Finite Group Databasebeta

← #26422369

Subgroups — #26422369

Order 12032.

2130 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251767C213yesmaximal, complemented
2#20251756C213yesmaximal, complemented
3#20251755C211yesmaximal, characteristic, complemented
4#20251706C216yesmaximal, complemented
5#20251704C212yesmaximal, complemented
6#20245938C216yesmaximal, complemented
7#20245936C212yesmaximal, complemented
8#20245877C213yesmaximal
9#20245869C213yesmaximal, complemented
10C43×D47C211yesmaximal, characteristic, complemented
11C47×#2863C211yesmaximal, characteristic, complemented
12C22×#10625354C2211yescharacteristic
13C2×#13094019C2216yes—
14C2×#13094018C2212yes—
15C2×#13093982C2213yes—
16C2×C42×D47C2211yescharacteristic
17C2×C42×D47C2213yes—
18C2×C42×D47C2213yes—
19#15689030C2213yes—
20#15689025C2213yes—
21#15689024C2213yes—
22#15689022C2213yes—
23#15689021C2213yes—
24#15689019C2213yes—
25#15689015C2216yes—
26#15689014C2216yes—
27#15689013C2216yes—
28#15689012C2216yes—
29#15689010C2216yes—
30#15689008C2216yes—
31#15689005C2216yes—
32#15689001C2216yes—
33#15689001C2216yes—
34#15688997C2216yes—
35#15688994C2216yes—
36#15688990C2216yes—
37C4⋊C4×Dic47C2216yes—
38#15688974C2216yes—
39#15688970C2216yes—
40#15688970C2216yes—
41C42×Dic47C2213yes—
42C42×Dic47C2211yescharacteristic
43C42×Dic47C2213yes—
44C47×#391C2213yes—
45C47×#389C2213yes—
46C47×#387C2216yes—
47C47×#383C2212yes—
48C43×C47C2211yescharacteristic
49C2×#10625354—212no—
50C22×D188C2312yes—
51C22×D188C2311yescharacteristic
52C22×C4×D47C2312yes—
53C22×C4×D47C2313yes—
54C22×C4×D47C2313yes—
55C22×C4×D47C2311yescharacteristic
56#13094019—224no—
57#13094018—28no—
58#13093982—212no—
59C2×C4⋊Dic47C2316yes—
60C2×C4⋊Dic47C2313yes—
61C2×Dic47⋊C4C2316yes—
62C2×Dic47⋊C4C2316yes—
63C2×(C2×D47)⋊C4C2316yes—
64C2×(C2×D47)⋊C4C2316yes—
65C2×(C2×D47)⋊C4C2316yes—
66C2×(C2×D47)⋊C4C2316yes—
67C2×(C2×D47)⋊C4C2316yes—
68C2×C4×Dic47C2313yes—
69C2×C4×Dic47C2313yes—
70C2×C4×Dic47C2313yes—
71C2×C4×Dic47C2313yes—
72C2×C4×Dic47C2313yes—
73C2×C4×Dic47C2313yes—
74C2×C4×Dic47C2316yes—
75C2×C4×Dic47C2313yes—
76C42×D47—212no—
77C42×D47—24no—
78C42×D47—212no—
79C47⋊#95C2316yes—
80C47⋊#95C2316yes—
81C47⋊#95C2316yes—
82C47⋊#95C2316yes—
83C47⋊#95C2316yes—
84C22×Q8×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2316yes—
86C2×C4⋊C4×C47C2313yes—
87C2×C42×C47C2313yes—
88C2×C42×C47C2313yes—
89C2×C42×C47C2311yescharacteristic
90#95×C47C2316yes—
91#95×C47C2316yes—
92#95×C47C2316yes—
93C23×D47C2412yes—
94C23×D47C2411yescharacteristic
95C2×Q8×C47—26no—
96C22×C4×C47C2416yes—
97C22×C4×C47C2412yes—
98C22×C4×C47C2413yes—
99C22×C4×C47C2413yes—
100C22×C4×C47C2411yescharacteristic
101C22×Dic47C2416yes—
102C22×Dic47C2413yes—
103C22×Dic47C2413yes—
104C22×Dic47C2411yescharacteristic
105#10625354—416no—
106C2×D188—212no—
107C2×D188—26no—
108C2×C4×D47—26no—
109C2×C4×D47—26no—
110C2×C4×D47—26no—
111C2×C4×D47—26no—
112C2×C4×D47—26no—
113C2×C4×D47—26no—
114C2×C4×D47—212no—
115C2×C4×D47#41112yes—
116C4⋊C4×C47—26no—
117C4⋊C4×C47—212no—
118C42×C47—26no—
119C42×C47—26no—
120C42×C47#4114yescomplemented
121(C2×D47)⋊C4—212no—
122(C2×D47)⋊C4—212no—
123(C2×D47)⋊C4—212no—
124(C2×D47)⋊C4—212no—
125(C2×D47)⋊C4—212no—
126C4⋊Dic47—26no—
127C4⋊Dic47—212no—
128Dic47⋊C4—212no—
129Dic47⋊C4—212no—
130C4×Dic47—26no—
131C4×Dic47—26no—
132C4×Dic47—26no—
133C4×Dic47—26no—
134C4×Dic47—26no—
135C4×Dic47—26no—
136C4×Dic47—212no—
137C4×Dic47#41112yescomplemented
138C23×C47C2511yescharacteristic
139C22×D47—23no—
140C22×D47—21no—
141C22×D47—26no—
142C22×D47—22no—
143C22×D47—26no—
144C22×D47C2×#4116yes—
145Q8×C47—44no—
146C2×C4×C47—23no—
147C2×C4×C47—23no—
148C2×C4×C47—23no—
149C2×C4×C47—23no—
150C2×C4×C47—26no—
151C2×C4×C47—26no—
152C2×C4×C47—26no—
153C2×C4×C47—26no—
154C2×C4×C47C2×#4116yes—
155C2×C4×C47C2×#4116yes—
156C2×C4×C47C2×#4116yes—
157C2×Dic47—23no—
158C2×Dic47—23no—
159C2×Dic47—23no—
160C2×Dic47—23no—
161C2×Dic47—26no—
162C2×Dic47—26no—
163C2×Dic47—26no—
164C2×Dic47C2×#4116yes—
165C2×Dic47C2×#4116yes—
166C2×Dic47C2×#4116yes—
167D188—48no—
168D188—44no—
169C4×D47—224no—
170C4×D47—224no—
171C4×D47—48no—
172C4×D47#126116yescomplemented
173#36641—471nomaximal, Sylow
174C22×C47C22×#4113yes—
175C22×C47C22×#4113yes—
176C22×C47C22×#4111yescharacteristic
177C2×D47—26no—
178C2×D47—26no—
179C2×D47—42no—
180C2×D47—46no—
181C2×D47—46no—
182C2×D47C2×#12614yes—
183C4×C47—26no—
184C4×C47—26no—
185C4×C47—42no—
186C4×C47—46no—
187C4×C47C2×#12614yes—
188Dic47—26no—
189Dic47—26no—
190Dic47—46no—
191Dic47C2×#12614yes—
192#2863—473no—
193#2863D4711yescharacteristic, complemented
194#2860—473no—
195#2860—471no—
196#2852—476no—
197#2852—472no—
198C4×#126—476no—
199C4×#126—472no—
200#2297—473no—
201#2296—473no—
202C2×C43—471no—
203C2×C47C22×#12611yescharacteristic
204C2×C47#344413yes—
205C2×C47#344413yes—
206D47—24no—
207D47—82no—
208C22×#41—471no—
209C2×#126—476no—
210C2×#126—472no—
211C2×#117—473no—
212C22×C42—473no—
213C22×C42—471no—
214C22×C42—473no—
215#391—473no—
216#391C2×D4713yes—
217#390—473no—
218#390—473no—
219#389—473no—
220#389—473no—
221#389—473no—
222#389C2×D4713yes—
223#388—476no—
224#388—476no—
225#388—476no—
226#388—476no—
227#387—476no—
228#387—476no—
229#387—476no—
230#387C2×D4716yes—
231#386—476no—
232#386—476no—
233#385—476no—
234#385—476no—
235#383—476no—
236#383C2×D4712yes—
237C4×C4⋊C4—476no—
238C4×C4⋊C4—476no—
239C4×C22⋊C4—476no—
240C4×C22⋊C4—476no—
241C43—473no—
242C43—471no—
243C43—473no—
244C43C2×D4711yescharacteristic
245C47#3664111yescharacteristic, complemented, Sylow
246C2×#41—9412no—
247C22×Q8C22×D4711yescharacteristic
248C22×D4—472no—
249C22×D4—471no—
250C23×C4—471no—
251C23×C4—472no—
252C23×C4—473no—
253C23×C4—473no—
254#126—9424no—
255#126—948no—
256#117—9412no—
257C2×C4⋊C4—473no—
258C2×C4⋊C4—476no—
259C2×C4⋊C4—476no—
260C2×C4⋊C4—476no—
261C2×C4⋊C4C22×D4713yes—
262C2×C4⋊C4C22×D4716yes—
263C2×C22⋊C4—476no—
264C2×C22⋊C4—476no—
265C2×C22⋊C4—476no—
266C2×C22⋊C4—476no—
267C2×C22⋊C4—476no—
268C2×C42—473no—
269C2×C42—476no—
270C2×C42—473no—
271C2×C42—473no—
272C2×C42—473no—
273C2×C42—473no—
274C2×C42—473no—
275C2×C42—473no—
276C2×C42—9412no—
277C2×C42—9412no—
278C2×C42—944no—
279C2×C42C22×D4713yes—
280C2×C42C22×D4713yes—
281C2×C42C22×D4711yescharacteristic
282#95—476no—
283#95—476no—
284#95—476no—
285#95—476no—
286#95—476no—
287#95C22×D4716yes—
288#95C22×D4716yes—
289#95C22×D4716yes—
290C24—471no—
291C24—472no—
292#41—18816no—
293C2×Q8—26no—
294C2×D4—9412no—
295C2×D4—946no—
296C22×C4—471no—
297C22×C4—4712no—
298C22×C4—473no—
299C22×C4—473no—
300C22×C4—476no—
301C22×C4—946no—
302C22×C4—946no—
303C22×C4—9412no—
304C22×C4—946no—
305C22×C4—946no—
306C22×C4—946no—
307C22×C4—946no—
308C22×C4C23×D4712yes—
309C22×C4C23×D4716yes—
310C22×C4C23×D4713yes—
311C22×C4C23×D4713yes—
312C22×C4C23×D4711yescharacteristic
313C4⋊C4—26no—
314C4⋊C4—212no—
315C4⋊C4—9412no—
316C4⋊C4—9412no—
317C4⋊C4—946no—
318C4⋊C4—9412no—
319C22⋊C4—9412no—
320C22⋊C4—9412no—
321C22⋊C4—9412no—
322C22⋊C4—9412no—
323C22⋊C4—9412no—
324C42—26no—
325C42—26no—
326C42—4712no—
327C42—946no—
328C42—946no—
329C42—946no—
330C42—946no—
331C42—9412no—
332C42—946no—
333C42—946no—
334C42#1062535414yescomplemented
335C23—476no—
336C23—943no—
337C23—941no—
338C23—946no—
339C23—946no—
340C23—942no—
341C23C24×D4711yescharacteristic
342Q8—44no—
343D4—1888no—
344D4—1884no—
345C2×C4—23no—
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—23no—
349C2×C4—26no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—26no—
353C2×C4—476no—
354C2×C4—4716no—
355C2×C4—476no—
356C2×C4—476no—
357C2×C4—9424no—
358C2×C4—9424no—
359C2×C4—943no—
360C2×C4—943no—
361C2×C4—943no—
362C2×C4—943no—
363C2×C4—946no—
364C2×C4—946no—
365C2×C4—946no—
366C2×C4—1888no—
367C2×C4#41×D4716yes—
368C2×C4#41×D4716yes—
369C2×C4C2×#1062535416yes—
370C22—474no—
371C22—946no—
372C22—946no—
373C22—1882no—
374C22—1886no—
375C22—1886no—
376C22C2×#41×D4713yes—
377C22C2×#41×D4713yes—
378C22C22×#1062535411yescharacteristic
379C4—26no—
380C4—26no—
381C4—42no—
382C4—46no—
383C4—474no—
384C4—946no—
385C4—946no—
386C4—1886no—
387C4#126×D4714yes—
388C2—944no—
389C2—3762no—
390C2C2×#126×D4711yescharacteristic
391C2#2025668213yes—
392C2#2025668513yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2863C2
prime radicalC22×#10625354C22
hypercenter#2863D47
hypocenterC47#36641
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2863

Complements

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

NH ≅ G/Ntype
1. #20251767C2semidirect
2. #20251756C2semidirect
3. #20251755C2semidirect
4. #20251706C2semidirect
5. #20251704C2semidirect
6. #20245938C2semidirect
7. #20245936C2semidirect
9. #20245869C2semidirect
10. C43×D47C2semidirect
11. C47×#2863C2semidirect
120. C42×C47#41semidirect
137. C4×Dic47#41semidirect
172. C4×D47#126semidirect
193. #2863D47semidirect
245. C47#36641semidirect
334. C42#10625354semidirect

Maximal subgroups

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

subgroupindex
#202517672
#202517562
#202517552
#202517062
#202517042
#202459382
#202459362
#202458772
#202458692
C43×D472
C47×#28632
#3664147