Finite Group Databasebeta

← #20255965

Subgroups — #20255965

Order 6016.

374 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#15689844C211yesmaximal, characteristic, complemented
2#15689774C211yesmaximal, characteristic
3#15689527C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689450C211yesmaximal, characteristic, complemented
6#15689448C211yesmaximal, characteristic, complemented
7#15689406C211yesmaximal, characteristic, complemented
8#15689402C211yesmaximal, characteristic, complemented
9#15689372C211yesmaximal, characteristic, complemented
10#15689371C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689164C211yesmaximal, characteristic, complemented
14#15689163C211yesmaximal, characteristic, complemented
15C47×#484C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625336C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094019—21no—
23#13094017—21no—
24#13094010—21no—
25#13094009—21no—
26#13094007—21no—
27#13094002—21no—
28#13094000C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32#13093989—21no—
33#13093986C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35#13093983C2211yescharacteristic
36#13093982C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47D411yescharacteristic
64#10625350—44no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47D411yescharacteristic
82#10625336—22no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102#10625329—22no—
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108C22×D47C2×D411yescharacteristic
109Q8×C47—21no—
110Q8×C47—21no—
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—42no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—22no—
121C22⋊D47—42no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128D188—21no—
129D188—21no—
130D188—42no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—42no—
134C4×D47—42no—
135Dic94—42no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47—21no—
139C47⋊C8—21no—
140C47⋊C8#4112yescomplemented
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—21no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C472−1+411yescharacteristic
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47AGL(1,ℤ/8)12yes—
164#3353—471nomaximal, Sylow
165C2×C47—41no—
166C2×C47#54711yescharacteristic
167C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C47#57811yescharacteristic
169D47—41no—
170D47—81no—
171#556—471no—
172#547—471no—
173#500—471no—
174#484—471no—
175#484D4711yescharacteristic, complemented
176#482—471no—
177#482—471no—
178#475—471no—
179#474—471no—
180#468—471no—
181#468—471no—
182C4×SD16—471no—
183#436—471no—
184#428—471no—
185#428—471no—
186C47#335311yescharacteristic, complemented, Sylow
187C2×#41—941no—
188C2×SD16—471no—
189C2×M16—471no—
190C2×M16—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193#126—941no—
194#126—941no—
195#124—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—941no—
200C22⋊Q8C2×D4711yescharacteristic
201#121—471no—
202#121—471no—
203C4×Q8—471no—
204C4×Q8—941no—
205C4×D4—471no—
206C4×D4—471no—
207#117—471no—
208#117—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4C2×D4711yescharacteristic
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107C2×D4711yescharacteristic
216#107C2×D4711yescharacteristic
217#106—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226#102—471no—
227C22⋊C8—471no—
228C22⋊C8C2×D4711yescharacteristic
229C4×C8—471no—
230#41—1884no—
231C2×Q8—941no—
232C2×Q8—941no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4—471no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4—941no—
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243SD16—942no—
244M16—942no—
245M16—942no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8C22×D4711yescharacteristic
249C2×C8C22×D4711yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
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⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—471no—
266C22⋊C4—471no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42—941no—
277C23—471no—
278C23—941no—
279C23D4×D4711yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—1882no—
283Q8—1882no—
284D4—942no—
285D4—941no—
286D4—941no—
287D4—1882no—
288D4—1882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—1882no—
305C2×C4—1882no—
306C2×C4D4×D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—21no—
310C8—472no—
311C8—941no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—941no—
316C22—941no—
317C22—941no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—472no—
328C4—941no—
329C4—941no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407111yescharacteristic
335C2—41no—
336C2—3761no—
337C2—1881no—
338C2#1568977111yescharacteristic
339C2AGL(1,ℤ/8)×D4711yescharacteristic
340C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3353
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #15689844C2semidirect
3. #15689527C2semidirect
4. #15689457C2semidirect
5. #15689450C2semidirect
6. #15689448C2semidirect
7. #15689406C2semidirect
8. #15689402C2semidirect
9. #15689372C2semidirect
10. #15689371C2semidirect
11. #15689208C2semidirect
12. #15689198C2semidirect
13. #15689164C2semidirect
14. #15689163C2semidirect
15. C47×#484C2semidirect
140. C47⋊C8#41semidirect
175. #484D47semidirect
186. C47#3353semidirect