Finite Group Databasebeta

← #20255897

Subgroups — #20255897

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689838C211yesmaximal, characteristic
2#15689533C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689447C211yesmaximal, characteristic, complemented
6#15689441C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic, complemented
8#15689408C211yesmaximal, characteristic, complemented
9#15689371C211yesmaximal, characteristic, complemented
10#15689354C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689163C211yesmaximal, characteristic, complemented
14#15689159C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094010—21no—
21#13094010—21no—
22#13093998C2211yescharacteristic
23#13093998C2211yescharacteristic
24#13093995—21no—
25C4×D188C2211yescharacteristic
26#13093983C2211yescharacteristic
27#13093983C2211yescharacteristic
28#13093982—21no—
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47—21no—
50#125×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47D411yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×Dic94—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×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89#10625336—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99#10625329—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—41no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×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—42no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—81no—
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130D188—21no—
131D188—21no—
132C4×D47—42no—
133Dic94—81no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C47⋊C8#4112yes—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
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×C472−1+411yescharacteristic
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3348—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47—41no—
164C2×C47#54711yescharacteristic
165C2×C47#57511yescharacteristic
166C2×C47#57711yescharacteristic
167D47—81no—
168#555—471no—
169#552D4711yescharacteristic, complemented
170#501—471no—
171#485—471no—
172#485—471no—
173#482—471no—
174#481—471no—
175#478—471no—
176#475—471no—
177#468—471no—
178#465—471no—
179#440—471no—
180#435—471no—
181#428—471no—
182#427—471no—
183C47#334811yescharacteristic, complemented, Sylow
184C2×SD16—471no—
185C2×M16—471no—
186C22×C8—471no—
187C4⋊Q8—471no—
188#126—21no—
189#125—21no—
190#125C2×D4711yescharacteristic
191#124—941no—
192#124—941no—
193#123—21no—
194C22⋊Q8C2×D4711yescharacteristic
195C22⋊Q8C2×D4711yescharacteristic
196#121—471no—
197#121—471no—
198#121—941no—
199C4×Q8C2×D4711yescharacteristic
200C4×D4—471no—
201C4×D4C2×D4711yescharacteristic
202#117—21no—
203#117—471no—
204#117—471no—
205#117—941no—
206#117C2×D4711yescharacteristic
207C2×C4⋊C4C2×D4711yescharacteristic
208#107—471no—
209#107—471no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214#106—471no—
215#106—471no—
216#106—471no—
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C2×Q8—941no—
228C2×Q8C22×D4711yescharacteristic
229C2×D4—471no—
230C2×D4—941no—
231C2×D4—941no—
232C2×D4C22⋊D4711yescharacteristic
233C22×C4—21no—
234C22×C4—941no—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
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—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—941no—
254C4⋊C4C22⋊D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4C22⋊D4711yescharacteristic
267C22⋊C4C22⋊D4711yescharacteristic
268C42—21no—
269C42—21no—
270C42—941no—
271C42—941no—
272C42C22×D4711yescharacteristic
273C23—941no—
274C23C2×C22⋊D4711yescharacteristic
275C23C2×C22⋊D4711yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—3761no—
279D4—41no—
280D4—941no—
281D4—941no—
282D4—3761no—
283D4—3761no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—1882no—
297C2×C4C2×C22⋊D4711yescharacteristic
298C2×C4C2×C22⋊D4711yescharacteristic
299C2×C4C2×C22⋊D4711yescharacteristic
300C2×C4C2×C22⋊D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—472no—
303C8—941no—
304C8—941no—
305C8—941no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—1881no—
313C22—1881no—
314C22—1881no—
315C22C22×C22⋊D4711yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4#41×D4711yescharacteristic
328C4#1309407111yescharacteristic
329C2—41no—
330C2—41no—
331C2—3761no—
332C2#1568977211yescharacteristic
333C2#1568992111yescharacteristic
334C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3348
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689461C2semidirect
4. #15689461C2semidirect
5. #15689447C2semidirect
6. #15689441C2semidirect
7. #15689420C2semidirect
8. #15689408C2semidirect
9. #15689371C2semidirect
10. #15689354C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689163C2semidirect
14. #15689159C2semidirect
15. C47×#552C2semidirect
169. #552D47semidirect
183. C47#3348semidirect