Finite Group Databasebeta

← #26108121

Subgroups — #26108121

Order 12032.

692 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256793C211yesmaximal, characteristic
2#20242046C212yesmaximal, complemented
3#20241790C212yesmaximal, complemented
4#20241702C211yesmaximal, characteristic
5C47×#1798C211yesmaximal, characteristic
6#15689754—21no—
7#15689754C412yes—
8#15689751—22no—
9#15689751—22no—
10#15689749—21no—
11#15689749C412yes—
12#15689680—21no—
13#15689680C2212yes—
14#15689676—24no—
15C2×#13093983—21no—
16#15689176C2212yes—
17#15688871—22no—
18#15688868—22no—
19#15688853—24no—
20#15688849—21no—
21#15688847—21no—
22C2×#117×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C22⋊C8×C47—21no—
26C47×#336—21no—
27#13094024—21no—
28#13094024—21no—
29#13094024D412yes—
30#13094024D412yes—
31#13094023—24no—
32#13094023—24no—
33#13094016—22no—
34#13094016—22no—
35#13094015—24no—
36#13094015—24no—
37#13094003—22no—
38#13094003—22no—
39#13094003—22no—
40#13094003C2×C414yes—
41#13094001—24no—
42#13094001—24no—
43#13094001—24no—
44#13094001—24no—
45C4×Dic94—22no—
46C4×Dic94—22no—
47C4×Dic94—22no—
48C4×Dic94D414yes—
49#13093983—22no—
50#13093983—22no—
51#13093983—22no—
52#13093983—22no—
53C2×C4⋊Dic47—21no—
54C2×C4⋊Dic47—21no—
55C2×C22⋊Dic47—22no—
56C2×C4×Dic47—22no—
57C4⋊(C47⋊C8)—22no—
58C22⋊(C47⋊C8)—22no—
59C4×C47⋊C8—22no—
60C23×C4×C47D411yescharacteristic
61C22×C8×C47—21no—
62C22×C8×C47—21no—
63#117×C47—22no—
64#117×C47—22no—
65C2×C4⋊C4×C47C2×C411yescharacteristic
66C2×C4⋊C4×C47D411yescharacteristic
67C2×C22⋊C4×C47C2×C411yescharacteristic
68C2×C22⋊C4×C47D411yescharacteristic
69C2×C42×C47D411yescharacteristic
70C2×C42×C47C2311yescharacteristic
71C4⋊C8×C47—22no—
72C4⋊C8×C47—22no—
73C22⋊C8×C47—42no—
74C24×C47C22⋊C411yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47SD1612yes—
83C22×C4×C47Q1612yes—
84C22×C4×C47C22×C411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×Dic47—22no—
88C22×Dic47—22no—
89C2×Dic94—22no—
90C2×Dic94—22no—
91C2×Dic94—22no—
92C2×Dic94C22⋊C414yes—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—22no—
101C22⋊C4×C47—22no—
102C22⋊C4×C47—22no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47C2×D412yes—
106C42×C47C2×D412yes—
107C22⋊Dic47—24no—
108C22⋊Dic47—24no—
109C4⋊Dic47—22no—
110C4⋊Dic47—22no—
111C4⋊Dic47—22no—
112C4⋊Dic47—22no—
113C4⋊Dic47—22no—
114C4⋊Dic47—22no—
115C4⋊Dic47—22no—
116C4⋊Dic47C22⋊C414yes—
117Dic47⋊C4—24no—
118Dic47⋊C4—24no—
119Dic47⋊C4—24no—
120Dic47⋊C4—24no—
121C4×Dic47—24no—
122C4×Dic47—24no—
123C2×C47⋊C8—42no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47#10312yes—
129C23×C47C2×C22⋊C411yescharacteristic
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47—22no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47#10312yes—
143C2×C4×C47C2×C22⋊C412yes—
144C2×C4×C47#12011yescharacteristic
145C2×C4×C47#12011yescharacteristic
146C2×C4×C47#12012yes—
147C2×C4×C47C2×SD1611yescharacteristic
148C2×C4×C47C2×Q1611yescharacteristic
149C2×C4×C47#13711yescharacteristic
150C2×C4×C47#13711yescharacteristic
151C2×Dic47—24no—
152C2×Dic47—24no—
153C2×Dic47—82no—
154C2×Dic47—82no—
155Dic94—44no—
156Dic94—82no—
157Dic94—82no—
158Dic94—82no—
159C8×C47—81no—
160C8×C47—81no—
161C47⋊C8—82no—
162#8410—471nomaximal, Sylow
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—22no—
166C22×C47—42no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—81no—
170C22×C47#37911yescharacteristic
171C22×C47C2×#10311yescharacteristic
172C22×C47#41911yescharacteristic
173C4×C47—22no—
174C4×C47—22no—
175C4×C47—22no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47#44811yescharacteristic
179C4×C47#44811yescharacteristic
180C4×C47#45111yescharacteristic
181C4×C47#45111yescharacteristic
182Dic47—44no—
183Dic47—44no—
184#3458—471no—
185#1798D4711yescharacteristic
186#1542—472no—
187#1481—472no—
188#1458—471no—
189C2×C47—21no—
190C2×C47—21no—
191C2×C47—42no—
192C2×C47#178711yescharacteristic
193C2×C47#179111yescharacteristic
194C2×C47#179411yescharacteristic
195#544—472no—
196#544—942no—
197#544—942no—
198#544—941no—
199#543—472no—
200#543—941no—
201#533—472no—
202#533—944no—
203#533—941no—
204C2×#117—941no—
205C2×#117C2×D4711yescharacteristic
206#431—472no—
207C2×C4⋊C8C2×D4711yescharacteristic
208C2×C4⋊C8C2×D4711yescharacteristic
209C2×C22⋊C8—21no—
210#336—21no—
211#333—942no—
212#332—942no—
213Q8⋊C8—944no—
214#324—941no—
215#323—941no—
216C47#841011yescharacteristic, complemented, Sylow
217C23×C4C22⋊D4711yescharacteristic
218C22×C8—21no—
219C22×C8—21no—
220C4⋊Q8—472no—
221C4⋊Q8—472no—
222C4⋊Q8—941no—
223C4⋊Q8—941no—
224C4⋊Q8—944no—
225C4⋊Q8—944no—
226#125—942no—
227#125—944no—
228#125—944no—
229#125—942no—
230C22⋊Q8—474no—
231C22⋊Q8—944no—
232C22⋊Q8—944no—
233C22⋊Q8—944no—
234C22⋊Q8—944no—
235C22⋊Q8—942no—
236C22⋊Q8—942no—
237C22⋊Q8—942no—
238C4×Q8—474no—
239C4×Q8—942no—
240C4×Q8—942no—
241C4×Q8—942no—
242#117—22no—
243#117—22no—
244#117—942no—
245#117—942no—
246#117—942no—
247#117—942no—
248C2×C4⋊C4—941no—
249C2×C4⋊C4—941no—
250C2×C4⋊C4C4×D4711yescharacteristic
251C2×C4⋊C4D18811yescharacteristic
252C2×C22⋊C4—942no—
253C2×C22⋊C4C4×D4711yescharacteristic
254C2×C22⋊C4D18811yescharacteristic
255C2×C42—942no—
256C2×C42C22⋊D4711yescharacteristic
257C2×C42C22×D4711yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—22no—
260C4⋊C8—942no—
261C22⋊C8—42no—
262C22⋊C8—942no—
263C4×C8—942no—
264C24(C2×D47)⋊C411yescharacteristic
265C2×Q8—474no—
266C2×Q8—942no—
267C2×Q8—942no—
268C2×Q8—942no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—942no—
274C22×C4—942no—
275C22×C4(C2×D47)⋊C411yescharacteristic
276C22×C4(C2×D47)⋊C411yescharacteristic
277C22×C4(C2×D47)⋊C411yescharacteristic
278C22×C4#1062533512yes—
279C22×C4#1062533712yes—
280C22×C4C2×C4×D4711yescharacteristic
281C22×C4C2×D18811yescharacteristic
282C22×C4C2×C22⋊D4711yescharacteristic
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—1882no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—474no—
293C4⋊C4—944no—
294C4⋊C4—944no—
295C4⋊C4—942no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—942no—
299C4⋊C4—944no—
300C4⋊C4—942no—
301C4⋊C4—942no—
302C4⋊C4—944no—
303C4⋊C4—942no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—944no—
307C22⋊C4—944no—
308C42—21no—
309C42—21no—
310C42—944no—
311C42—944no—
312C42D4×D4712yes—
313C42D4×D4712yes—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23#1309394712yes—
319C23C2×(C2×D47)⋊C411yescharacteristic
320Q8—3762no—
321Q8—3762no—
322Q8—3762no—
323Q8—1884no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—944no—
337C2×C4—944no—
338C2×C4—3762no—
339C2×C4—3762no—
340C2×C4#1309394712yes—
341C2×C4C22⋊C4×D4712yes—
342C2×C4#1309399211yescharacteristic
343C2×C4#1309399211yescharacteristic
344C2×C4#1309399412yes—
345C2×C4C2×#1062533511yescharacteristic
346C2×C4C2×#1062533711yescharacteristic
347C2×C4#1309405411yescharacteristic
348C2×C4#1309405411yescharacteristic
349C8—81no—
350C8—81no—
351C8—3762no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1568897811yescharacteristic
360C22C2×#1309394711yescharacteristic
361C22#1568913111yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—1884no—
368C4—1884no—
369C4#1568926111yescharacteristic
370C4#1568926111yescharacteristic
371C4#1568927811yescharacteristic
372C4#1568927811yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#2024332211yescharacteristic
377C2#2024333811yescharacteristic
378C2#2024335111yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1798C2
socleC22×C47#379
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1798D47
hypocenterC47#8410
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #20242046C2semidirect
3. #20241790C2semidirect
216. C47#8410semidirect

Maximal subgroups

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

subgroupindex
#202567932
#202420462
#202417902
#202417022
C47×#17982
#841047