Finite Group Databasebeta

← #20254053

Subgroups — #20254053

Order 6016.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689742C211yesmaximal, characteristic
2#15689734C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689477C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689378C211yesmaximal, characteristic, complemented
7#15689366C211yesmaximal, characteristic
8#15689361C211yesmaximal, characteristic, complemented
9#15689349C211yesmaximal, characteristic
10#15689230C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12Q16×Dic47C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#497C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094019—21no—
20#13094019—21no—
21#13094017—21no—
22#13094016C2211yescharacteristic
23#13094014—21no—
24#13094014—21no—
25#13094010—21no—
26#13094008—21no—
27#13094001—21no—
28#13094000C2211yescharacteristic
29#13094000C2211yescharacteristic
30#13094000C2211yescharacteristic
31#13093995C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33Q8×Dic47C2211yescharacteristic
34Q8×Dic47C2211yescharacteristic
35D4×Dic47C2211yescharacteristic
36#13093981C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C2×SD16×C47C2211yescharacteristic
56C4⋊Q8×C47C2211yescharacteristic
57#124×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67Q16×C47—22no—
68Q16×C47—22no—
69SD16×C47—22no—
70SD16×C47—22no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4D411yescharacteristic
84(C2×D47)⋊C4D411yescharacteristic
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—81no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135Dic94—81no—
136C8×C47#4112yes—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47C22×D411yescharacteristic
144C2×D47—21no—
145C2×D47—21no—
146C2×D47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×#4111yescharacteristic
153C4×C47C2×#4111yescharacteristic
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3178—471nomaximal, Sylow
162C2×C47—81no—
163C2×C47#53211yescharacteristic
164C2×C47#57711yescharacteristic
165C2×C47#57811yescharacteristic
166D47—41no—
167#542—471no—
168#541—471no—
169#501—471no—
170#497D4711yescharacteristic, complemented
171#488—471no—
172#487—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#441—471no—
178#440—471no—
179C4×Q16—471no—
180C4×SD16—471no—
181#405—471no—
182C47#317811yescharacteristic, complemented, Sylow
183C2×Q16C2×D4711yescharacteristic
184C2×Q16C2×D4711yescharacteristic
185C2×SD16C2×D4711yescharacteristic
186C2×SD16C2×D4711yescharacteristic
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8C2×D4711yescharacteristic
191#126—941no—
192#126—941no—
193#126—941no—
194#125—471no—
195#125—941no—
196#125—941no—
197#124—941no—
198#124C2×D4711yescharacteristic
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—941no—
204#121—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×D4—471no—
209#117—471no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#97—471no—
223#97C2×D4711yescharacteristic
224C4×C8—471no—
225C4×C8—471no—
226C2×Q8—941no—
227C2×Q8C22×D4711yescharacteristic
228C2×Q8C22×D4711yescharacteristic
229C2×Q8C22×D4711yescharacteristic
230C2×D4—941no—
231C2×D4C22×D4711yescharacteristic
232C22×C4—471no—
233C22×C4—941no—
234Q16—22no—
235Q16—22no—
236SD16—22no—
237SD16—22no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—471no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—21no—
276C23—471no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—3761no—
284D4—21no—
285D4—21no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—941no—
304C8—941no—
305C8#1062535212yes—
306C8#1062535212yes—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—941no—
311C22—941no—
312C22—941no—
313C22C2×D4×D4711yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—941no—
320C4—941no—
321C4—941no—
322C4—1881no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4C2×#1062535211yescharacteristic
327C4C2×#1062535211yescharacteristic
328C2—81no—
329C2—1881no—
330C2#1568967111yescharacteristic
331C2#1568993211yescharacteristic
332C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #15689734C2semidirect
3. #15689532C2semidirect
4. #15689477C2semidirect
5. #15689473C2semidirect
6. #15689378C2semidirect
8. #15689361C2semidirect
10. #15689230C2semidirect
11. #15689224C2semidirect
12. Q16×Dic47C2semidirect
13. SD16×Dic47C2semidirect
14. #15689080C2semidirect
15. C47×#497C2semidirect
170. #497D47semidirect
182. C47#3178semidirect