Finite Group Databasebeta

← #20254411

Subgroups — #20254411

Order 6016.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊Q8×D47C211yesmaximal, characteristic, complemented
2#15689652C211yesmaximal, characteristic
3#15689518C211yesmaximal, characteristic, complemented
4#15689492C211yesmaximal, characteristic, complemented
5#15689491C211yesmaximal, characteristic, complemented
6#15689331C212yesmaximal, complemented
7#15689326C212yesmaximal, complemented
8#15689277C212yesmaximal, complemented
9#15689260C212yesmaximal
10#15689178C211yesmaximal, characteristic, complemented
11C47×#497C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2212yes—
13C2×#10625337C2212yes—
14C2×#10625335C2212yes—
15#13094024C2211yescharacteristic
16#13094023—21no—
17#13094023—21no—
18#13094022C2212yes—
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094006—21no—
22#13094000C2211yescharacteristic
23#13093995C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25D4×Dic47C2211yescharacteristic
26(C22⋊D47)⋊C4—21no—
27#13093980—21no—
28C4⋊C4×D47—21no—
29C4⋊C4×D47—21no—
30C42×D47C2211yescharacteristic
31Dic47⋊C8C2212yes—
32#13093949C2212yes—
33#13093949C2212yes—
34#13093948C2212yes—
35#13093948C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C2×Q16×C47C2212yes—
39C2×SD16×C47C2212yes—
40C4⋊Q8×C47C2211yescharacteristic
41#124×C47C2211yescharacteristic
42#97×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C2×Q8×C47C2312yes—
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48Q8×D47—42no—
49Q8×D47—42no—
50C2×C4×D47—22no—
51C2×C4×D47D411yescharacteristic
52C2×C4×D47D411yescharacteristic
53C2×C4×D47C2311yescharacteristic
54C2×Dic94—22no—
55C2×Dic94C2312yes—
56Q16×C47—42no—
57SD16×C47—42no—
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47—21no—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—21no—
63C42×C47C2311yescharacteristic
64C22⋊Dic47—21no—
65C22⋊Dic47—21no—
66#10625337—42no—
67#10625335—42no—
68(C2×D47)⋊C4—21no—
69C4⋊Dic47—21no—
70C4⋊Dic47—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47C2311yescharacteristic
73C4⋊Dic47C2311yescharacteristic
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80C4×Dic47D411yescharacteristic
81C4×Dic47D411yescharacteristic
82C4×Dic47C2311yescharacteristic
83C2×C47⋊C8C2312yes—
84C23×C47—21no—
85C22×D47C2×D411yescharacteristic
86Q8×C47—22no—
87Q8×C47—22no—
88Q8×C47—22no—
89D4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—42no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—42no—
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C4×D47—22no—
104C4×D47—22no—
105C4×D47—22no—
106C4×D47—44no—
107Dic94—22no—
108Dic94—22no—
109Dic94—44no—
110C8×C47—22no—
111C47⋊C8—22no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—41no—
115C22×C47C22×D411yescharacteristic
116C2×D47—21no—
117C2×D47—21no—
118C2×D47#13712yes—
119C4×C47—21no—
120C4×C47—21no—
121C4×C47—42no—
122C4×C47—41no—
123C4×C47H(5,𝔽2)12yes—
124Dic47—21no—
125Dic47—21no—
126Dic47—42no—
127Dic47—41no—
128Dic47—41no—
129Dic47#13712yes—
130#3218—471nomaximal, Sylow
131C2×C47—81no—
132C2×C47#53511yescharacteristic
133C2×C47C2×#13711yescharacteristic
134C2×C47C2×#13711yescharacteristic
135D47—22no—
136C2×C4⋊Q8—471no—
137#529—471no—
138#497—471no—
139#497D4711yescharacteristic, complemented
140#491—471no—
141#491—471no—
142#462—472no—
143#461—472no—
144#451—472no—
145#448—472no—
146#432—471no—
147C47#321811yescharacteristic, complemented, Sylow
148C22×Q8—472no—
149C2×Q16—472no—
150C2×Q16C2×D4712yes—
151C2×SD16—472no—
152C2×SD16C2×D4712yes—
153C4⋊Q8—472no—
154C4⋊Q8—471no—
155C4⋊Q8—941no—
156C4⋊Q8—941no—
157C4⋊Q8C2×D4711yescharacteristic
158#126—941no—
159#125—471no—
160#124C2×D4711yescharacteristic
161#123—941no—
162C22⋊Q8—471no—
163#121—471no—
164C4×Q8—471no—
165C4×D4—471no—
166C4×D4—941no—
167#117—941no—
168C2×C4⋊C4—941no—
169C2×C4⋊C4—941no—
170C2×C42—471no—
171C4⋊C8—472no—
172#103—472no—
173#103—472no—
174#103—472no—
175#103—472no—
176C22⋊C8—472no—
177#97—471no—
178#97C2×D4711yescharacteristic
179C2×Q8—472no—
180C2×Q8—942no—
181C2×Q8—1882no—
182C2×Q8—1882no—
183C2×Q8C22×D4712yes—
184C2×Q8C22×D4711yescharacteristic
185C2×D4—941no—
186C2×D4C22×D4711yescharacteristic
187C22×C4—471no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—942no—
191C22×C4—941no—
192Q16—42no—
193Q16—1882no—
194SD16—42no—
195SD16—1882no—
196C2×C8—472no—
197C2×C8C22×D4712yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—471no—
201C4⋊C4—471no—
202C4⋊C4—942no—
203C4⋊C4—942no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4—941no—
209C4⋊C4—941no—
210C22⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C22⋊C4—941no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—21no—
221C23—471no—
222Q8—22no—
223Q8—22no—
224Q8—22no—
225Q8—942no—
226Q8—942no—
227Q8—1884no—
228D4—22no—
229D4—1882no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—471no—
233C2×C4—471no—
234C2×C4—471no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—942no—
241C2×C4—1884no—
242C2×C4—1882no—
243C2×C4D4×D4711yescharacteristic
244C2×C4D4×D4711yescharacteristic
245C2×C4C23×D4711yescharacteristic
246C8—22no—
247C8—942no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—472no—
252C22—941no—
253C22—941no—
254C22C2×D4×D4711yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—41no—
259C4—472no—
260C4—941no—
261C4—941no—
262C4—1881no—
263C4—1881no—
264C4—1882no—
265C4#1309406912yes—
266C2—81no—
267C2—942no—
268C2#1568968611yescharacteristic
269C2#137×D4711yescharacteristic
270C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3218
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
1. C4⋊Q8×D47C2semidirect
3. #15689518C2semidirect
4. #15689492C2semidirect
5. #15689491C2semidirect
6. #15689331C2semidirect
7. #15689326C2semidirect
8. #15689277C2semidirect
10. #15689178C2semidirect
11. C47×#497C2semidirect
139. #497D47semidirect
147. C47#3218semidirect