Finite Group Databasebeta

← #20249528

Subgroups — #20249528

Order 6016.

534 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13094012C211yesmaximal, characteristic, complemented
2#15689045C212yesmaximal, complemented
3#15689043C211yesmaximal, characteristic, complemented
4#15689040C211yesmaximal, characteristic, complemented
5#15689039C212yesmaximal, complemented
6#15689035C211yesmaximal, characteristic, complemented
7#15689032C211yesmaximal, characteristic
8#15689023C212yesmaximal, complemented
9#15689013C212yesmaximal, complemented
10C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
11C2×#126×C47C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×C22⋊D47C2212yes—
15#13094012—24no—
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29#126×C47—24no—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C42×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C23×D47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—24no—
46C2×C22⋊D47—42no—
47C2×C22⋊D47—42no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C2×D188—22no—
52C2×D188—42no—
53C2×Dic94—22no—
54C2×Dic94—42no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—22no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47—22no—
60C22⋊C4×C47—22no—
61C42×C47D414yescomplemented
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—42no—
67(C2×D47)⋊C4—42no—
68C4⋊Dic47—24no—
69Dic47⋊C4—42no—
70C4×Dic47—42no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47C2411yescharacteristic
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47C2×D412yes—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C22⋊D47—48no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47#4114yes—
108D188—44no—
109Dic94—44no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47C22×D411yescharacteristic
116C22×C47C2×#4112yes—
117C22×C47H(5,𝔽2)12yes—
118C22×C47H(5,𝔽2)11yescharacteristic
119C22×C472−1+411yescharacteristic
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—42no—
123C2×D47—42no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—42no—
127C4×C47—22no—
128C4×C47—22no—
129C4×C47—22no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47—41no—
133Dic47—24no—
134Dic47—42no—
135Dic47—42no—
136#2662—471nomaximal, Sylow
137C2×C47—81no—
138C2×C47#53211yescharacteristic
139C2×C47#53511yescharacteristic
140C2×C47#53711yescharacteristic
141C2×C47#53812yes—
142C2×C47#54212yes—
143D47—82no—
144C2×#126D4711yescharacteristic, complemented
145C2×#124—471no—
146#396—472no—
147#395—471no—
148#394—471no—
149#394—472no—
150#393—471no—
151#392—471no—
152#390—472no—
153#388—472no—
154C4×C4⋊C4—471no—
155C47#266211yescharacteristic, complemented, Sylow
156C22×Q8—471no—
157C22×D4—472no—
158C22×D4—471no—
159#126—24no—
160#124—944no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4C2×D4711yescharacteristic
164C2×C4⋊C4C2×D4711yescharacteristic
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4—472no—
170C2×C22⋊C4—472no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4C2×D4711yescharacteristic
173C2×C22⋊C4C2×D4711yescharacteristic
174C2×C22⋊C4C2×D4711yescharacteristic
175C2×C42—472no—
176C2×C42C2×D4711yescharacteristic
177#95—471no—
178#95—471no—
179#95—472no—
180#95—472no—
181C24—472no—
182C24C22×D4711yescharacteristic
183C2×Q8—942no—
184C2×Q8—1882no—
185C2×D4—944no—
186C2×D4—942no—
187C2×D4—1882no—
188C2×D4—1882no—
189C2×D4—1882no—
190C22×C4—472no—
191C22×C4—472no—
192C22×C4—472no—
193C22×C4C22×D4711yescharacteristic
194C22×C4C22×D4711yescharacteristic
195C22×C4C22×D4711yescharacteristic
196C22×C4C22×D4711yescharacteristic
197C22×C4C22×D4711yescharacteristic
198C22×C4C22×D4711yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—944no—
203C4⋊C4—1882no—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—944no—
208C22⋊C4—944no—
209C22⋊C4—944no—
210C22⋊C4—1882no—
211C22⋊C4—1882no—
212C22⋊C4—1882no—
213C42—1882no—
214C42C22⋊D4714yescomplemented
215C23—21no—
216C23—22no—
217C23—22no—
218C23—21no—
219C23—21no—
220C23—942no—
221C23—942no—
222C23—942no—
223C23—942no—
224C23—942no—
225C23—942no—
226C23—942no—
227C23C23×D4711yescharacteristic
228Q8—1884no—
229D4—1884no—
230D4—1888no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—474no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4C2×C22⋊D4712yes—
252C2×C4C2×C22⋊D4712yes—
253C2×C4C2×C22⋊D4712yes—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—1882no—
260C22—1882no—
261C22—1882no—
262C22—1882no—
263C22—1882no—
264C22—1882no—
265C22—1882no—
266C22C22×C22⋊D4711yescharacteristic
267C22#41×D4712yes—
268C22#1309407012yes—
269C22#1309407011yescharacteristic
270C22#1309407111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—944no—
278C4—1882no—
279C4—1882no—
280C2—81no—
281C2—3762no—
282C2#1568966911yescharacteristic
283C2#1568968711yescharacteristic
284C2#1568970111yescharacteristic
285C2#1568971212yes—
286C2#1568973912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#126×C47C2
hypercenterC2×#126D47
hypocenterC47#2662
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#13094012C2semidirect
2. #15689045C2semidirect
3. #15689043C2semidirect
4. #15689040C2semidirect
5. #15689039C2semidirect
6. #15689035C2semidirect
8. #15689023C2semidirect
9. #15689013C2semidirect
10. C4×C4⋊Dic47C2semidirect
11. C2×#126×C47C2semidirect
61. C42×C47D4semidirect
144. C2×#126D47semidirect
155. C47#2662semidirect
214. C42C22⋊D47semidirect