Finite Group Databasebeta

← #20255830

Subgroups — #20255830

Order 6016.

376 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#15689813C211yesmaximal, characteristic, complemented
2#15689777C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689454C211yesmaximal, characteristic, complemented
6#15689448C211yesmaximal, characteristic, complemented
7#15689437C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689419C211yesmaximal, characteristic, complemented
10#15689369C211yesmaximal, characteristic, complemented
11#15689352C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14C2×#13093958C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625325C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094014—21no—
22#13094008—21no—
23#13094008—21no—
24#13094005—21no—
25#13094004—21no—
26#13094003C2211yescharacteristic
27#13094003C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093983C2211yescharacteristic
33#13093980—21no—
34C2×C4⋊Dic47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093958C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093956C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67#10625352—44no—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72M16×C47—22no—
73C2×C8×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47D411yescharacteristic
79C22⋊C4×C47D411yescharacteristic
80C22⋊C4×C47D411yescharacteristic
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105#10625325—22no—
106C23×C47C2×D411yescharacteristic
107C23×C47C2×D411yescharacteristic
108C22×D47—21no—
109D4×C47—22no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—42no—
120C22⋊D47—42no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—42no—
129C2×Dic47—42no—
130C2×Dic47—42no—
131D188—21no—
132D188—21no—
133C4×D47—42no—
134Dic94—21no—
135Dic94—21no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47#4112yescomplemented
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47AGL(1,ℤ/8)12yes—
147C22×C47C22×D411yescharacteristic
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47C2×#4111yescharacteristic
156C4×C472−1+411yescharacteristic
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3343—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—41no—
167C2×C47#54711yescharacteristic
168C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C47#57811yescharacteristic
170D47—81no—
171#552—471no—
172#547—471no—
173#501—471no—
174#484—471no—
175#483—471no—
176#482—471no—
177#480—471no—
178#478—471no—
179#477—471no—
180#468—471no—
181#465—471no—
182#440—471no—
183#435D4711yescharacteristic, complemented
184#428—471no—
185C2×#107—471no—
186C47#334311yescharacteristic, complemented, Sylow
187C2×#41—941no—
188C2×SD16—471no—
189C2×M16C2×D4711yescharacteristic
190C22×C8C2×D4711yescharacteristic
191C4⋊Q8—471no—
192#126—941no—
193#125—471no—
194#125—941no—
195#123—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—941no—
201#121—471no—
202#121—471no—
203C4×Q8—471no—
204C4×D4—471no—
205C4×D4C2×D4711yescharacteristic
206#117—471no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220C4⋊C8C2×D4711yescharacteristic
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227C22⋊C8C2×D4711yescharacteristic
228C22⋊C8C2×D4711yescharacteristic
229#97C2×D4711yescharacteristic
230#41—1884no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×D4—471no—
234C2×D4—941no—
235C2×D4—941no—
236C2×D4D18811yescharacteristic
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243SD16—942no—
244M16—22no—
245C2×C8—22no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C2×C8C22×D4711yescharacteristic
249C2×C8C22×D4711yescharacteristic
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4D18811yescharacteristic
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4D18811yescharacteristic
273C22⋊C4D18811yescharacteristic
274C42—941no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—941no—
278C23C2×D18811yescharacteristic
279C23C2×D18811yescharacteristic
280Q8—941no—
281Q8—941no—
282Q8—1882no—
283D4—22no—
284D4—941no—
285D4—941no—
286D4—1882no—
287D4—1882no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4—1882no—
303C2×C4C2×D18811yescharacteristic
304C2×C4C2×D18811yescharacteristic
305C2×C4C2×D18811yescharacteristic
306C2×C4C2×D18811yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8#1062535212yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—1881no—
318C22—1881no—
319C22—1881no—
320C22#1309405212yes—
321C22C22×D18811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4C2×#1062535211yescharacteristic
334C4#1309407111yescharacteristic
335C2—22no—
336C2—41no—
337C2—3761no—
338C2#1568977711yescharacteristic
339C2C2×#1309405211yescharacteristic
340C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
3. #15689532C2semidirect
4. #15689459C2semidirect
5. #15689454C2semidirect
6. #15689448C2semidirect
7. #15689437C2semidirect
8. #15689424C2semidirect
9. #15689419C2semidirect
10. #15689369C2semidirect
11. #15689352C2semidirect
12. #15689225C2semidirect
13. #15689165C2semidirect
14. C2×#13093958C2semidirect
15. C47×#435C2semidirect
140. C8×C47#41semidirect
183. #435D47semidirect
186. C47#3343semidirect
311. C8#10625352semidirect