Finite Group Databasebeta

← #20247403

Subgroups — #20247403

Order 6016.

508 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
1C2×#13094002C211yesmaximal, characteristic
2#15689045C211yesmaximal, characteristic
3#15689043C211yesmaximal, characteristic, complemented
4#15689042C211yesmaximal, characteristic, complemented
5#15689034C211yesmaximal, characteristic
6#15689029C211yesmaximal, characteristic, complemented
7#15689018C211yesmaximal, characteristic, complemented
8#15689014C211yesmaximal, characteristic
9#15689014C211yesmaximal, characteristic
10#15689009C211yesmaximal, characteristic, complemented
11#15689007C211yesmaximal, characteristic, complemented
12#15689007C211yesmaximal, characteristic, complemented
13#15688994C211yesmaximal, characteristic
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic
15C2×C4×Q8×C47C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13094002—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C22×Q8×C47C2211yescharacteristic
46C4×Q8×C47—24no—
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C2×Q8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—22no—
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×Dic94—22no—
75C2×Dic94—22no—
76C2×Dic94—41no—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—22no—
79C4⋊C4×C47D414yes—
80C42×C47—22no—
81C42×C47—22no—
82C42×C47—22no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—22no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—41no—
88(C2×D47)⋊C4Q814yescomplemented
89C4⋊Dic47—41no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—22no—
94Dic47⋊C4—22no—
95Dic47⋊C4—41no—
96C4×Dic47—41no—
97C23×C47C2411yescharacteristic
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47C2×Q812yes—
105Q8×C47—28no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
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—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D412yes—
122C2×C4×C47C2×D412yes—
123C2×C4×C47C2×D412yes—
124C2×C4×C47C2×Q812yes—
125C2×C4×C47#4112yes—
126C2×C4×C47#4112yes—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
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—21no—
146C2×Dic47C2×Q812yes—
147C2×Dic47#4112yes—
148C4×D47—44no—
149Dic94—44no—
150C22×C47C22×D411yescharacteristic
151C22×C47C22×Q811yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47C2×#4111yescharacteristic
154C22×C47C2×#4111yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C472−1+411yescharacteristic
157C2×D47—22no—
158C2×D47—22no—
159C2×D47—22no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—22no—
170C4×C47—41no—
171Dic47—22no—
172Dic47—22no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#2465—471nomaximal, Sylow
179C2×C47#52511yescharacteristic
180C2×C47#53311yescharacteristic
181C2×C47#54211yescharacteristic
182C2×C47#54611yescharacteristic
183C2×C47D4×Q811yescharacteristic
184C2×C47#55411yescharacteristic
185C2×C47#55611yescharacteristic
186D47—42no—
187C2×C22⋊Q8—471no—
188C2×C4×Q8D4711yescharacteristic, complemented
189#396—471no—
190#395—471no—
191#395—471no—
192#393—471no—
193#391—471no—
194#389—471no—
195#388—471no—
196#388—471no—
197#387—471no—
198#387—471no—
199#387—471no—
200#385—471no—
201C4×C22⋊C4—471no—
202C47#246511yescharacteristic, complemented, Sylow
203C22×Q8—471no—
204C22×Q8C2×D4711yescharacteristic
205C23×C4—471no—
206C22⋊Q8—944no—
207C4×Q8—24no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4C2×D4711yescharacteristic
216C2×C4⋊C4C2×D4711yescharacteristic
217C2×C4⋊C4C2×D4711yescharacteristic
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C22⋊C4—471no—
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C42—471no—
225C2×C42C2×D4711yescharacteristic
226C2×C42C2×D4711yescharacteristic
227C2×C42C2×D4711yescharacteristic
228#95—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95—471no—
239#95—471no—
240C24—471no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—942no—
245C2×Q8—942no—
246C2×Q8—1881no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—942no—
255C22×C4—942no—
256C22×C4—1881no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C22×C4C22×D4711yescharacteristic
261C22×C4C22×D4711yescharacteristic
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—942no—
269C4⋊C4—942no—
270C4⋊C4—942no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C4⋊C4C22⋊D4714yes—
274C22⋊C4—474no—
275C22⋊C4—942no—
276C22⋊C4—942no—
277C22⋊C4—942no—
278C22⋊C4—942no—
279C22⋊C4—1881no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—1881no—
284C23—472no—
285C23—941no—
286C23—941no—
287C23—941no—
288C23—941no—
289C23—941no—
290C23—941no—
291C23C23×D4711yescharacteristic
292Q8—28no—
293Q8—1884no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
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—941no—
330C2×C4—1884no—
331C2×C4#1062535012yes—
332C2×C4#1062535012yes—
333C2×C4Q8×D4712yes—
334C2×C4C2×C22⋊D4712yes—
335C2×C4C2×C22⋊D4712yes—
336C2×C4C2×C22⋊D4712yes—
337C22—942no—
338C22—942no—
339C22—942no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22—1881no—
344C22C22×C22⋊D4711yescharacteristic
345C22C2×Q8×D4711yescharacteristic
346C22#41×D4711yescharacteristic
347C22C2×#1062535011yescharacteristic
348C22C2×#1062535011yescharacteristic
349C22#1309407011yescharacteristic
350C22#1309407211yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—942no—
359C4—942no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C2—1882no—
366C2#1568963411yescharacteristic
367C2#1568967711yescharacteristic
368C2#1568974511yescharacteristic
369C2#1568976111yescharacteristic
370C2Q8×C22⋊D4711yescharacteristic
371C2#1568983311yescharacteristic
372C2#1568984511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×Q8×C47C2
hypercenterC2×C4×Q8D47
hypocenterC47#2465
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #15689043C2semidirect
4. #15689042C2semidirect
6. #15689029C2semidirect
7. #15689018C2semidirect
10. #15689009C2semidirect
11. #15689007C2semidirect
12. #15689007C2semidirect
15. C2×C4×Q8×C47C2semidirect
88. (C2×D47)⋊C4Q8semidirect
188. C2×C4×Q8D47semidirect
202. C47#2465semidirect