Finite Group Databasebeta

← #26112567

Subgroups — #26112567

Order 12032.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253423C211yesmaximal, characteristic
2#20245865C211yesmaximal, characteristic
3#20241887C211yesmaximal, characteristic
4#20241816C211yesmaximal, characteristic
5#20241289C211yesmaximal, characteristic
6#20241221C211yesmaximal, characteristic
7C47×#1994C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9#15689456—21no—
10#15689415C412yescomplemented
11#15689330C412yescomplemented
12#15689278—21no—
13C4×#10625337—22no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16#15689029—21no—
17#15689021—21no—
18#15689007—22no—
19C4×Dic47⋊C4—21no—
20C4×C4⋊Dic47C2211yescharacteristic
21#15688969—21no—
22#15688860—22no—
23#15688853—22no—
24C47×#533C2211yescharacteristic
25C47×#423C2211yescharacteristic
26C43×C47C2211yescharacteristic
27C47×#339—21no—
28C47×#339—21no—
29C22×Dic94D411yescharacteristic
30C2×#10625337—22no—
31C4×Dic94—21no—
32C4×Dic94—21no—
33C4×Dic94C2×C412yes—
34C4×Dic94D412yes—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47D411yescharacteristic
37C2×Dic47⋊C4—21no—
38C2×Dic47⋊C4—22no—
39C2×C4×Dic47—21no—
40C2×C4×Dic47—21no—
41#13093957—22no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C412yes—
44#13093948—22no—
45#13093947—22no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C47⋊#95—22no—
51C47⋊#95—22no—
52C47⋊#95—22no—
53C47⋊#95D412yes—
54C2×M16×C47—21no—
55C4⋊Q8×C47C2×C411yescharacteristic
56C4⋊Q8×C47C2×C411yescharacteristic
57#125×C47—21no—
58C22⋊Q8×C47—21no—
59C22⋊Q8×C47—21no—
60C4×Q8×C47—21no—
61C4×Q8×C47—21no—
62#117×C47—21no—
63C2×C42×C47—21no—
64C2×C42×C47—21no—
65C2×C42×C47D411yescharacteristic
66C2×C42×C47D411yescharacteristic
67C2×C42×C47C2311yescharacteristic
68C4⋊C8×C47—21no—
69C4⋊C8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—22no—
80C2×Dic94—21no—
81C2×Dic94—42no—
82C2×Dic94C22⋊C412yes—
83M16×C47—41no—
84M16×C47—41no—
85C2×C8×C47—41no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C22⋊C4×C47—41no—
93C42×C47—21no—
94C42×C47—21no—
95C42×C47—21no—
96C42×C47—42no—
97C42×C47—42no—
98C42×C47—41no—
99C42×C47Q1612yescomplemented
100C42×C47C22×C411yescharacteristic
101C42×C47C2×D411yescharacteristic
102C42×C47#4111yescharacteristic
103C42×C47#4111yescharacteristic
104#10625337—44no—
105C4⋊Dic47—21no—
106C4⋊Dic47—42no—
107C4⋊Dic47C22⋊C412yes—
108Dic47⋊C4—22no—
109Dic47⋊C4—22no—
110Dic47⋊C4—44no—
111C4×Dic47—22no—
112C4×Dic47—22no—
113C4×Dic47—41no—
114C4×Dic47—41no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—41no—
117C23×C47#12011yescharacteristic
118Q8×C47—42no—
119Q8×C47—81no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47C2×C22⋊C411yescharacteristic
131C2×C4×C47C4×D411yescharacteristic
132C2×C4×C47C4×D411yescharacteristic
133C2×C4×C47#12111yescharacteristic
134C2×C4×C47#12111yescharacteristic
135C2×C4×C47#12311yescharacteristic
136C2×C4×C47C2×Q1611yescharacteristic
137C2×C4×C47#13511yescharacteristic
138C2×C4×C47#13711yescharacteristic
139C2×C4×C47#13711yescharacteristic
140C2×Dic47—22no—
141C2×Dic47—22no—
142C2×Dic47—42no—
143C2×Dic47—42no—
144C2×Dic47—42no—
145C2×Dic47—42no—
146C2×Dic47—42no—
147Dic94—22no—
148Dic94—22no—
149Dic94—42no—
150C8×C47—81no—
151C47⋊C8—42no—
152C47⋊C8—81no—
153#9236—471nomaximal, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#38611yescharacteristic
157C22×C47#45111yescharacteristic
158C22×C47#45211yescharacteristic
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—42no—
163C4×C47—42no—
164C4×C47—81no—
165C4×C47—81no—
166C4×C47#42112yes—
167C4×C47C4×Q1611yescharacteristic
168C4×C47#44111yescharacteristic
169C4×C47#46211yescharacteristic
170C4×C47#46411yescharacteristic
171Dic47—42no—
172Dic47—42no—
173Dic47—82no—
174#3104—471no—
175#2295—471no—
176#1994D4711yescharacteristic
177#1503—471no—
178#1487—471no—
179#1303—471no—
180#1276—471no—
181C2×C47—21no—
182C2×C47—21no—
183C2×C47#187811yescharacteristic
184C2×C47#189711yescharacteristic
185C2×C47#190611yescharacteristic
186#533C2×D4711yescharacteristic
187C2×C4×Q8—471no—
188#484—941no—
189#477—472no—
190#462—472no—
191#451—941no—
192C4×Q16—942no—
193#431—471no—
194#431—471no—
195#423C2×D4711yescharacteristic
196#391—941no—
197#389—941no—
198#387—942no—
199C4×C4⋊C4—471no—
200C4×C4⋊C4—941no—
201#376—941no—
202C43C2×D4711yescharacteristic
203#339—21no—
204#339—21no—
205#328—942no—
206Q8⋊C8—942no—
207C47#923611yescharacteristic, complemented, Sylow
208C22×Q8—471no—
209C2×Q16—942no—
210C2×M16—21no—
211C4⋊Q8C4×D4711yescharacteristic
212C4⋊Q8C4×D4711yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—472no—
219C4×Q8—472no—
220C4×Q8—941no—
221C4×Q8—941no—
222#117—21no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—941no—
225C2×C4⋊C4—942no—
226C2×C4⋊C4—941no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—941no—
230C2×C42—941no—
231C2×C42C22⋊D4711yescharacteristic
232C2×C42C22⋊D4711yescharacteristic
233C2×C42C22×D4711yescharacteristic
234#107—942no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—472no—
238C4⋊C8—941no—
239#103—942no—
240#103—942no—
241C22⋊C8—941no—
242C22⋊C8—941no—
243C4×C8—941no—
244C4×C8—941no—
245#95—472no—
246#95—942no—
247#95—942no—
248#95—942no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—472no—
252C2×Q8—941no—
253C2×Q8—1882no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—942no—
259C22×C4D4×D4711yescharacteristic
260C22×C4D4×D4711yescharacteristic
261C22×C4C2×C22⋊D4711yescharacteristic
262Q16—1884no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—942no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—472no—
275C4⋊C4—942no—
276C4⋊C4—942no—
277C4⋊C4—941no—
278C4⋊C4—1884no—
279C4⋊C4—1882no—
280C22⋊C4—41no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—42no—
285C42—42no—
286C42—41no—
287C42—942no—
288C42—942no—
289C42—1881no—
290C42—1881no—
291C42#1062533712yescomplemented
292C42C2×C4×D4711yescharacteristic
293C42#1062535011yescharacteristic
294C42D4×D4711yescharacteristic
295C42#1062535211yescharacteristic
296C23#1309399211yescharacteristic
297Q8—42no—
298Q8—81no—
299Q8—942no—
300Q8—942no—
301Q8—1882no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4—1882no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4C22⋊C4×D4711yescharacteristic
320C2×C4(C22⋊D47)⋊C411yescharacteristic
321C2×C4C4×C22⋊D4711yescharacteristic
322C2×C4#1309399511yescharacteristic
323C2×C4#1309399711yescharacteristic
324C2×C4#1309400611yescharacteristic
325C2×C4C2×#1062533711yescharacteristic
326C2×C4#1309404411yescharacteristic
327C2×C4#1309405411yescharacteristic
328C2×C4#1309405511yescharacteristic
329C8—81no—
330C8—3761no—
331C8—1882no—
332C22—21no—
333C22—21no—
334C22#1568899911yescharacteristic
335C22#1568927811yescharacteristic
336C22#1568928311yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—3762no—
345C4—1882no—
346C4—1882no—
347C4#1568913812yes—
348C4C4×#1062533711yescharacteristic
349C4#1568922811yescharacteristic
350C4#1568933011yescharacteristic
351C4#1568934211yescharacteristic
352C2—21no—
353C2—21no—
354C2#2024373211yescharacteristic
355C2#2024383311yescharacteristic
356C2#2024389211yescharacteristic
subgroupG/H
centerC2×C4#13093995
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#386
prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#1994D47
hypocenterC47#9236
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
10. #15689415C4semidirect
11. #15689330C4semidirect
99. C42×C47Q16semidirect
207. C47#9236semidirect
291. C42#10625337semidirect

Maximal subgroups

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

subgroupindex
#202534232
#202458652
#202418872
#202418162
#202412892
#202412212
C47×#19942
#923647