Finite Group Databasebeta

← #26226311

Subgroups — #26226311

Order 12032.

1094 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
2#20243999C214yesmaximal, complemented
3#20243994C214yesmaximal, complemented
4#20243366C212yesmaximal, complemented
5#20243297C212yesmaximal
6#20243150C211yesmaximal, characteristic, complemented
7C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×(C2×D47)⋊C4C412yes—
10C22×C4×Dic47C2211yescharacteristic
11C2×Dic47⋊C8C2214yescomplemented
12C2×C22⋊(C47⋊C8)C2212yes—
13C2×(C2×D47)⋊C8C2214yes—
14C2×(C2×D47)⋊C8C2214yes—
15C2×#13093935C2212yescomplemented
16C4×(C2×D47)⋊C4C412yes—
17C4×(C2×D47)⋊C4C412yes—
18C4×(C2×D47)⋊C4C2212yes—
19C4×(C2×D47)⋊C4C2212yes—
20C2×C47⋊#95C412yes—
21#15688878C2212yescomplemented
22#15688877C2214yescomplemented
23C22×C42×C47C2211yescharacteristic
24C2×C22⋊C8×C47C2212yes—
25C2×C4×C8×C47C2212yescomplemented
26C47×#336C2212yescomplemented
27C24×D47C2×C411yescharacteristic
28C23×Dic47C2×C412yes—
29C23×Dic47C2×C411yescharacteristic
30C22×C4×D47—24no—
31C22×C4×D47—42no—
32C22×C4×D47—42no—
33C22×C4×D47C2×C412yes—
34C22×C4×D47C2312yes—
35C22×C47⋊C8C2314yes—
36C2×(C2×D47)⋊C4—28no—
37C2×(C2×D47)⋊C4C2×C412yes—
38C2×(C2×D47)⋊C4C2×C412yes—
39C2×(C2×D47)⋊C4C2×C412yes—
40C2×(C2×D47)⋊C4C2×C412yes—
41C2×C4×Dic47—42no—
42C2×C4×Dic47C2×C411yescharacteristic
43C2×C4×Dic47C2×C411yescharacteristic
44C2×C4×Dic47C2312yes—
45Dic47⋊C8—44no—
46C22⋊(C47⋊C8)—24no—
47(C2×D47)⋊C8—44no—
48(C2×D47)⋊C8—44no—
49#13093935—42no—
50C47⋊#95C2×C412yes—
51C47⋊#95C2×C412yes—
52C47⋊#95C2×C412yes—
53C47⋊#95C2×C412yes—
54C23×C4×C47C2×C412yes—
55C23×C4×C47C2311yescharacteristic
56C22×C8×C47C2314yes—
57C2×C42×C47—42no—
58C2×C42×C47C2×C412yes—
59C2×C42×C47C2311yescharacteristic
60C2×C42×C47C2311yescharacteristic
61C22⋊C8×C47—24no—
62C4×C8×C47—42no—
63C24×C47C22×C411yescharacteristic
64C23×D47—22no—
65C23×D47—24no—
66C23×D47—24no—
67C23×D47—41no—
68C23×D47—41no—
69C23×D47C22×C412yes—
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—24no—
73C22×C4×C47—24no—
74C22×C4×C47—42no—
75C22×C4×C47C22×C412yes—
76C22×C4×C47C22×C411yescharacteristic
77C22×C4×C47C22×C412yes—
78C22×C4×C47#4114yes—
79C22×C4×C47C2411yescharacteristic
80C22×Dic47—22no—
81C22×Dic47—24no—
82C22×Dic47—24no—
83C22×Dic47—42no—
84C22×Dic47—41no—
85C22×Dic47—41no—
86C22×Dic47C22×C412yes—
87C22×Dic47C22×C412yes—
88C22×Dic47C22×C412yes—
89C2×C4×D47—24no—
90C2×C4×D47—24no—
91C2×C4×D47—24no—
92C2×C4×D47—24no—
93C2×C4×D47—42no—
94C2×C4×D47—42no—
95C2×C4×D47—416no—
96C2×C8×C47—24no—
97C2×C8×C47—24no—
98C2×C8×C47—24no—
99C42×C47—22no—
100C42×C47—22no—
101C42×C47—42no—
102(C2×D47)⋊C4—24no—
103(C2×D47)⋊C4—24no—
104(C2×D47)⋊C4—24no—
105(C2×D47)⋊C4M1618yes—
106C4×Dic47—24no—
107C4×Dic47—41no—
108C4×Dic47—41no—
109C2×C47⋊C8—24no—
110C2×C47⋊C8—24no—
111C2×C47⋊C8—24no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—22no—
115C23×C47#11712yes—
116C23×C47#13114yes—
117C23×C47C23×C411yescharacteristic
118C22×D47—28no—
119C22×D47—22no—
120C22×D47—22no—
121C22×D47—22no—
122C22×D47—22no—
123C22×D47—22no—
124C22×D47—22no—
125C22×D47—48no—
126C22×D47—48no—
127C22×D47—44no—
128C22×D47—44no—
129C22×D47C2×M1614yes—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47—22no—
134C2×C4×C47—28no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—48no—
139C2×C4×C47#11712yes—
140C2×C4×C47C2×M1614yes—
141C2×C4×C47C2×#4112yes—
142C2×C4×C47H(5,𝔽2)12yes—
143C2×C4×C47H(5,𝔽2)12yes—
144C2×Dic47—22no—
145C2×Dic47—22no—
146C2×Dic47—22no—
147C2×Dic47—22no—
148C2×Dic47—22no—
149C2×Dic47—22no—
150C2×Dic47—22no—
151C2×Dic47—22no—
152C2×Dic47—48no—
153C2×Dic47—44no—
154C2×Dic47C2×M1614yes—
155C4×D47—48no—
156C4×D47—48no—
157C8×C47—44no—
158C47⋊C8—44no—
159#21904—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—24no—
163C22×C47—24no—
164C22×C47#43314yes—
165C22×C47C2×#11711yescharacteristic
166C22×C47#51811yescharacteristic
167C22×C47#51811yescharacteristic
168C22×C47C22×M1612yes—
169C22×C47C2×#13112yes—
170C2×D47—24no—
171C2×D47—24no—
172C2×D47—24no—
173C2×D47—416no—
174C2×D47—42no—
175C2×D47—42no—
176C2×D47—42no—
177C2×D47—42no—
178C4×C47—22no—
179C4×C47—24no—
180C4×C47—42no—
181C4×C47#53814yes—
182Dic47—24no—
183Dic47—42no—
184Dic47—42no—
185C2×C4×C22⋊C4—471no—
186#1924—474no—
187#1923—474no—
188#1797—472no—
189#1779—472no—
190#1749—471no—
191C4×C22⋊C8D4711yescharacteristic, complemented
192C2×C47—24no—
193C2×C47#231211yescharacteristic
194C2×C47C2×#43311yescharacteristic
195C2×C47#292011yescharacteristic
196C2×C47#297412yes—
197C2×C47#297412yes—
198D47—44no—
199C24×C4—471no—
200C22×C22⋊C4—472no—
201C22×C42—471no—
202C22×C42C2×D4711yescharacteristic
203C2×C4⋊C8—474no—
204C2×C22⋊C8—472no—
205C2×C22⋊C8—474no—
206C2×C22⋊C8—474no—
207C2×C22⋊C8C2×D4712yes—
208C2×#97—472no—
209C2×C4×C8C2×D4712yescomplemented
210C4×C22⋊C4—472no—
211C4×C22⋊C4—472no—
212C4×C22⋊C4—472no—
213C4×C22⋊C4—472no—
214C2×#95—472no—
215#336—474no—
216#336—472no—
217#336C2×D4712yescomplemented
218C47#2190411yescharacteristic, complemented, Sylow
219C25—471no—
220C23×C4—472no—
221C23×C4—471no—
222C23×C4—472no—
223C23×C4—472no—
224C23×C4—944no—
225C23×C4—1882no—
226C23×C4—1882no—
227C23×C4C4×D4712yes—
228C23×C4C22×D4711yescharacteristic
229C22×C8—474no—
230C22×C8C22×D4714yes—
231C2×C22⋊C4—472no—
232C2×C22⋊C4—472no—
233C2×C22⋊C4—472no—
234C2×C22⋊C4—472no—
235C2×C22⋊C4—948no—
236C2×C42—42no—
237C2×C42—472no—
238C2×C42—471no—
239C2×C42—471no—
240C2×C42—1882no—
241C2×C42C4×D4712yes—
242C2×C42C22×D4711yescharacteristic
243C2×C42C22×D4711yescharacteristic
244C4⋊C8—1884no—
245C22⋊C8—24no—
246C22⋊C8—944no—
247C22⋊C8—1884no—
248C22⋊C8—1884no—
249#97—1882no—
250C4×C8—42no—
251#95—472no—
252#95—472no—
253#95—472no—
254#95—472no—
255C24—472no—
256C24—944no—
257C24—942no—
258C24—944no—
259C24—1881no—
260C24—1881no—
261C24C2×C4×D4711yescharacteristic
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—42no—
267C22×C4—472no—
268C22×C4—472no—
269C22×C4—472no—
270C22×C4—944no—
271C22×C4—942no—
272C22×C4—944no—
273C22×C4—944no—
274C22×C4—944no—
275C22×C4—944no—
276C22×C4—944no—
277C22×C4—1882no—
278C22×C4—1882no—
279C22×C4—18816no—
280C22×C4—1882no—
281C22×C4—1881no—
282C22×C4—1881no—
283C22×C4C2×C4×D4712yes—
284C22×C4C2×C4×D4711yescharacteristic
285C22×C4C2×C4×D4712yes—
286C22×C4#1062535014yes—
287C22×C4C23×D4711yescharacteristic
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—944no—
292C2×C8—944no—
293C2×C8—944no—
294C22⋊C4—478no—
295C22⋊C4—944no—
296C22⋊C4—944no—
297C22⋊C4—944no—
298C42—22no—
299C42—22no—
300C42—42no—
301C42—944no—
302C42—1881no—
303C42—1881no—
304C23—21no—
305C23—21no—
306C23—22no—
307C23—474no—
308C23—948no—
309C23—942no—
310C23—942no—
311C23—942no—
312C23—942no—
313C23—942no—
314C23—942no—
315C23—1888no—
316C23—1888no—
317C23—1884no—
318C23—1884no—
319C23#1309398112yes—
320C23#1309403014yes—
321C23C22×C4×D4711yescharacteristic
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—28no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—48no—
331C2×C4—474no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—942no—
335C2×C4—942no—
336C2×C4—942no—
337C2×C4—942no—
338C2×C4—942no—
339C2×C4—942no—
340C2×C4—1888no—
341C2×C4—1888no—
342C2×C4—1884no—
343C2×C4—1888no—
344C2×C4#1309398112yes—
345C2×C4M16×D4714yes—
346C2×C4C2×#1062535012yes—
347C2×C4#1309406912yes—
348C2×C4#1309407012yes—
349C8—44no—
350C8—1884no—
351C22—24no—
352C22—24no—
353C22—22no—
354C22—22no—
355C22—944no—
356C22—944no—
357C22—944no—
358C22—18816no—
359C22—1882no—
360C22—1882no—
361C22—1882no—
362C22—1882no—
363C22#1568918214yes—
364C22C2×#1309398111yescharacteristic
365C22#1568959611yescharacteristic
366C22#1568959711yescharacteristic
367C22C2×M16×D4712yes—
368C22C2×#1309403012yes—
369C4—24no—
370C4—22no—
371C4—42no—
372C4—944no—
373C4—1882no—
374C4—1882no—
375C4#1568970614yes—
376C2—24no—
377C2—1884no—
378C2#2024598311yescharacteristic
379C2C2×#1568918211yescharacteristic
380C2#2025201911yescharacteristic
381C2#2025241912yes—
382C2#2025242212yes—
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC4×C22⋊C8×C47C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC4×C22⋊C8D47
hypocenterC47#21904
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #20243999C2semidirect
3. #20243994C2semidirect
4. #20243366C2semidirect
6. #20243150C2semidirect
7. C4×C22⋊C8×C47C2semidirect
11. C2×Dic47⋊C8C22semidirect
15. C2×#13093935C22semidirect
21. #15688878C22semidirect
22. #15688877C22semidirect
25. C2×C4×C8×C47C22semidirect
26. C47×#336C22semidirect
191. C4×C22⋊C8D47semidirect
209. C2×C4×C8C2×D47semidirect
217. #336C2×D47semidirect
218. C47#21904semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D47)⋊C42
#202439992
#202439942
#202433662
#202432972
#202431502
C4×C22⋊C8×C472
#2190447