Finite Group Databasebeta

← #20254903

Subgroups — #20254903

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
2C22×#10625325C211yesmaximal, characteristic, complemented
3D4×Dic94C211yesmaximal, characteristic, complemented
4#15689769C211yesmaximal, characteristic
5#15689517C211yesmaximal, characteristic, complemented
6#15689369C211yesmaximal, characteristic, complemented
7#15689364C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689329C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689276C211yesmaximal, characteristic, complemented
13#15689264C211yesmaximal, characteristic, complemented
14#15689225C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C22×Dic94C2211yescharacteristic, complemented
19C22×D188C2211yescharacteristic
20#13094057—24no—
21C2×Dic188C2211yescharacteristic, complemented
22C2×Dic188C2211yescharacteristic, complemented
23C2×Dic188C2211yescharacteristic, complemented
24C2×#10625325—24no—
25C2×#10625325C2211yescharacteristic
26C2×#10625325C2211yescharacteristic
27C2×#10625325C2211yescharacteristic
28C2×#10625325C2211yescharacteristic
29C2×#10625325C2211yescharacteristic
30C2×#10625325C2211yescharacteristic
31#13094024C2211yescharacteristic, complemented
32#13094023—21no—
33#13094012C2211yescharacteristic
34#13094009—21no—
35#13094003C2211yescharacteristic
36#13094003C2211yescharacteristic
37#13094003C2211yescharacteristic, complemented
38#13094001—21no—
39#13094001—21no—
40#13093998C2211yescharacteristic
41#13093997—21no—
42#13093992—21no—
43C4×Dic94C2211yescharacteristic, complemented
44C4×D188C2211yescharacteristic
45D4×Dic47—21no—
46C22⋊C4×D47—21no—
47#13093958C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093949C2211yescharacteristic, complemented
51#13093949C2211yescharacteristic, complemented
52#13093946C2211yescharacteristic
53#13093946C2211yescharacteristic
54C2×M16×C47C2211yescharacteristic, complemented
55C22×C8×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C4⋊C8×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C22⋊C8×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×D4×C47D411yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625350—22no—
70#10625350—41no—
71C2×D188—22no—
72C2×D188—21no—
73C2×D188—41no—
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×Dic94—22no—
79C2×Dic94—22no—
80C2×Dic94—21no—
81C2×Dic94—21no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×Dic94C2311yescharacteristic
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88M16×C47—22no—
89C2×C8×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47D411yescharacteristic
95C22⋊C4×C47D411yescharacteristic
96C22⋊C4×C47D411yescharacteristic
97C42×C47C2311yescharacteristic
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2311yescharacteristic
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113C4×Dic47—21no—
114Dic188—22no—
115Dic188—22no—
116Dic188—41no—
117#10625325—22no—
118#10625325—22no—
119#10625325—22no—
120#10625325—22no—
121#10625325—41no—
122#10625325D414yescomplemented
123C23×C47C2×D411yescharacteristic
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130D4×C47—22no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—42no—
141C22⋊D47—81no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150D188—21no—
151D188—21no—
152D188—21no—
153D188—42no—
154D188C2×D412yes—
155C4×D47—42no—
156C4×D47—81no—
157Dic94—21no—
158Dic94—21no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—42no—
165Dic94—42no—
166Dic94C2×D412yes—
167C8×C47—21no—
168C8×C47—21no—
169C8×C47—21no—
170C8×C47C2×D412yes—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47#13712yescomplemented
177C22×C47C22×D411yescharacteristic
178C2×D47—22no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—84no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—21no—
189C4×C47C22×D411yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—22no—
192Dic47—41no—
193Dic47—41no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—22no—
199C2×C47—41no—
200C2×C47D4211yescharacteristic
201C2×C47C2×#13711yescharacteristic
202C2×C47#57711yescharacteristic
203D47—42no—
204D47—81no—
205C2×#137—471no—
206C22×SD16—471no—
207D4×Q8—471no—
208#546—471no—
209#497—471no—
210#468—471no—
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#435D4711yescharacteristic, complemented
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—471no—
235C2×SD16—944no—
236C2×M16C2×D4711yescharacteristic, complemented
237C22×C8C2×D4711yescharacteristic
238C4⋊Q8—471no—
239C4⋊Q8—941no—
240#124—471no—
241#123—941no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—471no—
245C22⋊Q8—941no—
246C22⋊Q8—941no—
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—941no—
253C4×D4C2×D4711yescharacteristic
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8C2×D4711yescharacteristic, complemented
257#103—471no—
258#103—471no—
259#103—471no—
260#103—471no—
261#102—471no—
262#102—471no—
263C22⋊C8C2×D4711yescharacteristic
264C22⋊C8C2×D4711yescharacteristic, complemented
265#97C2×D4711yescharacteristic, complemented
266C24—941no—
267#41—942no—
268#41—1881no—
269C2×Q8—471no—
270C2×Q8—471no—
271C2×Q8—471no—
272C2×Q8—471no—
273C2×Q8—942no—
274C2×Q8—942no—
275C2×Q8—941no—
276C2×Q8—941no—
277C2×Q8—1881no—
278C2×Q8—1881no—
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—942no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—1881no—
286C2×D4D18811yescharacteristic
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4C22×D4711yescharacteristic
292C22×C4C22×D4711yescharacteristic
293Q16—942no—
294Q16—942no—
295Q16—1881no—
296SD16—474no—
297SD16—942no—
298SD16—942no—
299SD16—942no—
300SD16—942no—
301SD16—1881no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D4711yescharacteristic
305C2×C8C22×D4711yescharacteristic
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—471no—
309C4⋊C4—471no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4D18811yescharacteristic
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4D18811yescharacteristic
325C22⋊C4D18811yescharacteristic
326C42—941no—
327C42C22×D4711yescharacteristic
328C23—941no—
329C23—941no—
330C23—3761no—
331C23—1882no—
332C23—1882no—
333C23C2×D18811yescharacteristic
334C23C2×D18811yescharacteristic
335Q8—472no—
336Q8—941no—
337Q8—941no—
338Q8—941no—
339Q8—941no—
340Q8—941no—
341Q8—941no—
342Q8—941no—
343Q8—1882no—
344Q8—1882no—
345D4—22no—
346D4—472no—
347D4—941no—
348D4—941no—
349D4—941no—
350D4—3761no—
351D4—1882no—
352D4—1882no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—3761no—
364C2×C4—1882no—
365C2×C4—1882no—
366C2×C4—1882no—
367C2×C4C2×D18811yescharacteristic
368C2×C4C2×D18811yescharacteristic
369C2×C4C2×D18811yescharacteristic
370C2×C4C2×D18811yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D4712yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—942no—
382C22—3764no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22#1309405712yescomplemented
389C22C22×D18811yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—942no—
395C4—1881no—
396C4—1881no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309407011yescharacteristic
402C2—22no—
403C2—41no—
404C2—3761no—
405C2—1882no—
406C2D4×D18811yescharacteristic
407C2C2×#1309405711yescharacteristic
408C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C22×#10625325C2semidirect
3. D4×Dic94C2semidirect
5. #15689517C2semidirect
6. #15689369C2semidirect
7. #15689364C2semidirect
8. #15689346C2semidirect
9. #15689329C2semidirect
10. #15689287C2semidirect
11. #15689281C2semidirect
12. #15689276C2semidirect
13. #15689264C2semidirect
14. #15689225C2semidirect
15. C47×#435C2semidirect
18. C22×Dic94C22semidirect
21. C2×Dic188C22semidirect
22. C2×Dic188C22semidirect
23. C2×Dic188C22semidirect
31. #13094024C22semidirect
37. #13094003C22semidirect
43. C4×Dic94C22semidirect
47. #13093958C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093949C22semidirect
51. #13093949C22semidirect
54. C2×M16×C47C22semidirect
57. C4⋊C8×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. #97×C47C22semidirect
122. #10625325D4semidirect
176. C22×C47#137semidirect
219. #435D47semidirect
220. C47#3266semidirect
236. C2×M16C2×D47semidirect
256. C4⋊C8C2×D47semidirect
264. C22⋊C8C2×D47semidirect
265. #97C2×D47semidirect
388. C22#13094057semidirect