Finite Group Databasebeta

← #26374503

Subgroups — #26374503

Order 12032.

3598 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
1C2×C4×#10625352C213yesmaximal
2#20245752C213yesmaximal, complemented
3#20245751C211yesmaximal, characteristic, complemented
4#20245749C213yesmaximal, complemented
5#20245747C216yesmaximal, complemented
6#20245746C212yesmaximal, complemented
7C4×#13093982C213yesmaximal, complemented
8C4×#13093980C216yesmaximal, complemented
9C2×#15688968C212yesmaximal, complemented
10#376×D47C211yesmaximal, characteristic, complemented
11C47×#2275C211yesmaximal, characteristic, complemented
12C22×#10625352C2211yescharacteristic
13C4×#10625352C4148yescomplemented
14C2×C4×Dic94C2213yes—
15C2×#13093989C2213yes—
16C2×D4×Dic47C2213yes—
17C2×C4×C22⋊D47C2216yes—
18C2×(C22⋊D47)⋊C4C2216yes—
19C2×#13093982C2213yes—
20C2×#13093980C2216yes—
21C22×C4×Dic47C2216yes—
22C2×C42×D47C2213yes—
23C4⋊C4×Dic47C2216yes—
24C4×Dic47⋊C4C22112yes—
25C4×C4⋊Dic47C2213yes—
26#15688974C2216yes—
27#15688974C2216yes—
28C22⋊C4×Dic47C22112yes—
29C4×(C2×D47)⋊C4C2216yes—
30C4×C22⋊Dic47C2216yes—
31#15688970C2216yes—
32#15688969C2213yes—
33#15688968C2211yescharacteristic
34#15688968C2213yes—
35#15688968C2216yes—
36#15688968C2212yes—
37#15688968C2216yes—
38C2×C47⋊#95C2216yes—
39#95×D47C2211yescharacteristic
40#95×D47C2213yes—
41C42×Dic47C2216yes—
42C2×C4×D4×C47C2213yes—
43C4×C4⋊C4×C47C2213yes—
44C4×C22⋊C4×C47C2216yes—
45C47×#376C2211yescharacteristic
46C2×#95×C47C2212yes—
47C2×#10625352C2×C4124yes—
48C22×Dic94C2311yescharacteristic
49C22×C22⋊D47C2312yes—
50C23×Dic47C2316yes—
51C23×Dic47C2312yes—
52C22×C4×D47C2313yes—
53C22×C4×D47C2313yes—
54C22×C4×D47C2311yescharacteristic
55C4×Dic94C2×C4124yescomplemented
56#13093989C2×C4124yescomplemented
57D4×Dic47C2×C4124yescomplemented
58C4×C22⋊D47C2×C4148yescomplemented
59(C22⋊D47)⋊C4C2×C4148yescomplemented
60#13093982C2×C4124yescomplemented
61#13093980C2×C4148yescomplemented
62C2×C4⋊Dic47C2313yes—
63C2×Dic47⋊C4C2316yes—
64C2×Dic47⋊C4C2316yes—
65C2×C22⋊Dic47C2316yes—
66C2×(C2×D47)⋊C4C2316yes—
67C2×C4×Dic47C2×C4148yescomplemented
68C2×C4×Dic47C23112yes—
69C2×C4×Dic47C2316yes—
70C2×C4×Dic47C2313yes—
71C2×C4×Dic47C2316yes—
72C2×C4×Dic47C2313yes—
73C2×C4×Dic47C2316yes—
74C2×C4×Dic47C2316yes—
75C2×C4×Dic47C2313yes—
76C42×D47C2×C4124yescomplemented
77C47⋊#95C2313yes—
78C47⋊#95C2313yes—
79C47⋊#95C2316yes—
80C47⋊#95C2316yes—
81C47⋊#95C23112yes—
82C22×D4×C47C2311yescharacteristic
83C23×C4×C47C2316yes—
84C4×D4×C47C2×C4124yescomplemented
85C2×C4⋊C4×C47C2313yes—
86C2×C22⋊C4×C47C2316yes—
87C2×C42×C47C2316yes—
88C2×C42×C47C2313yes—
89#95×C47C2311yescharacteristic
90#95×C47C2313yes—
91#95×C47C2316yes—
92C24×C47C2412yes—
93C23×D47C2411yescharacteristic
94C2×D4×C47C22×C4112yes—
95C22×C4×C47—412no—
96C22×C4×C47C22×C4124yes—
97C22×C4×C47C2413yes—
98C22×C4×C47C2416yes—
99C22×C4×C47C2413yes—
100C22×C4×C47C2411yescharacteristic
101C2×C22⋊D47C22×C4124yes—
102C22×Dic47—46no—
103C22×Dic47—46no—
104C22×Dic47C22×C4124yes—
105C22×Dic47C22×C4124yes—
106C22×Dic47C2413yes—
107C22×Dic47C2416yes—
108C22×Dic47C2413yes—
109C22×Dic47C2411yescharacteristic
110C22×Dic47C2412yes—
111#10625352C42164yescomplemented
112C2×C4×D47—46no—
113C2×C4×D47—43no—
114C2×C4×D47—43no—
115C2×C4×D47C22×C4112yes—
116C2×C4×D47C22×C4112yes—
117C2×C4×D47C22×C4112yes—
118C2×Dic94C22×C4112yes—
119C4⋊C4×C47C22×C4112yes—
120C22⋊C4×C47C22×C4124yes—
121C42×C47—46no—
122C42×C47C22×C4112yes—
123C22⋊Dic47C22×C4124yes—
124(C2×D47)⋊C4C22×C4124yes—
125C4⋊Dic47C22×C4112yes—
126Dic47⋊C4C22×C4124yes—
127Dic47⋊C4C22×C4124yes—
128C4×Dic47—412no—
129C4×Dic47—46no—
130C4×Dic47C22×C4112yes—
131C4×Dic47C22×C4112yes—
132C4×Dic47C22×C4112yes—
133C4×Dic47C22×C4124yes—
134C4×Dic47C22×C4124yes—
135C4×Dic47C22×C4124yes—
136C23×C47—22no—
137C23×C47—26no—
138C23×C47C23×C4112yes—
139C23×C47C2511yescharacteristic
140C22×D47—23no—
141C22×D47—21no—
142C22×D47C23×C416yes—
143D4×C47C2×C42116yes—
144C2×C4×C47—23no—
145C2×C4×C47—212no—
146C2×C4×C47—23no—
147C2×C4×C47—26no—
148C2×C4×C47—424no—
149C2×C4×C47C23×C416yes—
150C2×C4×C47C23×C4112yes—
151C2×C4×C47C23×C416yes—
152C2×C4×C47C23×C416yes—
153C22⋊D47C2×C42132yes—
154C2×Dic47—26no—
155C2×Dic47—26no—
156C2×Dic47—26no—
157C2×Dic47—23no—
158C2×Dic47—23no—
159C2×Dic47—424no—
160C2×Dic47C2×C42132yes—
161C2×Dic47C23×C416yes—
162C2×Dic47C23×C416yes—
163C2×Dic47C23×C4112yes—
164C2×Dic47C23×C416yes—
165C2×Dic47C23×C4112yes—
166C4×D47—412no—
167C4×D47—412no—
168C4×D47C2×C42116yes—
169Dic94C2×C42116yes—
170#33999—471nomaximal, Sylow
171C22×C47—212no—
172C22×C47—212no—
173C22×C47C22×C4218yes—
174C22×C47C24×C413yes—
175C22×C47#58513yes—
176C22×C47#58511yescharacteristic
177C2×D47—26no—
178C2×D47—26no—
179C2×D47C22×C4214yes—
180C4×C47—26no—
181C4×C47—26no—
182C4×C47—212no—
183C4×C47C22×C4214yes—
184Dic47—26no—
185Dic47—26no—
186Dic47—212no—
187Dic47C22×C4218yes—
188Dic47C22×C4214yes—
189C2×C4×#41—473no—
190#2276—473no—
191#2276—471no—
192#2275—476no—
193#2275—472no—
194#2275—473no—
195#2275D4711yescharacteristic, complemented
196C4×#117—473no—
197C4×#117—476no—
198C2×#376—471no—
199C2×#376—472no—
200C2×C47—28no—
201C2×C47C23×C4211yescharacteristic
202C2×C47#342813yes—
203C2×C47#342813yes—
204D47—24no—
205C22×#41—471no—
206C4×#41—4748no—
207C2×C4×Q8—473no—
208C2×C4×Q8—473no—
209C2×C4×D4—473no—
210C2×C4×D4—476no—
211C2×C4×D4—476no—
212C2×C4×D4C2×D4713yes—
213C2×#117—473no—
214C2×#117—476no—
215C22×C42—476no—
216C22×C42—473no—
217C4×C4⋊C4—476no—
218C4×C4⋊C4—473no—
219C4×C4⋊C4—4712no—
220C4×C4⋊C4—476no—
221C4×C4⋊C4—476no—
222C4×C4⋊C4C2×D4713yes—
223C4×C22⋊C4—476no—
224C4×C22⋊C4—4712no—
225C4×C22⋊C4—476no—
226C4×C22⋊C4—476no—
227C4×C22⋊C4C2×D4716yes—
228#376—473no—
229#376—471no—
230#376—473no—
231#376—476no—
232#376—476no—
233#376—472no—
234#376C2×D4711yescharacteristic
235C2×#95—476no—
236C2×#95—473no—
237C2×#95—471no—
238C2×#95C2×D4712yes—
239C43—476no—
240C47#3399911yescharacteristic, complemented, Sylow
241C2×#41—4724no—
242C22×Q8—471no—
243C22×D4—472no—
244C22×D4C22×D4711yescharacteristic
245C23×C4—472no—
246C23×C4—471no—
247C23×C4—476no—
248C23×C4—473no—
249C23×C4—473no—
250C23×C4C22×D4716yes—
251C4×Q8—4724no—
252C4×Q8—4724no—
253C4×D4—4724no—
254C4×D4—4748no—
255C4×D4—4748no—
256C4×D4C4×D47124yescomplemented
257#117—4724no—
258#117—4748no—
259C2×C4⋊C4—476no—
260C2×C4⋊C4—476no—
261C2×C4⋊C4—473no—
262C2×C4⋊C4C22×D4713yes—
263C2×C22⋊C4—476no—
264C2×C22⋊C4—476no—
265C2×C22⋊C4C22×D4716yes—
266C2×C42—4748no—
267C2×C42—476no—
268C2×C42—473no—
269C2×C42—476no—
270C2×C42—476no—
271C2×C42—473no—
272C2×C42—473no—
273C2×C42—4724no—
274C2×C42—4712no—
275C2×C42—476no—
276C2×C42C22×D4716yes—
277C2×C42C22×D4713yes—
278#95—473no—
279#95—4712no—
280#95—476no—
281#95—473no—
282#95—476no—
283#95C22×D4711yescharacteristic
284#95C22×D4713yes—
285#95C22×D4716yes—
286C24—471no—
287C24C23×D4712yes—
288#41—4764no—
289C2×Q8—4712no—
290C2×D4—4724no—
291C2×D4C2×C4×D47112yes—
292C22×C4—412no—
293C22×C4—4724no—
294C22×C4—471no—
295C22×C4—472no—
296C22×C4—4712no—
297C22×C4—473no—
298C22×C4—473no—
299C22×C4—476no—
300C22×C4—4724no—
301C22×C4—4712no—
302C22×C4—4712no—
303C22×C4—1883no—
304C22×C4—1886no—
305C22×C4—1883no—
306C22×C4—1886no—
307C22×C4—1886no—
308C22×C4C2×C4×D47124yes—
309C22×C4C23×D4713yes—
310C22×C4C23×D4716yes—
311C22×C4C23×D4713yes—
312C22×C4C23×D4711yescharacteristic
313C4⋊C4—4724no—
314C4⋊C4—4724no—
315C4⋊C4—4712no—
316C4⋊C4C2×C4×D47112yes—
317C22⋊C4—4724no—
318C22⋊C4—4724no—
319C22⋊C4C2×C4×D47124yes—
320C42—46no—
321C42—4712no—
322C42—4724no—
323C42—4712no—
324C42—4724no—
325C42—4724no—
326C42—4712no—
327C42—18812no—
328C42—1886no—
329C42C2×C4×D47112yes—
330C23—26no—
331C23—22no—
332C23—476no—
333C23—943no—
334C23—941no—
335C23C22×C4×D47112yes—
336C23C24×D4711yescharacteristic
337Q8—4716no—
338D4—4732no—
339D4C42×D47116yes—
340C2×C4—23no—
341C2×C4—212no—
342C2×C4—26no—
343C2×C4—23no—
344C2×C4—424no—
345C2×C4—4732no—
346C2×C4—476no—
347C2×C4—4712no—
348C2×C4—4716no—
349C2×C4—476no—
350C2×C4—476no—
351C2×C4—4712no—
352C2×C4—946no—
353C2×C4—946no—
354C2×C4—943no—
355C2×C4—946no—
356C2×C4—943no—
357C2×C4—18812no—
358C2×C4—18812no—
359C2×C4—18824no—
360C2×C4C22×C4×D4716yes—
361C2×C4C22×C4×D47112yes—
362C2×C4C22×C4×D4716yes—
363C2×C4C22×C4×D4716yes—
364C22—212no—
365C22—212no—
366C22—474no—
367C22—946no—
368C22—946no—
369C22C2×C42×D4718yes—
370C22C23×C4×D4713yes—
371C22#1568995813yes—
372C22#1568996011yescharacteristic
373C4—26no—
374C4—212no—
375C4—26no—
376C4—474no—
377C4—478no—
378C4—946no—
379C4—946no—
380C4—9412no—
381C4C2×C42×D4714yes—
382C2—28no—
383C2—944no—
384C2C22×C42×D4711yescharacteristic
385C2#2025658613yes—
386C2#2025658813yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC2×C47C23×C42
FittingC47×#2275C2
socle, cosocleC23×C47C25
prime radicalC22×#10625352C22
hypercenter#2275D47
hypocenterC47#33999
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #20245752C2semidirect
3. #20245751C2semidirect
4. #20245749C2semidirect
5. #20245747C2semidirect
6. #20245746C2semidirect
7. C4×#13093982C2semidirect
8. C4×#13093980C2semidirect
9. C2×#15688968C2semidirect
10. #376×D47C2semidirect
11. C47×#2275C2semidirect
13. C4×#10625352C4semidirect
55. C4×Dic94C2×C4semidirect
56. #13093989C2×C4semidirect
57. D4×Dic47C2×C4semidirect
58. C4×C22⋊D47C2×C4semidirect
59. (C22⋊D47)⋊C4C2×C4semidirect
60. #13093982C2×C4semidirect
61. #13093980C2×C4semidirect
67. C2×C4×Dic47C2×C4semidirect
76. C42×D47C2×C4semidirect
84. C4×D4×C47C2×C4semidirect
111. #10625352C42semidirect
195. #2275D47semidirect
240. C47#33999semidirect
256. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
#202457522
#202457512
#202457492
#202457472
#202457462
C4×#130939822
C4×#130939802
C2×#156889682
#376×D472
C47×#22752
#3399947