Finite Group Databasebeta

← #20249077

Subgroups — #20249077

Order 6016.

576 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13093981C211yesmaximal, characteristic, complemented
2#15689042C211yesmaximal, characteristic, complemented
3#15689037C211yesmaximal, characteristic, complemented
4#15689034C211yesmaximal, characteristic, complemented
5#15689031C211yesmaximal, characteristic
6#15689023C212yesmaximal, complemented
7#15689017C212yesmaximal, complemented
8#15689011C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#15688969C211yesmaximal, characteristic, complemented
11C2×#124×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2212yes—
13C22×C4×D47C2211yescharacteristic
14#13093981—24no—
15C2×Dic47⋊C4C2211yescharacteristic
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×Q8×C47C2211yescharacteristic
32C22×D4×C47C2211yescharacteristic
33#124×C47—24no—
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36C2×C42×C47C2211yescharacteristic
37C24×C47C2312yes—
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C2×D4×C47—22no—
42C2×D4×C47—42no—
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—42no—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—22no—
58C22⋊C4×C47—24no—
59C22⋊C4×C47—24no—
60C42×C47D414yescomplemented
61C22⋊Dic47—24no—
62C22⋊Dic47—24no—
63C22⋊Dic47—42no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—42no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—42no—
70C4×Dic47—22no—
71C4×Dic47—24no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47C2411yescharacteristic
80C22×D47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47#4112yes—
85Q8×C47—44no—
86D4×C47—44no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D412yes—
96C2×C4×C47C2×D412yes—
97C22⋊D47—48no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47#4114yes—
110C2×Dic47#4112yes—
111C4×D47—28no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47C22×D411yescharacteristic
120C22×C47C2×#4111yescharacteristic
121C22×C47C2×#4111yescharacteristic
122C22×C47C2×#4112yes—
123C22×C47H(5,𝔽2)12yes—
124C2×D47—22no—
125C2×D47—24no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—42no—
129C4×C47—22no—
130C4×C47—22no—
131C4×C47—22no—
132C4×C47—42no—
133Dic47—22no—
134Dic47—24no—
135Dic47—41no—
136Dic47—41no—
137Dic47—42no—
138#2610—471nomaximal, Sylow
139C2×C47—82no—
140C2×C47#52511yescharacteristic
141C2×C47#53211yescharacteristic
142C2×C47#53511yescharacteristic
143C2×C47#55112yes—
144C2×C47#55512yes—
145D47—42no—
146C2×#124D4711yescharacteristic, complemented
147C2×#117—471no—
148#395—471no—
149#394—471no—
150#393—471no—
151#392—471no—
152#390—472no—
153#388—472no—
154#388—472no—
155#386—472no—
156#376—471no—
157C47#261011yescharacteristic, complemented, Sylow
158C22×Q8C2×D4711yescharacteristic
159C22×D4—472no—
160C22×D4C2×D4711yescharacteristic
161C23×C4—471no—
162#124—24no—
163#117—944no—
164C2×C4⋊C4—471no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4C2×D4712yes—
174C2×C22⋊C4C2×D4712yes—
175C2×C42—471no—
176C2×C42—472no—
177C2×C42C2×D4711yescharacteristic
178#95—472no—
179#95—471no—
180#95—471no—
181#95—472no—
182#95—472no—
183C24—471no—
184C24C22×D4712yes—
185C2×Q8—22no—
186C2×Q8—42no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—944no—
190C2×D4—944no—
191C2×D4—1882no—
192C22×C4—472no—
193C22×C4—471no—
194C22×C4—472no—
195C22×C4—471no—
196C22×C4—471no—
197C22×C4—942no—
198C22×C4—942no—
199C22×C4—942no—
200C22×C4C22×D4712yes—
201C22×C4C22×D4711yescharacteristic
202C22×C4C22×D4711yescharacteristic
203C22×C4C22×D4711yescharacteristic
204C4⋊C4—942no—
205C4⋊C4—942no—
206C4⋊C4—1882no—
207C22⋊C4—24no—
208C22⋊C4—24no—
209C22⋊C4—944no—
210C22⋊C4—944no—
211C22⋊C4—942no—
212C22⋊C4—942no—
213C22⋊C4—1882no—
214C22⋊C4—1882no—
215C42—944no—
216C42—942no—
217C42C22⋊D4714yescomplemented
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—472no—
226C23—941no—
227C23—941no—
228C23—942no—
229C23—942no—
230C23C23×D4711yescharacteristic
231Q8—44no—
232D4—44no—
233D4—1888no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—474no—
242C2×C4—472no—
243C2×C4—948no—
244C2×C4—941no—
245C2×C4—941no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—941no—
249C2×C4—941no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4C2×C22⋊D4712yes—
256C2×C4C2×C22⋊D4712yes—
257C2×C4C2×C22⋊D4712yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—944no—
266C22—942no—
267C22—1882no—
268C22—1881no—
269C22—1881no—
270C22C22×C22⋊D4711yescharacteristic
271C22#41×D4711yescharacteristic
272C22#41×D4712yes—
273C22#41×D4711yescharacteristic
274C22#1309406912yes—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—42no—
279C4—944no—
280C4—942no—
281C4—1882no—
282C4—1881no—
283C4—1881no—
284C2—82no—
285C2—1882no—
286C2#1568963011yescharacteristic
287C2#1568966911yescharacteristic
288C2#1568969011yescharacteristic
289C2#1568980312yes—
290C2#1568983512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#124×C47C2
hypercenterC2×#124D47
hypocenterC47#2610
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13093981C2semidirect
2. #15689042C2semidirect
3. #15689037C2semidirect
4. #15689034C2semidirect
6. #15689023C2semidirect
7. #15689017C2semidirect
8. #15689011C2semidirect
9. #15688999C2semidirect
10. #15688969C2semidirect
11. C2×#124×C47C2semidirect
60. C42×C47D4semidirect
146. C2×#124D47semidirect
157. C47#2610semidirect
217. C42C22⋊D47semidirect