Finite Group Databasebeta

← #20256135

Subgroups — #20256135

Order 6016.

358 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#15689833C211yesmaximal, characteristic, complemented
2#15689487C211yesmaximal, characteristic, complemented
3#15689482C211yesmaximal, characteristic, complemented
4#15689477C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689403C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689335C211yesmaximal, characteristic, complemented
10#15689315C211yesmaximal, characteristic
11#15689254C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14C4×#10625334C211yesmaximal, characteristic, complemented
15C47×#559C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094002—21no—
23#13094002—21no—
24#13094000—21no—
25C4×D188C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C4×D188C2211yescharacteristic
28C4⋊C4×D47—21no—
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093955C2211yescharacteristic
32C4⋊(C47⋊C8)C2211yescharacteristic
33C4⋊(C47⋊C8)C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#127×C47C2211yescharacteristic
49#124×C47—21no—
50#124×C47C2211yescharacteristic
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53#123×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4×D4×C47—21no—
57C4×D4×C47C2211yescharacteristic
58C4×D4×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87#10625336—22no—
88#10625334—22no—
89#10625334—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
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106C23×C47—21no—
107C22×D47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110Q8×C47—41no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—42no—
116D4×C47—81no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131D188—21no—
132D188#4112yes—
133C4×D47—42no—
134C4×D47—81no—
135C4×D47—81no—
136Dic94—81no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—22no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C472−1+411yescharacteristic
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3370—471nomaximal, Sylow
165C2×C47—81no—
166C2×C47—81no—
167C2×C47#54811yescharacteristic
168C2×C47#57511yescharacteristic
169C2×C47#57611yescharacteristic
170D47—42no—
171#559D4711yescharacteristic, complemented
172#554—471no—
173#490—471no—
174#489—471no—
175#488—471no—
176#479—471no—
177#478—471no—
178#474—471no—
179#463—471no—
180#463—471no—
181#459—471no—
182#446—471no—
183#442—471no—
184#440—471no—
185C4×D8—471no—
186C47#337011yescharacteristic, complemented, Sylow
187C2×SD16—471no—
188C2×D8—471no—
189C2×D8—471no—
190C4⋊Q8—471no—
191#127C2×D4711yescharacteristic
192#125—471no—
193#125—471no—
194#124—21no—
195#124C2×D4711yescharacteristic
196#124C2×D4711yescharacteristic
197#123—21no—
198#123—21no—
199C22⋊Q8—941no—
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C4×Q8C2×D4711yescharacteristic
203C4×Q8C2×D4711yescharacteristic
204C4×D4—21no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4C2×D4711yescharacteristic
209C4×D4C2×D4711yescharacteristic
210C2×C4⋊C4—941no—
211#107—471no—
212#107—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#97—471no—
228#97—471no—
229C4×C8—471no—
230C2×Q8—941no—
231C2×Q8C22⋊D4711yescharacteristic
232C2×Q8C22×D4711yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—471no—
236C2×D4C22×D4711yescharacteristic
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243SD16—942no—
244D8—942no—
245D8—942no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—471no—
250C4⋊C4—21no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22⋊D4711yescharacteristic
260C4⋊C4C22⋊D4711yescharacteristic
261C4⋊C4C22⋊D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C42—21no—
273C42C22×D4711yescharacteristic
274C42C22×D4711yescharacteristic
275C42C22×D4711yescharacteristic
276C23—21no—
277C23—21no—
278C23—941no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—3761no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—472no—
290D4—941no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—1882no—
301C2×C4C2×C22⋊D4711yescharacteristic
302C2×C4C2×C22⋊D4711yescharacteristic
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C2×C22⋊D4711yescharacteristic
306C2×C4C2×C22⋊D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—941no—
309C8—941no—
310C8—941no—
311C8—941no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—942no—
319C22—1881no—
320C22—1881no—
321C22C22×C22⋊D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407111yescharacteristic
335C2—81no—
336C2—81no—
337C2—1882no—
338C2#1568978011yescharacteristic
339C2#1568992111yescharacteristic
340C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#559C2
socleC22×C47C22×D4
hypercenter#559D47
hypocenterC47#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #15689833C2semidirect
2. #15689487C2semidirect
3. #15689482C2semidirect
4. #15689477C2semidirect
5. #15689430C2semidirect
6. #15689423C2semidirect
7. #15689403C2semidirect
8. #15689335C2semidirect
9. #15689335C2semidirect
11. #15689254C2semidirect
12. #15689233C2semidirect
13. #15689221C2semidirect
14. C4×#10625334C2semidirect
15. C47×#559C2semidirect
171. #559D47semidirect
186. C47#3370semidirect