Finite Group Databasebeta

← #20252669

Subgroups — #20252669

Order 6016.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094072C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic, complemented
3C2×SD16×D47C211yesmaximal, characteristic, complemented
4#15689689C211yesmaximal, characteristic, complemented
5#15689271C211yesmaximal, characteristic, complemented
6#15689270C211yesmaximal, characteristic, complemented
7#15689267C211yesmaximal, characteristic, complemented
8#15689266C211yesmaximal, characteristic, complemented
9#15689263C211yesmaximal, characteristic, complemented
10#15689262C211yesmaximal, characteristic, complemented
11#15689260C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#448C211yesmaximal, characteristic, complemented
16#13094072—24no—
17#13094072—24no—
18C2×#10625354—21no—
19C2×#10625354C2211yescharacteristic
20C2×#10625354C2211yescharacteristic, complemented
21C2×#10625350—21no—
22C2×#10625350—21no—
23C2×#10625350C2211yescharacteristic
24C2×#10625350C2211yescharacteristic, complemented
25C2×Q8×D47—21no—
26C2×Q8×D47C2211yescharacteristic
27C2×Q8×D47C2211yescharacteristic, complemented
28C2×D4×D47C2211yescharacteristic
29#13094051—24no—
30C2×#10625325C2211yescharacteristic
31C2×#10625335C2211yescharacteristic
32C2×#10625336C2211yescharacteristic
33C2×#10625336C2211yescharacteristic
34SD16×D47—24no—
35C2×D376C2211yescharacteristic
36C2×#10625334C2211yescharacteristic
37C2×#10625324C2211yescharacteristic
38C2×C8×D47C2211yescharacteristic
39#13094020—21no—
40#13094010—21no—
41#13093999C2211yescharacteristic
42#13093998C2211yescharacteristic
43#13093995C2211yescharacteristic
44#13093994—21no—
45#13093992—21no—
46#13093982C2211yescharacteristic
47#13093949C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#13093944C2211yescharacteristic, complemented
53C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55(C2×D47)⋊C8C2211yescharacteristic, complemented
56C22×Q8×C47C2211yescharacteristic, complemented
57C2×SD16×C47C2211yescharacteristic
58C2×SD16×C47C2211yescharacteristic
59#121×C47C2211yescharacteristic
60#103×C47C2211yescharacteristic, complemented
61#103×C47C2211yescharacteristic, complemented
62C22⋊C8×C47C2211yescharacteristic, complemented
63C23×D47—21no—
64C2×Q8×C47—22no—
65C2×Q8×C47—22no—
66C2×Q8×C47—21no—
67C2×Q8×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47D411yescharacteristic
78C2×C22⋊D47D411yescharacteristic
79#10625354—28no—
80#10625354—22no—
81#10625354—22no—
82#10625354—22no—
83#10625354D414yescomplemented
84Q8×D47—28no—
85Q8×D47—22no—
86Q8×D47—22no—
87Q8×D47—22no—
88Q8×D47D414yescomplemented
89D4×D47—22no—
90D4×D47—22no—
91#10625350—28no—
92#10625350—28no—
93#10625350—22no—
94#10625350—22no—
95#10625350—22no—
96#10625350—22no—
97C2×D188—21no—
98C2×D188—21no—
99C2×D188—21no—
100C2×D188D411yescharacteristic
101C2×D188C2311yescharacteristic
102C2×D188C2311yescharacteristic
103C2×C4×D47—21no—
104C2×C4×D47—21no—
105C2×C4×D47—21no—
106C2×C4×D47—21no—
107C2×C4×D47—21no—
108C2×C4×D47C2311yescharacteristic
109C2×C4×D47C2311yescharacteristic
110C2×Dic94—21no—
111C2×Dic94—21no—
112C2×Dic94D411yescharacteristic
113C2×Dic94C2311yescharacteristic
114SD16×C47—22no—
115SD16×C47—22no—
116C2×C8×C47C2311yescharacteristic
117C2×C8×C47C2311yescharacteristic
118C4⋊C4×C47C2311yescharacteristic
119C22⋊C4×C47—21no—
120C22⋊Dic47—21no—
121#10625336—22no—
122#10625336—22no—
123#10625335—22no—
124#10625334—22no—
125(C2×D47)⋊C4—21no—
126(C2×D47)⋊C4—21no—
127(C2×D47)⋊C4—21no—
128C4⋊Dic47C2311yescharacteristic
129C4×Dic47—21no—
130C2×C47⋊C8C2311yescharacteristic
131C2×C47⋊C8C2311yescharacteristic
132D376—22no—
133#10625325—22no—
134#10625324—22no—
135C8×D47—22no—
136C23×C47—21no—
137C23×C47C2×D411yescharacteristic
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—42no—
141C22×D47—81no—
142C22×D47—81no—
143C22×D47C2×D411yescharacteristic
144C22×D47C2×D411yescharacteristic
145Q8×C47—24no—
146Q8×C47—21no—
147Q8×C47—21no—
148Q8×C47C2×D412yes—
149Q8×C47C2×D412yes—
150D4×C47—21no—
151D4×C47—21no—
152D4×C47—81no—
153C2×C4×C47—24no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47C2×D411yescharacteristic
160C2×C4×C47C2411yescharacteristic
161C22⋊D47—24no—
162C22⋊D47—22no—
163C22⋊D47—22no—
164C22⋊D47—42no—
165C22⋊D47—81no—
166C22⋊D47—81no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47C2×D411yescharacteristic
170C2×Dic47C2×D411yescharacteristic
171D188—24no—
172D188—24no—
173D188—22no—
174D188—21no—
175D188—21no—
176D188—21no—
177D188—81no—
178D188C2×D412yes—
179C4×D47—24no—
180C4×D47—24no—
181C4×D47—24no—
182C4×D47—24no—
183C4×D47—21no—
184C4×D47—21no—
185C4×D47—24no—
186C4×D47C2×D412yes—
187C4×D47C2×D412yes—
188Dic94—24no—
189Dic94—21no—
190Dic94—24no—
191Dic94—22no—
192Dic94C2×D412yes—
193C8×C47—21no—
194C8×C47—21no—
195C47⋊C8—21no—
196C47⋊C8—21no—
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47C22×D411yescharacteristic
204C2×D47—21no—
205C2×D47—21no—
206C2×D47—21no—
207C2×D47—22no—
208C2×D47—21no—
209C2×D47—21no—
210C2×D47—41no—
211C2×D47—41no—
212C2×D47—41no—
213C2×D47—41no—
214C2×D47—41no—
215C2×D47—84no—
216C2×D47#12012yes—
217C4×C47—22no—
218C4×C47—22no—
219C4×C47—21no—
220C4×C47—41no—
221C4×C47C22×D411yescharacteristic
222C4×C47C22×D411yescharacteristic
223Dic47—21no—
224Dic47—22no—
225Dic47—41no—
226Dic47#12012yes—
227#3010—471nomaximal, Sylow
228C2×C47—41no—
229C2×C47—81no—
230C2×C47C2×#12011yescharacteristic
231C2×C47#57711yescharacteristic
232C2×C47#57711yescharacteristic
233D47—22no—
234D47—41no—
235D47—42no—
236D47—81no—
237C2×2−1+4—471no—
238C2×AGL(1,ℤ/8)—471no—
239C22×SD16—471no—
240#535—471no—
241#449—471no—
242#449—471no—
243#449—471no—
244#449—471no—
245#448—471no—
246#448—471no—
247#448—471no—
248#448D4711yescharacteristic, complemented
249#419—471no—
250#416—471no—
251#408—471no—
252C47#301011yescharacteristic, complemented, Sylow
2532−1+4—944no—
2542−1+4—944no—
255C2×#41—471no—
256C2×#41—471no—
257C2×#41—471no—
258C2×#41—471no—
259C2×#41—941no—
260C2×#41—941no—
261C2×#41—941no—
262C22×Q8—471no—
263C22×Q8—471no—
264C22×Q8—941no—
265C22×Q8C2×D4711yescharacteristic, complemented
266C22×D4—471no—
267AGL(1,ℤ/8)—944no—
268C2×SD16—471no—
269C2×SD16—471no—
270C2×SD16—471no—
271C2×SD16—471no—
272C2×SD16—944no—
273C2×SD16C2×D4711yescharacteristic
274C2×SD16C2×D4711yescharacteristic
275C2×D8—471no—
276C2×D8—471no—
277C2×M16—471no—
278C22×C8—471no—
279#127—941no—
280#124—941no—
281#121—471no—
282#121—471no—
283#121—471no—
284#121C2×D4711yescharacteristic
285#120—941no—
286#120—941no—
287#117—471no—
288#103—471no—
289#103—471no—
290#103—471no—
291#103—471no—
292#103C2×D4711yescharacteristic, complemented
293#103C2×D4711yescharacteristic, complemented
294#102—471no—
295#102—471no—
296C22⋊C8—471no—
297C22⋊C8—471no—
298C22⋊C8—471no—
299C22⋊C8C2×D4711yescharacteristic, complemented
300C24—941no—
301#41—474no—
302#41—942no—
303#41—942no—
304#41—942no—
305#41—942no—
306#41—948no—
307#41—948no—
308#41—942no—
309#41—942no—
310#41—948no—
311#41—942no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—21no—
315C2×Q8—471no—
316C2×Q8—474no—
317C2×Q8—471no—
318C2×Q8—941no—
319C2×Q8—941no—
320C2×Q8—942no—
321C2×Q8—942no—
322C2×Q8—948no—
323C2×Q8—942no—
324C2×Q8C22×D4711yescharacteristic
325C2×Q8C22×D4711yescharacteristic
326C2×D4—21no—
327C2×D4—471no—
328C2×D4—471no—
329C2×D4—471no—
330C2×D4—471no—
331C2×D4—471no—
332C2×D4—941no—
333C2×D4—941no—
334C2×D4—941no—
335C2×D4—942no—
336C2×D4—942no—
337C2×D4—941no—
338C2×D4—941no—
339C2×D4—941no—
340C2×D4—941no—
341C2×D4C22×D4711yescharacteristic
342C22×C4—21no—
343C22×C4—471no—
344C22×C4—471no—
345C22×C4—941no—
346C22×C4—941no—
347C22×C4—941no—
348C22×C4—941no—
349C22×C4—941no—
350C22×C4C22×D4711yescharacteristic
351SD16—22no—
352SD16—22no—
353SD16—942no—
354SD16—942no—
355SD16—942no—
356SD16—942no—
357D8—942no—
358D8—942no—
359M16—942no—
360C2×C8—471no—
361C2×C8—471no—
362C2×C8—942no—
363C2×C8C22×D4711yescharacteristic
364C2×C8C22×D4711yescharacteristic
365C4⋊C4—471no—
366C4⋊C4C22×D4711yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—941no—
369C22⋊C4—941no—
370C22⋊C4—941no—
371C22⋊C4—941no—
372C42—941no—
373C23—21no—
374C23—471no—
375C23—471no—
376C23—941no—
377C23—941no—
378C23—3761no—
379C23—3761no—
380C23—1882no—
381C23D4×D4711yescharacteristic
382Q8—24no—
383Q8—21no—
384Q8—21no—
385Q8—472no—
386Q8—944no—
387Q8—942no—
388Q8—944no—
389Q8—941no—
390Q8D4×D4712yes—
391Q8D4×D4712yes—
392D4—21no—
393D4—21no—
394D4—81no—
395D4—472no—
396D4—942no—
397D4—944no—
398D4—944no—
399D4—942no—
400D4—942no—
401D4—944no—
402D4—941no—
403D4—941no—
404D4—941no—
405D4—3761no—
406D4—3761no—
407D4—3761no—
408D4—1882no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—471no—
416C2×C4—472no—
417C2×C4—472no—
418C2×C4—471no—
419C2×C4—944no—
420C2×C4—944no—
421C2×C4—944no—
422C2×C4—944no—
423C2×C4—944no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4D4×D4711yescharacteristic
429C2×C4C23×D4711yescharacteristic
430C8—21no—
431C8—21no—
432C8—941no—
433C8—941no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—472no—
441C22—941no—
442C22—941no—
443C22—942no—
444C22—941no—
445C22—941no—
446C22—941no—
447C22—3764no—
448C22—1881no—
449C22—1881no—
450C22—1881no—
451C22—1881no—
452C22—1881no—
453C22C2×D4×D4711yescharacteristic
454C4—22no—
455C4—22no—
456C4—21no—
457C4—41no—
458C4—472no—
459C4—941no—
460C4—942no—
461C4—1881no—
462C4C2×D4×D4711yescharacteristic
463C4C2×D4×D4711yescharacteristic
464C2—41no—
465C2—81no—
466C2—942no—
467C2—3761no—
468C2—1881no—
469C2—1882no—
470C2#120×D4711yescharacteristic
471C2#1568992911yescharacteristic
472C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#448C2
socleC22×C47C22×D4
hypercenter#448D47
hypocenterC47#3010
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. C2×#13094051C2semidirect
3. C2×SD16×D47C2semidirect
4. #15689689C2semidirect
5. #15689271C2semidirect
6. #15689270C2semidirect
7. #15689267C2semidirect
8. #15689266C2semidirect
9. #15689263C2semidirect
10. #15689262C2semidirect
11. #15689260C2semidirect
12. #15689130C2semidirect
13. #15689118C2semidirect
14. #15689088C2semidirect
15. C47×#448C2semidirect
20. C2×#10625354C22semidirect
24. C2×#10625350C22semidirect
27. C2×Q8×D47C22semidirect
47. #13093949C22semidirect
48. #13093948C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
51. #13093946C22semidirect
52. #13093944C22semidirect
53. C22⋊(C47⋊C8)C22semidirect
54. (C2×D47)⋊C8C22semidirect
55. (C2×D47)⋊C8C22semidirect
56. C22×Q8×C47C22semidirect
60. #103×C47C22semidirect
61. #103×C47C22semidirect
62. C22⋊C8×C47C22semidirect
83. #10625354D4semidirect
88. Q8×D47D4semidirect
248. #448D47semidirect
252. C47#3010semidirect
265. C22×Q8C2×D47semidirect
292. #103C2×D47semidirect
293. #103C2×D47semidirect
299. C22⋊C8C2×D47semidirect