Finite Group Databasebeta

← #20253754

Subgroups — #20253754

Order 6016.

372 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#15689753C211yesmaximal, characteristic, complemented
2#15689698C211yesmaximal, characteristic
3#15689490C211yesmaximal, characteristic, complemented
4#15689484C211yesmaximal, characteristic, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689480C211yesmaximal, characteristic, complemented
7#15689479C211yesmaximal, characteristic, complemented
8#15689473C211yesmaximal, characteristic, complemented
9#15689472C211yesmaximal, characteristic, complemented
10#15689130C211yesmaximal, characteristic, complemented
11#15689123C211yesmaximal, characteristic
12#15689118C211yesmaximal, characteristic
13#103×D47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#491C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094023—21no—
22#13094023C2211yescharacteristic
23#13094022C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094013C2211yescharacteristic
27#13094012C2211yescharacteristic
28#13094009—21no—
29#13094009—21no—
30#13094004—21no—
31#13094002—21no—
32#13094002—21no—
33#13094002—21no—
34#13093982C2211yescharacteristic
35#13093981C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093949C2211yescharacteristic
38#13093949C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61#10625354—22no—
62#10625354—22no—
63Q8×D47—22no—
64Q8×D47—22no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C42×C47C2311yescharacteristic
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
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—21no—
128D188—21no—
129D188—42no—
130C4×D47—42no—
131C4×D47—42no—
132C4×D47—81no—
133C4×D47#4112yes—
134C4×D47#4112yes—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138Dic94—81no—
139Dic94—81no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47#12412yes—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47C2×#4111yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47#12412yes—
165#3137—471nomaximal, Sylow
166C2×C47C2×#12411yescharacteristic
167C2×C47#57711yescharacteristic
168C2×C47#57811yescharacteristic
169D47—22no—
170D47—81no—
171#544—471no—
172#536—471no—
173#491—471no—
174#491D4711yescharacteristic, complemented
175#489—471no—
176#489—471no—
177#488—471no—
178#488—471no—
179#487—471no—
180#487—471no—
181#419—471no—
182#417—471no—
183#416—471no—
184C2×#103—471no—
185#405—471no—
186C47#313711yescharacteristic, complemented, Sylow
187C2×#41—471no—
188C22×Q8—471no—
189C2×M16—471no—
190C22×C8—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194C4⋊Q8—941no—
195C4⋊Q8C2×D4711yescharacteristic
196#125—471no—
197#125—941no—
198#125C2×D4711yescharacteristic
199#124—471no—
200#124—471no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204C22⋊Q8—941no—
205C22⋊Q8—941no—
206C22⋊Q8—941no—
207#117—471no—
208#117—471no—
209C2×C4⋊C4—471no—
210#103—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103C2×D4711yescharacteristic
219#103C2×D4711yescharacteristic
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226#97—471no—
227#97C2×D4711yescharacteristic
228C4×C8—471no—
229C4×C8—471no—
230#41—942no—
231#41—942no—
232C2×Q8—471no—
233C2×Q8—941no—
234C2×Q8—941no—
235C2×Q8—942no—
236C2×Q8—942no—
237C2×Q8—941no—
238C2×Q8C22×D4711yescharacteristic
239C2×Q8C22×D4711yescharacteristic
240C2×D4—471no—
241C2×D4—941no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246M16—942no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—942no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—471no—
270C22⋊C4—471no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—471no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—471no—
280C23—941no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—941no—
286Q8—941no—
287Q8—3761no—
288Q8—3761no—
289Q8—1882no—
290D4—941no—
291D4—941no—
292D4—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—471no—
298C2×C4—472no—
299C2×C4—472no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—3761no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—472no—
316C22—941no—
317C22—941no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—472no—
329C4—941no—
330C4—941no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4#41×D4711yescharacteristic
336C2—942no—
337C2—3761no—
338C2#124×D4711yescharacteristic
339C2#1568993211yescharacteristic
340C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #15689753C2semidirect
3. #15689490C2semidirect
4. #15689484C2semidirect
5. #15689483C2semidirect
6. #15689480C2semidirect
7. #15689479C2semidirect
8. #15689473C2semidirect
9. #15689472C2semidirect
10. #15689130C2semidirect
13. #103×D47C2semidirect
14. #15689080C2semidirect
15. C47×#491C2semidirect
174. #491D47semidirect
186. C47#3137semidirect