Finite Group Databasebeta

← #20254058

Subgroups — #20254058

Order 6016.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic
2#15689533C211yesmaximal, characteristic, complemented
3#15689515C211yesmaximal, characteristic, complemented
4#15689480C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic
8#15689362C211yesmaximal, characteristic, complemented
9#15689354C211yesmaximal, characteristic
10#15689228C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625336C211yesmaximal, characteristic, complemented
14#15689079C211yesmaximal, characteristic, complemented
15C47×#541C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094019—21no—
24#13094012C2211yescharacteristic
25#13094010—21no—
26#13094006—21no—
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13093998C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093935C2211yescharacteristic
45#13093935C2211yescharacteristic
46C4×C47⋊C8C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#125×C47—21no—
52#125×C47—21no—
53#125×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×Dic94—21no—
66C2×Dic94C2311yescharacteristic
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C42×C47—21no—
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625337—22no—
89#10625337—22no—
90#10625336—22no—
91#10625336—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102#10625329—22no—
103C2×C47⋊C8—22no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
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×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130D188—21no—
131D188—21no—
132C4×D47—81no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C47⋊C8#4112yes—
139C47⋊C8#4112yes—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47C22×D411yescharacteristic
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C47C2×#4111yescharacteristic
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3178—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47#53211yescharacteristic
164C2×C47#57711yescharacteristic
165C2×C47#57811yescharacteristic
166D47—81no—
167#542—471no—
168#541D4711yescharacteristic, complemented
169#501—471no—
170#497—471no—
171#488—471no—
172#487—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#441—471no—
178#440—471no—
179C4×Q16—471no—
180C4×SD16—471no—
181#405—471no—
182C47#317811yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×Q16—471no—
185C2×SD16—471no—
186C2×SD16—471no—
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8C2×D4711yescharacteristic
191#126—21no—
192#126—21no—
193#126—941no—
194#125—21no—
195#125—21no—
196#125C2×D4711yescharacteristic
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—941no—
202C22⋊Q8C2×D4711yescharacteristic
203C22⋊Q8C2×D4711yescharacteristic
204#121—471no—
205C4×Q8—471no—
206C4×Q8C2×D4711yescharacteristic
207C4×Q8C2×D4711yescharacteristic
208C4×D4—471no—
209#117C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#97—471no—
223#97—471no—
224C4×C8—471no—
225C4×C8—471no—
226C2×Q8—471no—
227C2×Q8—941no—
228C2×Q8C22×D4711yescharacteristic
229C2×Q8C22×D4711yescharacteristic
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—941no—
233C22×C4C22×D4711yescharacteristic
234Q16—942no—
235Q16—942no—
236SD16—942no—
237SD16—942no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—471no—
242C2×C8—471no—
243C2×C8—942no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4C22⋊D4711yescharacteristic
258C4⋊C4C22⋊D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4C22⋊D4711yescharacteristic
269C22⋊C4C22⋊D4711yescharacteristic
270C42—21no—
271C42—21no—
272C42—941no—
273C42C22×D4711yescharacteristic
274C42C22×D4711yescharacteristic
275C23—941no—
276C23C2×C22⋊D4711yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—941no—
282Q8—941no—
283Q8—3761no—
284D4—941no—
285D4—941no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4C2×C22⋊D4711yescharacteristic
298C2×C4C2×C22⋊D4711yescharacteristic
299C2×C4C2×C22⋊D4711yescharacteristic
300C2×C4C2×C22⋊D4711yescharacteristic
301C2×C4C2×C22⋊D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—472no—
304C8—472no—
305C8—941no—
306C8—941no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C22×C22⋊D4711yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#41×D4711yescharacteristic
327C4#41×D4711yescharacteristic
328C2—41no—
329C2—3761no—
330C2#1568966911yescharacteristic
331C2#1568993111yescharacteristic
332C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689515C2semidirect
4. #15689480C2semidirect
5. #15689473C2semidirect
6. #15689379C2semidirect
8. #15689362C2semidirect
10. #15689228C2semidirect
11. #15689221C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625336C2semidirect
14. #15689079C2semidirect
15. C47×#541C2semidirect
168. #541D47semidirect
182. C47#3178semidirect