Finite Group Databasebeta

← #20246748

Subgroups — #20246748

Order 6016.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×Q8×D47C211yesmaximal, characteristic, complemented
2C2×#13094002C212yesmaximal, complemented
3C2×#13093986C211yesmaximal, characteristic
4#15689043C211yesmaximal, characteristic, complemented
5#15689036C211yesmaximal, characteristic, complemented
6#15689034C211yesmaximal, characteristic, complemented
7#15689027C212yesmaximal, complemented
8#15689001C212yesmaximal
9#15688994C212yesmaximal, complemented
10#15688982C211yesmaximal, characteristic, complemented
11C47×#395C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2212yes—
14C2×Q8×D47—24no—
15C2×Q8×D47—28no—
16C22×D188C2211yescharacteristic
17C22×C4×D47C2212yes—
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094002—28no—
21#13093986—24no—
22C2×Dic47⋊C4C2212yes—
23C2×Dic47⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C47⋊#95C2212yes—
34C22×Q8×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2212yes—
36C2×C4⋊C4×C47C2211yescharacteristic
37#95×C47C2211yescharacteristic
38#95×C47C2212yes—
39C23×D47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C2×Q8×C47—22no—
42C2×Q8×C47—24no—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2312yes—
47C22×C4×C47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52Q8×D47—232no—
53C2×D188—22no—
54C2×D188—22no—
55C2×D188Q814yescomplemented
56C2×C4×D47—24no—
57C2×C4×D47—24no—
58C2×C4×D47—24no—
59C2×C4×D47—24no—
60C2×C4×D47—22no—
61C2×C4×D47—24no—
62C2×C4×D47D414yes—
63C2×Dic94—22no—
64C2×Dic94—24no—
65C2×Dic94—24no—
66C2×Dic94—24no—
67C2×Dic94D418yescomplemented
68C4⋊C4×C47—22no—
69C4⋊C4×C47—24no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—24no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—24no—
75Dic47⋊C4—24no—
76Dic47⋊C4—24no—
77C4×Dic47—22no—
78C23×C47C2411yescharacteristic
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—21no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47C2×D412yes—
86C22×D47C2×Q812yes—
87C22×D47C2×Q812yescomplemented
88C22×D47#4112yes—
89Q8×C47—28no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—21no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2×D414yes—
102C2×C4×C47C2×Q812yescomplemented
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47C2×D414yes—
111C2×Dic47C2×D412yes—
112C2×Dic47C2×D414yes—
113D188—28no—
114C4×D47—216no—
115C4×D47—28no—
116C4×D47—44no—
117Dic94—28no—
118Dic94—216no—
119C22×C47C22×D411yescharacteristic
120C22×C47C22×D412yes—
121C22×C47C22×Q811yescharacteristic
122C22×C47C2×#4111yescharacteristic
123C22×C472−1+412yes—
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—24no—
127C2×D47—24no—
128C2×D47—22no—
129C2×D47—24no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—42no—
133C2×D47C22⋊Q814yescomplemented
134C4×C47—22no—
135C4×C47—24no—
136C4×C47—22no—
137C4×C47—41no—
138C4×C47—42no—
139Dic47—24no—
140Dic47—41no—
141Dic47—42no—
142Dic47#12014yes—
143#2409—471nomaximal, Sylow
144C2×C47C2×#12011yescharacteristic
145C2×C47C2×C22⋊Q811yescharacteristic
146C2×C47#53611yescharacteristic
147C2×C47#54812yes—
148C2×C47D4×Q812yes—
149D47—24no—
150D47—42no—
151C23×Q8—471no—
152C2×C22⋊Q8—472no—
153C2×C4×D4—471no—
154#395—471no—
155#395D4711yescharacteristic, complemented
156#393—471no—
157#393—471no—
158#391—472no—
159#386—472no—
160#385—472no—
161#380—471no—
162C47#240911yescharacteristic, complemented, Sylow
163C22×Q8—472no—
164C22×Q8—471no—
165C22×Q8—944no—
166C22×Q8—948no—
167C22×Q8C2×D4711yescharacteristic
168C22×D4—471no—
169C23×C4—471no—
170C23×C4—471no—
171C23×C4—472no—
172C22⋊Q8—948no—
173C4×D4—944no—
174C2×C4⋊C4—472no—
175C2×C4⋊C4—472no—
176C2×C4⋊C4C2×D4711yescharacteristic
177C2×C4⋊C4C2×D4712yes—
178C2×C22⋊C4—471no—
179C2×C22⋊C4—471no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—472no—
183C2×C42—471no—
184#95—471no—
185#95—472no—
186#95—472no—
187#95—472no—
188#95C2×D4711yescharacteristic
189#95C2×D4712yes—
190C24—471no—
191C24—471no—
192C2×Q8—22no—
193C2×Q8—24no—
194C2×Q8—478no—
195C2×Q8—944no—
196C2×Q8—944no—
197C2×Q8—944no—
198C2×Q8—9432no—
199C2×Q8—942no—
200C2×D4—474no—
201C2×D4—942no—
202C2×D4—942no—
203C22×C4—471no—
204C22×C4—472no—
205C22×C4—474no—
206C22×C4—471no—
207C22×C4—472no—
208C22×C4—944no—
209C22×C4—944no—
210C22×C4—942no—
211C22×C4—944no—
212C22×C4—944no—
213C22×C4—944no—
214C22×C4C22×D4712yes—
215C22×C4C22×D4711yescharacteristic
216C22×C4C22×D4711yescharacteristic
217C22×C4C22×D4712yes—
218C22×C4C22×D4711yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—24no—
221C4⋊C4—944no—
222C4⋊C4—944no—
223C22⋊C4—944no—
224C22⋊C4—944no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C22⋊C4—944no—
228C42—942no—
229C23—472no—
230C23—472no—
231C23—472no—
232C23—472no—
233C23—942no—
234C23—942no—
235C23—942no—
236C23—941no—
237C23—941no—
238C23—942no—
239C23C23×D4711yescharacteristic
240Q8—28no—
241Q8—9416no—
242Q8—948no—
243D4—948no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—472no—
255C2×C4—474no—
256C2×C4—474no—
257C2×C4—948no—
258C2×C4—9416no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—1884no—
267C2×C4D4×D4712yes—
268C2×C4D4×D4714yes—
269C2×C4Q8×D4712yescomplemented
270C22—474no—
271C22—944no—
272C22—944no—
273C22—942no—
274C22—942no—
275C22—944no—
276C22—942no—
277C22—1882no—
278C22—1881no—
279C22—1881no—
280C22C2×D4×D4712yes—
281C22C2×D4×D4711yescharacteristic
282C22C2×Q8×D4711yescharacteristic
283C22#41×D4711yescharacteristic
284C22#1309407212yes—
285C4—22no—
286C4—24no—
287C4—22no—
288C4—42no—
289C4—41no—
290C4—474no—
291C4—944no—
292C4—1882no—
293C4—1881no—
294C2—944no—
295C2—1882no—
296C2#120×D4711yescharacteristic
297C2C22⋊Q8×D4711yescharacteristic
298C2#1568969811yescharacteristic
299C2#1568978312yes—
300C2#1568978812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2409
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D47C2semidirect
2. C2×#13094002C2semidirect
4. #15689043C2semidirect
5. #15689036C2semidirect
6. #15689034C2semidirect
7. #15689027C2semidirect
9. #15688994C2semidirect
10. #15688982C2semidirect
11. C47×#395C2semidirect
55. C2×D188Q8semidirect
67. C2×Dic94D4semidirect
87. C22×D47C2×Q8semidirect
102. C2×C4×C47C2×Q8semidirect
133. C2×D47C22⋊Q8semidirect
155. #395D47semidirect
162. C47#2409semidirect
269. C2×C4Q8×D47semidirect