Finite Group Databasebeta

← #20256107

Subgroups — #20256107

Order 6016.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689845C211yesmaximal, characteristic, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689484C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689418C211yesmaximal, characteristic, complemented
7#15689417C211yesmaximal, characteristic, complemented
8#15689402C211yesmaximal, characteristic, complemented
9#15689340C211yesmaximal, characteristic
10#15689338C211yesmaximal, characteristic
11#15689326C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689203C211yesmaximal, characteristic
15C47×#440C211yesmaximal, characteristic, complemented
16C22×Dic94—21no—
17C2×#10625335C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094019—21no—
24#13094018—21no—
25#13094013C2211yescharacteristic
26#13094012C2211yescharacteristic
27#13094003—21no—
28#13094002—21no—
29#13094001—21no—
30#13094001—21no—
31C4×Dic94C2211yescharacteristic
32#13093989C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093981—21no—
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—44no—
70C2×Dic94D411yescharacteristic
71C2×Dic94C2311yescharacteristic
72SD16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83#10625335—22no—
84#10625334—22no—
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—
90C4⋊Dic47—21no—
91C4⋊Dic47D411yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C22×D47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—21no—
111D4×C47#4112yes—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—42no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—42no—
123C2×Dic47—42no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128D188—21no—
129D188—21no—
130C4×D47—42no—
131Dic94—22no—
132Dic94—21no—
133Dic94—21no—
134Dic94—42no—
135Dic94—42no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47—21no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—22no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47C22×D411yescharacteristic
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47AGL(1,ℤ/8)12yes—
162#3367—471nomaximal, Sylow
163C2×C47—42no—
164C2×C47#54811yescharacteristic
165C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
166C2×C47#57811yescharacteristic
167D47—81no—
168#556—471no—
169D4×Q8—471no—
170#489—471no—
171#489—471no—
172#487—471no—
173#477—471no—
174#477—471no—
175#474—471no—
176#463—471no—
177#463—471no—
178#461—471no—
179#446—471no—
180#440—471no—
181#440D4711yescharacteristic, complemented
182C4×D8—471no—
183C47#336711yescharacteristic, complemented, Sylow
184C22×Q8—941no—
185C2×SD16—471no—
186C2×SD16C2×D4711yescharacteristic
187C2×D8—471no—
188C4⋊Q8—471no—
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191C4⋊Q8—471no—
192#126—941no—
193#126—941no—
194#124—471no—
195#124—471no—
196C22⋊Q8—941no—
197C22⋊Q8—941no—
198C22⋊Q8—941no—
199C22⋊Q8—941no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8C2×D4711yescharacteristic
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—471no—
206C4×D4C2×D4711yescharacteristic
207#117—941no—
208#107—471no—
209#107—471no—
210#107C2×D4711yescharacteristic
211C4⋊C8—471no—
212C4⋊C8—471no—
213C4⋊C8—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103C2×D4711yescharacteristic
220#102—471no—
221#102—471no—
222#102—471no—
223#102C2×D4711yescharacteristic
224#97—471no—
225#97C2×D4711yescharacteristic
226C4×C8—471no—
227C2×Q8—471no—
228C2×Q8—471no—
229C2×Q8—941no—
230C2×Q8—941no—
231C2×Q8—941no—
232C2×Q8—1884no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4—471no—
235C2×D4C22×D4711yescharacteristic
236C22×C4—21no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240SD16—22no—
241SD16—942no—
242D8—942no—
243C2×C8—471no—
244C2×C8—471no—
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—21no—
270C42—471no—
271C42—471no—
272C42—941no—
273C42C22×D4711yescharacteristic
274C23—21no—
275C23—941no—
276Q8—21no—
277Q8—21no—
278Q8—942no—
279Q8—941no—
280Q8—941no—
281Q8—1882no—
282Q8—1882no—
283Q8—1882no—
284D4—21no—
285D4—941no—
286D4—941no—
287D4#1062535012yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4D4×D4711yescharacteristic
303C2×C4D4×D4711yescharacteristic
304C2×C4C23×D4711yescharacteristic
305C8—21no—
306C8—21no—
307C8—941no—
308C8—941no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—1881no—
313C22—1881no—
314C22—1881no—
315C22C2×D4×D4711yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—472no—
322C4—941no—
323C4—941no—
324C4—941no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C4C2×#1062535011yescharacteristic
329C4#1309407111yescharacteristic
330C2—42no—
331C2—3761no—
332C2#1568978211yescharacteristic
333C2AGL(1,ℤ/8)×D4711yescharacteristic
334C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3367
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689845C2semidirect
2. D4×Dic94C2semidirect
3. #15689484C2semidirect
4. #15689483C2semidirect
5. #15689472C2semidirect
6. #15689418C2semidirect
7. #15689417C2semidirect
8. #15689402C2semidirect
11. #15689326C2semidirect
12. #15689251C2semidirect
13. #15689220C2semidirect
15. C47×#440C2semidirect
181. #440D47semidirect
183. C47#3367semidirect