Finite Group Databasebeta

← #20247206

Subgroups — #20247206

Order 6016.

584 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×#13094001C211yesmaximal, characteristic, complemented
2#15689062C211yesmaximal, characteristic, complemented
3#15689056C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689035C211yesmaximal, characteristic, complemented
6#15689029C211yesmaximal, characteristic, complemented
7#15689007C211yesmaximal, characteristic, complemented
8#15689003C211yesmaximal, characteristic
9#15689003C211yesmaximal, characteristic
10#15688998C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688996C211yesmaximal, characteristic, complemented
13#15688983C211yesmaximal, characteristic, complemented
14C2×C47⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×D4×C47C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19#13094001—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊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×D4×C47C2211yescharacteristic
46C23×C4×C47C2211yescharacteristic
47C23×C4×C47C2211yescharacteristic
48C4×D4×C47—24no—
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C2×D4×C47—22no—
56C2×D4×C47—22no—
57C2×D4×C47Q814yescomplemented
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×Dic47—22no—
70C22×Dic47—22no—
71C22×Dic47—22no—
72C22×Dic47—41no—
73C22×Dic47—41no—
74C22×Dic47—41no—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C2×Dic94—22no—
84C2×Dic94—22no—
85C2×Dic94—41no—
86C4⋊C4×C47—22no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47D414yes—
89C42×C47—22no—
90C22⋊Dic47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—41no—
94C22⋊Dic47—41no—
95C22⋊Dic47—41no—
96C4⋊Dic47—22no—
97C4⋊Dic47—41no—
98C4⋊Dic47—41no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4—41no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47C2×D412yes—
114C23×C47C2×Q812yes—
115C23×C47C2×Q812yes—
116C23×C47#4112yes—
117C23×C47C2411yescharacteristic
118D4×C47—28no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
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—44no—
131C2×C4×C47—44no—
132C2×C4×C47C2×D412yes—
133C2×C4×C47C2×D412yes—
134C2×C4×C47C2×Q812yes—
135C2×C4×C47#4112yes—
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×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×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—44no—
160C2×Dic47—44no—
161C2×Dic47#4112yes—
162Dic94—44no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—22no—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22⋊Q814yes—
177C22×C47C22×D411yescharacteristic
178C22×C47C22×Q811yescharacteristic
179C22×C47C2×#4111yescharacteristic
180C22×C47C2×#4111yescharacteristic
181C22×C47C2×#4111yescharacteristic
182C22×C47H(5,𝔽2)11yescharacteristic
183C22×C47H(5,𝔽2)11yescharacteristic
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—22no—
187C4×C47—22no—
188C4×C47—41no—
189Dic47—22no—
190Dic47—41no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197#2450—471nomaximal, Sylow
198C2×C47—24no—
199C2×C47—42no—
200C2×C47C2×C22⋊Q811yescharacteristic
201C2×C47#52911yescharacteristic
202C2×C47#53811yescharacteristic
203C2×C47#54611yescharacteristic
204C2×C47#54611yescharacteristic
205C2×C47#55411yescharacteristic
206C2×C47#55411yescharacteristic
207C2×C22⋊Q8—471no—
208C2×C4×D4D4711yescharacteristic
209#400—471no—
210#398—471no—
211#396—471no—
212#393—471no—
213#391—471no—
214#387—471no—
215#386—471no—
216#386—471no—
217#385—471no—
218#385—471no—
219#385—471no—
220#380—471no—
221C2×#95—471no—
222C47#245011yescharacteristic, complemented, Sylow
223C22×Q8—471no—
224C22×D4C2×D4711yescharacteristic
225C23×C4—471no—
226C23×C4—471no—
227C23×C4C2×D4711yescharacteristic
228C23×C4C2×D4711yescharacteristic
229C22⋊Q8—944no—
230C4×D4—24no—
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⋊C4C2×D4711yescharacteristic
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4C2×D4711yescharacteristic
246C2×C22⋊C4C2×D4711yescharacteristic
247C2×C42C2×D4711yescharacteristic
248#95—471no—
249#95—471no—
250#95—471no—
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259#95—471no—
260C24C22×D4711yescharacteristic
261C24C22×D4711yescharacteristic
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—1881no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4Dic9414yescomplemented
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4—942no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4—1881no—
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291C22×C4C22×D4711yescharacteristic
292C22×C4C22×D4711yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—1881no—
299C4⋊C4—1881no—
300C4⋊C4—1881no—
301C22⋊C4—22no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—942no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C22⋊C4C22⋊D4714yes—
309C42—22no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×Dic9412yes—
321C23C2×Dic9412yes—
322C23#1062535012yes—
323C23C2×C22⋊D4712yes—
324C23C23×D4711yescharacteristic
325Q8—1884no—
326D4—28no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
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—44no—
339C2×C4—44no—
340C2×C4—472no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
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—1884no—
365C2×C4—1884no—
366C2×C4C2×Dic9412yes—
367C2×C4#1062535212yes—
368C2×C4C2×C22⋊D4712yes—
369C2×C4C2×C22⋊D4712yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#1309400314yes—
384C22C22×C22⋊D4711yescharacteristic
385C22C22×Dic9411yescharacteristic
386C22#41×D4711yescharacteristic
387C22C2×#1062535211yescharacteristic
388C22C2×#1062535011yescharacteristic
389C22#1309406911yescharacteristic
390C22#1309407011yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—942no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C4—1881no—
401C4—1881no—
402C4—1881no—
403C4—1881no—
404C2—24no—
405C2—42no—
406C2C2×#1309400311yescharacteristic
407C2#1568965311yescharacteristic
408C2#1568970611yescharacteristic
409C2#1568976111yescharacteristic
410C2#1568976711yescharacteristic
411C2#1568983011yescharacteristic
412C2#1568983211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2450
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094001C2semidirect
2. #15689062C2semidirect
3. #15689056C2semidirect
4. #15689046C2semidirect
5. #15689035C2semidirect
6. #15689029C2semidirect
7. #15689007C2semidirect
10. #15688998C2semidirect
11. #15688996C2semidirect
12. #15688996C2semidirect
13. #15688983C2semidirect
14. C2×C47⋊#95C2semidirect
57. C2×D4×C47Q8semidirect
222. C47#2450semidirect
267. C2×D4Dic94semidirect