Finite Group Databasebeta

← C2×#20249164 #26382633

Subgroups — C2×#20249164 #26382633

Order 12032.

4378 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093993C211yesmaximal, characteristic
2C23×C22⋊Dic47C211yesmaximal, characteristic, complemented
3#20249164C2116yesmaximal, direct product factor
4C2×#15689048C214yesmaximal, complemented
5C2×#15689039C214yesmaximal, complemented
6C2×#15689000C212yesmaximal, complemented
7C2×#15688998C212yesmaximal, complemented
8C2×C47×#379C211yesmaximal, characteristic, complemented
9C23×C22⋊D47C2211yescharacteristic
10C23×C22⋊D47C2212yes—
11C24×Dic47C2212yes—
12C2×#13093993—28no—
13C2×#13093993C2218yes—
14C22×C4⋊Dic47C2214yescomplemented
15C22×C22⋊Dic47—28no—
16C22×C22⋊Dic47C2214yes—
17C22×C22⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2212yes—
19C22×C22⋊Dic47C2218yescomplemented
20C22×(C2×D47)⋊C4C2214yescomplemented
21#15689048C22132yescomplemented
22#15689039C22132yescomplemented
23#15689000C22116yescomplemented
24#15688998C22116yescomplemented
25C2×C47⋊#95C2214yescomplemented
26C2×C47⋊#95C2214yescomplemented
27C26×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2212yes—
29C22×C22⋊C4×C47C2214yes—
30C47×#379C2218yescomplemented
31C24×D47C2311yescharacteristic
32C22×C22⋊D47—28no—
33C22×C22⋊D47—24no—
34C22×C22⋊D47—28no—
35C22×C22⋊D47—48no—
36C22×C22⋊D47C2314yes—
37C22×C22⋊D47C2318yes—
38C23×Dic47—28no—
39C23×Dic47—48no—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2314yes—
42C23×Dic47C2312yes—
43C23×Dic47C2318yes—
44#13093993—232no—
45C2×C4⋊Dic47—48no—
46C2×C4⋊Dic47C23116yescomplemented
47C2×C22⋊Dic47—216no—
48C2×C22⋊Dic47—232no—
49C2×C22⋊Dic47—28no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47C2314yes—
52C2×C22⋊Dic47C23116yes—
53C2×C22⋊Dic47C2318yes—
54C2×(C2×D47)⋊C4—48no—
55C2×(C2×D47)⋊C4C23116yescomplemented
56C47⋊#95C23116yescomplemented
57C47⋊#95C23116yescomplemented
58C25×C47—28no—
59C25×C47—48no—
60C25×C47D418yes—
61C25×C47C2312yes—
62C25×C47C2311yescharacteristic
63C25×C47C2314yes—
64C23×C4×C47C2314yes—
65C2×C22⋊C4×C47—28no—
66C2×C22⋊C4×C47—48no—
67C2×C22⋊C4×C47C2318yes—
68C2×C22⋊C4×C47C23116yes—
69C24×C47—28no—
70C24×C47—232no—
71C24×C47—216no—
72C24×C47—28no—
73C24×C47—28no—
74C24×C47—28no—
75C24×C47—432no—
76C24×C47—416no—
77C24×C47—464no—
78C24×C47C2×D418yes—
79C24×C47C2×D414yes—
80C24×C47C2×D4116yes—
81C24×C47#4118yes—
82C24×C47C2414yes—
83C24×C47C2412yes—
84C24×C47C2411yescharacteristic
85C23×D47—22no—
86C23×D47—24no—
87C23×D47—28no—
88C23×D47C2412yes—
89C22×C4×C47—28no—
90C22×C4×C47—28no—
91C22×C4×C47—28no—
92C22×C4×C47C2418yes—
93C2×C22⋊D47—216no—
94C2×C22⋊D47—28no—
95C2×C22⋊D47—216no—
96C2×C22⋊D47—416no—
97C2×C22⋊D47—432no—
98C2×C22⋊D47—416no—
99C22×Dic47—216no—
100C22×Dic47—28no—
101C22×Dic47—22no—
102C22×Dic47—24no—
103C22×Dic47—24no—
104C22×Dic47—28no—
105C22×Dic47—28no—
106C22×Dic47—28no—
107C22×Dic47—416no—
108C22×Dic47—432no—
109C22×Dic47C2412yes—
110C22×Dic47C2418yes—
111C22×Dic47C2414yes—
112C22⋊C4×C47—216no—
113C22⋊C4×C47—416no—
114C22⋊Dic47—232no—
115C22⋊Dic47—216no—
116C22⋊Dic47—28no—
117(C2×D47)⋊C4—416no—
118C4⋊Dic47—416no—
119C23×C47—216no—
120C23×C47—232no—
121C23×C47—28no—
122C23×C47—232no—
123C23×C47—216no—
124C23×C47—216no—
125C23×C47—216no—
126C23×C47—28no—
127C23×C47—28no—
128C23×C47—28no—
129C23×C47—432no—
130C23×C47—4128no—
131C23×C47—464no—
132C23×C47—432no—
133C23×C47#123116yes—
134C23×C47C22×D418yes—
135C23×C47C22×D414yes—
136C23×C47C22×D412yes—
137C23×C47C2×#4118yes—
138C23×C47C2×#4114yes—
139C23×C47H(5,𝔽2)18yes—
140C23×C47C2511yescharacteristic
141C22×D47—22no—
142C22×D47—24no—
143C22×D47—28no—
144C22×D47—44no—
145C22×D47—48no—
146C22×D47—416no—
147C2×C4×C47—28no—
148C2×C4×C47—28no—
149C2×C4×C47—28no—
150C2×C4×C47—416no—
151C22⋊D47—432no—
152C22⋊D47—416no—
153C2×Dic47—28no—
154C2×Dic47—22no—
155C2×Dic47—24no—
156C2×Dic47—24no—
157C2×Dic47—28no—
158C2×Dic47—28no—
159C2×Dic47—28no—
160C2×Dic47—432no—
161C2×Dic47—44no—
162C2×Dic47—416no—
163C2×Dic47—48no—
164C2×#2622—471nomaximal, Sylow
165C22×C47—232no—
166C22×C47—28no—
167C22×C47—216no—
168C22×C47—28no—
169C22×C47—28no—
170C22×C47—28no—
171C22×C47—464no—
172C22×C47—432no—
173C22×C47—416no—
174C22×C47C2×#12318yes—
175C22×C47C2×#12314yes—
176C22×C47#53418yes—
177C22×C47#538116yes—
178C22×C47C23×D411yescharacteristic
179C22×C47C22×#4112yes—
180C22×C47C2×H(5,𝔽2)14yes—
181C2×D47—42no—
182C2×D47—44no—
183C2×D47—48no—
184C2×D47—88no—
185C4×C47—48no—
186Dic47—42no—
187Dic47—48no—
188Dic47—44no—
189C22×#120—471no—
190C23×C22⋊C4—471no—
191#2622—4716no—
192C2×#397—474no—
193C2×#394—474no—
194C2×#386—472no—
195C2×#385—472no—
196C2×#379D4711yescharacteristic, complemented
197C2×C47—28no—
198C2×C47—48no—
199C2×C47#262218yescomplemented
200C2×C47C22×#12311yescharacteristic
201C2×C47C2×#53412yes—
202C2×C47C2×#53814yes—
203D47—82no—
204C26C2×D4711yescharacteristic
205C23×D4—471no—
206C23×D4—472no—
207C24×C4—472no—
208C2×#120—478no—
209C2×#120—948no—
210C22×C4⋊C4—474no—
211C22×C22⋊C4—478no—
212C22×C22⋊C4—474no—
213C22×C22⋊C4—472no—
214C22×C22⋊C4—471no—
215C22×C22⋊C4—474no—
216C22×C22⋊C4—948no—
217C22×C22⋊C4C2×D4712yes—
218C22×C22⋊C4C2×D4714yes—
219#397—4732no—
220#394—4732no—
221#386—4716no—
222#385—4716no—
223#379C2×D4718yescomplemented
224C2×#95—474no—
225C2×#95—474no—
226C47C2×#262211yescharacteristic, complemented, Sylow
227C25—28no—
228C25—48no—
229C25—471no—
230C25D18818yes—
231C25C22×D4712yes—
232C25C22×D4711yescharacteristic
233C25C22×D4714yes—
234C22×D4—474no—
235C22×D4—478no—
236C22×D4—948no—
237C22×D4—944no—
238C22×D4—948no—
239C22×D4—1888no—
240C23×C4—474no—
241C23×C4—472no—
242C23×C4—471no—
243C23×C4—478no—
244C23×C4—948no—
245C23×C4—1888no—
246C23×C4C22×D4714yes—
247#120—9432no—
248C2×C4⋊C4—4716no—
249C2×C4⋊C4—1888no—
250C2×C22⋊C4—28no—
251C2×C22⋊C4—48no—
252C2×C22⋊C4—4716no—
253C2×C22⋊C4—474no—
254C2×C22⋊C4—478no—
255C2×C22⋊C4—4716no—
256C2×C22⋊C4—9416no—
257C2×C22⋊C4—9432no—
258C2×C22⋊C4—948no—
259C2×C22⋊C4—944no—
260C2×C22⋊C4—1888no—
261C2×C22⋊C4C22×D4718yes—
262C2×C22⋊C4C22×D47116yes—
263#95—4716no—
264#95—4716no—
265C24—28no—
266C24—232no—
267C24—216no—
268C24—28no—
269C24—28no—
270C24—28no—
271C24—432no—
272C24—416no—
273C24—464no—
274C24—472no—
275C24—942no—
276C24—944no—
277C24—948no—
278C24C2×D18818yes—
279C24C2×D18814yes—
280C24C2×D188116yes—
281C24#1062535218yes—
282C24C23×D4714yes—
283C24C23×D4712yes—
284C24C23×D4711yescharacteristic
285C2×D4—9416no—
286C2×D4—948no—
287C2×D4—9416no—
288C2×D4—18816no—
289C2×D4—18832no—
290C2×D4—18816no—
291C22×C4—28no—
292C22×C4—28no—
293C22×C4—28no—
294C22×C4—472no—
295C22×C4—478no—
296C22×C4—474no—
297C22×C4—9416no—
298C22×C4—948no—
299C22×C4—942no—
300C22×C4—944no—
301C22×C4—944no—
302C22×C4—948no—
303C22×C4—948no—
304C22×C4—948no—
305C22×C4—18816no—
306C22×C4—18832no—
307C22×C4C23×D4718yes—
308C4⋊C4—18816no—
309C22⋊C4—216no—
310C22⋊C4—416no—
311C22⋊C4—9432no—
312C22⋊C4—9416no—
313C22⋊C4—948no—
314C22⋊C4—18816no—
315C23—216no—
316C23—28no—
317C23—232no—
318C23—232no—
319C23—216no—
320C23—216no—
321C23—216no—
322C23—28no—
323C23—28no—
324C23—28no—
325C23—432no—
326C23—4128no—
327C23—464no—
328C23—432no—
329C23—942no—
330C23—944no—
331C23—948no—
332C23—1884no—
333C23—1888no—
334C23—18816no—
335C23#13094008116yes—
336C23C22×D18818yes—
337C23C22×D18814yes—
338C23C22×D18812yes—
339C23C2×#1062535218yes—
340C23C2×#1062535214yes—
341C23#1309406918yes—
342C23C24×D4711yescharacteristic
343D4—18832no—
344D4—18816no—
345C2×C4—28no—
346C2×C4—28no—
347C2×C4—28no—
348C2×C4—416no—
349C2×C4—948no—
350C2×C4—942no—
351C2×C4—944no—
352C2×C4—944no—
353C2×C4—948no—
354C2×C4—948no—
355C2×C4—948no—
356C2×C4—18832no—
357C2×C4—1884no—
358C2×C4—18816no—
359C2×C4—1888no—
360C22—232no—
361C22—28no—
362C22—216no—
363C22—28no—
364C22—28no—
365C22—28no—
366C22—464no—
367C22—432no—
368C22—416no—
369C22—3768no—
370C22—1882no—
371C22—1884no—
372C22—1888no—
373C22C2×#1309400818yes—
374C22C2×#1309400814yes—
375C22#1568968518yes—
376C22#15689708116yes—
377C22C23×D18811yescharacteristic
378C22C22×#1062535212yes—
379C22C2×#1309406914yes—
380C4—48no—
381C4—1882no—
382C4—1888no—
383C4—1884no—
384C2—28no—
385C2—48no—
386C2—3762no—
387C2#2024916418yesdirect product factor
388C2C22×#1309400811yescharacteristic
389C2C2×#1568968512yes—
390C2C2×#1568970814yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#379C2
socleC24×C47C24
prime radicalC22×#13093993C2
hypercenterC2×#379D47
hypocenterC47C2×#2622
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊Dic47C2semidirect
3. #20249164C2direct (N × H)
4. C2×#15689048C2semidirect
5. C2×#15689039C2semidirect
6. C2×#15689000C2semidirect
7. C2×#15688998C2semidirect
8. C2×C47×#379C2semidirect
14. C22×C4⋊Dic47C22semidirect
19. C22×C22⋊Dic47C22semidirect
20. C22×(C2×D47)⋊C4C22semidirect
21. #15689048C22semidirect
22. #15689039C22semidirect
23. #15689000C22semidirect
24. #15688998C22semidirect
25. C2×C47⋊#95C22semidirect
26. C2×C47⋊#95C22semidirect
30. C47×#379C22semidirect
46. C2×C4⋊Dic47C23semidirect
55. C2×(C2×D47)⋊C4C23semidirect
56. C47⋊#95C23semidirect
57. C47⋊#95C23semidirect
196. C2×#379D47semidirect
199. C2×C47#2622semidirect
223. #379C2×D47semidirect
226. C47C2×#2622semidirect
387. C2#20249164direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939932
C23×C22⋊Dic472
#202491642
C2×#156890482
C2×#156890392
C2×#156890002
C2×#156889982
C2×C47×#3792
C2×#262247