Finite Group Databasebeta

← #20254899

Subgroups — #20254899

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×#13094055C211yesmaximal, characteristic, complemented
2C22×#10625336C211yesmaximal, characteristic, complemented
3#15689769C211yesmaximal, characteristic
4#15689515C211yesmaximal, characteristic, complemented
5#15689371C211yesmaximal, characteristic, complemented
6#15689362C211yesmaximal, characteristic, complemented
7#15689345C211yesmaximal, characteristic, complemented
8#15689325C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689273C211yesmaximal, characteristic, complemented
12#15689262C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15D4×Q8×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18#13094055—24no—
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625336—24no—
23C2×#10625336C2211yescharacteristic
24C2×#10625336C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic
28C2×#10625336C2211yescharacteristic
29C2×#10625329C2211yescharacteristic, complemented
30C22×C47⋊C8C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094009—21no—
33#13094003C2211yescharacteristic
34#13093998C2211yescharacteristic
35#13093997—21no—
36#13093992—21no—
37C4×D188C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093957C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C22×Q8×C47C2211yescharacteristic
51C22×Q8×C47C2211yescharacteristic, complemented
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56C22⋊Q8×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic, complemented
58C4×Q8×C47C2211yescharacteristic, complemented
59C4×D4×C47—21no—
60C4×D4×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47—21no—
63C2×Q8×C47—21no—
64C2×Q8×C47—22no—
65C2×Q8×C47—22no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×Q8×C47C2311yescharacteristic
69C2×Q8×C47C2311yescharacteristic
70C2×Q8×C47C2311yescharacteristic
71C2×D4×C47D411yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78#10625350—22no—
79#10625350—41no—
80C2×D188—22no—
81C2×D188—21no—
82C2×D188—41no—
83C2×D188C2311yescharacteristic
84C2×D188C2311yescharacteristic
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×Dic94C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47D411yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47D411yescharacteristic
98C22⋊C4×C47D411yescharacteristic
99C42×C47—21no—
100C42×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102#10625337—22no—
103#10625337—22no—
104#10625337—41no—
105#10625336—22no—
106#10625336—22no—
107#10625336—22no—
108#10625336—22no—
109#10625336—41no—
110#10625336D414yescomplemented
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4—21no—
115C4⋊Dic47C2311yescharacteristic
116Dic47⋊C4—21no—
117#10625329—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47C2×D411yescharacteristic
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130Q8×C47—21no—
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—42no—
136Q8×C47—42no—
137Q8×C47C2×D412yes—
138D4×C47—22no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—42no—
148C2×C4×C47—42no—
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2×D411yescharacteristic
152C2×C4×C47C2×D411yescharacteristic
153C2×C4×C47C2411yescharacteristic
154C22⋊D47—42no—
155C22⋊D47—81no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158D188—21no—
159D188—21no—
160D188—21no—
161D188—42no—
162D188C2×D412yes—
163C4×D47—42no—
164C4×D47—81no—
165Dic94—21no—
166Dic94—21no—
167C47⋊C8—21no—
168C47⋊C8—21no—
169C47⋊C8—21no—
170C47⋊C8C2×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—22no—
188C4×C47—21no—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47C22×D411yescharacteristic
194C4×C47H(5,𝔽2)11yescharacteristic
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×Q8D4711yescharacteristic, complemented
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#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C22×Q8C2×D4711yescharacteristic
223C22×Q8C2×D4711yescharacteristic, complemented
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×M16—471no—
237C22×C8—471no—
238C4⋊Q8—21no—
239C4⋊Q8C2×D4711yescharacteristic, complemented
240#124—471no—
241#123—941no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—471no—
245C22⋊Q8C2×D4711yescharacteristic
246C22⋊Q8C2×D4711yescharacteristic, complemented
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8C2×D4711yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—471no—
253C4×D4C2×D4711yescharacteristic
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103—471no—
260#103—471no—
261#102—471no—
262#102—471no—
263C22⋊C8—471no—
264C22⋊C8—471no—
265#97—471no—
266C24—941no—
267#41—942no—
268#41—1881no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—471no—
276C2×Q8C22×D4711yescharacteristic
277C2×Q8C22×D4711yescharacteristic
278C2×Q8C22×D4711yescharacteristic
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—942no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—1881no—
286C2×D4C22⋊D4711yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
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—942no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—471no—
306C2×C8—471no—
307C2×C8—942no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—471no—
314C4⋊C4—941no—
315C4⋊C4C22⋊D4711yescharacteristic
316C4⋊C4C22×D4711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4C22⋊D4711yescharacteristic
325C22⋊C4C22⋊D4711yescharacteristic
326C42—21no—
327C42C22×D4711yescharacteristic
328C23—941no—
329C23—941no—
330C23—3761no—
331C23—1882no—
332C23—1882no—
333C23C2×C22⋊D4711yescharacteristic
334C23C2×C22⋊D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—42no—
342Q8—941no—
343Q8—941no—
344Q8D4×D4712yes—
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—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—3761no—
366C2×C4—1882no—
367C2×C4C2×C22⋊D4711yescharacteristic
368C2×C4C2×C22⋊D4711yescharacteristic
369C2×C4C2×C22⋊D4711yescharacteristic
370C2×C4C2×C22⋊D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—472no—
373C8—941no—
374C8—941no—
375C8—941no—
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#1309405512yescomplemented
389C22C22×C22⋊D4711yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309406911yescharacteristic
402C2—22no—
403C2—41no—
404C2—3761no—
405C2—1882no—
406C2D4×C22⋊D4711yescharacteristic
407C2C2×#1309405511yescharacteristic
408C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD4×Q8×C47C2
socleC22×C47C22×D4
hypercenterD4×Q8D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C22×#10625336C2semidirect
4. #15689515C2semidirect
5. #15689371C2semidirect
6. #15689362C2semidirect
7. #15689345C2semidirect
8. #15689325C2semidirect
9. #15689283C2semidirect
10. #15689279C2semidirect
11. #15689273C2semidirect
12. #15689262C2semidirect
13. #15689221C2semidirect
14. #15689195C2semidirect
15. D4×Q8×C47C2semidirect
19. C2×#10625337C22semidirect
20. C2×#10625337C22semidirect
21. C2×#10625337C22semidirect
29. C2×#10625329C22semidirect
39. #13093957C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
43. #13093948C22semidirect
44. #13093947C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
51. C22×Q8×C47C22semidirect
53. C4⋊Q8×C47C22semidirect
57. C22⋊Q8×C47C22semidirect
58. C4×Q8×C47C22semidirect
110. #10625336D4semidirect
176. C22×C47#137semidirect
207. D4×Q8D47semidirect
220. C47#3266semidirect
223. C22×Q8C2×D47semidirect
239. C4⋊Q8C2×D47semidirect
246. C22⋊Q8C2×D47semidirect
250. C4×Q8C2×D47semidirect
388. C22#13094055semidirect