Finite Group Databasebeta

← #26138984

Subgroups — #26138984

Order 12032.

2078 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093983C211yesmaximal, characteristic
2C22×C47⋊#95C211yesmaximal, characteristic
3#20241657C212yesmaximal, complemented
4#20241655C212yesmaximal, complemented
5#20241612C214yesmaximal, complemented
6#20241610C214yesmaximal
7C2×C47×#381C211yesmaximal, characteristic
8C24×Dic47C2212yes—
9C2×#13093983—24no—
10C2×#13093983—24no—
11C2×#13093983C418yescomplemented
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C22⋊Dic47C2212yes—
15C22×C4×Dic47C2212yes—
16C2×C47⋊#95—24no—
17C2×C47⋊#95C2218yes—
18C2×C47⋊#95C2212yes—
19C2×C47⋊#95C2212yes—
20C2×C47⋊#95C2218yes—
21C24×C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2212yes—
23C47×#381—24no—
24C2×#95×C47C2212yes—
25C2×#95×C47C2212yes—
26C23×Dic47—24no—
27C23×Dic47—28no—
28C23×Dic47—28no—
29C23×Dic47—44no—
30C23×Dic47C2312yes—
31C23×Dic47C2312yes—
32C23×Dic47C2314yes—
33#13093983—232no—
34C2×C4⋊Dic47—22no—
35C2×C4⋊Dic47—22no—
36C2×C4⋊Dic47—22no—
37C2×C4⋊Dic47—22no—
38C2×C4⋊Dic47C2×C414yescomplemented
39C2×C4⋊Dic47C2×C414yescomplemented
40C2×C22⋊Dic47—24no—
41C2×C22⋊Dic47—24no—
42C2×C22⋊Dic47C2×C418yes—
43C2×C4×Dic47—24no—
44C2×C4×Dic47—24no—
45C2×C4×Dic47C2×C418yescomplemented
46C47⋊#95—24no—
47C47⋊#95—24no—
48C47⋊#95—216no—
49C47⋊#95—48no—
50C25×C47C2311yescharacteristic
51C23×C4×C47—28no—
52C23×C4×C47C2×C414yes—
53C23×C4×C47D414yes—
54C23×C4×C47D414yes—
55C23×C4×C47C2314yes—
56C23×C4×C47C2311yescharacteristic
57C23×C4×C47C2311yescharacteristic
58C2×C22⋊C4×C47—24no—
59C2×C22⋊C4×C47—28no—
60#95×C47—24no—
61#95×C47—24no—
62C24×C47—24no—
63C24×C47—22no—
64C24×C47—22no—
65C24×C47C22×C412yes—
66C24×C47C2×D412yes—
67C24×C47C2×D412yes—
68C24×C47#4118yes—
69C24×C47C2411yescharacteristic
70C22×C4×C47—216no—
71C22×C4×C47—216no—
72C22×C4×C47—216no—
73C22×C4×C47—24no—
74C22×C4×C47—24no—
75C22×C4×C47—24no—
76C22×C4×C47—28no—
77C22×C4×C47—28no—
78C22×C4×C47—24no—
79C22×C4×C47—24no—
80C22×C4×C47C22⋊C4116yes—
81C22×C4×C47C22×C412yes—
82C22×C4×C47C22×C412yes—
83C22×C4×C47C2×D412yes—
84C22×C4×C47C2×D412yes—
85C22×C4×C47C2×D412yes—
86C22×C4×C47C2×D412yes—
87C22×Dic47—216no—
88C22×Dic47—24no—
89C22×Dic47—22no—
90C22×Dic47—22no—
91C22×Dic47—22no—
92C22×Dic47—22no—
93C22×Dic47—28no—
94C22×Dic47—24no—
95C22×Dic47—28no—
96C22×Dic47—24no—
97C22×Dic47—28no—
98C22×Dic47—24no—
99C22×Dic47—432no—
100C22×Dic47—48no—
101C22×Dic47—48no—
102C22×Dic47C22×C414yes—
103C22×Dic47C22×C414yes—
104C22×Dic47#4118yes—
105C22⋊C4×C47—48no—
106C22⋊Dic47—216no—
107C4⋊Dic47—28no—
108C4⋊Dic47—28no—
109C4×Dic47—216no—
110C23×C47—24no—
111C23×C47—24no—
112C23×C47—24no—
113C23×C47—24no—
114C23×C47—22no—
115C23×C47—22no—
116C23×C47—24no—
117C23×C47—216no—
118C23×C47—216no—
119C23×C47C2×C22⋊C414yes—
120C23×C47#11718yes—
121C23×C47#12318yes—
122C23×C47#12318yes—
123C23×C47C23×C411yescharacteristic
124C23×C47C22×D411yescharacteristic
125C23×C47C22×D411yescharacteristic
126C23×C47C2×#4114yes—
127C23×C47C2×#4114yes—
128C23×C47H(5,𝔽2)12yes—
129C23×C472−1+412yes—
130C2×C4×C47—24no—
131C2×C4×C47—24no—
132C2×C4×C47—24no—
133C2×C4×C47—24no—
134C2×C4×C47—24no—
135C2×C4×C47—24no—
136C2×C4×C47—232no—
137C2×C4×C47—44no—
138C2×C4×C47—44no—
139C2×C4×C47—44no—
140C2×C4×C47—48no—
141C2×C4×C47—48no—
142C2×C4×C47C2×C22⋊C414yes—
143C2×C4×C47C2×C22⋊C414yes—
144C2×Dic47—24no—
145C2×Dic47—24no—
146C2×Dic47—28no—
147C2×Dic47—28no—
148C2×Dic47—28no—
149C2×Dic47—216no—
150C2×Dic47—432no—
151C2×Dic47—44no—
152C2×Dic47—44no—
153C2×Dic47—44no—
154C2×Dic47—42no—
155C2×Dic47—44no—
156C2×Dic47—42no—
157C2×Dic47—44no—
158C2×Dic47—48no—
159#13958—471nomaximal, Sylow
160C22×C47—24no—
161C22×C47—216no—
162C22×C47—28no—
163C22×C47—28no—
164C22×C47—216no—
165C22×C47—24no—
166C22×C47#38118yes—
167C22×C47C22×C22⋊C411yescharacteristic
168C22×C47C2×#11712yes—
169C22×C47C4×#4112yes—
170C22×C47#52012yes—
171C22×C47C2×#12312yes—
172C22×C47C2×#12312yes—
173C22×C47#52512yes—
174C22×C47#53212yes—
175C22×C47#53511yescharacteristic
176C22×C47#53611yescharacteristic
177C22×C47#53712yes—
178C22×C47#55118yes—
179C22×C47#55218yes—
180C4×C47—24no—
181C4×C47—24no—
182C4×C47—84no—
183Dic47—44no—
184Dic47—48no—
185Dic47—44no—
186C22×#117—471no—
187C2×#381D4711yescharacteristic
188C22×#95—471no—
189#1445—472no—
190#1445—472no—
191#1434—474no—
192C22⋊#95—474no—
193C2×C47—28no—
194C2×C47C2×#38111yescharacteristic
195C2×C47#229711yescharacteristic
196C2×C47#231111yescharacteristic
197C2×C47#234314yes—
198C2×C47#248212yes—
199C2×C47#248412yes—
200C2×C47#249814yes—
201C24×C4—472no—
202C24×C4C2×D4711yescharacteristic
203C2×#117—478no—
204C2×#117—944no—
205C2×#117—944no—
206C22×C4⋊C4—471no—
207C22×C4⋊C4—471no—
208C22×C22⋊C4—472no—
209C22×C22⋊C4C2×D4712yes—
210C22×C42—472no—
211#381—24no—
212C2×#95—478no—
213C2×#95—472no—
214C2×#95—472no—
215C2×#95—478no—
216C2×#95—944no—
217C2×#95C2×D4712yes—
218C2×#95C2×D4712yes—
219C47#1395811yescharacteristic, complemented, Sylow
220C25C22×D4711yescharacteristic
221C23×C4—28no—
222C23×C4—472no—
223C23×C4—472no—
224C23×C4—474no—
225C23×C4—948no—
226C23×C4—944no—
227C23×C4—948no—
228C23×C4—1884no—
229C23×C4C4×D4714yes—
230C23×C4D18814yes—
231C23×C4C22⋊D4714yes—
232C23×C4C22×D4714yes—
233C23×C4C22×D4711yescharacteristic
234C23×C4C22×D4711yescharacteristic
235#117—9432no—
236C2×C4⋊C4—474no—
237C2×C4⋊C4—474no—
238C2×C4⋊C4—942no—
239C2×C4⋊C4—942no—
240C2×C4⋊C4—942no—
241C2×C4⋊C4—942no—
242C2×C22⋊C4—28no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4—478no—
245C2×C22⋊C4—944no—
246C2×C22⋊C4—944no—
247C2×C42—478no—
248C2×C42—944no—
249C2×C42—944no—
250#95—24no—
251#95—24no—
252#95—9416no—
253#95—944no—
254#95—944no—
255#95—1888no—
256C24—24no—
257C24—22no—
258C24—22no—
259C24C2×C4×D4712yes—
260C24C2×D18812yes—
261C24#1062535218yes—
262C24C2×C22⋊D4712yes—
263C24C23×D4711yescharacteristic
264C22×C4—216no—
265C22×C4—216no—
266C22×C4—216no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—474no—
275C22×C4—474no—
276C22×C4—478no—
277C22×C4—9416no—
278C22×C4—942no—
279C22×C4—942no—
280C22×C4—944no—
281C22×C4—942no—
282C22×C4—942no—
283C22×C4—948no—
284C22×C4—944no—
285C22×C4—948no—
286C22×C4—944no—
287C22×C4—948no—
288C22×C4—944no—
289C22×C4—18832no—
290C22×C4—1888no—
291C22×C4—1888no—
292C22×C4(C2×D47)⋊C4116yes—
293C22×C4C2×C4×D4712yes—
294C22×C4C2×C4×D4712yes—
295C22×C4C2×D18812yes—
296C22×C4C2×D18812yes—
297C22×C4C2×C22⋊D4712yes—
298C22×C4C2×C22⋊D4712yes—
299C4⋊C4—948no—
300C4⋊C4—948no—
301C22⋊C4—48no—
302C22⋊C4—9416no—
303C42—9416no—
304C23—216no—
305C23—216no—
306C23—24no—
307C23—24no—
308C23—24no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—24no—
313C23C2×(C2×D47)⋊C414yes—
314C23#1309398018yes—
315C23#1309400518yes—
316C23#1309400818yes—
317C23C22×C4×D4711yescharacteristic
318C23C22×C22⋊D4711yescharacteristic
319C23C22×D18811yescharacteristic
320C23#41×D4714yes—
321C23C2×#1062535214yes—
322C23#1309407012yes—
323C23#1309407112yes—
324C2×C4—232no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—48no—
332C2×C4—48no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—9416no—
337C2×C4—944no—
338C2×C4—944no—
339C2×C4—948no—
340C2×C4—948no—
341C2×C4—948no—
342C2×C4—18832no—
343C2×C4—1888no—
344C2×C4—1884no—
345C2×C4—1884no—
346C2×C4—1884no—
347C2×C4—1882no—
348C2×C4—1884no—
349C2×C4—1882no—
350C2×C4—1884no—
351C2×C4C2×(C2×D47)⋊C414yes—
352C2×C4C2×(C2×D47)⋊C414yes—
353C22—216no—
354C22—28no—
355C22—24no—
356C22—28no—
357C22—24no—
358C22—216no—
359C22#1568898418yes—
360C22C22×(C2×D47)⋊C411yescharacteristic
361C22C2×#1309398012yes—
362C22#1568959112yes—
363C22#1568960312yes—
364C22C2×#1309400512yes—
365C22C2×#1309400812yes—
366C22#1568963512yes—
367C22#1568966912yes—
368C22#1568969211yescharacteristic
369C22#1568969911yescharacteristic
370C22#1568970112yes—
371C22#1568979618yes—
372C22#1568981018yes—
373C4—24no—
374C4—24no—
375C4—84no—
376C4—1888no—
377C4—1884no—
378C4—1884no—
379C2—28no—
380C2C2×#1568898411yescharacteristic
381C2#2024587611yescharacteristic
382C2#2024597611yescharacteristic
383C2#2024625014yes—
384C2#2024766412yes—
385C2#2024767712yes—
386C2#2024783414yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#381C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#381D47
hypocenterC47#13958
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #20241657C2semidirect
4. #20241655C2semidirect
5. #20241612C2semidirect
11. C2×#13093983C4semidirect
38. C2×C4⋊Dic47C2×C4semidirect
39. C2×C4⋊Dic47C2×C4semidirect
45. C2×C4×Dic47C2×C4semidirect
219. C47#13958semidirect

Maximal subgroups

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

subgroupindex
C22×#130939832
C22×C47⋊#952
#202416572
#202416552
#202416122
#202416102
C2×C47×#3812
#1395847