Finite Group Databasebeta

← #20253413

Subgroups — #20253413

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689658C211yesmaximal, characteristic, complemented
2C4×#10625354C211yesmaximal, characteristic, complemented
3#15689466C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689345C211yesmaximal, characteristic, complemented
7#15689339C211yesmaximal, characteristic, complemented
8#15689288C211yesmaximal, characteristic, complemented
9#15689271C211yesmaximal, characteristic
10#15689215C211yesmaximal, characteristic, complemented
11#15689210C211yesmaximal, characteristic, complemented
12#15689208C211yesmaximal, characteristic, complemented
13#15689205C211yesmaximal, characteristic, complemented
14#15689175C211yesmaximal, characteristic, complemented
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094019—21no—
22#13094012C2211yescharacteristic
23#13094009—21no—
24#13094004C2211yescharacteristic
25#13093999C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27#13093989C2211yescharacteristic
28C4×D188—21no—
29C4×D188C2211yescharacteristic
30#13093986—21no—
31#13093986—21no—
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093982—21no—
35#13093982—21no—
36#13093982C2211yescharacteristic
37C42×D47—21no—
38C42×D47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60#10625354—22no—
61#10625354—22no—
62C2×D188—21no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47D411yescharacteristic
71C2×C4×D47D411yescharacteristic
72C2×C4×D47C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84#10625337—22no—
85#10625336—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106D376—22no—
107#10625325—22no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111Q8×C47—21no—
112Q8×C47#4112yes—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125D188—24no—
126D188—21no—
127D188—21no—
128D188—21no—
129D188—42no—
130D188#4112yes—
131C4×D47—24no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—22no—
135C4×D47—41no—
136C4×D47—42no—
137C4×D47—42no—
138C4×D47—42no—
139Dic94—21no—
140Dic94—21no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47C22×D411yescharacteristic
146C2×D47—21no—
147C2×D47—22no—
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—22no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47#13512yes—
168#3102—471nomaximal, Sylow
169C2×C47#52511yescharacteristic
170C2×C47C2×#13511yescharacteristic
171C2×C47#57511yescharacteristic
172D47—41no—
173D47—42no—
174D47—81no—
175#529—471no—
176C4×#41—471no—
177#485—471no—
178#482—471no—
179#479D4711yescharacteristic, complemented
180#478—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185C4×Q16—471no—
186C4×SD16—471no—
187C4×SD16—471no—
188C4×D8—471no—
189#431—471no—
190C47#310211yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196#126—941no—
197#125C2×D4711yescharacteristic
198#124—471no—
199#123—941no—
200C22⋊Q8—471no—
201#121—471no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4—941no—
211#117—471no—
212#117—941no—
213#117—941no—
214C2×C42—471no—
215C2×C42—941no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#106—471no—
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221C4⋊C8C2×D4711yescharacteristic
222#103—471no—
223#103—471no—
224#103C2×D4711yescharacteristic
225#103C2×D4711yescharacteristic
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8—471no—
232C4×C8—471no—
233C4×C8—471no—
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—471no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4—941no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—21no—
276C42—471no—
277C42—471no—
278C42—471no—
279C42—941no—
280C42—941no—
281C42—941no—
282C42C22×D4711yescharacteristic
283C23—471no—
284C23—941no—
285C23—941no—
286Q8—21no—
287Q8—941no—
288Q8—941no—
289Q8#1062535412yes—
290D4—472no—
291D4—944no—
292D4—941no—
293D4—941no—
294D4—941no—
295D4—1882no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—942no—
304C2×C4—944no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—1881no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4D4×D4711yescharacteristic
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—942no—
321C22—941no—
322C22—941no—
323C22—941no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22C2×D4×D4711yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—472no—
337C4—941no—
338C4—941no—
339C4—1881no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4C2×#1062535411yescharacteristic
343C2—3761no—
344C2—1881no—
345C2—1882no—
346C2#1568963611yescharacteristic
347C2#135×D4711yescharacteristic
348C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #15689658C2semidirect
2. C4×#10625354C2semidirect
3. #15689466C2semidirect
4. #15689449C2semidirect
5. #15689420C2semidirect
6. #15689345C2semidirect
7. #15689339C2semidirect
8. #15689288C2semidirect
10. #15689215C2semidirect
11. #15689210C2semidirect
12. #15689208C2semidirect
13. #15689205C2semidirect
14. #15689175C2semidirect
15. C47×#479C2semidirect
179. #479D47semidirect
190. C47#3102semidirect