Finite Group Databasebeta

← #26111777

Subgroups — #26111777

Order 12032.

498 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252468C211yesmaximal, characteristic
2#20246107C211yesmaximal, characteristic
3#20241784C211yesmaximal, characteristic
4#20241782C211yesmaximal, characteristic
5#20241711C211yesmaximal, characteristic
6#20241217C211yesmaximal, characteristic
7C47×#1274C211yesmaximal, characteristic
8C2×#13094024C411yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10C2×C4×Dic94C2211yescharacteristic
11C8×Dic94—22no—
12#15689247—22no—
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15#15689173—22no—
16#15689029C411yescharacteristic
17#15689029C411yescharacteristic
18#15689008—22no—
19#15689008—22no—
20#15688989C411yescharacteristic
21#15688855—22no—
22#15688853—22no—
23#15688848—22no—
24C47×#431C2211yescharacteristic
25C47×#431C2211yescharacteristic
26C47×#376C2211yescharacteristic
27C22×Dic94C2×C411yescharacteristic
28C22×Dic94C2×C411yescharacteristic
29#13094024—22no—
30#13094024C814yescomplemented
31C4×Dic94—21no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C4×Dic94—21no—
35C4×Dic94—21no—
36C4×Dic94—21no—
37C4×Dic94—21no—
38C4×Dic94—21no—
39C2×C4⋊Dic47—22no—
40C2×C4⋊Dic47C2×C411yescharacteristic
41C2×C4⋊Dic47C2×C411yescharacteristic
42C2×Dic47⋊C4—21no—
43C2×Dic47⋊C4D412yes—
44C2×C4×Dic47—21no—
45C2×C4×Dic47D412yes—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48Dic47⋊C8—24no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C4×C47⋊C8—21no—
52C4×C47⋊C8D412yes—
53C8×Dic47—24no—
54C47⋊#95—22no—
55C47⋊#95—22no—
56C47⋊#95—22no—
57C2×C42×C47C2×C411yescharacteristic
58C2×C42×C47C2×C411yescharacteristic
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64C4×C8×C47—21no—
65C4×C8×C47D412yes—
66#95×C47—21no—
67#95×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47C22⋊C412yes—
76C22×Dic47C22⋊C412yes—
77C2×Dic94—21no—
78C2×Dic94—21no—
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94—21no—
82C2×Dic94—21no—
83C2×Dic94—21no—
84C2×Dic94—21no—
85C2×Dic94—21no—
86C2×Dic94C2×C812yes—
87C2×Dic94C2×C812yes—
88C2×Dic94M1612yes—
89C2×C8×C47—22no—
90C2×C8×C47—41no—
91C42×C47—21no—
92C42×C47—21no—
93C42×C47—21no—
94C42×C47C2×C812yes—
95C42×C47C2×D411yescharacteristic
96C42×C47C2×D411yescharacteristic
97C42×C47#4111yescharacteristic
98C42×C47#4111yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47—28no—
102C4⋊Dic47—21no—
103C4⋊Dic47—21no—
104Dic47⋊C4—22no—
105Dic47⋊C4—22no—
106Dic47⋊C4—41no—
107Dic47⋊C4—41no—
108C4×Dic47—22no—
109C4×Dic47—22no—
110C4×Dic47—41no—
111C4×Dic47—41no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8—41no—
114C23×C47C2×C22⋊C411yescharacteristic
115C2×C4×C47—22no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47C4×D411yescharacteristic
124C2×C4×C47C4×D411yescharacteristic
125C2×C4×C47#12011yescharacteristic
126C2×C4×C47#12111yescharacteristic
127C2×C4×C47#12111yescharacteristic
128C2×C4×C47#12311yescharacteristic
129C2×C4×C47C22×C811yescharacteristic
130C2×C4×C47C2×M1611yescharacteristic
131C2×C4×C47#13111yescharacteristic
132C2×C4×C47#13111yescharacteristic
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—22no—
136C2×Dic47—22no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141C2×Dic47—41no—
142C2×Dic47C22⋊C814yes—
143Dic94—22no—
144Dic94—22no—
145Dic94—22no—
146Dic94—22no—
147Dic94—22no—
148Dic94—22no—
149Dic94—41no—
150Dic94—41no—
151C8×C47—42no—
152C8×C47—81no—
153C47⋊C8—42no—
154C47⋊C8—81no—
155#9100—471nomaximal, Sylow
156C22×C47—21no—
157C22×C47—21no—
158C22×C47#38611yescharacteristic
159C22×C47C2×C22⋊C811yescharacteristic
160C22×C47#40811yescharacteristic
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—42no—
166C4×C47—81no—
167C4×C47C8×D411yescharacteristic
168C4×C47C8×D411yescharacteristic
169C4×C47#43511yescharacteristic
170C4×C47#43511yescharacteristic
171Dic47—24no—
172Dic47—42no—
173Dic47—42no—
174Dic47—81no—
175#2982—471no—
176#2327—471no—
177#1479—471no—
178#1479—471no—
179#1461—471no—
180#1274—471no—
181#1274D4711yescharacteristic
182C2×C47—21no—
183C2×C47—21no—
184C2×C47#186911yescharacteristic
185C2×C47#190911yescharacteristic
186C2×C47#191211yescharacteristic
187C2×C4⋊Q8—471no—
188C2×C4×Q8—471no—
189C2×C4×Q8—471no—
190C8×Q8—942no—
191C8×Q8—942no—
192#431—471no—
193#431—471no—
194#431—942no—
195#431C2×D4711yescharacteristic
196#431C2×D4711yescharacteristic
197#391—471no—
198#391—471no—
199#387—942no—
200#387—942no—
201#382—471no—
202#376C2×D4711yescharacteristic
203Q8⋊C8—942no—
204Q8⋊C8—942no—
205#324—942no—
206C47#910011yescharacteristic, complemented, Sylow
207C22×Q8—471no—
208C22×Q8—471no—
209C4⋊Q8—474no—
210C4⋊Q8—942no—
211C4×Q8—941no—
212C4×Q8—941no—
213C4×Q8—941no—
214C4×Q8—941no—
215C4×Q8—941no—
216C4×Q8—941no—
217C4×Q8—941no—
218C4×Q8—941no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—472no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—942no—
223C2×C4⋊C4—941no—
224C2×C42—472no—
225C2×C42—941no—
226C2×C42C4×D4711yescharacteristic
227C2×C42C4×D4711yescharacteristic
228C2×C42C22×D4711yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—944no—
232C4⋊C8—941no—
233C4⋊C8—941no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—941no—
237C22⋊C8—941no—
238C4×C8—21no—
239C4×C8—472no—
240C4×C8—944no—
241C4×C8—941no—
242C4×C8D18812yes—
243#95—21no—
244#95—21no—
245#95—942no—
246#95—942no—
247#95—942no—
248C2×Q8—472no—
249C2×Q8—472no—
250C2×Q8—472no—
251C2×Q8—941no—
252C2×Q8—941no—
253C2×Q8—941no—
254C2×Q8—941no—
255C2×Q8—941no—
256C2×Q8—941no—
257C2×Q8—941no—
258C2×Q8—941no—
259C2×Q8—941no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—472no—
263C22×C4—472no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C2×C4×D4711yescharacteristic
267C22×C4D4×D4711yescharacteristic
268C22×C4D4×D4711yescharacteristic
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—942no—
272C2×C8—1881no—
273C4⋊C4—948no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—942no—
277C4⋊C4—942no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—942no—
286C42—942no—
287C42—1881no—
288C42—1881no—
289C42C8×D4712yes—
290C42C2×D18811yescharacteristic
291C42#1062535011yescharacteristic
292C42D4×D4711yescharacteristic
293C42#1062535411yescharacteristic
294C23C22⋊C4×D4711yescharacteristic
295Q8—942no—
296Q8—942no—
297Q8—942no—
298Q8—942no—
299Q8—942no—
300Q8—942no—
301Q8—1881no—
302Q8—1881no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—474no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—1882no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1882no—
321C2×C4#1309398611yescharacteristic
322C2×C4C4×D18811yescharacteristic
323C2×C4#1309399411yescharacteristic
324C2×C4#1309399711yescharacteristic
325C2×C4#1309399911yescharacteristic
326C2×C4#1309400911yescharacteristic
327C2×C4C2×C8×D4711yescharacteristic
328C2×C4M16×D4711yescharacteristic
329C2×C4#1309403011yescharacteristic
330C2×C4#1309403211yescharacteristic
331C8—42no—
332C8—81no—
333C8—3761no—
334C8—1882no—
335C22—21no—
336C22—21no—
337C22#1568900111yescharacteristic
338C22C22⋊C8×D4711yescharacteristic
339C22#1568908811yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—42no—
345C4—81no—
346C4—944no—
347C4—3761no—
348C4—1882no—
349C4—1882no—
350C4#1568918811yescharacteristic
351C4C8×D18811yescharacteristic
352C4#1568919311yescharacteristic
353C4#1568919611yescharacteristic
354C2—21no—
355C2—21no—
356C2#2024367911yescharacteristic
357C2#2024390911yescharacteristic
358C2#2024392411yescharacteristic
subgroupG/H
centerC22#15689001
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1274C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1274D47
hypocenterC47#9100
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
30. #13094024C8semidirect
206. C47#9100semidirect

Maximal subgroups

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

subgroupindex
#202524682
#202461072
#202417842
#202417822
#202417112
#202412172
C47×#12742
#910047