Finite Group Databasebeta

← #26379137

Subgroups — #26379137

Order 12032.

2410 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×#15689671C211yesmaximal, characteristic
2#20246568C212yesmaximal, complemented
3#20246565C211yesmaximal, characteristic, complemented
4#20246497C214yesmaximal, complemented
5#20246315C218yesmaximal, complemented
6#20246149C218yesmaximal, complemented
7#20245975C214yesmaximal, complemented
8#20245785C212yesmaximal, complemented
9C47×#2380C211yesmaximal, characteristic, complemented
10C22×#10625352C2212yes—
11#15689671C4116yescomplemented
12C2×#13094024C2211yescharacteristic
13C2×#13094011C2212yes—
14C2×#13093995C2214yes—
15C2×D4×Dic47C2214yes—
16C2×#13093980C2214yes—
17C22×Dic47⋊C4C2214yes—
18C2×C42×D47C2211yescharacteristic
19#15689027C2218yes—
20#15689023C2218yes—
21#15689017C2218yes—
22#15689011C2218yes—
23#15689008C2218yes—
24#15689006C2218yes—
25#15689003C2218yes—
26#15689003C2214yes—
27#15689002C2214yes—
28#15689000C2214yes—
29#15688991C2212yes—
30#15688987C2214yes—
31#15688985C2214yes—
32#15688982C2214yes—
33#15688981C2218yes—
34#15688974C2214yes—
35C22⋊C4×Dic47C2218yes—
36C4×C22⋊Dic47C2218yes—
37#15688970C2214yes—
38#15688968C2214yes—
39C2×#127×C47C2211yescharacteristic
40C47×#386C2218yes—
41C47×#386C2214yes—
42C47×#383C2212yes—
43C2×#10625352—44no—
44C2×#10625352—44no—
45C2×#10625352C2×C4116yescomplemented
46C22×Dic94C2312yes—
47C22×C22⋊D47C2314yes—
48C23×Dic47C2314yes—
49C23×Dic47C2314yes—
50C22×C4×D47C2311yescharacteristic
51C22×C4×D47C2312yes—
52#13094024C2×C418yescomplemented
53#13094011C2×C4116yescomplemented
54#13093995C2×C4132yescomplemented
55D4×Dic47C2×C4132yescomplemented
56#13093980—48no—
57C2×C4⋊Dic47C2314yes—
58C2×Dic47⋊C4—48no—
59C2×Dic47⋊C4C2318yes—
60C2×Dic47⋊C4C2318yes—
61C2×C22⋊Dic47C2318yes—
62C2×C22⋊Dic47C2314yes—
63C2×C22⋊Dic47C2318yes—
64C2×(C2×D47)⋊C4C2318yes—
65C2×C4×Dic47C2318yes—
66C2×C4×Dic47C2318yes—
67C2×C4×Dic47C2311yescharacteristic
68C2×C4×Dic47C2312yes—
69C42×D47C2×C418yescomplemented
70C47⋊#95C2318yes—
71C47⋊#95C2314yes—
72C47⋊#95C2314yes—
73C47⋊#95C2318yes—
74C47⋊#95C2318yes—
75C47⋊#95C2314yes—
76C22×D4×C47C2314yes—
77C22×D4×C47C2312yes—
78C23×C4×C47C2314yes—
79#127×C47C2×C418yes—
80C2×C22⋊C4×C47C2318yes—
81C2×C22⋊C4×C47C2314yes—
82C2×C42×C47C2311yescharacteristic
83#95×C47C2314yes—
84#95×C47C2314yes—
85#95×C47C2314yes—
86C24×C47C2414yes—
87C23×D47C2411yescharacteristic
88C2×D4×C47—44no—
89C2×D4×C47—44no—
90C2×D4×C47—42no—
91C2×D4×C47—42no—
92C2×D4×C47C22×C4116yes—
93C2×D4×C47C22×C418yes—
94C22×C4×C47—48no—
95C22×C4×C47—44no—
96C22×C4×C47C2418yes—
97C22×C4×C47C2412yes—
98C22×C4×C47C2411yescharacteristic
99C2×C22⋊D47—44no—
100C2×C22⋊D47—44no—
101C2×C22⋊D47C22×C4116yes—
102C22×Dic47—28no—
103C22×Dic47—28no—
104C22×Dic47—44no—
105C22×Dic47—48no—
106C22×Dic47C22×C4116yes—
107C22×Dic47C2418yes—
108C22×Dic47C2412yes—
109C22×Dic47C2414yes—
110C22×Dic47C2411yescharacteristic
111#10625352—432no—
112C2×C4×D47—24no—
113C2×C4×D47—44no—
114C2×C4×D47C22×C414yes—
115C2×C4×D47C22×C418yes—
116C2×Dic94—42no—
117C2×Dic94—42no—
118C2×Dic94C22×C418yes—
119C22⋊C4×C47—48no—
120C22⋊C4×C47—44no—
121C42×C47C22×C414yes—
122C22⋊Dic47—48no—
123C22⋊Dic47—44no—
124C22⋊Dic47C22×C4132yes—
125(C2×D47)⋊C4—48no—
126C4⋊Dic47C22×C4116yes—
127Dic47⋊C4—216no—
128Dic47⋊C4—48no—
129C4×Dic47—48no—
130C4×Dic47—48no—
131C4×Dic47C22×C418yes—
132C4×Dic47C22×C414yes—
133C23×C47—24no—
134C23×C47—24no—
135C23×C47—28no—
136C23×C47—28no—
137C23×C47C23×C418yes—
138C23×C47C2511yescharacteristic
139C22×D47—22no—
140C22×D47—24no—
141C22×D47C23×C412yes—
142D4×C47—48no—
143D4×C47—416no—
144C2×C4×C47—22no—
145C2×C4×C47—24no—
146C2×C4×C47—28no—
147C2×C4×C47—28no—
148C2×C4×C47—28no—
149C2×C4×C47—88no—
150C2×C4×C47C23×C414yes—
151C2×C4×C47C23×C412yes—
152C22⋊D47—416no—
153C2×Dic47—24no—
154C2×Dic47—24no—
155C2×Dic47—24no—
156C2×Dic47—232no—
157C2×Dic47—28no—
158C2×Dic47—28no—
159C2×Dic47—28no—
160C2×Dic47—88no—
161C2×Dic47C23×C414yes—
162C2×Dic47C23×C418yes—
163C2×Dic47C23×C412yes—
164C2×Dic47H(5,𝔽2)14yes—
165C4×D47—28no—
166C4×D47—48no—
167Dic94—48no—
168#34369—471nomaximal, Sylow
169C22×C47—28no—
170C22×C47—216no—
171C22×C47—44no—
172C22×C47—48no—
173C22×C47—44no—
174C22×C47C24×C411yescharacteristic
175C22×C47C2×H(5,𝔽2)12yes—
176C22×C47#58514yes—
177C2×D47—22no—
178C2×D47—24no—
179C2×D47—44no—
180C4×C47—22no—
181C4×C47—24no—
182C4×C47—48no—
183Dic47—28no—
184Dic47—24no—
185Dic47—48no—
186Dic47#51814yes—
187C2×#532—471no—
188#2381—472no—
189#2380—471no—
190#2380D4711yescharacteristic, complemented
191#2372—474no—
192#2352—478no—
193#2333—478no—
194#2311—474no—
195#2283—472no—
196C2×C47—48no—
197C2×C47C2×#51811yescharacteristic
198C2×C47#342812yes—
199C2×C47#355114yes—
200D47—42no—
201C22×#41—472no—
202#532—4716no—
203C2×C4⋊Q8—471no—
204C2×#127C2×D4711yescharacteristic
205C2×#124—472no—
206C2×#121—474no—
207C2×C4×D4—474no—
208C2×#117—474no—
209C22×C4⋊C4—474no—
210C22×C42—471no—
211#391—478no—
212#390—478no—
213#388—478no—
214#388—478no—
215#387—478no—
216#387—478no—
217#386—474no—
218#386—478no—
219#386—474no—
220#386—474no—
221#386C2×D4714yes—
222#386C2×D4718yes—
223#383—472no—
224#383C2×D4712yes—
225#382—474no—
226#381—474no—
227#380—478no—
228#380—474no—
229C4×C4⋊C4—474no—
230C4×C22⋊C4—478no—
231C4×C22⋊C4—478no—
232C4×C22⋊C4—474no—
233#376—474no—
234C47#3436911yescharacteristic, complemented, Sylow
235C2×#41—4716no—
236C2×#41—1884no—
237C2×#41—1884no—
238C22×Q8—472no—
239C22×D4—474no—
240C22×D4C22×D4714yes—
241C22×D4C22×D4712yes—
242C23×C4—474no—
243C23×C4—471no—
244C23×C4—472no—
245C23×C4—474no—
246C23×C4C22×D4714yes—
247C4⋊Q8—478no—
248#127C4×D4718yes—
249#124—4716no—
250#121—4732no—
251C4×D4—4732no—
252#117—1888no—
253C2×C4⋊C4—474no—
254C2×C4⋊C4—478no—
255C2×C4⋊C4—478no—
256C2×C4⋊C4—1888no—
257C2×C22⋊C4—478no—
258C2×C22⋊C4—474no—
259C2×C22⋊C4—478no—
260C2×C22⋊C4—478no—
261C2×C22⋊C4C22×D4714yes—
262C2×C22⋊C4C22×D4718yes—
263C2×C42—472no—
264C2×C42—471no—
265C2×C42—478no—
266C2×C42—478no—
267C2×C42—478no—
268C2×C42C22×D4711yescharacteristic
269#95—478no—
270#95—474no—
271#95—478no—
272#95—478no—
273#95—474no—
274#95—474no—
275#95C22×D4714yes—
276#95C22×D4714yes—
277#95C22×D4714yes—
278C24—471no—
279C24C23×D4714yes—
280#41—18832no—
281C2×Q8—478no—
282C2×Q8—1882no—
283C2×Q8—1882no—
284C2×D4—44no—
285C2×D4—44no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—4716no—
289C2×D4—1884no—
290C2×D4—1884no—
291C2×D4C2×C4×D47116yes—
292C2×D4C2×C4×D4718yes—
293C22×C4—44no—
294C22×C4—48no—
295C22×C4—471no—
296C22×C4—4716no—
297C22×C4—472no—
298C22×C4—474no—
299C22×C4—474no—
300C22×C4—478no—
301C22×C4—478no—
302C22×C4—944no—
303C22×C4—948no—
304C22×C4—948no—
305C22×C4—1884no—
306C22×C4—1884no—
307C22×C4—1888no—
308C22×C4C23×D4718yes—
309C22×C4C23×D4712yes—
310C22×C4C23×D4711yescharacteristic
311C4⋊C4—4716no—
312C4⋊C4—9416no—
313C4⋊C4—1888no—
314C22⋊C4—48no—
315C22⋊C4—44no—
316C22⋊C4—4732no—
317C22⋊C4—1888no—
318C22⋊C4—1888no—
319C22⋊C4—1884no—
320C42—478no—
321C42—474no—
322C42—1888no—
323C42—1888no—
324C42C2×C4×D4714yes—
325C23—24no—
326C23—24no—
327C23—28no—
328C23—28no—
329C23—472no—
330C23—942no—
331C23—944no—
332C23C22×C4×D4718yes—
333C23C24×D4711yescharacteristic
334Q8—1888no—
335D4—416no—
336D4—48no—
337D4—18816no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—88no—
344C2×C4—472no—
345C2×C4—474no—
346C2×C4—474no—
347C2×C4—478no—
348C2×C4—948no—
349C2×C4—9432no—
350C2×C4—944no—
351C2×C4—944no—
352C2×C4—944no—
353C2×C4—948no—
354C2×C4—948no—
355C2×C4—948no—
356C2×C4—3768no—
357C2×C4—1888no—
358C2×C4C22×C4×D4714yes—
359C2×C4C22×C4×D4712yes—
360C22—28no—
361C22—216no—
362C22—44no—
363C22—48no—
364C22—44no—
365C22—942no—
366C22—944no—
367C22—1884no—
368C22C23×C4×D4711yescharacteristic
369C22H(5,𝔽2)×D4712yes—
370C22#1568995814yes—
371C4—22no—
372C4—24no—
373C4—48no—
374C4—474no—
375C4—948no—
376C4—944no—
377C4—1888no—
378C2—48no—
379C2—1882no—
380C2#518×D4711yescharacteristic
381C2#2025658612yes—
382C2#2025780714yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2380C2
socle, cosocleC23×C47C25
prime radicalC2×#15689671C2
hypercenter#2380D47
hypocenterC47#34369
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2380

Complements

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

NH ≅ G/Ntype
2. #20246568C2semidirect
3. #20246565C2semidirect
4. #20246497C2semidirect
5. #20246315C2semidirect
6. #20246149C2semidirect
7. #20245975C2semidirect
8. #20245785C2semidirect
9. C47×#2380C2semidirect
11. #15689671C4semidirect
45. C2×#10625352C2×C4semidirect
52. #13094024C2×C4semidirect
53. #13094011C2×C4semidirect
54. #13093995C2×C4semidirect
55. D4×Dic47C2×C4semidirect
69. C42×D47C2×C4semidirect
190. #2380D47semidirect
234. C47#34369semidirect

Maximal subgroups

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

subgroupindex
C2×#156896712
#202465682
#202465652
#202464972
#202463152
#202461492
#202459752
#202457852
C47×#23802
#3436947