Finite Group Databasebeta

← #20254933

Subgroups — #20254933

Order 6016.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094052C211yesmaximal, characteristic, complemented
2C2×#13094046C211yesmaximal, characteristic, complemented
3#15689794C211yesmaximal, characteristic, complemented
4#15689769C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689369C211yesmaximal, characteristic, complemented
7#15689359C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689319C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689270C211yesmaximal, characteristic, complemented
12#15689270C211yesmaximal, characteristic, complemented
13#15689259C211yesmaximal, characteristic, complemented
14#15689225C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C2×#10625350C2211yescharacteristic, complemented
19C22×D188C2211yescharacteristic
20#13094052—24no—
21#13094046—24no—
22C2×Dic188C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625325C2211yescharacteristic
25C2×#10625325C2211yescharacteristic, complemented
26C2×#10625325C2211yescharacteristic, complemented
27C2×D376C2211yescharacteristic
28C2×D376C2211yescharacteristic
29C2×D376C2211yescharacteristic
30C2×D376C2211yescharacteristic
31#13094021C2211yescharacteristic, complemented
32#13094020—21no—
33#13094012C2211yescharacteristic
34#13094009—21no—
35#13094003C2211yescharacteristic
36#13093998C2211yescharacteristic
37#13093998C2211yescharacteristic
38#13093998C2211yescharacteristic, complemented
39#13093997—21no—
40#13093997—21no—
41#13093997—21no—
42#13093992—21no—
43C4×Dic94C2211yescharacteristic, complemented
44C4×D188C2211yescharacteristic
45#13093986—21no—
46C22⋊C4×D47—21no—
47#13093958C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52#13093946C2211yescharacteristic, complemented
53#13093946C2211yescharacteristic, complemented
54C2×M16×C47C2211yescharacteristic
55C22×C8×C47C2211yescharacteristic, complemented
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—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71#10625350—22no—
72#10625350—22no—
73#10625350—22no—
74#10625350—41no—
75#10625350—41no—
76#10625350—41no—
77C2×D188—22no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—41no—
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×D188C2311yescharacteristic
85C2×D188C2311yescharacteristic
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×Dic94C2311yescharacteristic
91C2×Dic94C2311yescharacteristic
92M16×C47—22no—
93C2×C8×C47—22no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C4⋊C4×C47D411yescharacteristic
99C22⋊C4×C47D411yescharacteristic
100C22⋊C4×C47D411yescharacteristic
101C42×C47C2311yescharacteristic
102C22⋊Dic47—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109C4⋊Dic47C2311yescharacteristic
110C4⋊Dic47C2311yescharacteristic
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113C4×Dic47—21no—
114Dic188—22no—
115D376—22no—
116D376—22no—
117D376—22no—
118D376—41no—
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—21no—
128C22×D47—21no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—81no—
132D4×C47—41no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C22⋊D47—81no—
146C22⋊D47—81no—
147C22⋊D47—81no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—21no—
156D188—21no—
157D188—21no—
158D188—21no—
159D188—42no—
160D188—42no—
161D188—81no—
162D188C2×D412yes—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C4×D47—81no—
167Dic94—21no—
168Dic94—21no—
169Dic94—21no—
170Dic94C2×D412yes—
171C8×C47—21no—
172C8×C47—21no—
173C8×C47—21no—
174C8×C47C2×D412yes—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47C22×D411yescharacteristic
182C2×D47—22no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—21no—
199C4×C47C22×D411yescharacteristic
200C4×C47H(5,𝔽2)11yescharacteristic
201Dic47—22no—
202Dic47—41no—
203Dic47—41no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—41no—
207C2×C47—41no—
208C2×C47D4211yescharacteristic
209C2×C47#57511yescharacteristic
210C2×C47#57611yescharacteristic
211D47—42no—
212D47—81no—
213D47—81no—
214D47—81no—
215C2×AGL(1,ℤ/8)—471no—
216C2×#135—471no—
217#550—471no—
218#546—471no—
219#496—471no—
220#468—471no—
221#466—471no—
222#464—471no—
223#459—471no—
224#452—471no—
225#449—471no—
226#449—471no—
227#447—471no—
228#440—471no—
229#435D4711yescharacteristic, complemented
230C47#326811yescharacteristic, complemented, Sylow
231C2×#41—471no—
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235AGL(1,ℤ/8)—944no—
236#135—944no—
237C2×Q16—471no—
238C2×SD16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×D8—471no—
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×M16C2×D4711yescharacteristic
247C22×C8C2×D4711yescharacteristic, complemented
248#127—471no—
249#127—941no—
250#124—471no—
251#123—941no—
252C22⋊Q8—471no—
253#121—471no—
254#121—471no—
255#121—471no—
256#121—941no—
257#121—941no—
258#121—941no—
259#120—941no—
260C4×Q8—471no—
261C4×D4—471no—
262C4×D4—941no—
263C4×D4C2×D4711yescharacteristic
264C2×C22⋊C4—941no—
265#107—471no—
266C4⋊C8C2×D4711yescharacteristic, complemented
267#103—471no—
268#103—471no—
269#102—471no—
270#102—471no—
271#102—471no—
272#102—471no—
273C22⋊C8C2×D4711yescharacteristic
274C22⋊C8C2×D4711yescharacteristic, complemented
275#97C2×D4711yescharacteristic, complemented
276C24—941no—
277#41—942no—
278#41—942no—
279#41—942no—
280#41—1881no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8—471no—
285C2×D4—471no—
286C2×D4—471no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—942no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—1881no—
300C2×D4D18811yescharacteristic
301C22×C4—941no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306C22×C4C22×D4711yescharacteristic
307Q16—942no—
308SD16—474no—
309SD16—942no—
310SD16—942no—
311SD16—1881no—
312D8—942no—
313D8—942no—
314D8—942no—
315D8—1881no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D4711yescharacteristic
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C4⋊C4D18811yescharacteristic
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4D18811yescharacteristic
335C22⋊C4D18811yescharacteristic
336C42—941no—
337C42C22×D4711yescharacteristic
338C23—941no—
339C23—941no—
340C23—941no—
341C23—941no—
342C23—3761no—
343C23—1882no—
344C23—1882no—
345C23C2×D18811yescharacteristic
346C23C2×D18811yescharacteristic
347Q8—472no—
348Q8—941no—
349Q8—941no—
350Q8—941no—
351D4—41no—
352D4—472no—
353D4—941no—
354D4—941no—
355D4—941no—
356D4—941no—
357D4—941no—
358D4—941no—
359D4—941no—
360D4—3761no—
361D4—3761no—
362D4—3761no—
363D4—3761no—
364D4—1882no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4—1882no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—3761no—
378C2×C4—1882no—
379C2×C4—1882no—
380C2×C4—1882no—
381C2×C4C2×D18811yescharacteristic
382C2×C4C2×D18811yescharacteristic
383C2×C4C2×D18811yescharacteristic
384C2×C4C2×D18811yescharacteristic
385C2×C4C23×D4711yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D4712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—942no—
397C22—3764no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22—1881no—
402C22—1881no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22C22×D18811yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—942no—
415C4—1881no—
416C4—1881no—
417C4—1881no—
418C4C2×D4×D4711yescharacteristic
419C4#1309407011yescharacteristic
420C2—41no—
421C2—41no—
422C2—3761no—
423C2—3761no—
424C2—3761no—
425C2—1882no—
426C2D4×D18811yescharacteristic
427C2#1568992311yescharacteristic
428C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3268
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×#13094052C2semidirect
2. C2×#13094046C2semidirect
3. #15689794C2semidirect
4. #15689769C2semidirect
5. #15689512C2semidirect
6. #15689369C2semidirect
7. #15689359C2semidirect
8. #15689346C2semidirect
9. #15689319C2semidirect
10. #15689287C2semidirect
11. #15689270C2semidirect
12. #15689270C2semidirect
13. #15689259C2semidirect
14. #15689225C2semidirect
15. C47×#435C2semidirect
18. C2×#10625350C22semidirect
22. C2×Dic188C22semidirect
25. C2×#10625325C22semidirect
26. C2×#10625325C22semidirect
31. #13094021C22semidirect
38. #13093998C22semidirect
43. C4×Dic94C22semidirect
47. #13093958C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
52. #13093946C22semidirect
53. #13093946C22semidirect
55. C22×C8×C47C22semidirect
57. C4⋊C8×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. #97×C47C22semidirect
122. #10625325D4semidirect
229. #435D47semidirect
230. C47#3268semidirect
247. C22×C8C2×D47semidirect
266. C4⋊C8C2×D47semidirect
274. C22⋊C8C2×D47semidirect
275. #97C2×D47semidirect