Finite Group Databasebeta

← #26109052

Subgroups — #26109052

Order 12032.

456 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×Dic47C211yesmaximal, characteristic
2#20243242C211yesmaximal, characteristic
3#20243242C211yesmaximal, characteristic
4C2×#15688865C211yesmaximal, characteristic
5#20241270C211yesmaximal, characteristic
6#20241270C211yesmaximal, characteristic
7C2×C47×#330C211yesmaximal, characteristic
8C2×Dic47⋊C8—21no—
9C2×Dic47⋊C8—21no—
10C2×#13093935C2211yescharacteristic
11C2×#13093935C2211yescharacteristic
12#15689022C411yescharacteristic
13#15689022C411yescharacteristic
14#15689009—21no—
15#15689009—21no—
16#15688989C2211yescharacteristic
17C4⋊C4×Dic47—21no—
18C4⋊C4×Dic47—21no—
19C4⋊C4×Dic47C411yescharacteristic
20C4⋊C4×Dic47C411yescharacteristic
21C42×Dic47C2211yescharacteristic
22#15688877—21no—
23#15688877—21no—
24#15688865—22no—
25C2×#125×C47C2211yescharacteristic
26C2×#97×C47C2211yescharacteristic
27C2×#97×C47C2211yescharacteristic
28C47×#330—22no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×C4⋊Dic47C2×C411yescharacteristic
35C2×C4×Dic47—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47C2×C411yescharacteristic
38C2×C4×Dic47C2×C411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47D411yescharacteristic
42C2×C4×Dic47D411yescharacteristic
43Dic47⋊C8—24no—
44Dic47⋊C8—24no—
45#13093935—21no—
46#13093935—21no—
47#13093935—21no—
48#13093935—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C47⋊#95—21no—
55C22×C8×C47—21no—
56C22×C8×C47—21no—
57#125×C47—21no—
58#125×C47—21no—
59#125×C47D412yes—
60#125×C47Q812yes—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47C2×C411yescharacteristic
64C2×C4⋊C4×C47C2×C411yescharacteristic
65C2×C42×C47C2311yescharacteristic
66#97×C47—21no—
67#97×C47—21no—
68#97×C47—21no—
69#97×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47C22×C411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47C22⋊C411yescharacteristic
78C22×Dic47C22⋊C411yescharacteristic
79C22×Dic47C22⋊C411yescharacteristic
80C22×Dic47C22⋊C411yescharacteristic
81C2×C8×C47—22no—
82C2×C8×C47—22no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—22no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47C4⋊C412yes—
94C4⋊C4×C47C4⋊C412yes—
95C42×C47C2×D411yescharacteristic
96C42×C47C2×Q811yescharacteristic
97C42×C47#4111yescharacteristic
98C42×C47#4111yescharacteristic
99C4⋊Dic47—42no—
100C4⋊Dic47—42no—
101C4⋊Dic47—41no—
102C4⋊Dic47—41no—
103C4×Dic47—22no—
104C4×Dic47—22no—
105C4×Dic47—22no—
106C4×Dic47—41no—
107C4×Dic47—41no—
108C4×Dic47—41no—
109C4×Dic47—42no—
110C4×Dic47—42no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8—41no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C23×C47C2×C22⋊C411yescharacteristic
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47C2×C4⋊C411yescharacteristic
131C2×C4×C47#11711yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47#12111yescharacteristic
134C2×C4×C47C22⋊Q811yescharacteristic
135C2×C4×C47C22⋊Q811yescharacteristic
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47#10112yes—
152C2×Dic47#10412yes—
153C2×Dic47#10412yes—
154C8×C47—42no—
155C8×C47—42no—
156C47⋊C8—42no—
157C47⋊C8—42no—
158#8582—471nomaximal, Sylow
159C22×C47#38011yescharacteristic
160C22×C47C2×#10111yescharacteristic
161C22×C47#41311yescharacteristic
162C22×C47C2×#10411yescharacteristic
163C22×C47C2×#10411yescharacteristic
164C22×C47#42111yescharacteristic
165C22×C47#42111yescharacteristic
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—42no—
173C4×C47—42no—
174Dic47—22no—
175Dic47—22no—
176Dic47—22no—
177Dic47—41no—
178Dic47—81no—
179Dic47—81no—
180C4×#125—471no—
181#1767—471no—
182#1767—471no—
183C2×#330—471no—
184C2×#330D4711yescharacteristic
185#1295—471no—
186#1295—471no—
187C2×C47#152411yescharacteristic
188C2×C47#152811yescharacteristic
189C2×C47#153111yescharacteristic
190C2×C47#153511yescharacteristic
191C2×C47#180111yescharacteristic
192C2×C47#180611yescharacteristic
193C2×C47#180611yescharacteristic
194C2×#125C2×D4711yescharacteristic
195C2×C4⋊C8—941no—
196C2×C4⋊C8—941no—
197C2×#97—471no—
198C2×#97—471no—
199C2×#97C2×D4711yescharacteristic
200C2×#97C2×D4711yescharacteristic
201#389—471no—
202#389—471no—
203#387—941no—
204#387—941no—
205#382—471no—
206C4×C4⋊C4—471no—
207C4×C4⋊C4—471no—
208C4×C4⋊C4—941no—
209C4×C4⋊C4—941no—
210C43—471no—
211#336—941no—
212#336—941no—
213#330—22no—
214#330—942no—
215C47#858211yescharacteristic, complemented, Sylow
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—941no—
219C22×C8—941no—
220#125—21no—
221#125—21no—
222#125Dic9412yes—
223#125C22⋊D4712yes—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—941no—
229C2×C4⋊C4—941no—
230C2×C4⋊C4C4×D4711yescharacteristic
231C2×C4⋊C4C4×D4711yescharacteristic
232C2×C42—471no—
233C2×C42—471no—
234C2×C42—471no—
235C2×C42—471no—
236C2×C42—471no—
237C2×C42—471no—
238C2×C42—941no—
239C2×C42—941no—
240C2×C42C22×D4711yescharacteristic
241C4⋊C8—944no—
242C4⋊C8—944no—
243#97—21no—
244#97—21no—
245#97—21no—
246#97—21no—
247#97—941no—
248#97—941no—
249#97—941no—
250#97—941no—
251#95—941no—
252#95—941no—
253#95—941no—
254#95—941no—
255#95—941no—
256#95—941no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4C2×C4×D4711yescharacteristic
266C22×C4D4×D4711yescharacteristic
267C22×C4D4×D4711yescharacteristic
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—942no—
275C2×C8—942no—
276C2×C8—1881no—
277C2×C8—1881no—
278C2×C8—1881no—
279C2×C8—1881no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C4⋊C4—1882no—
289C4⋊C4—1882no—
290C4⋊C4Dic47⋊C412yes—
291C4⋊C4Dic47⋊C412yes—
292C42—942no—
293C42—942no—
294C42—942no—
295C42—1881no—
296C42—1881no—
297C42—1881no—
298C42—1882no—
299C42—1882no—
300C42C2×Dic9411yescharacteristic
301C42#1062535211yescharacteristic
302C42#1062535211yescharacteristic
303C42C2×C22⋊D4711yescharacteristic
304C23C22⋊C4×D4711yescharacteristic
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—472no—
318C2×C4—472no—
319C2×C4—472no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4—1881no—
334C2×C4—1881no—
335C2×C4C2×Dic47⋊C411yescharacteristic
336C2×C4#1309398011yescharacteristic
337C2×C4#1309399611yescharacteristic
338C2×C4#1309399611yescharacteristic
339C2×C4#1309400111yescharacteristic
340C2×C4#1309400111yescharacteristic
341C8—42no—
342C8—42no—
343C8—1882no—
344C8—1882no—
345C22#1568898111yescharacteristic
346C22#101×D4711yescharacteristic
347C22#1568910611yescharacteristic
348C22#104×D4711yescharacteristic
349C22#104×D4711yescharacteristic
350C22#1568913811yescharacteristic
351C22#1568913811yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—942no—
361C4—942no—
362C4—942no—
363C4—3761no—
364C4—3761no—
365C4—1881no—
366C2#2024197511yescharacteristic
367C2#2024198811yescharacteristic
368C2#2024200111yescharacteristic
369C2#2024201811yescharacteristic
370C2#2024338211yescharacteristic
371C2#2024340611yescharacteristic
372C2#2024340611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#330C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#330D47
hypocenterC47#8582
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
215. C47#8582semidirect

Maximal subgroups

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

subgroupindex
#125×Dic472
#202432422
C2×#156888652
#202412702
C2×C47×#3302
#858247