Finite Group Databasebeta

← #20249668

Subgroups — #20249668

Order 6016.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic
3C2×#13094006C211yesmaximal, characteristic
4C2×#13094000C211yesmaximal, characteristic, complemented
5#15689059C211yesmaximal, characteristic, complemented
6#15689052C211yesmaximal, characteristic, complemented
7#15689046C211yesmaximal, characteristic, complemented
8#15689044C211yesmaximal, characteristic, complemented
9#15689038C211yesmaximal, characteristic
10#15689020C211yesmaximal, characteristic, complemented
11#15689017C211yesmaximal, characteristic, complemented
12#15689012C211yesmaximal, characteristic, complemented
13#15689010C211yesmaximal, characteristic, complemented
14#15688997C211yesmaximal, characteristic, complemented
15C47×#393C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13094022—24no—
20#13094010—24no—
21#13094006—24no—
22#13094000—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C2×C4×Dic47C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—41no—
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—22no—
67C2×C22⋊D47—22no—
68C2×C22⋊D47—41no—
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—41no—
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94—41no—
82C22⋊C4×C47—22no—
83C22⋊C4×C47—22no—
84C22⋊C4×C47—41no—
85C22⋊Dic47—22no—
86C22⋊Dic47—22no—
87C22⋊Dic47—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4D414yes—
93C4⋊Dic47—22no—
94C4⋊Dic47—22no—
95C4⋊Dic47—41no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4D414yes—
103C4×Dic47—22no—
104C4×Dic47—22no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47C2411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47C2×D412yes—
120Q8×C47—44no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47C2×D412yes—
138C2×C4×C47C2×D412yes—
139C22⋊D47—44no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47C2×D412yes—
158C2×Dic47C2×D412yes—
159C2×Dic47C2×D412yes—
160C2×Dic47#4112yes—
161C4×D47—44no—
162Dic94—44no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47C22×D411yescharacteristic
171C22×C47C22×D411yescharacteristic
172C22×C47C2×#4111yescharacteristic
173C22×C47H(5,𝔽2)11yescharacteristic
174C22×C472−1+411yescharacteristic
175C22×C472−1+411yescharacteristic
176C22×C472−1+411yescharacteristic
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190Dic47—22no—
191Dic47—22no—
192Dic47—22no—
193Dic47—22no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197#2674—471nomaximal, Sylow
198C2×C47—81no—
199C2×C47#53611yescharacteristic
200C2×C47#53611yescharacteristic
201C2×C47#54211yescharacteristic
202C2×C47D4211yescharacteristic
203C2×C47#54711yescharacteristic
204C2×C47#54811yescharacteristic
205C2×C47#56311yescharacteristic
206D47—42no—
207C2×C4⋊Q8—471no—
208C2×#124—471no—
209C2×#123—471no—
210C2×C22⋊Q8—471no—
211#399—471no—
212#397—471no—
213#396—471no—
214#395—471no—
215#394—471no—
216#393D4711yescharacteristic, complemented
217#389—471no—
218#388—471no—
219#388—471no—
220#387—471no—
221#385—471no—
222C47#267411yescharacteristic, complemented, Sylow
223C22×Q8—471no—
224C22×Q8C2×D4711yescharacteristic
225C22×D4—471no—
226C23×C4—471no—
227C4⋊Q8—944no—
228#124—944no—
229#123—944no—
230C22⋊Q8—944no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—471no—
240C2×C4⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4—471no—
247C2×C22⋊C4—471no—
248C2×C22⋊C4—471no—
249C2×C22⋊C4C2×D4711yescharacteristic
250C2×C22⋊C4C2×D4711yescharacteristic
251C2×C22⋊C4C2×D4711yescharacteristic
252C2×C42—471no—
253C2×C42—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259#95C2×D4711yescharacteristic
260#95C2×D4711yescharacteristic
261#95C2×D4711yescharacteristic
262C24—471no—
263C24C22×D4711yescharacteristic
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—942no—
268C2×Q8—942no—
269C2×Q8—1881no—
270C2×D4—942no—
271C2×D4—942no—
272C2×D4—1881no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—942no—
281C22×C4—942no—
282C22×C4—1881no—
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—474no—
290C4⋊C4—942no—
291C4⋊C4—942no—
292C4⋊C4—942no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—1881no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—474no—
303C22⋊C4—942no—
304C22⋊C4—942no—
305C22⋊C4—942no—
306C22⋊C4—942no—
307C22⋊C4—942no—
308C22⋊C4—942no—
309C22⋊C4—942no—
310C42—942no—
311C42—942no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—472no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23—941no—
324C23—941no—
325C23—941no—
326C23C23×D4711yescharacteristic
327Q8—44no—
328Q8—1884no—
329D4—1884no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—472no—
347C2×C4—472no—
348C2×C4—472no—
349C2×C4—472no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—1884no—
368C2×C4D4×D4712yes—
369C2×C4D4×D4712yes—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—942no—
378C22—942no—
379C22—942no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22C2×D4×D4711yescharacteristic
385C22C2×D4×D4711yescharacteristic
386C22#41×D4711yescharacteristic
387C22#1309406911yescharacteristic
388C22#1309407111yescharacteristic
389C22#1309407111yescharacteristic
390C22#1309407211yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—942no—
398C4—942no—
399C4—942no—
400C4—942no—
401C4—1881no—
402C4—1881no—
403C4—1881no—
404C2—81no—
405C2—1882no—
406C2#1568969311yescharacteristic
407C2#1568969611yescharacteristic
408C2#1568973711yescharacteristic
409C2#1568975511yescharacteristic
410C2#1568977511yescharacteristic
411C2#1568978111yescharacteristic
412C2#1568987411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2674
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
4. C2×#13094000C2semidirect
5. #15689059C2semidirect
6. #15689052C2semidirect
7. #15689046C2semidirect
8. #15689044C2semidirect
10. #15689020C2semidirect
11. #15689017C2semidirect
12. #15689012C2semidirect
13. #15689010C2semidirect
14. #15688997C2semidirect
15. C47×#393C2semidirect
216. #393D47semidirect
222. C47#2674semidirect