Finite Group Databasebeta

← #20251419

Subgroups — #20251419

Order 6016.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094002C211yesmaximal, characteristic, complemented
2C2×#13093995C211yesmaximal, characteristic
3#15689059C212yesmaximal, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689053C211yesmaximal, characteristic, complemented
6#15689039C212yesmaximal, complemented
7#15689038C212yesmaximal, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15689035C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C4×D47C2211yescharacteristic
15#13094002—24no—
16#13093995—24no—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C23×D47C2311yescharacteristic
39C2×D4×C47—22no—
40C2×D4×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—24no—
46C2×C22⋊D47—42no—
47C2×C22⋊D47—42no—
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C2×C4×D47—42no—
54C2×C4×D47D414yes—
55C2×Dic94—22no—
56C2×Dic94—42no—
57C4⋊C4×C47—22no—
58C22⋊C4×C47—42no—
59C22⋊C4×C47—42no—
60C22⋊Dic47—24no—
61C22⋊Dic47—42no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—42no—
66C4⋊Dic47—22no—
67C4⋊Dic47—42no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—42no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2411yescharacteristic
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47C2×D412yes—
84D4×C47—44no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47C2×D412yes—
95C22⋊D47—48no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47C2×D412yes—
109C4×D47—44no—
110Dic94—44no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47C22×D411yescharacteristic
119C22×C47H(5,𝔽2)12yes—
120C22×C47H(5,𝔽2)11yescharacteristic
121C22×C47H(5,𝔽2)11yescharacteristic
122C22×C472−1+412yes—
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—42no—
127C2×D47—42no—
128C4×C47—22no—
129C4×C47—41no—
130C4×C47—41no—
131C4×C47—42no—
132Dic47—22no—
133Dic47—41no—
134Dic47—41no—
135Dic47—42no—
136Dic47—42no—
137#2816—471nomaximal, Sylow
138C2×C47—82no—
139C2×C47#53411yescharacteristic
140C2×C47#53511yescharacteristic
141C2×C47#53611yescharacteristic
142C2×C47#56212yes—
143C2×C47#56212yes—
144D47—42no—
145C2×C22⋊Q8—471no—
146C2×#121—471no—
147#399—472no—
148#398—471no—
149#398—471no—
150#394—471no—
151#394—472no—
152#394—472no—
153#394D4711yescharacteristic, complemented
154#393—472no—
155#381—471no—
156C47#281611yescharacteristic, complemented, Sylow
157C22×Q8—471no—
158C22×D4—472no—
159C22×D4C2×D4711yescharacteristic
160C23×C4—471no—
161C22⋊Q8—944no—
162#121—944no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—471no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—472no—
167C2×C4⋊C4—472no—
168C2×C4⋊C4C2×D4711yescharacteristic
169C2×C22⋊C4—472no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—471no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4C2×D4712yes—
176C2×C22⋊C4C2×D4712yes—
177#95—472no—
178#95—471no—
179#95—472no—
180#95—472no—
181#95C2×D4711yescharacteristic
182C24—471no—
183C24C22×D4712yes—
184C2×Q8—942no—
185C2×Q8—1882no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—944no—
189C2×D4—1882no—
190C2×D4—1882no—
191C22×C4—471no—
192C22×C4—474no—
193C22×C4—472no—
194C22×C4—471no—
195C22×C4—472no—
196C22×C4—471no—
197C22×C4—1882no—
198C22×C4C22×D4712yes—
199C22×C4C22×D4711yescharacteristic
200C22×C4C22×D4711yescharacteristic
201C22×C4C22×D4711yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—942no—
204C4⋊C4—942no—
205C4⋊C4—942no—
206C4⋊C4—1882no—
207C4⋊C4—1882no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—944no—
213C22⋊C4—1882no—
214C22⋊C4—1882no—
215C22⋊C4—1882no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—472no—
224C23—942no—
225C23—941no—
226C23—941no—
227C23—942no—
228C23C23×D4711yescharacteristic
229Q8—1884no—
230D4—44no—
231D4—1888no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—472no—
242C2×C4—942no—
243C2×C4—941no—
244C2×C4—942no—
245C2×C4—941no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—941no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—1884no—
255C2×C4D4×D4712yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—942no—
264C22—942no—
265C22—942no—
266C22—1882no—
267C22—1882no—
268C22C2×D4×D4711yescharacteristic
269C22#1309406911yescharacteristic
270C22#1309406912yes—
271C22#1309407011yescharacteristic
272C22#1309407112yes—
273C4—22no—
274C4—42no—
275C4—41no—
276C4—41no—
277C4—942no—
278C4—1882no—
279C4—1881no—
280C4—1882no—
281C4—1881no—
282C2—82no—
283C2—1882no—
284C2#1568968311yescharacteristic
285C2#1568968911yescharacteristic
286C2#1568969311yescharacteristic
287C2#1568986812yes—
288C2#1568987012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2816
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
3. #15689059C2semidirect
4. #15689055C2semidirect
5. #15689053C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689037C2semidirect
9. #15689035C2semidirect
10. #15688985C2semidirect
11. C47×#394C2semidirect
153. #394D47semidirect
156. C47#2816semidirect