Finite Group Databasebeta

← C4×C47⋊#564 #26378999

Subgroups — C4×C47⋊#564 #26378999

Order 12032.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47⋊#564C211yesmaximal, characteristic
2#20246574C211yesmaximal, characteristic
3#20246573C212yesmaximal
4#20246572C214yesmaximal
5#20246571C214yesmaximal
6#20246570C214yesmaximal
7C4×#13094016C212yesmaximal
8C4×#13094015C214yesmaximal
9C4×#13094014C214yesmaximal
10C4×#13094014C214yesmaximal
11C4×#125×C47C211yesmaximal, characteristic
12C47⋊#564C4116yesdirect product factor
13C2×#13094016C2212yes—
14C2×#13094015C2214yes—
15C2×#13094014C2214yes—
16C2×#13094014C2214yes—
17#15689022C2214yes—
18#15689021C2212yes—
19#15689021C2212yes—
20#15689020C2214yes—
21#15689020C2214yes—
22#15689019C2214yes—
23#15689018C2214yes—
24#15689018C2214yes—
25#15689010C2214yes—
26#15689010C2214yes—
27#15689009C2214yes—
28#15689009C2214yes—
29#15689008C2214yes—
30#15689008C2214yes—
31#15689007C2214yes—
32#15689007C2214yes—
33#15689006C2214yes—
34#15689006C2214yes—
35#15689005C2214yes—
36#15689005C2214yes—
37#15689004C2214yes—
38#15689004C2214yes—
39#15688989C2212yes—
40#15688988C2214yes—
41#15688987C2214yes—
42#15688987C2214yes—
43C4×Dic47⋊C4C2214yes—
44C4×Dic47⋊C4C2214yes—
45C4×Dic47⋊C4C2214yes—
46C4×Dic47⋊C4C2214yes—
47C4×C4⋊Dic47C2212yes—
48C4×C4⋊Dic47C2214yes—
49C4×C4⋊Dic47C2212yes—
50C42×Dic47C2214yes—
51C2×#125×C47C2211yescharacteristic
52C47×#389C2212yes—
53C47×#387C2214yes—
54C47×#382C2211yescharacteristic
55C4×C4⋊C4×C47C2212yes—
56C4×C4⋊C4×C47C2214yes—
57C43×C47C2211yescharacteristic
58#13094016C2×C4116yes—
59#13094015C2×C4132yes—
60#13094014C2×C4132yes—
61#13094014C2×C4132yes—
62C2×C4⋊Dic47C2314yes—
63C2×C4⋊Dic47C2312yes—
64C2×C4⋊Dic47C2312yes—
65C2×C4⋊Dic47C2312yes—
66C2×C4⋊Dic47C2314yes—
67C2×C4⋊Dic47C2312yes—
68C2×Dic47⋊C4C2314yes—
69C2×Dic47⋊C4C2314yes—
70C2×Dic47⋊C4C2314yes—
71C2×Dic47⋊C4C2314yes—
72C2×Dic47⋊C4C2314yes—
73C2×Dic47⋊C4C2314yes—
74C2×Dic47⋊C4C2314yes—
75C2×Dic47⋊C4C2314yes—
76C2×C4×Dic47C2314yes—
77C2×C4×Dic47C2314yes—
78C2×C4×Dic47C2314yes—
79C2×C4×Dic47C2314yes—
80C2×C4×Dic47C2314yes—
81C2×C4×Dic47C2314yes—
82C47⋊#95C2314yes—
83C47⋊#95C2314yes—
84C47⋊#95C2314yes—
85C47⋊#95C2314yes—
86C47⋊#95C2314yes—
87C47⋊#95C2314yes—
88C47⋊#95C2314yes—
89C47⋊#95C2314yes—
90C47⋊#95C2314yes—
91C47⋊#95C2314yes—
92C47⋊#95C2314yes—
93C47⋊#95C2314yes—
94#125×C47C2×C418yes—
95C2×C4⋊C4×C47C2314yes—
96C2×C4⋊C4×C47C2312yes—
97C2×C4⋊C4×C47C2312yes—
98C2×C4⋊C4×C47C2314yes—
99C2×C42×C47C2314yes—
100C2×C42×C47C2312yes—
101C2×C42×C47C2311yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2312yes—
104C2×C42×C47C2311yescharacteristic
105#95×C47C2314yes—
106#95×C47C2314yes—
107#95×C47C2314yes—
108C22×C4×C47C2412yes—
109C22×C4×C47C2411yescharacteristic
110C22×C4×C47C2414yes—
111C22×C4×C47C2411yescharacteristic
112C22×C4×C47C2412yes—
113C22×C4×C47C2414yes—
114C22×C4×C47C2411yescharacteristic
115C22×Dic47C2414yes—
116C22×Dic47C2414yes—
117C22×Dic47C2414yes—
118C22×Dic47C2414yes—
119C4⋊C4×C47—44no—
120C4⋊C4×C47—42no—
121C4⋊C4×C47C22×C418yes—
122C4⋊C4×C47C22×C4116yes—
123C42×C47—28no—
124C42×C47—24no—
125C42×C47—22no—
126C42×C47—42no—
127C42×C47—41no—
128C42×C47C22×C414yes—
129C4⋊Dic47—42no—
130C4⋊Dic47—44no—
131C4⋊Dic47—42no—
132C4⋊Dic47C22×C418yes—
133C4⋊Dic47C22×C4116yes—
134C4⋊Dic47C22×C418yes—
135Dic47⋊C4—44no—
136Dic47⋊C4—44no—
137Dic47⋊C4—44no—
138Dic47⋊C4—44no—
139Dic47⋊C4C22×C4116yes—
140Dic47⋊C4C22×C4116yes—
141Dic47⋊C4C22×C4116yes—
142Dic47⋊C4C22×C4116yes—
143C4×Dic47—28no—
144C4×Dic47—28no—
145C4×Dic47—44no—
146C4×Dic47—44no—
147C4×Dic47—44no—
148C4×Dic47C22×C4116yes—
149C23×C47C2511yescharacteristic
150C2×C4×C47—22no—
151C2×C4×C47—24no—
152C2×C4×C47—21no—
153C2×C4×C47—24no—
154C2×C4×C47—22no—
155C2×C4×C47—21no—
156C2×C4×C47—22no—
157C2×C4×C47—24no—
158C2×C4×C47—21no—
159C2×C4×C47—24no—
160C2×C4×C47—24no—
161C2×C4×C47—22no—
162C2×C4×C47—22no—
163C2×C4×C47—22no—
164C2×C4×C47C23×C418yes—
165C2×C4×C47C23×C412yes—
166C2×C4×C47C23×C414yes—
167C2×C4×C472−1+414yes—
168C2×C4×C472−1+412yes—
169C2×Dic47—24no—
170C2×Dic47—24no—
171C2×Dic47—24no—
172C2×Dic47—24no—
173C2×Dic47—24no—
174C2×Dic47—24no—
175C2×Dic47—24no—
176C2×Dic47—24no—
177C2×Dic47—24no—
178C2×Dic47—24no—
179C2×Dic47C23×C418yes—
180C2×Dic47C23×C418yes—
181C4×#564—471nomaximal, Sylow
182C22×C47C24×C411yescharacteristic
183C22×C47C2×2−1+412yes—
184C22×C47C2×2−1+411yescharacteristic
185C22×C47#58512yes—
186C22×C47#58511yescharacteristic
187C4×C47—28no—
188C4×C47—24no—
189C4×C47—22no—
190C4×C47—44no—
191C4×C47—42no—
192C4×C47—41no—
193C4×C47#56414yescomplemented
194Dic47—28no—
195Dic47—28no—
196Dic47—44no—
197Dic47—44no—
198C2×#564—471no—
199#2382—474no—
200#2382—474no—
201#2382—474no—
202#2382—472no—
203#2382—471no—
204C4×#125—474no—
205C4×#125—474no—
206C4×#125—474no—
207C4×#125—472no—
208C4×#125D4711yescharacteristic
209C2×C47C4×2−1+412yes—
210C2×C47C4×2−1+411yescharacteristic
211C2×C47C2×#56411yescharacteristic
212C2×C47#353112yes—
213C2×C47#353111yescharacteristic
214#564—4716no—
215C2×#125—474no—
216C2×#125—474no—
217C2×#125—474no—
218C2×#125—472no—
219C2×#125C2×D4711yescharacteristic
220#389—474no—
221#389—474no—
222#389—474no—
223#389—474no—
224#389—472no—
225#389—472no—
226#389—474no—
227#389—474no—
228#389C2×D4712yes—
229#387—474no—
230#387—474no—
231#387—474no—
232#387—474no—
233#387—474no—
234#387—474no—
235#387—474no—
236#387—474no—
237#387—474no—
238#387—474no—
239#387—474no—
240#387—474no—
241#387—474no—
242#387—474no—
243#387C2×D4714yes—
244#382—474no—
245#382—472no—
246#382—474no—
247#382—474no—
248#382C2×D4711yescharacteristic
249C4×C4⋊C4—474no—
250C4×C4⋊C4—472no—
251C4×C4⋊C4—472no—
252C4×C4⋊C4—474no—
253C4×C4⋊C4—474no—
254C4×C4⋊C4—474no—
255C4×C4⋊C4—474no—
256C4×C4⋊C4C2×D4714yes—
257C4×C4⋊C4C2×D4712yes—
258C43—474no—
259C43C2×D4711yescharacteristic
260C47C4×#56411yescharacteristic, complemented, Sylow
261#125—4732no—
262#125—4732no—
263#125—4732no—
264#125—4716no—
265#125C4×D4718yes—
266C2×C4⋊C4—474no—
267C2×C4⋊C4—474no—
268C2×C4⋊C4—474no—
269C2×C4⋊C4—474no—
270C2×C4⋊C4—474no—
271C2×C4⋊C4—472no—
272C2×C4⋊C4—472no—
273C2×C4⋊C4—474no—
274C2×C4⋊C4—474no—
275C2×C4⋊C4—474no—
276C2×C4⋊C4—474no—
277C2×C4⋊C4—474no—
278C2×C4⋊C4—472no—
279C2×C4⋊C4—472no—
280C2×C4⋊C4C22×D4714yes—
281C2×C4⋊C4C22×D4712yes—
282C2×C4⋊C4C22×D4712yes—
283C2×C4⋊C4C22×D4714yes—
284C2×C42—474no—
285C2×C42—474no—
286C2×C42—474no—
287C2×C42—474no—
288C2×C42—474no—
289C2×C42—474no—
290C2×C42C22×D4714yes—
291C2×C42C22×D4712yes—
292C2×C42C22×D4711yescharacteristic
293C2×C42C22×D4711yescharacteristic
294C2×C42C22×D4712yes—
295C2×C42C22×D4711yescharacteristic
296#95—474no—
297#95—474no—
298#95—474no—
299#95—474no—
300#95—474no—
301#95—474no—
302#95—474no—
303#95—474no—
304#95—474no—
305#95—474no—
306#95—474no—
307#95—474no—
308#95C22×D4714yes—
309#95C22×D4714yes—
310#95C22×D4714yes—
311C22×C4—474no—
312C22×C4—474no—
313C22×C4—474no—
314C22×C4—474no—
315C22×C4C23×D4712yes—
316C22×C4C23×D4714yes—
317C22×C4C23×D4711yescharacteristic
318C22×C4C23×D4711yescharacteristic
319C22×C4C23×D4714yes—
320C22×C4C23×D4712yes—
321C22×C4C23×D4711yescharacteristic
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—4716no—
325C4⋊C4—4716no—
326C4⋊C4—4716no—
327C4⋊C4—4716no—
328C4⋊C4—4716no—
329C4⋊C4—478no—
330C4⋊C4—478no—
331C4⋊C4—1884no—
332C4⋊C4—1884no—
333C4⋊C4—1884no—
334C4⋊C4—1884no—
335C4⋊C4—1882no—
336C4⋊C4—1882no—
337C4⋊C4—1884no—
338C4⋊C4C2×C4×D4718yes—
339C4⋊C4C2×C4×D47116yes—
340C42—28no—
341C42—24no—
342C42—22no—
343C42—41no—
344C42—42no—
345C42—4716no—
346C42—948no—
347C42—948no—
348C42—1884no—
349C42—1884no—
350C42—1884no—
351C42C2×C4×D4714yes—
352C23C24×D4711yescharacteristic
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—478no—
368C2×C4—478no—
369C2×C4—944no—
370C2×C4—944no—
371C2×C4—944no—
372C2×C4—944no—
373C2×C4—944no—
374C2×C4—944no—
375C2×C4—944no—
376C2×C4—944no—
377C2×C4—944no—
378C2×C4—944no—
379C2×C4C22×C4×D4718yes—
380C2×C4C22×C4×D4714yes—
381C2×C4C22×C4×D4712yes—
382C2×C4#1309407114yes—
383C2×C4#1309407212yes—
384C22C23×C4×D4711yescharacteristic
385C22C2×#1309407112yes—
386C22C2×#1309407211yescharacteristic
387C22#1568995912yes—
388C22#1568995911yescharacteristic
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—948no—
396C4—948no—
397C4—1884no—
398C4—1884no—
399C4C47⋊#56414yesdirect product factor
400C2C4×#1309407112yes—
401C2C4×#1309407211yescharacteristic
402C2C2×C47⋊#56411yescharacteristic
403C2#2025753312yes—
404C2#2025753511yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×#125×C47C2
socle, prime radical, cosocleC23×C47C25
hypercenterC4×#125D47
hypocenterC47C4×#564
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
12. C47⋊#564C4direct (N × H)
193. C4×C47#564semidirect
260. C47C4×#564semidirect
399. C4C47⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47⋊#5642
#202465742
#202465732
#202465722
#202465712
#202465702
C4×#130940162
C4×#130940152
C4×#130940142
C4×#125×C472
C4×#56447