Finite Group Databasebeta

← #20253457

Subgroups — #20253457

Order 6016.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2C4×#10625354C211yesmaximal, characteristic
3#15689466C211yesmaximal, characteristic, complemented
4#15689462C211yesmaximal, characteristic, complemented
5#15689406C211yesmaximal, characteristic, complemented
6#15689402C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689327C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic
10#15689284C211yesmaximal, characteristic
11C4×#10625337C211yesmaximal, characteristic, complemented
12C4×#10625325C211yesmaximal, characteristic, complemented
13C4×#10625336C211yesmaximal, characteristic, complemented
14#15689174C211yesmaximal, characteristic, complemented
15C4×Q16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094014—21no—
23#13094004C2211yescharacteristic
24#13094002—21no—
25#13094000C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94C2211yescharacteristic
29C4×D188—21no—
30C4×D188C2211yescharacteristic
31#13093986—21no—
32#13093986C2211yescharacteristic
33#13093982—21no—
34#13093982C2211yescharacteristic
35#13093981—21no—
36C42×D47—21no—
37C42×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61#10625354—22no—
62#10625354—22no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47D411yescharacteristic
69C2×C4×D47D411yescharacteristic
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73Q16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C42×C47—21no—
81C42×C47—21no—
82C42×C47C2311yescharacteristic
83#10625337—22no—
84#10625336—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—24no—
128D188—21no—
129D188#4112yes—
130C4×D47—24no—
131C4×D47—22no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—22no—
135C4×D47—42no—
136C4×D47—42no—
137Dic94—21no—
138Dic94—21no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—21no—
146C2×D47—22no—
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—22no—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47#13712yes—
157C4×C47C2×#4111yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47#13512yes—
165#3107—471nomaximal, Sylow
166C2×C47#52511yescharacteristic
167C2×C47C2×#13511yescharacteristic
168C2×C47C2×#13711yescharacteristic
169D47—41no—
170D47—42no—
171#533—471no—
172C4×#41—471no—
173#485—471no—
174#485—471no—
175#475—471no—
176#474—471no—
177#462—471no—
178#461—471no—
179#452—471no—
180#452—471no—
181C4×Q16—471no—
182C4×Q16D4711yescharacteristic, complemented
183C4×SD16—471no—
184C4×SD16—471no—
185#431—471no—
186C47#310711yescharacteristic, complemented, Sylow
187C2×#41—471no—
188C2×Q16—471no—
189C2×Q16C2×D4711yescharacteristic
190C2×SD16—471no—
191C2×SD16—471no—
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194#125—941no—
195C22⋊Q8—471no—
196C22⋊Q8—471no—
197C22⋊Q8—941no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—941no—
201C4×Q8C2×D4711yescharacteristic
202C4×Q8C2×D4711yescharacteristic
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—941no—
206C4×D4—941no—
207#117—471no—
208#117—941no—
209#117—941no—
210C2×C42—471no—
211C2×C42—941no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#106—471no—
215#106—471no—
216C4⋊C8—471no—
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226C22⋊C8—471no—
227C22⋊C8—471no—
228C4×C8—471no—
229C4×C8C2×D4711yescharacteristic
230#41—942no—
231#41—942no—
232C2×Q8—471no—
233C2×Q8—941no—
234C2×Q8C22×D4711yescharacteristic
235C2×Q8C22×D4711yescharacteristic
236C2×D4—471no—
237C2×D4—941no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244Q16—22no—
245Q16—942no—
246SD16—942no—
247SD16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—21no—
272C42—471no—
273C42—471no—
274C42—471no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—471no—
280C23—941no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—941no—
285Q8—941no—
286Q8—1882no—
287Q8#1062535012yes—
288D4—472no—
289D4—944no—
290D4—941no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—944no—
300C2×C4—942no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—942no—
316C22—941no—
317C22—941no—
318C22—941no—
319C22—1881no—
320C22—1881no—
321C22C2×D4×D4711yescharacteristic
322C4—22no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—472no—
328C4—941no—
329C4—941no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#1309405612yes—
334C4#41×D4711yescharacteristic
335C4C2×#1062535011yescharacteristic
336C2—1881no—
337C2—1882no—
338C2#1568963211yescharacteristic
339C2#135×D4711yescharacteristic
340C2C2×#1309405611yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3107
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689466C2semidirect
4. #15689462C2semidirect
5. #15689406C2semidirect
6. #15689402C2semidirect
7. #15689331C2semidirect
8. #15689327C2semidirect
11. C4×#10625337C2semidirect
12. C4×#10625325C2semidirect
13. C4×#10625336C2semidirect
14. #15689174C2semidirect
15. C4×Q16×C47C2semidirect
182. C4×Q16D47semidirect
186. C47#3107semidirect