Finite Group Databasebeta

← #20248571

Subgroups — #20248571

Order 6016.

584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13094004C211yesmaximal, characteristic, complemented
2C2×#13093986C211yesmaximal, characteristic
3#15689058C211yesmaximal, characteristic, complemented
4#15689043C211yesmaximal, characteristic, complemented
5#15689036C211yesmaximal, characteristic, complemented
6#15689010C212yesmaximal, complemented
7#15689001C212yesmaximal
8#15688997C212yesmaximal, complemented
9#15688982C212yesmaximal, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#400C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×C4×D47C2212yes—
15C22×C4×D47C2211yescharacteristic
16C22×C4×D47C2211yescharacteristic
17#13094004—24no—
18#13093986—24no—
19C2×C4⋊Dic47C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C2×D188—22no—
49C2×D188—22no—
50C2×D188Q814yescomplemented
51C2×C4×D47—24no—
52C2×C4×D47—22no—
53C2×C4×D47—24no—
54C2×C4×D47—42no—
55C2×C4×D47—42no—
56C2×C4×D47—42no—
57C2×C4×D47D414yes—
58C2×Dic94—22no—
59C2×Dic94—42no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—42no—
67C4⋊Dic47—24no—
68Dic47⋊C4—24no—
69Dic47⋊C4—42no—
70C4×Dic47—22no—
71C23×C47C2411yescharacteristic
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—21no—
77C22×D47—22no—
78C22×D47C2×D412yes—
79C22×D47C2×Q812yes—
80C22×D47C2×Q812yes—
81C22×D47#4112yes—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×Q812yes—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47C2×D412yes—
104C2×Dic47#4114yes—
105D188—28no—
106C4×D47—44no—
107C4×D47—48no—
108C4×D47—44no—
109Dic94—44no—
110C22×C47C22×D411yescharacteristic
111C22×C47C22×Q811yescharacteristic
112C22×C47C2×#4111yescharacteristic
113C22×C47C2×#4112yes—
114C22×C47H(5,𝔽2)12yes—
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—24no—
118C2×D47—24no—
119C2×D47—22no—
120C2×D47—24no—
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—42no—
124C2×D47C22⋊Q814yes—
125C4×C47—22no—
126C4×C47—22no—
127C4×C47—42no—
128C4×C47—41no—
129C4×C47—42no—
130Dic47—22no—
131Dic47—24no—
132Dic47—41no—
133Dic47—42no—
134#2564—471nomaximal, Sylow
135C2×C47C2×C22⋊Q811yescharacteristic
136C2×C47#53211yescharacteristic
137C2×C47#53411yescharacteristic
138C2×C47#55112yes—
139C2×C47#55412yes—
140D47—24no—
141D47—42no—
142C2×C22⋊Q8—471no—
143C2×C4×D4—471no—
144#400D4711yescharacteristic, complemented
145#399—471no—
146#395—471no—
147#393—471no—
148#387—472no—
149#386—472no—
150#385—472no—
151#380—472no—
152C2×#95—471no—
153C47#256411yescharacteristic, complemented, Sylow
154C22×Q8—471no—
155C22×D4—471no—
156C23×C4—471no—
157C23×C4—472no—
158C23×C4—471no—
159C22⋊Q8—944no—
160C4×D4—944no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—472no—
164C2×C4⋊C4C2×D4711yescharacteristic
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4—471no—
167C2×C22⋊C4—471no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4—472no—
170C2×C22⋊C4—472no—
171C2×C42—471no—
172#95—472no—
173#95—471no—
174#95—472no—
175#95—472no—
176#95C2×D4711yescharacteristic
177#95C2×D4712yes—
178#95C2×D4712yes—
179C24—471no—
180C24—471no—
181C2×Q8—942no—
182C2×Q8—1882no—
183C2×D4—474no—
184C2×D4—942no—
185C2×D4—942no—
186C22×C4—472no—
187C22×C4—471no—
188C22×C4—474no—
189C22×C4—471no—
190C22×C4—472no—
191C22×C4—942no—
192C22×C4—944no—
193C22×C4—944no—
194C22×C4—1882no—
195C22×C4—1882no—
196C22×C4—1882no—
197C22×C4C22×D4712yes—
198C22×C4C22×D4712yes—
199C22×C4C22×D4711yescharacteristic
200C22×C4C22×D4711yescharacteristic
201C22×C4C22×D4711yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—944no—
205C4⋊C4—944no—
206C4⋊C4—1882no—
207C22⋊C4—944no—
208C22⋊C4—942no—
209C22⋊C4—944no—
210C22⋊C4—942no—
211C22⋊C4—1882no—
212C42—942no—
213C23—472no—
214C23—472no—
215C23—472no—
216C23—472no—
217C23—942no—
218C23—942no—
219C23—941no—
220C23—942no—
221C23—941no—
222C23—942no—
223C23C23×D4711yescharacteristic
224Q8—1884no—
225D4—948no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—472no—
238C2×C4—474no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—941no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—1884no—
248C2×C4—1888no—
249C2×C4—1884no—
250C2×C4D4×D4712yes—
251C2×C4Q8×D4712yes—
252C22—474no—
253C22—944no—
254C22—944no—
255C22—942no—
256C22—942no—
257C22—944no—
258C22—942no—
259C22—1882no—
260C22—1881no—
261C22—1881no—
262C22C2×D4×D4711yescharacteristic
263C22C2×Q8×D4711yescharacteristic
264C22#41×D4711yescharacteristic
265C22#41×D4712yes—
266C22#1309407012yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—41no—
272C4—944no—
273C4—942no—
274C4—1881no—
275C4—1882no—
276C2—944no—
277C2—1882no—
278C2C22⋊Q8×D4711yescharacteristic
279C2#1568967211yescharacteristic
280C2#1568968411yescharacteristic
281C2#1568979812yes—
282C2#1568982912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2564
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13094004C2semidirect
3. #15689058C2semidirect
4. #15689043C2semidirect
5. #15689036C2semidirect
6. #15689010C2semidirect
8. #15688997C2semidirect
9. #15688982C2semidirect
10. #95×D47C2semidirect
11. C47×#400C2semidirect
50. C2×D188Q8semidirect
144. #400D47semidirect
153. C47#2564semidirect