Finite Group Databasebeta

← #20255890

Subgroups — #20255890

Order 6016.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689838C211yesmaximal, characteristic, complemented
2#15689819C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689448C211yesmaximal, characteristic, complemented
7#15689437C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689404C211yesmaximal, characteristic, complemented
10#15689376C211yesmaximal, characteristic, complemented
11#15689359C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689161C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×D376C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094019—21no—
19#13094016C2211yescharacteristic
20#13094010—21no—
21#13094010—21no—
22#13094006—21no—
23#13093998C2211yescharacteristic
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093996—21no—
28#13093995—21no—
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic
31(C22⋊D47)⋊C4—21no—
32#13093983C2211yescharacteristic
33#13093983C2211yescharacteristic
34#13093983C2211yescharacteristic
35#13093982—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093956C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
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—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C2×D188C2311yescharacteristic
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×Dic94—21no—
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—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104D376—22no—
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108C22×D47—21no—
109D4×C47—41no—
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—81no—
121C22⋊D47—81no—
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130D188—21no—
131D188—21no—
132D188—21no—
133D188—21no—
134C4×D47—42no—
135C4×D47—81no—
136Dic94—81no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47#4112yes—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47C22×D411yescharacteristic
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3347—471nomaximal, Sylow
167C2×C47—41no—
168C2×C47—41no—
169C2×C47#54711yescharacteristic
170C2×C47#57511yescharacteristic
171C2×C47#57611yescharacteristic
172D47—81no—
173D47—81no—
174#555—471no—
175#553—471no—
176#501—471no—
177#482—471no—
178#482—471no—
179#482—471no—
180#480—471no—
181#478—471no—
182#474—471no—
183#469—471no—
184#466—471no—
185#442—471no—
186#435D4711yescharacteristic, complemented
187#428—471no—
188#427—471no—
189C47#334711yescharacteristic, complemented, Sylow
190C2×D8—471no—
191C2×M16C2×D4711yescharacteristic
192C22×C8C2×D4711yescharacteristic
193C4⋊Q8—471no—
194#126—941no—
195#125—471no—
196#124—941no—
197#124—941no—
198#123—941no—
199#121—471no—
200#121—471no—
201#121—471no—
202#121—471no—
203#121—941no—
204#121—941no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—941no—
208C4×D4C2×D4711yescharacteristic
209#117—471no—
210#117—471no—
211#117—471no—
212#117—941no—
213C2×C4⋊C4—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#107—471no—
218#107—471no—
219#106—471no—
220#106—471no—
221#106—471no—
222#106—471no—
223C4⋊C8C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8C2×D4711yescharacteristic
231C22⋊C8C2×D4711yescharacteristic
232#97C2×D4711yescharacteristic
233C2×Q8—941no—
234C2×D4—471no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4—941no—
240C2×D4D18811yescharacteristic
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246D8—942no—
247M16—22no—
248C2×C8—22no—
249C2×C8C22×D4711yescharacteristic
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4D18811yescharacteristic
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4D18811yescharacteristic
274C22⋊C4D18811yescharacteristic
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—941no—
280C23—941no—
281C23C2×D18811yescharacteristic
282C23C2×D18811yescharacteristic
283Q8—3761no—
284D4—41no—
285D4—941no—
286D4—941no—
287D4—941no—
288D4—941no—
289D4—3761no—
290D4—3761no—
291D4—3761no—
292D4—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—3761no—
304C2×C4—3761no—
305C2×C4—1882no—
306C2×C4C2×D18811yescharacteristic
307C2×C4C2×D18811yescharacteristic
308C2×C4C2×D18811yescharacteristic
309C2×C4C2×D18811yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#1062535212yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—1881no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C22×D18811yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—1881no—
333C4—1881no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4C2×#1062535211yescharacteristic
339C4#1309407111yescharacteristic
340C2—41no—
341C2—41no—
342C2—3761no—
343C2—3761no—
344C2#1568977711yescharacteristic
345C2#1568992311yescharacteristic
346C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3347
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. #15689838C2semidirect
2. #15689819C2semidirect
3. #15689532C2semidirect
4. #15689448C2semidirect
5. #15689448C2semidirect
6. #15689448C2semidirect
7. #15689437C2semidirect
8. #15689424C2semidirect
9. #15689404C2semidirect
10. #15689376C2semidirect
11. #15689359C2semidirect
12. #15689236C2semidirect
13. #15689165C2semidirect
14. #15689161C2semidirect
15. C47×#435C2semidirect
186. #435D47semidirect
189. C47#3347semidirect