Finite Group Databasebeta

← #20246629

Subgroups — #20246629

Order 6016.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×#13093986C212yesmaximal, complemented
2C2×#13093986C211yesmaximal, characteristic, complemented
3C2×#13093982C211yesmaximal, characteristic, complemented
4#15689049C211yesmaximal, characteristic, complemented
5#15689045C212yesmaximal, complemented
6#15689041C212yesmaximal, complemented
7#15689040C211yesmaximal, characteristic, complemented
8#15689033C211yesmaximal, characteristic
9#15688974C211yesmaximal, characteristic, complemented
10#15688970C212yesmaximal, complemented
11C47×#398C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×D188C2212yes—
14C22×C4×D47C2212yes—
15C22×C4×D47C2211yescharacteristic
16#13093986—28no—
17#13093986—24no—
18#13093982—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2212yes—
30C2×C4×Dic47C2211yescharacteristic
31C47⋊#95C2212yes—
32C47⋊#95C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35C2×C4⋊C4×C47C2211yescharacteristic
36#95×C47C2212yes—
37#95×C47C2211yescharacteristic
38C23×D47C2311yescharacteristic
39C23×D47C2312yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C2×D188—24no—
50C2×D188—24no—
51C2×D188—24no—
52C2×D188—22no—
53C2×D188—24no—
54C2×C4×D47—22no—
55C2×C4×D47—22no—
56C2×C4×D47—24no—
57C2×C4×D47—24no—
58C2×C4×D47—24no—
59C2×C4×D47D414yescomplemented
60C4⋊C4×C47—22no—
61C4⋊C4×C47—24no—
62C4⋊C4×C47—22no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—24no—
67(C2×D47)⋊C4—24no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—24no—
70C4⋊Dic47—22no—
71Dic47⋊C4—24no—
72C4×Dic47—22no—
73C4×Dic47—24no—
74C4×Dic47D414yescomplemented
75C23×C47C2411yescharacteristic
76C22×D47—21no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47C2×D412yes—
87C22×D47#4114yes—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D412yes—
100C2×C4×C47#4114yes—
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47C2×D412yes—
108C2×Dic47C2×D412yes—
109C2×Dic47C2×D412yes—
110C2×Dic47#4112yes—
111D188—28no—
112D188—216no—
113C4×D47—28no—
114C4×D47—48no—
115C22×C47C22×D411yescharacteristic
116C22×C47C22×D411yescharacteristic
117C22×C47C2×#4111yescharacteristic
118C22×C47C2×#4112yes—
119C22×C47C2×#4112yes—
120C2×D47—22no—
121C2×D47—24no—
122C2×D47—24no—
123C2×D47—24no—
124C2×D47—24no—
125C2×D47—42no—
126C2×D47—41no—
127C2×D47—42no—
128C2×D47—42no—
129C2×D47—42no—
130C2×D47—41no—
131C2×D47—42no—
132C4×C47—22no—
133C4×C47—22no—
134C4×C47—24no—
135C4×C47—42no—
136C4×C47—41no—
137Dic47—22no—
138Dic47—42no—
139Dic47—41no—
140Dic47#12114yes—
141#2392—471nomaximal, Sylow
142C2×C47C2×#12111yescharacteristic
143C2×C47#52511yescharacteristic
144C2×C47#52512yes—
145C2×C47#52912yes—
146C2×C47#53211yescharacteristic
147D47—42no—
148D47—44no—
149C2×C4×D4—471no—
150C2×C4×D4—472no—
151C2×#117—471no—
152#398D4711yescharacteristic, complemented
153#397—471no—
154#396—472no—
155#394—471no—
156#394—472no—
157#392—471no—
158C4×C4⋊C4—471no—
159C4×C22⋊C4—472no—
160C47#239211yescharacteristic, complemented, Sylow
161C22×D4—471no—
162C22×D4—472no—
163C23×C4—471no—
164C23×C4—472no—
165C4×D4—944no—
166C4×D4—948no—
167#117—944no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4C2×D4711yescharacteristic
171C2×C4⋊C4C2×D4712yes—
172C2×C4⋊C4C2×D4711yescharacteristic
173C2×C22⋊C4—471no—
174C2×C22⋊C4—471no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C42—471no—
181C2×C42—471no—
182C2×C42—472no—
183#95—472no—
184#95—471no—
185#95C2×D4712yes—
186#95C2×D4711yescharacteristic
187C24—471no—
188C24—472no—
189C2×D4—944no—
190C2×D4—944no—
191C2×D4—944no—
192C2×D4—942no—
193C2×D4—944no—
194C22×C4—471no—
195C22×C4—471no—
196C22×C4—474no—
197C22×C4—472no—
198C22×C4—471no—
199C22×C4—942no—
200C22×C4—942no—
201C22×C4—944no—
202C22×C4—944no—
203C22×C4—944no—
204C22×C4C22×D4712yes—
205C22×C4C22×D4711yescharacteristic
206C22×C4C22×D4711yescharacteristic
207C22×C4C22×D4711yescharacteristic
208C22×C4C22×D4712yes—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—942no—
213C4⋊C4—944no—
214C22⋊C4—942no—
215C22⋊C4—944no—
216C22⋊C4—944no—
217C22⋊C4—944no—
218C22⋊C4—942no—
219C22⋊C4—944no—
220C22⋊C4—944no—
221C42—474no—
222C42—942no—
223C42—944no—
224C23—472no—
225C23—474no—
226C23—941no—
227C23—942no—
228C23—942no—
229C23—941no—
230C23—942no—
231C23—942no—
232C23—942no—
233C23—942no—
234C23—942no—
235C23—942no—
236C23C23×D4711yescharacteristic
237D4—948no—
238D4—9416no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—472no—
250C2×C4—472no—
251C2×C4—472no—
252C2×C4—472no—
253C2×C4—948no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—941no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—1888no—
261C2×C4D4×D4712yes—
262C2×C4D4×D4712yes—
263C2×C4#1062535414yes—
264C22—942no—
265C22—944no—
266C22—944no—
267C22—944no—
268C22—944no—
269C22—1882no—
270C22—1881no—
271C22—1882no—
272C22—1882no—
273C22—1882no—
274C22—1881no—
275C22—1882no—
276C22C2×D4×D4711yescharacteristic
277C22C2×D4×D4711yescharacteristic
278C22#41×D4711yescharacteristic
279C22#41×D4712yes—
280C22C2×#1062535412yes—
281C4—22no—
282C4—22no—
283C4—24no—
284C4—42no—
285C4—41no—
286C4—474no—
287C4—942no—
288C4—1882no—
289C4—1881no—
290C2—1882no—
291C2—1884no—
292C2#121×D4711yescharacteristic
293C2#1568963111yescharacteristic
294C2#1568963612yes—
295C2#1568965812yes—
296C2#1568967411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2392
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13093986C2semidirect
2. C2×#13093986C2semidirect
3. C2×#13093982C2semidirect
4. #15689049C2semidirect
5. #15689045C2semidirect
6. #15689041C2semidirect
7. #15689040C2semidirect
9. #15688974C2semidirect
10. #15688970C2semidirect
11. C47×#398C2semidirect
59. C2×C4×D47D4semidirect
74. C4×Dic47D4semidirect
152. #398D47semidirect
160. C47#2392semidirect