Finite Group Databasebeta

← #20254416

Subgroups — #20254416

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#15689658C211yesmaximal, characteristic
3#15689517C211yesmaximal, characteristic, complemented
4#15689515C211yesmaximal, characteristic, complemented
5#15689493C211yesmaximal, characteristic, complemented
6#15689332C212yesmaximal, complemented
7#15689327C212yesmaximal, complemented
8#15689280C212yesmaximal, complemented
9#15689263C212yesmaximal
10#15689178C211yesmaximal, characteristic, complemented
11C47×#491C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2212yes—
13C2×Dic188C2212yes—
14C2×#10625337C2212yes—
15C2×#10625325C2212yes—
16C2×#10625336C2212yes—
17#13094024C2211yescharacteristic
18#13094023—21no—
19#13094023—21no—
20#13094022C2212yes—
21#13094019—21no—
22#13094012C2211yescharacteristic
23#13094009—21no—
24#13094004C2211yescharacteristic
25#13093999C2211yescharacteristic
26#13093989C2211yescharacteristic
27#13093986—21no—
28#13093986C2211yescharacteristic
29#13093982—21no—
30C4⋊C4×D47—21no—
31C4⋊C4×D47—21no—
32C42×D47C2211yescharacteristic
33Dic47⋊C8C2212yes—
34#13093947C2212yes—
35#13093947C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#103×C47C2212yes—
41#103×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47C2312yes—
44Q8×D47—42no—
45Q8×D47—42no—
46C2×D188—21no—
47C2×D188C2311yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47—21no—
50C2×C4×D47D411yescharacteristic
51C2×C4×D47D411yescharacteristic
52C2×C4×D47C2311yescharacteristic
53C2×Dic94—22no—
54C2×Dic94C2312yes—
55C2×Dic94C2311yescharacteristic
56C2×C8×C47C2312yes—
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47—21no—
60C4⋊C4×C47—21no—
61C4⋊C4×C47C2311yescharacteristic
62C4⋊C4×C47C2311yescharacteristic
63C42×C47C2311yescharacteristic
64#10625337—42no—
65#10625336—42no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47—21no—
73C4⋊Dic47—21no—
74Dic47⋊C4—22no—
75Dic47⋊C4—22no—
76Dic47⋊C4—21no—
77C4×Dic47—21no—
78C4×Dic47D411yescharacteristic
79C4×Dic47D411yescharacteristic
80C4×Dic47C2311yescharacteristic
81C2×C47⋊C8C2312yes—
82Dic188—42no—
83#10625325—42no—
84C22×D47—21no—
85C22×D47C2×D411yescharacteristic
86Q8×C47—22no—
87Q8×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2411yescharacteristic
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99D188—22no—
100D188—42no—
101C4×D47—22no—
102C4×D47—22no—
103C4×D47—22no—
104C4×D47—44no—
105C4×D47—42no—
106Dic94—22no—
107Dic94—22no—
108Dic94—22no—
109Dic94—44no—
110C8×C47—22no—
111C47⋊C8—22no—
112C22×C47C22×D411yescharacteristic
113C2×D47—21no—
114C2×D47—21no—
115C2×D47—41no—
116C2×D47—41no—
117C2×D47—41no—
118C2×D47#13712yes—
119C4×C47—21no—
120C4×C47—21no—
121C4×C47—42no—
122C4×C47—41no—
123C4×C47—41no—
124C4×C47H(5,𝔽2)12yes—
125Dic47—21no—
126Dic47—21no—
127Dic47—42no—
128Dic47—41no—
129Dic47#13712yes—
130#3218—471nomaximal, Sylow
131C2×C47#53511yescharacteristic
132C2×C47C2×#13711yescharacteristic
133C2×C47C2×#13711yescharacteristic
134D47—22no—
135D47—81no—
136C2×C4⋊Q8—471no—
137#529—471no—
138#497—471no—
139#497—471no—
140#491—471no—
141#491D4711yescharacteristic, complemented
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×Q16—472no—
151C2×SD16—472no—
152C2×SD16—472no—
153C4⋊Q8—472no—
154C4⋊Q8—471no—
155C4⋊Q8—941no—
156C4⋊Q8—941no—
157C4⋊Q8C2×D4711yescharacteristic
158#126—941no—
159#125C2×D4711yescharacteristic
160#124—471no—
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#103C2×D4712yes—
175#103C2×D4712yes—
176C22⋊C8—472no—
177#97—471no—
178#97C2×D4711yescharacteristic
179C2×Q8—472no—
180C2×Q8—471no—
181C2×Q8—942no—
182C2×Q8—1882no—
183C2×Q8—1882no—
184C2×Q8C22×D4712yes—
185C2×D4—471no—
186C2×D4—941no—
187C22×C4—471no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—941no—
191C22×C4—942no—
192Q16—1882no—
193Q16—1882no—
194SD16—1882no—
195SD16—1882no—
196C2×C8—472no—
197C2×C8C22×D4712yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—942no—
203C4⋊C4—942no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4C22×D4711yescharacteristic
209C4⋊C4C22×D4711yescharacteristic
210C22⋊C4—941no—
211C22⋊C4—941no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C22⋊C4—941no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—471no—
221C23—941no—
222Q8—22no—
223Q8—22no—
224Q8—942no—
225Q8—942no—
226Q8—942no—
227Q8—1884no—
228D4—942no—
229D4—1882no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—471no—
234C2×C4—471no—
235C2×C4—471no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—941no—
240C2×C4—942no—
241C2×C4—1882no—
242C2×C4—1884no—
243C2×C4D4×D4711yescharacteristic
244C2×C4D4×D4711yescharacteristic
245C2×C4C23×D4711yescharacteristic
246C8—22no—
247C8—942no—
248C22—472no—
249C22—941no—
250C22—941no—
251C22—1881no—
252C22—1881no—
253C22—1881no—
254C22C2×D4×D4711yescharacteristic
255C4—21no—
256C4—21no—
257C4—41no—
258C4—41no—
259C4—42no—
260C4—472no—
261C4—941no—
262C4—941no—
263C4—1882no—
264C4—1881no—
265C4#1309407012yes—
266C2—942no—
267C2—3761no—
268C2#1568969111yescharacteristic
269C2#137×D4711yescharacteristic
270C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3218
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D47C2semidirect
3. #15689517C2semidirect
4. #15689515C2semidirect
5. #15689493C2semidirect
6. #15689332C2semidirect
7. #15689327C2semidirect
8. #15689280C2semidirect
10. #15689178C2semidirect
11. C47×#491C2semidirect
141. #491D47semidirect
147. C47#3218semidirect