Finite Group Databasebeta

← #26126902

Subgroups — #26126902

Order 12032.

462 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248564C211yesmaximal, characteristic
2#20241729C211yesmaximal, characteristic
3#20241411C212yesmaximal, complemented
4#20241408C212yesmaximal, complemented
5C4×#99×C47C211yesmaximal, characteristic
6C2×#13094003C411yescharacteristic, complemented
7#15689180—21no—
8#15689062C411yescharacteristic, complemented
9#15689059C2211yescharacteristic
10#15689043C411yescharacteristic, complemented
11#15689035C2211yescharacteristic
12#15689007—21no—
13#15689003—21no—
14#15688996—21no—
15#15688981—21no—
16C2×C47⋊#95C411yescharacteristic, complemented
17#15688847—21no—
18#15688847C2212yes—
19C2×C4×D4×C47C2211yescharacteristic
20C2×#99×C47—21no—
21C4×C22⋊C4×C47—21no—
22C47×#342C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C23×Dic47—21no—
25#13094003—41no—
26#13094003—41no—
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×C22⋊Dic47—21no—
32C2×C22⋊Dic47—21no—
33C2×C22⋊Dic47—21no—
34C4⋊(C47⋊C8)—41no—
35C22⋊(C47⋊C8)—22no—
36#13093935—41no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95C2×C411yescharacteristic
43C47⋊#95C2×C411yescharacteristic
44C22×D4×C47D411yescharacteristic
45C23×C4×C47C2×C411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C4×D4×C47—41no—
48C4×D4×C47—41no—
49C2×C4⋊C4×C47C2×C411yescharacteristic
50C2×C22⋊C4×C47—22no—
51C2×C22⋊C4×C47D411yescharacteristic
52C2×C22⋊C4×C47C2311yescharacteristic
53C2×C42×C47—41no—
54C2×C42×C47D411yescharacteristic
55#99×C47—24no—
56#95×C47—41no—
57C24×C47C22⋊C411yescharacteristic
58C24×C47C2×D411yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—41no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—42no—
67C22×C4×C47—81no—
68C22×C4×C47—81no—
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22×C411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—42no—
79C22×Dic47—42no—
80C22×Dic47—81no—
81C2×Dic94—41no—
82C2×Dic94—81no—
83C4⋊C4×C47—41no—
84C22⋊C4×C47—24no—
85C22⋊C4×C47—41no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—42no—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—82no—
91C22⋊Dic47—42no—
92C22⋊Dic47—42no—
93C22⋊Dic47—81no—
94C4⋊Dic47—41no—
95Dic47⋊C4—42no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98Dic47⋊C4—81no—
99C2×C47⋊C8—42no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—41no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47—41no—
108C23×C47#10412yes—
109C23×C47C2×C22⋊C411yescharacteristic
110C23×C47#13712yes—
111D4×C47—44no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—41no—
119C2×C4×C47—42no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—44no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—82no—
128C2×C4×C47—82no—
129C2×C4×C47#9911yescharacteristic
130C2×C4×C47#9911yescharacteristic
131C2×Dic47—22no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—84no—
144Dic94—82no—
145C47⋊C8—82no—
146#11789—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—81no—
159C22×C47C2×#9911yescharacteristic
160C22×C47#41911yescharacteristic
161C22×C47C2×#10411yescharacteristic
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—84no—
169Dic47—42no—
170Dic47—81no—
171Dic47—81no—
172Dic47—81no—
173#2564—471no—
174C4×#99D4711yescharacteristic
175#1466—471no—
176#1352—472no—
177#1351—472no—
178C2×C47—21no—
179C2×C47—21no—
180C2×C47—42no—
181C2×C47—42no—
182C2×C47#150811yescharacteristic
183C2×C47#212111yescharacteristic
184C2×C47#212611yescharacteristic
185C2×C22⋊Q8—471no—
186C2×C4×D4C2×D4711yescharacteristic
187#432—941no—
188C2×#99—21no—
189#400—471no—
190#399—471no—
191#395—471no—
192#393—471no—
193#387—941no—
194#386—941no—
195#385—941no—
196#380—941no—
197C4×C22⋊C4—21no—
198C2×#95—471no—
199#342C2×D4712yes—
200#323—472no—
201#323—941no—
202C47#1178911yescharacteristic, complemented, Sylow
203C22×Q8—471no—
204C22×D4C22⋊D4711yescharacteristic
205C23×C4—941no—
206C23×C4C4×D4711yescharacteristic
207C23×C4C22⋊D4711yescharacteristic
208C22⋊Q8—1881no—
209C22⋊Q8—1881no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4C4×D4711yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—941no—
219C2×C22⋊C4—941no—
220C2×C22⋊C4—941no—
221C2×C22⋊C4D18811yescharacteristic
222C2×C22⋊C4C22×D4711yescharacteristic
223C2×C42—41no—
224C2×C42D18811yescharacteristic
225C4⋊C8—1881no—
226#99—24no—
227C22⋊C8—942no—
228#97—1881no—
229#95—41no—
230#95—471no—
231#95—471no—
232#95—941no—
233#95—941no—
234#95—941no—
235#95—941no—
236#95—941no—
237C24(C2×D47)⋊C411yescharacteristic
238C24C2×C22⋊D4711yescharacteristic
239C2×Q8—3761no—
240C2×Q8—1881no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—3761no—
256C22×C4—1882no—
257C22×C4—1882no—
258C22×C4(C2×D47)⋊C411yescharacteristic
259C22×C4(C2×D47)⋊C411yescharacteristic
260C22×C4(C2×D47)⋊C411yescharacteristic
261C22×C4C2×C4×D4711yescharacteristic
262C22×C4C2×D18811yescharacteristic
263C2×C8—1882no—
264C4⋊C4—41no—
265C4⋊C4—3761no—
266C4⋊C4—1881no—
267C4⋊C4—1882no—
268C4⋊C4—1881no—
269C4⋊C4—1881no—
270C22⋊C4—24no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—3761no—
275C22⋊C4—1882no—
276C22⋊C4—1882no—
277C42—21no—
278C42—21no—
279C42—82no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#1309395212yes—
289C23C2×(C2×D47)⋊C411yescharacteristic
290C23#1309405412yes—
291Q8—3762no—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—942no—
311C2×C4—3764no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1881no—
321C2×C4—1881no—
322C2×C4—1881no—
323C2×C4#1309393811yescharacteristic
324C2×C4#1309393811yescharacteristic
325C8—3762no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#1309393811yescharacteristic
339C22#1568913111yescharacteristic
340C22C2×#1309395211yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—84no—
348C4—3761no—
349C4—3761no—
350C4—3761no—
351C4—1882no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#2024190711yescharacteristic
357C2#2024503211yescharacteristic
358C2#2024505111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C22⋊C4C22×D47
FittingC4×#99×C47C2
socleC22×C47C2×#99
prime radicalC22×D4×C47D4
cosocleC2×C22⋊C4×C47C23
hypercenterC4×#99D47
hypocenterC47#11789
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #20241411C2semidirect
4. #20241408C2semidirect
6. C2×#13094003C4semidirect
8. #15689062C4semidirect
10. #15689043C4semidirect
16. C2×C47⋊#95C4semidirect
202. C47#11789semidirect

Maximal subgroups

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

subgroupindex
#202485642
#202417292
#202414112
#202414082
C4×#99×C472
#1178947