Finite Group Databasebeta

← #20256203

Subgroups — #20256203

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#15689856C211yesmaximal, characteristic
2Q8×Dic94C211yesmaximal, characteristic, complemented
3#15689483C211yesmaximal, characteristic, complemented
4#15689481C211yesmaximal, characteristic, complemented
5#15689468C211yesmaximal, characteristic
6#15689417C211yesmaximal, characteristic, complemented
7#15689403C211yesmaximal, characteristic, complemented
8#15689402C211yesmaximal, characteristic, complemented
9#15689345C211yesmaximal, characteristic, complemented
10#15689343C211yesmaximal, characteristic, complemented
11#15689321C211yesmaximal, characteristic
12#15689251C211yesmaximal, characteristic, complemented
13#15689226C211yesmaximal, characteristic, complemented
14#15689215C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18#13094024—21no—
19#13094024C2211yescharacteristic
20#13094023—21no—
21#13094023—21no—
22#13094023C2211yescharacteristic
23#13094023C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094011C2211yescharacteristic
27#13094010—21no—
28#13094007—21no—
29#13094006—21no—
30Q8×Dic47C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32C4×Dic94—21no—
33C4×Dic94C2211yescharacteristic
34#13093989C2211yescharacteristic
35#13093986C2211yescharacteristic
36C4×C22⋊D47—21no—
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
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—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94D411yescharacteristic
70C2×Dic94C2311yescharacteristic
71SD16×C47—22no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C42×C47—21no—
79C42×C47C2311yescharacteristic
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82#10625337—22no—
83#10625336—22no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106C22×D47—21no—
107Q8×C47—21no—
108Q8×C47#4112yes—
109D4×C47—21no—
110D4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—81no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—42no—
119C22⋊D47—81no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—21no—
128D188—21no—
129C4×D47—81no—
130Dic94—22no—
131Dic94—21no—
132Dic94—21no—
133Dic94—81no—
134Dic94—81no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47C22×D411yescharacteristic
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—22no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×#4111yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47#13712yes—
161#3375—471nomaximal, Sylow
162C2×C47—81no—
163C2×C47#54811yescharacteristic
164C2×C47C2×#13711yescharacteristic
165C2×C47#57611yescharacteristic
166D47—81no—
167#559—471no—
168Q82—471no—
169#489—471no—
170#489—471no—
171#486—471no—
172#477—471no—
173#474—471no—
174#474—471no—
175#464—471no—
176#464—471no—
177#460—471no—
178#446—471no—
179#440—471no—
180#440D4711yescharacteristic, complemented
181C4×Q16—471no—
182C47#337511yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×SD16—471no—
185C2×SD16C2×D4711yescharacteristic
186C4⋊Q8—471no—
187C4⋊Q8—471no—
188C4⋊Q8—471no—
189C4⋊Q8—941no—
190C4⋊Q8—941no—
191C4⋊Q8—941no—
192#127—471no—
193#124—471no—
194#124—471no—
195#124—941no—
196#123—941no—
197#123—941no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×Q8C2×D4711yescharacteristic
204C4×D4—471no—
205C4×D4—941no—
206C4×D4C2×D4711yescharacteristic
207#107—471no—
208#107—471no—
209#107C2×D4711yescharacteristic
210C4⋊C8—471no—
211C4⋊C8—471no—
212C4⋊C8—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103C2×D4711yescharacteristic
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#102—471no—
222#102C2×D4711yescharacteristic
223#97—471no—
224#97C2×D4711yescharacteristic
225C4×C8—471no—
226C2×Q8—471no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×Q8—941no—
230C2×Q8—941no—
231C2×Q8C22×D4711yescharacteristic
232C2×D4—471no—
233C2×D4—941no—
234C2×D4—941no—
235C2×D4C22×D4711yescharacteristic
236C22×C4—21no—
237C22×C4—941no—
238Q16—942no—
239SD16—22no—
240SD16—942no—
241C2×C8—471no—
242C2×C8—471no—
243C2×C8C22×D4711yescharacteristic
244C2×C8C22×D4711yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—21no—
266C42—471no—
267C42—471no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42C22×D4711yescharacteristic
272C23—21no—
273C23—941no—
274Q8—21no—
275Q8—942no—
276Q8—941no—
277Q8—941no—
278Q8—3761no—
279Q8—3761no—
280Q8—3761no—
281Q8#1062535012yes—
282D4—21no—
283D4—21no—
284D4—941no—
285D4—941no—
286D4—3761no—
287D4—1882no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—21no—
304C8—21no—
305C8—941no—
306C8—941no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C2×D4×D4711yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—472no—
320C4—941no—
321C4—941no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4C2×#1062535011yescharacteristic
327C4#1309407111yescharacteristic
328C2—81no—
329C2—3761no—
330C2#1568978211yescharacteristic
331C2#137×D4711yescharacteristic
332C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3375
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
2. Q8×Dic94C2semidirect
3. #15689483C2semidirect
4. #15689481C2semidirect
6. #15689417C2semidirect
7. #15689403C2semidirect
8. #15689402C2semidirect
9. #15689345C2semidirect
10. #15689343C2semidirect
12. #15689251C2semidirect
13. #15689226C2semidirect
14. #15689215C2semidirect
15. C47×#440C2semidirect
180. #440D47semidirect
182. C47#3375semidirect