4—944no—
346C2×C4—944no—
347C2×C4—944no—
348C2×C4—944no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—942no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4—1881no—
360C2×C4—1881no—
361C2×C4—1881no—
362C2×C4—1881no—
363C2×C4—1881no—
364C2×C4C2×C8×D4711yescharacteristic
365C2×C4M16×D4711yescharacteristic
366C2×C4#1309404311yescharacteristic
367C2×C4#1309404511yescharacteristic
368C2×C4#1309405111yescharacteristic
369C2×C4#1309405611yescharacteristic
370C8—42no—
371C8—81no—
372C8—3761no—
373C8—1882no—
374C22—474no—
375C22—942no—
376C22—942no—
377C22—942no—
378C22—942no—
379C22—942no—
380C22—942no—
381C22C22⋊C8×D4711yescharacteristic
382C22#99×D4711yescharacteristic
383C22#101×D4711yescharacteristic
384C22#1568911611yescharacteristic
385C22#1568912311yescharacteristic
386C22#104×D4711yescharacteristic
387C22#1568913811yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—942no—
397C4—942no—
398C4—3761no—
399C4—1881no—
400C4—1882no—
401C2—944no—
402C2#324×D4711yescharacteristic
403C2#2024176711yescharacteristic
404C2#2024177411yescharacteristic
405C2#2024189111yescharacteristic
406C2#2024194111yescharacteristic
407C2#2024200111yescharacteristic
408C2#2024208511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1271C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1271D47
hypocenterC47#7579
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #20241212C2semidirect
5. #20241211C2semidirect
6. #20241210C2semidirect
7. C47×#1271C2semidirect
37. #13093982C8semidirect
95. C4⋊C4×C47C2×C8semidirect
102. C4⋊Dic47C2×C8semidirect
203. #1271D47semidirect
231. C47#7579semidirect
314. C4⋊C4C8×D47semidirect

Maximal subgroups

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

subgroupindex
#202458692
#202434552
#336×D472
#202412122
#202412112
#202412102
C47×#12712
#757947