Finite Group Databasebeta

← #20255585

Subgroups — #20255585

Order 6016.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689817C211yesmaximal, characteristic, complemented
2#15689767C211yesmaximal, characteristic, complemented
3#15689476C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689337C211yesmaximal, characteristic, complemented
10#15689269C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689203C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#418C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625325C2211yescharacteristic, complemented
18C2×#10625334C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21#13094018—21no—
22#13094015C2211yescharacteristic, complemented
23#13094011C2211yescharacteristic
24#13094006—21no—
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13093999C2211yescharacteristic, complemented
28#13093998C2211yescharacteristic
29#13093997—21no—
30#13093996—21no—
31#13093995C2211yescharacteristic
32#13093993—21no—
33C4×D188—21no—
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic, complemented
36C4×C22⋊D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic, complemented
38C2×C22⋊Dic47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C24×C47—21no—
60C2×D4×C47—22no—
61C2×D4×C47—21no—
62C2×D4×C47—41no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72#10625352—22no—
73#10625352—41no—
74C2×D188—21no—
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47C2311yescharacteristic
79C2×Dic94C2311yescharacteristic
80M16×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C42×C47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47D411yescharacteristic
93#10625334—22no—
94#10625334—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625325—41no—
110#10625324—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C22×D47—21no—
118C22×D47C2×D411yescharacteristic
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123D4×C47#4112yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—41no—
131C22⋊D47—42no—
132C22⋊D47—81no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47—81no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142D188—21no—
143D188—21no—
144D188—42no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—81no—
148C4×D47—81no—
149Dic94—21no—
150Dic94—21no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—22no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—84no—
165C22×C47C22×D411yescharacteristic
166C2×D47—21no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47C2×#4111yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177Dic47—21no—
178Dic47—21no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3322—471nomaximal, Sylow
184C2×C47—41no—
185C2×C47—42no—
186C2×C47—81no—
187C2×C47#54611yescharacteristic
188C2×C47#57511yescharacteristic
189C2×C47#57611yescharacteristic
190D47—41no—
191D47—81no—
192#553—471no—
193#546—471no—
194#488—471no—
195#485—471no—
196#480—471no—
197#478—471no—
198#469—471no—
199#468—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203C4×D8—471no—
204#436—471no—
205#418D4711yescharacteristic, complemented
206#417—471no—
207C47#332211yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4C2×D4711yescharacteristic
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C2×M16—471no—
214C2×M16C2×D4711yescharacteristic
215#126—941no—
216#125—471no—
217#124—471no—
218#123—941no—
219#123—941no—
220C22⋊Q8—471no—
221#121—471no—
222#121—471no—
223#121—471no—
224#121—941no—
225#121—941no—
226#120—941no—
227C4×D4—471no—
228C4×D4—471no—
229C4×D4—471no—
230C4×D4—941no—
231#117C2×D4711yescharacteristic
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234#107—471no—
235#107—471no—
236#106—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102C2×D4711yescharacteristic
245#102C2×D4711yescharacteristic
246#102C2×D4711yescharacteristic
247#102C2×D4711yescharacteristic
248C22⋊C8—471no—
249C22⋊C8—471no—
250C4×C8—471no—
251C24—21no—
252#41—942no—
253#41—1881no—
254C2×Q8—471no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—471no—
259C2×D4—471no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4C22×D4711yescharacteristic
265C2×D4C22×D4711yescharacteristic
266C22×C4—471no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272SD16—1881no—
273D8—942no—
274D8—1881no—
275M16—41no—
276M16—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—471no—
292C22⋊C4—471no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—21no—
302C42—471no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—471no—
309C23—941no—
310C23D4×D4711yescharacteristic
311Q8—941no—
312Q8—941no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—941no—
318D4—941no—
319D4—3761no—
320D4—3761no—
321D4—1882no—
322D4—1881no—
323D4—1882no—
324D4#1062535012yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—471no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—3761no—
338C2×C4—3761no—
339C2×C4—3761no—
340C2×C4—1882no—
341C2×C4D4×D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—941no—
346C8—941no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—941no—
358C22—941no—
359C22—941no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—941no—
368C4—941no—
369C4—941no—
370C4—1881no—
371C4—1881no—
372C4—1881no—
373C4C2×#1062535011yescharacteristic
374C4#1309406911yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3761no—
379C2—1881no—
380C2#1568976311yescharacteristic
381C2#1568991911yescharacteristic
382C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3322
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689817C2semidirect
2. #15689767C2semidirect
3. #15689476C2semidirect
4. #15689464C2semidirect
5. #15689435C2semidirect
6. #15689421C2semidirect
7. #15689375C2semidirect
8. #15689369C2semidirect
9. #15689337C2semidirect
10. #15689269C2semidirect
11. #15689257C2semidirect
12. #15689203C2semidirect
13. #15689199C2semidirect
14. #15689121C2semidirect
15. C47×#418C2semidirect
17. C2×#10625325C22semidirect
20. C2×#10625324C22semidirect
22. #13094015C22semidirect
27. #13093999C22semidirect
35. #13093986C22semidirect
37. C4⋊C4×D47C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093955C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
45. #13093947C22semidirect
46. #13093946C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
205. #418D47semidirect
207. C47#3322semidirect