Finite Group Databasebeta

← #20255159

Subgroups — #20255159

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689938C211yesmaximal, characteristic, complemented
2#15689931C211yesmaximal, characteristic, complemented
3#15689930C211yesmaximal, characteristic, complemented
4#15689516C211yesmaximal, characteristic, complemented
5#15689396C211yesmaximal, characteristic, complemented
6#15689395C211yesmaximal, characteristic, complemented
7#15689388C211yesmaximal, characteristic, complemented
8#15689386C211yesmaximal, characteristic, complemented
9#15689306C211yesmaximal, characteristic, complemented
10#15689304C211yesmaximal, characteristic, complemented
11#15689299C211yesmaximal, characteristic, complemented
12#15689296C211yesmaximal, characteristic, complemented
13#15689245C211yesmaximal, characteristic, complemented
14#15689243C211yesmaximal, characteristic, complemented
15C47×#578C211yesmaximal, characteristic, complemented
16#13094071C2211yescharacteristic
17#13094070C2211yescharacteristic
18#13094056—21no—
19#13094055—21no—
20#13094055—21no—
21#13094055C2211yescharacteristic
22#13094055C2211yescharacteristic
23#13094054—21no—
24#13094054C2211yescharacteristic
25#13094054C2211yescharacteristic, complemented
26#13094049—21no—
27#13094049C2211yescharacteristic
28#13094049C2211yescharacteristic
29#13094048—21no—
30#13094045—21no—
31#13094044—21no—
32#13094044—21no—
33#13094044C2211yescharacteristic
34C2×#10625337—21no—
35C2×#10625337C2211yescharacteristic, complemented
36C2×#10625325C2211yescharacteristic
37C2×#10625336—21no—
38C2×#10625336C2211yescharacteristic
39SD16×D47—21no—
40#13094031C2211yescharacteristic
41#13094031C2211yescharacteristic, complemented
42#13094030C2211yescharacteristic
43#13094022C2211yescharacteristic, complemented
44#13094013C2211yescharacteristic
45#13093960C2211yescharacteristic, complemented
46#13093959C2211yescharacteristic, complemented
47#13093951C2211yescharacteristic
48#13093951C2211yescharacteristic, complemented
49#13093951C2211yescharacteristic, complemented
50#13093950C2211yescharacteristic
51#13093943C2211yescharacteristic, complemented
52#13093943C2211yescharacteristic, complemented
53#13093942C2211yescharacteristic, complemented
54#13093940C2211yescharacteristic
55#13093934C2211yescharacteristic, complemented
562−1+4×C47C2211yescharacteristic
572−1+4×C47C2211yescharacteristic, complemented
58#137×C47—21no—
59#137×C47—21no—
60#137×C47C2211yescharacteristic
61#137×C47C2211yescharacteristic, complemented
62#135×C47—21no—
63#135×C47C2211yescharacteristic
64C2×Q16×C47—21no—
65C2×Q16×C47C2211yescharacteristic, complemented
66#131×C47C2211yescharacteristic, complemented
67#41×C47—21no—
68#41×C47—21no—
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—41no—
72#41×C47—41no—
73#41×C47C2311yescharacteristic
74#41×C47C2311yescharacteristic
75#41×C47C2311yescharacteristic
76C2×Q8×C47—21no—
77C2×Q8×C47—21no—
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47C2311yescharacteristic
81C2×Q8×C47C2311yescharacteristic
82#10625354—21no—
83Q8×D47—21no—
84#10625352—21no—
85#10625352—41no—
86D4×D47—21no—
87D4×D47—41no—
88#10625350—21no—
89#10625350—21no—
90#10625350C2311yescharacteristic
91C2×D188—21no—
92C2×D188C2311yescharacteristic
93C2×Dic94—21no—
94C2×Dic94C2311yescharacteristic
95Q16×C47—21no—
96Q16×C47—21no—
97Q16×C47—21no—
98Q16×C47—21no—
99Q16×C47D411yescharacteristic
100SD16×C47—21no—
101SD16×C47—21no—
102SD16×C47D411yescharacteristic
103SD16×C47D411yescharacteristic
104D8×C47D411yescharacteristic
105M16×C47—21no—
106M16×C47C2311yescharacteristic
107C2×C8×C47—21no—
108C2×C8×C47C2311yescharacteristic
109#10625337—21no—
110#10625337—21no—
111#10625337—21no—
112#10625337—21no—
113#10625337—21no—
114#10625337—21no—
115#10625337D411yescharacteristic
116#10625336—21no—
117#10625336—21no—
118#10625336—21no—
119#10625336—21no—
120#10625336—21no—
121#10625336—21no—
122#10625336D411yescharacteristic
123#10625335—21no—
124#10625335—21no—
125#10625335D411yescharacteristic
126#10625334—21no—
127#10625334—21no—
128#10625334D411yescharacteristic
129(C2×D47)⋊C4—41no—
130Dic47⋊C4—41no—
131C4×Dic47C2311yescharacteristic
132#10625329—21no—
133#10625329—21no—
134#10625329C2311yescharacteristic
135#10625329C2311yescharacteristic
136#10625329C2311yescharacteristic
137C2×C47⋊C8—21no—
138C2×C47⋊C8—21no—
139C2×C47⋊C8C2311yescharacteristic
140#10625325—21no—
141#10625325—21no—
142#10625324—21no—
143C8×D47—21no—
144C22×D47—21no—
145C22×D47—41no—
146Q8×C47—21no—
147Q8×C47—21no—
148Q8×C47—21no—
149Q8×C47—21no—
150Q8×C47—41no—
151Q8×C47—41no—
152Q8×C47C2×D411yescharacteristic
153Q8×C47C2×D411yescharacteristic
154Q8×C47C2×D411yescharacteristic
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47—41no—
159D4×C47—41no—
160D4×C47C2×D411yescharacteristic
161D4×C47C2×D411yescharacteristic
162D4×C47C2×D411yescharacteristic
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47C2411yescharacteristic
173C22⋊D47—21no—
174C22⋊D47—41no—
175C22⋊D47—41no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—41no—
179D188—21no—
180D188—21no—
181D188—41no—
182D188C2×D411yescharacteristic
183C4×D47—21no—
184C4×D47—41no—
185C4×D47—41no—
186Dic94—21no—
187Dic94—21no—
188Dic94—41no—
189Dic94C2×D411yescharacteristic
190C8×C47—21no—
191C8×C47C2×D411yescharacteristic
192C8×C47C2×D411yescharacteristic
193C47⋊C8—21no—
194C47⋊C8—21no—
195C47⋊C8—21no—
196C47⋊C8C2×D411yescharacteristic
197C47⋊C8C2×D411yescharacteristic
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47H(5,𝔽2)11yescharacteristic
202C2×D47—21no—
203C2×D47—41no—
204C2×D47—81no—
205C2×D47—161no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—41no—
210C4×C47—41no—
211C4×C47C22×D411yescharacteristic
212C4×C47C22×D411yescharacteristic
213Dic47—21no—
214Dic47—41no—
215Dic47—41no—
216#3289—471nomaximal, Sylow
217C2×C47—21no—
218C2×C47—41no—
219C2×C47—41no—
220C2×C47—41no—
221C2×C47D4211yescharacteristic
222D47—41no—
223D47—81no—
224#578—471no—
225#578D4711yescharacteristic, complemented
226#577—471no—
227#577—471no—
228#497—471no—
229#473—471no—
230#473—471no—
231#471—471no—
232#471—471no—
233#456—471no—
234#456—471no—
235#455—471no—
236#454—471no—
237#444—471no—
238#444—471no—
239C47#328911yescharacteristic, complemented, Sylow
2402−1+4—471no—
2412−1+4C2×D4711yescharacteristic
2422−1+4C2×D4711yescharacteristic, complemented
243H(5,𝔽2)—471no—
244#137—21no—
245#137—21no—
246#137—471no—
247#137—471no—
248#137—471no—
249#137—471no—
250#137—941no—
251#137—941no—
252#137—941no—
253#137—941no—
254#137C2×D4711yescharacteristic
255#137C2×D4711yescharacteristic, complemented
256AGL(1,ℤ/8)—471no—
257AGL(1,ℤ/8)—471no—
258AGL(1,ℤ/8)—941no—
259AGL(1,ℤ/8)—941no—
260#135—21no—
261#135—471no—
262#135—941no—
263#135—941no—
264#135—941no—
265#135C2×D4711yescharacteristic
266C2×Q16—21no—
267C2×Q16—471no—
268C2×Q16—941no—
269C2×Q16C2×D4711yescharacteristic, complemented
270C2×SD16—471no—
271C2×SD16—471no—
272C2×SD16—941no—
273C2×SD16—941no—
274#131—471no—
275#131—471no—
276#131—471no—
277#131C2×D4711yescharacteristic, complemented
278C4⋊Q8—471no—
279#124—471no—
280#108—471no—
281#108—471no—
282#104—471no—
283#104—471no—
284#104—471no—
285#104—471no—
286#101—471no—
287#101—471no—
288#101—471no—
289#100—471no—
290#97—471no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—41no—
297#41—471no—
298#41—941no—
299#41—941no—
300#41—941no—
301#41—941no—
302#41—1881no—
303#41C22×D4711yescharacteristic
304#41C22×D4711yescharacteristic
305#41C22×D4711yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—471no—
311C2×Q8—941no—
312C2×Q8—941no—
313C2×Q8C22×D4711yescharacteristic
314C2×Q8C22×D4711yescharacteristic
315C2×D4—471no—
316C2×D4—941no—
317C2×D4—941no—
318C2×D4—1881no—
319Q16—21no—
320Q16—21no—
321Q16—21no—
322Q16—21no—
323Q16—471no—
324Q16—941no—
325Q16—941no—
326Q16—941no—
327Q16—941no—
328Q16—941no—
329Q16—941no—
330Q16C22⋊D4711yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—471no—
334SD16—471no—
335SD16—941no—
336SD16—941no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16—941no—
345SD16C22⋊D4711yescharacteristic
346SD16C22⋊D4711yescharacteristic
347D8—471no—
348D8—941no—
349D8—941no—
350D8C22⋊D4711yescharacteristic
351M16—21no—
352M16—471no—
353M16—471no—
354M16—471no—
355M16—941no—
356M16—941no—
357M16—941no—
358M16C22×D4711yescharacteristic
359C2×C8—21no—
360C2×C8—471no—
361C2×C8—941no—
362C2×C8—941no—
363C2×C8—941no—
364C2×C8C22×D4711yescharacteristic
365C4⋊C4—1881no—
366C22⋊C4—1881no—
367C42—471no—
368C23—941no—
369C23—1881no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—41no—
376Q8—471no—
377Q8—941no—
378Q8—941no—
379Q8—1881no—
380Q8D4×D4711yescharacteristic
381Q8C2×C22⋊D4711yescharacteristic
382Q8C2×C22⋊D4711yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—471no—
389D4—941no—
390D4—941no—
391D4—941no—
392D4—1881no—
393D4—1881no—
394D4—1881no—
395D4D4×D4711yescharacteristic
396D4C2×C22⋊D4711yescharacteristic
397D4C2×C22⋊D4711yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—1881no—
411C2×C4—1881no—
412C2×C4—1881no—
413C2×C4C23×D4711yescharacteristic
414C8—21no—
415C8—471no—
416C8—471no—
417C8—941no—
418C8—941no—
419C8—941no—
420C8C2×C22⋊D4711yescharacteristic
421C8C2×C22⋊D4711yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—941no—
426C22—3761no—
427C22—1881no—
428C22—7521no—
429C22#1309406911yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—941no—
436C4—1881no—
437C4—1881no—
438C4C2×D4×D4711yescharacteristic
439C4C22×C22⋊D4711yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—3761no—
445C2—1881no—
446C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#578C2
socleC2×C47D42
hypercenter#578D47
hypocenterC47#3289
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #15689938C2semidirect
2. #15689931C2semidirect
3. #15689930C2semidirect
4. #15689516C2semidirect
5. #15689396C2semidirect
6. #15689395C2semidirect
7. #15689388C2semidirect
8. #15689386C2semidirect
9. #15689306C2semidirect
10. #15689304C2semidirect
11. #15689299C2semidirect
12. #15689296C2semidirect
13. #15689245C2semidirect
14. #15689243C2semidirect
15. C47×#578C2semidirect
25. #13094054C22semidirect
35. C2×#10625337C22semidirect
41. #13094031C22semidirect
43. #13094022C22semidirect
45. #13093960C22semidirect
46. #13093959C22semidirect
48. #13093951C22semidirect
49. #13093951C22semidirect
51. #13093943C22semidirect
52. #13093943C22semidirect
53. #13093942C22semidirect
55. #13093934C22semidirect
57. 2−1+4×C47C22semidirect
61. #137×C47C22semidirect
65. C2×Q16×C47C22semidirect
66. #131×C47C22semidirect
225. #578D47semidirect
239. C47#3289semidirect
242. 2−1+4C2×D47semidirect
255. #137C2×D47semidirect
269. C2×Q16C2×D47semidirect
277. #131C2×D47semidirect