Finite Group Databasebeta

← #20248336

Subgroups — #20248336

Order 6016.

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

normal subgroups only

This group has 676 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
1C2×#13094023C211yesmaximal, characteristic, complemented
2C2×#13094002C212yesmaximal, complemented
3C2×#13094001C212yesmaximal, complemented
4C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
5#15689060C211yesmaximal, characteristic, complemented
6#15689059C211yesmaximal, characteristic, complemented
7#15689058C211yesmaximal, characteristic, complemented
8#15689023C212yesmaximal
9#15688992C212yesmaximal, complemented
10#15688974C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic, complemented
12C22×Dic94C2212yes—
13C22×C22⋊D47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16#13094023—24no—
17#13094002—28no—
18#13094001—28no—
19(C22⋊D47)⋊C4—24no—
20C2×C4⋊Dic47C2212yes—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2212yes—
25C2×Dic47⋊C4C2212yes—
26C2×Dic47⋊C4C2212yes—
27C2×C22⋊Dic47C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×(C2×D47)⋊C4C2212yes—
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×C4×Dic47C2212yes—
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C2×C22⋊C4×C47C2211yescharacteristic
38#95×C47C2211yescharacteristic
39C24×C47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47Q814yescomplemented
48C22×Dic47—22no—
49C22×Dic47—24no—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2312yes—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C2×C4×D47—22no—
56C2×C4×D47—24no—
57C2×Dic94—24no—
58C2×Dic94—24no—
59C2×Dic94—24no—
60C4⋊C4×C47—24no—
61C4⋊C4×C47—22no—
62C22⋊C4×C47—22no—
63C22⋊C4×C47—24no—
64C22⋊Dic47—24no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—24no—
67(C2×D47)⋊C4—24no—
68C4⋊Dic47—24no—
69C4⋊Dic47—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—24no—
72Dic47⋊C4—24no—
73Dic47⋊C4—24no—
74Dic47⋊C4D418yescomplemented
75C4×Dic47—24no—
76C4×Dic47D414yes—
77C23×C47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47C2×Q812yes—
82C23×C47C2411yescharacteristic
83C22×D47—22no—
84C22×D47—21no—
85C22×D47—21no—
86C22×D47—22no—
87C22×D47C2×Q812yes—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D414yes—
98C22⋊D47—28no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—22no—
106C2×Dic47—44no—
107C2×Dic47C2×D414yes—
108C2×Dic47C2×D412yes—
109C2×Dic47C2×D412yes—
110C2×Dic47C2×D414yes—
111C2×Dic47C2×Q812yes—
112C2×Dic47#4112yes—
113C4×D47—44no—
114Dic94—48no—
115C22×C47—22no—
116C22×C47—24no—
117C22×C47—41no—
118C22×C47—41no—
119C22×C47—42no—
120C22×C47C22×D411yescharacteristic
121C22×C47C22×D412yes—
122C22×C47C22×Q811yescharacteristic
123C22×C47C2×#4111yescharacteristic
124C22×C472−1+412yes—
125C2×D47—22no—
126C2×D47—24no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C4×C47—22no—
131C4×C47—24no—
132C4×C47—42no—
133C4×C47—41no—
134Dic47—24no—
135Dic47—42no—
136Dic47—41no—
137Dic47C22⋊Q814yescomplemented
138Dic47#12714yes—
139#2542—471nomaximal, Sylow
140C2×C47—42no—
141C2×C47C2×C22⋊Q811yescharacteristic
142C2×C47C2×#12711yescharacteristic
143C2×C47#53611yescharacteristic
144C2×C47#54712yes—
145C2×C47D4×Q812yes—
146D47—42no—
147C2×C4⋊Q8—471no—
148C2×C22⋊Q8—472no—
149C2×C22⋊Q8—472no—
150C2×C4×D4—471no—
151#399—471no—
152#399—471no—
153#399—471no—
154#399D4711yescharacteristic, complemented
155#390—472no—
156#384—472no—
157C4×C4⋊C4—471no—
158C47#254211yescharacteristic, complemented, Sylow
159C22×Q8—472no—
160C22×D4—471no—
161C23×C4—471no—
162C23×C4—471no—
163C4⋊Q8—944no—
164C22⋊Q8—948no—
165C22⋊Q8—948no—
166C4×D4—944no—
167C2×C4⋊C4—472no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4—472no—
172C2×C4⋊C4—472no—
173C2×C4⋊C4—471no—
174C2×C4⋊C4C2×D4712yes—
175C2×C4⋊C4C2×D4711yescharacteristic
176C2×C22⋊C4—472no—
177C2×C22⋊C4—471no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4C2×D4711yescharacteristic
181C2×C22⋊C4C2×D4712yes—
182C2×C42—471no—
183C2×C42—472no—
184#95—471no—
185#95C2×D4711yescharacteristic
186C24—471no—
187C24C22×D4711yescharacteristic
188C2×Q8—944no—
189C2×Q8—944no—
190C2×Q8—944no—
191C2×D4—474no—
192C2×D4—942no—
193C2×D4—942no—
194C22×C4—471no—
195C22×C4—471no—
196C22×C4—472no—
197C22×C4—472no—
198C22×C4—471no—
199C22×C4—942no—
200C22×C4—944no—
201C22×C4—942no—
202C22×C4—944no—
203C22×C4C22×D4712yes—
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4711yescharacteristic
206C22×C4C22×D4712yes—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—478no—
210C4⋊C4—942no—
211C4⋊C4—944no—
212C4⋊C4—944no—
213C4⋊C4—944no—
214C4⋊C4—944no—
215C4⋊C4—942no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—944no—
219C22⋊C4—944no—
220C22⋊C4—942no—
221C22⋊C4—944no—
222C42—474no—
223C42—944no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—472no—
229C23—942no—
230C23—941no—
231C23—941no—
232C23—942no—
233C23Q8×D4712yes—
234C23C23×D4711yescharacteristic
235Q8—1888no—
236D4—948no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—472no—
246C2×C4—472no—
247C2×C4—474no—
248C2×C4—472no—
249C2×C4—472no—
250C2×C4—474no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—941no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—1884no—
259C2×C4—1884no—
260C2×C4D4×D4712yes—
261C2×C4D4×D4714yes—
262C22—24no—
263C22—22no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—944no—
268C22—942no—
269C22—1882no—
270C22—1881no—
271C22—1881no—
272C22C2×D4×D4712yes—
273C22C2×D4×D4711yescharacteristic
274C22C2×Q8×D4711yescharacteristic
275C22#41×D4711yescharacteristic
276C22#1309407112yes—
277C4—24no—
278C4—22no—
279C4—41no—
280C4—42no—
281C4—474no—
282C4—474no—
283C4—944no—
284C4—1881no—
285C4—1882no—
286C2—42no—
287C2—1882no—
288C2C22⋊Q8×D4711yescharacteristic
289C2#127×D4711yescharacteristic
290C2#1568969511yescharacteristic
291C2#1568977112yes—
292C2#1568978612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2542
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
2. C2×#13094002C2semidirect
3. C2×#13094001C2semidirect
5. #15689060C2semidirect
6. #15689059C2semidirect
7. #15689058C2semidirect
9. #15688992C2semidirect
10. #15688974C2semidirect
11. C47×#399C2semidirect
47. C2×C22⋊D47Q8semidirect
74. Dic47⋊C4D4semidirect
137. Dic47C22⋊Q8semidirect
154. #399D47semidirect
158. C47#2542semidirect