Finite Group Databasebeta

← #20254891

Subgroups — #20254891

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×#13094056C211yesmaximal, characteristic, complemented
2C22×#10625336C211yesmaximal, characteristic, complemented
3Q8×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689764C211yesmaximal, characteristic
5#15689516C211yesmaximal, characteristic, complemented
6#15689372C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689347C211yesmaximal, characteristic, complemented
9#15689327C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11#15689276C211yesmaximal, characteristic, complemented
12#15689263C211yesmaximal, characteristic, complemented
13#15689226C211yesmaximal, characteristic, complemented
14#15689191C211yesmaximal, characteristic, complemented
15C47×#451C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic, complemented
18C22×D188C2211yescharacteristic
19#13094056—24no—
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625325C2211yescharacteristic
22C2×#10625325C2211yescharacteristic
23C2×#10625336—24no—
24C2×#10625336C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic
28C2×#10625324C2211yescharacteristic, complemented
29C22×C47⋊C8C2211yescharacteristic
30#13094022—21no—
31#13094022C2211yescharacteristic, complemented
32#13094013C2211yescharacteristic
33#13094009—21no—
34#13094003—21no—
35#13094003C2211yescharacteristic
36#13094000—21no—
37#13094000C2211yescharacteristic, complemented
38#13093999—21no—
39#13093999C2211yescharacteristic
40#13093994—21no—
41Q8×Dic47C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic
43C4×C22⋊D47—21no—
44C4×C22⋊D47C2211yescharacteristic
45C22⋊C4×D47—21no—
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093934C2211yescharacteristic, complemented
54C22×Q8×C47C2211yescharacteristic
55C2×Q16×C47C2211yescharacteristic, complemented
56C2×Q16×C47C2211yescharacteristic, complemented
57C22⋊Q8×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47—21no—
63C2×Q8×C47—22no—
64C2×Q8×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C22×C4×C47—21no—
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47D411yescharacteristic
71#10625354—22no—
72#10625354—41no—
73Q8×D47—22no—
74Q8×D47—41no—
75C2×D188—22no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—41no—
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87C2×Dic94C2311yescharacteristic
88Q16×C47—22no—
89Q16×C47—41no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47—21no—
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47D411yescharacteristic
97#10625337—22no—
98#10625336—22no—
99#10625336—22no—
100#10625336—22no—
101#10625336D414yescomplemented
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4D411yescharacteristic
108C4⋊Dic47—21no—
109C4⋊Dic47C2311yescharacteristic
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4D411yescharacteristic
115C4×Dic47—21no—
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120#10625325—22no—
121#10625325—41no—
122#10625324—22no—
123C23×C47C2×D411yescharacteristic
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—42no—
136Q8×C47C2×D412yes—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—42no—
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—22no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151C2×Dic47C2×D411yescharacteristic
152D188—21no—
153D188—21no—
154D188—21no—
155D188—42no—
156D188—42no—
157D188—81no—
158D188C2×D412yes—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—42no—
162C4×D47—42no—
163C4×D47—81no—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167C8×C47—21no—
168C8×C47—21no—
169C47⋊C8—21no—
170C47⋊C8C2×D412yes—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47#13712yescomplemented
174C22×C47C22×D411yescharacteristic
175C2×D47—21no—
176C2×D47—22no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—84no—
185C4×C47—22no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47C22×D411yescharacteristic
191C4×C47H(5,𝔽2)11yescharacteristic
192Dic47—21no—
193Dic47—21no—
194Dic47—21no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—22no—
199C2×C47D4211yescharacteristic
200C2×C47C2×#13711yescharacteristic
201C2×C47#57711yescharacteristic
202D47—41no—
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#451D4711yescharacteristic, complemented
216#450—471no—
217#448—471no—
218#440—471no—
219#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C22×Q8—471no—
223C22×Q8C2×D4711yescharacteristic
224C22×D4—471no—
225#137—944no—
226C2×Q16—471no—
227C2×Q16C2×D4711yescharacteristic, complemented
228C2×Q16C2×D4711yescharacteristic, complemented
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—944no—
236C2×M16—471no—
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
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—941no—
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103C2×D4711yescharacteristic, complemented
260#103C2×D4711yescharacteristic, complemented
261#102—471no—
262#102—471no—
263C22⋊C8—471no—
264C22⋊C8C2×D4711yescharacteristic
265#97—471no—
266C24—941no—
267#41—942no—
268#41—1881no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—471no—
273C2×Q8—941no—
274C2×Q8—942no—
275C2×Q8—1881no—
276C2×Q8C22×D4711yescharacteristic
277C2×Q8C22×D4711yescharacteristic
278C2×Q8C22×D4711yescharacteristic
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—942no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—1881no—
287C22×C4—21no—
288C22×C4—471no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292C22×C4C22×D4711yescharacteristic
293Q16—22no—
294Q16—41no—
295Q16—942no—
296SD16—474no—
297SD16—942no—
298SD16—942no—
299SD16—942no—
300SD16—942no—
301SD16—1881no—
302M16—942no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—942no—
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—471no—
310C4⋊C4—471no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4C22×D4711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—471no—
319C22⋊C4—471no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—471no—
327C42—941no—
328C23—471no—
329C23—941no—
330C23—941no—
331C23—3761no—
332C23—1882no—
333C23—1882no—
334C23D4×D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—941no—
342Q8—941no—
343Q8—1882no—
344Q8D4×D4712yes—
345D4—472no—
346D4—942no—
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—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—471no—
361C2×C4—471no—
362C2×C4—471no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—3761no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4D4×D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—21no—
374C8—472no—
375C8—941no—
376C22—21no—
377C22—21no—
378C22—941no—
379C22—942no—
380C22—941no—
381C22—941no—
382C22—3764no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22#1309405612yescomplemented
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—941no—
396C4—941no—
397C4—941no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309406911yescharacteristic
402C2—22no—
403C2—3761no—
404C2—1881no—
405C2—1882no—
406C2#1568975511yescharacteristic
407C2C2×#1309405611yescharacteristic
408C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C22×#10625336C2semidirect
3. Q8×C22⋊D47C2semidirect
5. #15689516C2semidirect
6. #15689372C2semidirect
7. #15689362C2semidirect
8. #15689347C2semidirect
9. #15689327C2semidirect
10. #15689284C2semidirect
11. #15689276C2semidirect
12. #15689263C2semidirect
13. #15689226C2semidirect
14. #15689191C2semidirect
15. C47×#451C2semidirect
17. C2×Q8×D47C22semidirect
20. C2×#10625337C22semidirect
28. C2×#10625324C22semidirect
31. #13094022C22semidirect
37. #13094000C22semidirect
41. Q8×Dic47C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093948C22semidirect
49. #13093947C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093934C22semidirect
55. C2×Q16×C47C22semidirect
56. C2×Q16×C47C22semidirect
58. #103×C47C22semidirect
59. #103×C47C22semidirect
101. #10625336D4semidirect
173. C22×C47#137semidirect
215. #451D47semidirect
220. C47#3266semidirect
227. C2×Q16C2×D47semidirect
228. C2×Q16C2×D47semidirect
259. #103C2×D47semidirect
260. #103C2×D47semidirect
388. C22#13094056semidirect