Finite Group Databasebeta

← #20254905

Subgroups — #20254905

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094057C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689786C211yesmaximal, characteristic, complemented
4#15689770C211yesmaximal, characteristic
5#15689514C211yesmaximal, characteristic, complemented
6#15689365C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689327C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689280C211yesmaximal, characteristic, complemented
11#15689275C211yesmaximal, characteristic, complemented
12#15689261C211yesmaximal, characteristic, complemented
13#15689222C211yesmaximal, characteristic, complemented
14#15689192C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic, complemented
18C2×Q8×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094057—24no—
21C2×Dic188C2211yescharacteristic, complemented
22C2×Dic188C2211yescharacteristic, complemented
23C2×#10625337C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic
25C2×#10625325C2211yescharacteristic
26C2×#10625335C2211yescharacteristic
27C2×#10625335C2211yescharacteristic
28C2×#10625336C2211yescharacteristic
29SD16×D47—24no—
30C2×C8×D47C2211yescharacteristic
31#13094023—21no—
32#13094022C2211yescharacteristic, complemented
33#13094011C2211yescharacteristic
34#13094006—21no—
35#13094004C2211yescharacteristic
36#13094004C2211yescharacteristic
37#13094002—21no—
38#13094001—21no—
39#13093995—21no—
40#13093992—21no—
41#13093989C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic
43C4×C22⋊D47C2211yescharacteristic
44(C22⋊D47)⋊C4—21no—
45C22⋊C4×D47—21no—
46Dic47⋊C8C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic
51C22⋊(C47⋊C8)C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53#13093934C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C2×M16×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#107×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70Q8×D47—22no—
71Q8×D47—41no—
72D4×D47—22no—
73D4×D47—41no—
74#10625350—22no—
75#10625350—41no—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—22no—
82C2×Dic94—21no—
83C2×Dic94—21no—
84C2×Dic94—41no—
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88SD16×C47—22no—
89M16×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47—21no—
93C4⋊C4×C47C2311yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47D411yescharacteristic
100#10625337—41no—
101#10625336—22no—
102#10625335—22no—
103#10625335—41no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4D411yescharacteristic
108C4⋊Dic47—21no—
109C4⋊Dic47—21no—
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4D411yescharacteristic
114C4×Dic47—21no—
115C4×Dic47C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118Dic188—22no—
119Dic188—22no—
120#10625325—22no—
121#10625325D414yescomplemented
122C8×D47—22no—
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—81no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—22no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151C2×Dic47C2×D411yescharacteristic
152D188—21no—
153D188C2×D412yes—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—42no—
157C4×D47—42no—
158C4×D47—81no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—42no—
165Dic94—42no—
166Dic94C2×D412yes—
167C8×C47—21no—
168C8×C47C2×D412yes—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47C22×D411yescharacteristic
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—22no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47#13712yescomplemented
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—22no—
192Dic47—21no—
193Dic47—21no—
194Dic47—21no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—41no—
199C2×C47—81no—
200C2×C47D4211yescharacteristic
201C2×C47C2×#13711yescharacteristic
202C2×C47#57711yescharacteristic
203D47—22no—
204D47—42no—
205C2×#137—471no—
206C22×SD16—471no—
207D4×Q8—471no—
208#546—471no—
209#497—471no—
210#468D4711yescharacteristic, complemented
211#467—471no—
212#464—471no—
213#461—471no—
214#452—471no—
215#451—471no—
216#450—471no—
217#448—471no—
218#440—471no—
219#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C22×Q8—471no—
223C22×Q8—471no—
224C22×D4—471no—
225#137—944no—
226C2×Q16—471no—
227C2×Q16—471no—
228C2×Q16—471no—
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—471no—
234C2×SD16—944no—
235C2×SD16C2×D4711yescharacteristic
236C2×M16C2×D4711yescharacteristic, complemented
237C22×C8—471no—
238C4⋊Q8—471no—
239C4⋊Q8—941no—
240#124—471no—
241#123—941no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—941no—
245C22⋊Q8—941no—
246C22⋊Q8C2×D4711yescharacteristic, complemented
247#121—941no—
248#121C2×D4711yescharacteristic
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—941no—
254C2×C22⋊C4—941no—
255#107C2×D4711yescharacteristic, complemented
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103—471no—
260#103C2×D4711yescharacteristic, complemented
261#102—471no—
262#102C2×D4711yescharacteristic
263C22⋊C8—471no—
264C22⋊C8—471no—
265#97—471no—
266C24—941no—
267#41—942no—
268#41—1881no—
269C2×Q8—471no—
270C2×Q8—471no—
271C2×Q8—471no—
272C2×Q8—941no—
273C2×Q8—942no—
274C2×Q8—941no—
275C2×Q8—942no—
276C2×Q8—1881no—
277C2×Q8—1881no—
278C2×Q8C22×D4711yescharacteristic
279C2×D4—21no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—941no—
283C2×D4—942no—
284C2×D4—941no—
285C2×D4—1881no—
286C2×D4C22×D4711yescharacteristic
287C22×C4—471no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292C22×C4C22×D4711yescharacteristic
293Q16—942no—
294Q16—942no—
295Q16—1881no—
296SD16—22no—
297SD16—474no—
298SD16—942no—
299SD16—942no—
300SD16—942no—
301SD16—1881no—
302M16—22no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—942no—
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—471no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4C22×D4711yescharacteristic
316C4⋊C4C22×D4711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—471no—
320C22⋊C4—471no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—471no—
327C42—941no—
328C23—21no—
329C23—471no—
330C23—941no—
331C23—3761no—
332C23—1882no—
333C23—1882no—
334C23D4×D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—472no—
338Q8—941no—
339Q8—941no—
340Q8—941no—
341Q8—941no—
342Q8—941no—
343Q8—1882no—
344Q8—1882no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—472no—
349D4—942no—
350D4—941no—
351D4—1882no—
352D4—1882no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—471no—
359C2×C4—471no—
360C2×C4—471no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—3761no—
367C2×C4—1882no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4D4×D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—941no—
374C8—941no—
375C8D4×D4712yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—472no—
383C22—941no—
384C22—941no—
385C22—942no—
386C22—3764no—
387C22—1881no—
388C22—1881no—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—941no—
395C4—942no—
396C4—941no—
397C4—941no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309407011yescharacteristic
402C2—41no—
403C2—81no—
404C2—942no—
405C2—1882no—
406C2#1568975711yescharacteristic
407C2#137×D4711yescharacteristic
408C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689786C2semidirect
5. #15689514C2semidirect
6. #15689365C2semidirect
7. #15689344C2semidirect
8. #15689327C2semidirect
9. #15689283C2semidirect
10. #15689280C2semidirect
11. #15689275C2semidirect
12. #15689261C2semidirect
13. #15689222C2semidirect
14. #15689192C2semidirect
15. C47×#468C2semidirect
17. C22×Dic94C22semidirect
21. C2×Dic188C22semidirect
22. C2×Dic188C22semidirect
23. C2×#10625337C22semidirect
32. #13094022C22semidirect
41. #13093989C22semidirect
46. Dic47⋊C8C22semidirect
47. #13093947C22semidirect
48. #13093947C22semidirect
49. #13093947C22semidirect
51. C22⋊(C47⋊C8)C22semidirect
53. #13093934C22semidirect
55. C2×M16×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #107×C47C22semidirect
59. #103×C47C22semidirect
121. #10625325D4semidirect
184. C2×D47#137semidirect
210. #468D47semidirect
220. C47#3266semidirect
236. C2×M16C2×D47semidirect
246. C22⋊Q8C2×D47semidirect
255. #107C2×D47semidirect
260. #103C2×D47semidirect