Finite Group Databasebeta

← #20255476

Subgroups — #20255476

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689833C211yesmaximal, characteristic, complemented
2#15689766C211yesmaximal, characteristic
3#15689482C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689404C211yesmaximal, characteristic, complemented
7#15689366C211yesmaximal, characteristic, complemented
8#15689361C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625324C2211yescharacteristic, complemented
20C2×C8×D47C2211yescharacteristic
21#13094024C2211yescharacteristic, complemented
22#13094016—21no—
23#13094006—21no—
24#13094002—21no—
25#13094002—21no—
26#13094000C2211yescharacteristic
27#13094000C2211yescharacteristic
28#13094000C2211yescharacteristic, complemented
29#13093997—21no—
30#13093995C2211yescharacteristic
31#13093994—21no—
32C4×D188—21no—
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C22⋊C4×D47—21no—
38#13093958C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093935C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65#10625354—22no—
66#10625354—41no—
67D4×D47—22no—
68D4×D47—41no—
69C2×D188—21no—
70C2×D188D411yescharacteristic
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79Q16×C47—41no—
80SD16×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47—21no—
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90#10625336—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47—21no—
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—81no—
116C22×D47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—22no—
138D188—21no—
139D188—42no—
140D188#4112yes—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—42no—
146C4×D47—81no—
147C4×D47—81no—
148C4×D47—81no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—22no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—84no—
167C2×D47#13712yes—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C2×#4111yescharacteristic
174C4×C47H(5,𝔽2)11yescharacteristic
175Dic47—21no—
176Dic47—21no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—81no—
182C2×C47#54611yescharacteristic
183C2×C47C2×#13711yescharacteristic
184C2×C47#57611yescharacteristic
185D47—22no—
186D47—41no—
187D47—42no—
188#554—471no—
189#546—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#474—471no—
194#468—471no—
195#467—471no—
196#464D4711yescharacteristic, complemented
197#452—471no—
198#450—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4—471no—
206C2×Q16C2×D4711yescharacteristic, complemented
207C2×SD16—471no—
208C2×SD16C2×D4711yescharacteristic
209C2×M16—471no—
210C22×C8—471no—
211C4⋊Q8—471no—
212#125—941no—
213#124C2×D4711yescharacteristic
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218C22⋊Q8—941no—
219C22⋊Q8—941no—
220#121—471no—
221#121—941no—
222#120—941no—
223C4×Q8C2×D4711yescharacteristic, complemented
224C4×D4—471no—
225C4×D4—471no—
226C4×D4—941no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—941no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8C2×D4711yescharacteristic, complemented
234#103—471no—
235#103—471no—
236#103—471no—
237#103C2×D4711yescharacteristic, complemented
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—941no—
251C2×Q8C22×D4711yescharacteristic
252C2×Q8C22×D4711yescharacteristic
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4C22×D4711yescharacteristic
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267Q16—41no—
268SD16—41no—
269SD16—942no—
270M16—1881no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—1881no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—21no—
298C42C22×D4711yescharacteristic
299C23—21no—
300C23—471no—
301C23—471no—
302C23—941no—
303C23—3761no—
304C23—1882no—
305C23—1882no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—3761no—
311D4—21no—
312D4—21no—
313D4—472no—
314D4—942no—
315D4—941no—
316D4—3761no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—1882no—
335C2×C4D4×D4711yescharacteristic
336C2×C4D4×D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—941no—
341C8—941no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—472no—
346C22—941no—
347C22—941no—
348C22—941no—
349C22—942no—
350C22—941no—
351C22—941no—
352C22—3764no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—941no—
362C4—941no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309406911yescharacteristic
368C2—81no—
369C2—942no—
370C2—1881no—
371C2—1882no—
372C2#1568977011yescharacteristic
373C2#137×D4711yescharacteristic
374C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #15689833C2semidirect
3. #15689482C2semidirect
4. #15689457C2semidirect
5. #15689435C2semidirect
6. #15689404C2semidirect
7. #15689366C2semidirect
8. #15689361C2semidirect
9. #15689284C2semidirect
10. #15689272C2semidirect
11. #15689221C2semidirect
12. #15689193C2semidirect
13. #15689123C2semidirect
14. #102×D47C2semidirect
15. C47×#464C2semidirect
19. C2×#10625324C22semidirect
21. #13094024C22semidirect
28. #13094000C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093958C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
43. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. C2×Q16×C47C22semidirect
55. C4×Q8×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
196. #464D47semidirect
203. C47#3314semidirect
206. C2×Q16C2×D47semidirect
223. C4×Q8C2×D47semidirect
233. C4⋊C8C2×D47semidirect
237. #103C2×D47semidirect