Finite Group Databasebeta

← #20255893

Subgroups — #20255893

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#15689823C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689446C211yesmaximal, characteristic, complemented
5#15689446C211yesmaximal, characteristic, complemented
6#15689445C211yesmaximal, characteristic, complemented
7#15689435C211yesmaximal, characteristic, complemented
8#15689423C211yesmaximal, characteristic, complemented
9#15689403C211yesmaximal, characteristic, complemented
10#15689373C211yesmaximal, characteristic, complemented
11#15689356C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689162C211yesmaximal, characteristic, complemented
14#15689158C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094010—21no—
22#13094010—21no—
23#13094007—21no—
24#13093998—21no—
25#13093997—21no—
26#13093995C2211yescharacteristic
27#13093995C2211yescharacteristic
28#13093995C2211yescharacteristic
29#13093995C2211yescharacteristic
30C4×D188C2211yescharacteristic
31C4×C22⋊D47—21no—
32#13093983—21no—
33#13093982C2211yescharacteristic
34#13093982C2211yescharacteristic
35#13093982C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093955C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×D188D411yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72D8×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C42×C47C2311yescharacteristic
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103#10625324—22no—
104C8×D47—22no—
105C23×C47—21no—
106C23×C47—21no—
107C22×D47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—42no—
116C2×C4×C47—81no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C22⋊D47—81no—
122C22⋊D47—81no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—41no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—81no—
136Dic94—81no—
137C8×C47—21no—
138C8×C47#4112yes—
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—21no—
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3347—471nomaximal, Sylow
167C2×C47—81no—
168C2×C47—81no—
169C2×C47#54711yescharacteristic
170C2×C47#57511yescharacteristic
171C2×C47#57611yescharacteristic
172D47—41no—
173D47—41no—
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#442D4711yescharacteristic, complemented
186#435—471no—
187#428—471no—
188#427—471no—
189C47#334711yescharacteristic, complemented, Sylow
190C2×D8C2×D4711yescharacteristic
191C2×M16—471no—
192C22×C8—471no—
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—941no—
207C4×D4C2×D4711yescharacteristic
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#106C2×D4711yescharacteristic
223C4⋊C8—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102C2×D4711yescharacteristic
229#102C2×D4711yescharacteristic
230C22⋊C8—471no—
231C22⋊C8—471no—
232#97C2×D4711yescharacteristic
233C2×Q8—941no—
234C2×D4—471no—
235C2×D4—941no—
236C2×D4—941no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C2×D4C22×D4711yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—941no—
246D8—22no—
247M16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8—942no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—471no—
267C22⋊C4—471no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—21no—
280C23—21no—
281C23—471no—
282C23—471no—
283Q8—3761no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—3761no—
289D4—3761no—
290D4—3761no—
291D4—1881no—
292D4—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—941no—
313C8—941no—
314C8#1062535012yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—941no—
322C22—941no—
323C22—941no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4C2×#1062535011yescharacteristic
339C4#1309407111yescharacteristic
340C2—81no—
341C2—81no—
342C2—1881no—
343C2—1881no—
344C2#1568977811yescharacteristic
345C2#1568991911yescharacteristic
346C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3347
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. #15689823C2semidirect
3. #15689532C2semidirect
4. #15689446C2semidirect
5. #15689446C2semidirect
6. #15689445C2semidirect
7. #15689435C2semidirect
8. #15689423C2semidirect
9. #15689403C2semidirect
10. #15689373C2semidirect
11. #15689356C2semidirect
12. #15689196C2semidirect
13. #15689162C2semidirect
14. #15689158C2semidirect
15. C47×#442C2semidirect
185. #442D47semidirect
189. C47#3347semidirect