Finite Group Databasebeta

← #20256463

Subgroups — #20256463

Order 6016.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689846C211yesmaximal, characteristic, complemented
2#15689518C211yesmaximal, characteristic, complemented
3#15689515C211yesmaximal, characteristic, complemented
4#15689505C211yesmaximal, characteristic
5#15689345C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic
8#15689335C211yesmaximal, characteristic
9#15689333C211yesmaximal, characteristic, complemented
10#15689330C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689223C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14C4×#10625337C211yesmaximal, characteristic, complemented
15C47×#556C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625336C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25#13094024C2211yescharacteristic
26#13094019—21no—
27#13094019—21no—
28#13094012C2211yescharacteristic
29#13094012C2211yescharacteristic
30#13094000—21no—
31C4×Dic94C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093982—21no—
35#13093957C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#124×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53C22⋊Q8×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47—21no—
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C42×C47C2311yescharacteristic
85C42×C47C2311yescharacteristic
86#10625337—22no—
87#10625337—41no—
88#10625337—41no—
89#10625337—41no—
90#10625336—22no—
91#10625336—41no—
92#10625335—22no—
93#10625335—41no—
94#10625334—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—41no—
118D4×C47—21no—
119D4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—42no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134D188—21no—
135D188—21no—
136C4×D47—42no—
137Dic94—21no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8#4112yes—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47H(5,𝔽2)11yescharacteristic
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3402—471nomaximal, Sylow
167C2×C47—81no—
168C2×C47#55011yescharacteristic
169C2×C47#57511yescharacteristic
170C2×C47#57811yescharacteristic
171D47—81no—
172#556—471no—
173#556D4711yescharacteristic, complemented
174#497—471no—
175#497—471no—
176#495—471no—
177#464—471no—
178#464—471no—
179#463—471no—
180#463—471no—
181#462—471no—
182#462—471no—
183#446—471no—
184#440—471no—
185#440—471no—
186C4×Q16—471no—
187C47#340211yescharacteristic, complemented, Sylow
188C2×Q16—471no—
189C2×Q16—471no—
190C2×Q16—471no—
191C2×Q16—471no—
192C2×SD16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×SD16—471no—
196C2×D8—471no—
197C4⋊Q8—471no—
198C4⋊Q8C2×D4711yescharacteristic
199#126—21no—
200#126—21no—
201#126—941no—
202#126—941no—
203#124—471no—
204#124—471no—
205#124C2×D4711yescharacteristic
206#124C2×D4711yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—941no—
209C4×Q8—471no—
210C4×Q8—471no—
211C4×Q8C2×D4711yescharacteristic
212C4×Q8C2×D4711yescharacteristic
213C4×Q8C2×D4711yescharacteristic
214C4×D4—471no—
215C4×D4C2×D4711yescharacteristic
216#117—21no—
217#117—941no—
218#107—471no—
219C4⋊C8—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#97—471no—
229#97—471no—
230C4×C8—471no—
231C2×Q8—471no—
232C2×Q8—471no—
233C2×Q8C22⋊D4711yescharacteristic
234C2×Q8C22×D4711yescharacteristic
235C2×Q8C22×D4711yescharacteristic
236C2×D4—471no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—941no—
240Q16—942no—
241Q16—1881no—
242Q16—1881no—
243Q16—1881no—
244SD16—942no—
245SD16—942no—
246SD16—1881no—
247SD16—1881no—
248D8—1881no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8—471no—
252C2×C8—471no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22⋊D4711yescharacteristic
263C4⋊C4C22⋊D4711yescharacteristic
264C4⋊C4C22⋊D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—21no—
277C42—21no—
278C42—941no—
279C42—941no—
280C42C22×D4711yescharacteristic
281C42C22×D4711yescharacteristic
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—941no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—941no—
291Q8—941no—
292Q8—941no—
293Q8—941no—
294D4—21no—
295D4—21no—
296D4—941no—
297D4—941no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—1882no—
306C2×C4C2×C22⋊D4711yescharacteristic
307C2×C4C2×C22⋊D4711yescharacteristic
308C2×C4C2×C22⋊D4711yescharacteristic
309C2×C4C2×C22⋊D4711yescharacteristic
310C2×C4C2×C22⋊D4711yescharacteristic
311C2×C4C2×C22⋊D4711yescharacteristic
312C2×C4C23×D4711yescharacteristic
313C8—472no—
314C8—941no—
315C8—941no—
316C8—941no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—1881no—
321C22—1881no—
322C22—1881no—
323C22C22×C22⋊D4711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1881no—
334C4—1881no—
335C4—1881no—
336C4#41×D4711yescharacteristic
337C4#1309407011yescharacteristic
338C2—81no—
339C2—3761no—
340C2#1568979211yescharacteristic
341C2#1568992111yescharacteristic
342C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3402
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #15689846C2semidirect
2. #15689518C2semidirect
3. #15689515C2semidirect
5. #15689345C2semidirect
6. #15689342C2semidirect
9. #15689333C2semidirect
10. #15689330C2semidirect
11. #15689254C2semidirect
12. #15689223C2semidirect
13. #15689221C2semidirect
14. C4×#10625337C2semidirect
15. C47×#556C2semidirect
173. #556D47semidirect
187. C47#3402semidirect