Finite Group Databasebeta

← #20254642

Subgroups — #20254642

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689750C211yesmaximal, characteristic, complemented
2#15689729C211yesmaximal, characteristic
3#15689522C211yesmaximal, characteristic, complemented
4#15689488C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689450C211yesmaximal, characteristic, complemented
7#15689449C211yesmaximal, characteristic, complemented
8#15689443C211yesmaximal, characteristic, complemented
9#15689438C211yesmaximal, characteristic, complemented
10#15689426C211yesmaximal, characteristic, complemented
11#15689422C211yesmaximal, characteristic, complemented
12#15689412C211yesmaximal, characteristic, complemented
13#15689402C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic, complemented
15C47×#501C211yesmaximal, characteristic, complemented
16#13094023C2211yescharacteristic
17#13094022—21no—
18#13094021C2211yescharacteristic
19#13094016C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094014—21no—
22#13094009—21no—
23#13094009—21no—
24#13094002—21no—
25#13094000—21no—
26#13093999—21no—
27#13093999—21no—
28#13093999C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093986C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35#13093957C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093955C2211yescharacteristic
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093946C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D188—21no—
61C2×D188—21no—
62C2×D188—21no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C42×C47C2311yescharacteristic
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C22×D47—21no—
103C22×D47—21no—
104C22×D47C2×D411yescharacteristic
105Q8×C47—81no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47C2×D411yescharacteristic
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118D188—21no—
119D188—21no—
120D188—21no—
121D188—21no—
122D188—81no—
123D188—81no—
124D188—81no—
125D188—81no—
126C4×D47—21no—
127C4×D47—21no—
128C4×D47—81no—
129C4×D47—81no—
130C4×D47—81no—
131Dic94—81no—
132C8×C47—21no—
133C8×C47—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C22×C47C22×D411yescharacteristic
137C2×D47—21no—
138C2×D47—21no—
139C2×D47—21no—
140C2×D47—41no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C472−1+411yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159#3241—471nomaximal, Sylow
160C2×C47#53611yescharacteristic
161C2×C47#57611yescharacteristic
162C2×C47#57711yescharacteristic
163D47—41no—
164D47—81no—
165D47—81no—
166#544—471no—
167#540—471no—
168#501D4711yescharacteristic, complemented
169#499—471no—
170#490—471no—
171#486—471no—
172#482—471no—
173#482—471no—
174#481—471no—
175#480—471no—
176#478—471no—
177#478—471no—
178#476—471no—
179#474—471no—
180#433—471no—
181C47#324111yescharacteristic, complemented, Sylow
182C4⋊Q8—471no—
183C4⋊Q8—941no—
184C4⋊Q8C2×D4711yescharacteristic
185#127—471no—
186#125—471no—
187#125—471no—
188#125—941no—
189#125C2×D4711yescharacteristic
190#123—941no—
191#123—941no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—471no—
195#121—471no—
196#121—941no—
197#121—941no—
198C4×D4—471no—
199C4×D4—471no—
200#117—471no—
201#117—471no—
202C2×C4⋊C4—471no—
203#107—471no—
204#107—471no—
205#107C2×D4711yescharacteristic
206#107C2×D4711yescharacteristic
207#106—471no—
208#106—471no—
209#106C2×D4711yescharacteristic
210#106C2×D4711yescharacteristic
211C4⋊C8—471no—
212C4⋊C8—471no—
213#102—471no—
214#102—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221C22⋊C8—471no—
222C22⋊C8—471no—
223#97C2×D4711yescharacteristic
224C4×C8—471no—
225C2×Q8—21no—
226C2×Q8—941no—
227C2×D4—471no—
228C2×D4—471no—
229C2×D4—941no—
230C2×D4—941no—
231C2×D4—941no—
232C2×D4—941no—
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—471no—
259C22⋊C4—471no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—471no—
266C42—941no—
267C42C22×D4711yescharacteristic
268C23—471no—
269C23—941no—
270C23—941no—
271Q8—81no—
272Q8—3761no—
273D4—941no—
274D4—941no—
275D4—941no—
276D4—941no—
277D4—3761no—
278D4—3761no—
279D4—3761no—
280D4—3761no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4D4×D4711yescharacteristic
296C2×C4D4×D4711yescharacteristic
297C2×C4C23×D4711yescharacteristic
298C8—21no—
299C8—21no—
300C8—941no—
301C8—941no—
302C22—941no—
303C22—941no—
304C22—941no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22—1881no—
310C22—1881no—
311C22C2×D4×D4711yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—941no—
319C4—941no—
320C4—941no—
321C4—1881no—
322C4—1881no—
323C4#1309407211yescharacteristic
324C4#1309407211yescharacteristic
325C2—3761no—
326C2—3761no—
327C2—1881no—
328C2#1568969811yescharacteristic
329C2#1568992711yescharacteristic
330C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689522C2semidirect
4. #15689488C2semidirect
5. #15689471C2semidirect
6. #15689450C2semidirect
7. #15689449C2semidirect
8. #15689443C2semidirect
9. #15689438C2semidirect
10. #15689426C2semidirect
11. #15689422C2semidirect
12. #15689412C2semidirect
13. #15689402C2semidirect
14. #15689185C2semidirect
15. C47×#501C2semidirect
168. #501D47semidirect
181. C47#3241semidirect