Finite Group Databasebeta

← #20249973

Subgroups — #20249973

Order 6016.

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

normal subgroups only

This group has 612 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×#13093996C212yesmaximal, complemented
2#15689053C211yesmaximal, characteristic, complemented
3#15689040C211yesmaximal, characteristic, complemented
4#15689039C212yesmaximal, complemented
5#15689032C212yesmaximal, complemented
6#15689014C212yesmaximal, complemented
7#15689000C212yesmaximal, complemented
8#15688984C212yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C22×C22⋊D47C2212yes—
13C23×Dic47C2212yes—
14#13093996—28no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C47⋊#95C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C22×D4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2212yes—
31C2×C42×C47C2211yescharacteristic
32C24×C47C2312yes—
33C23×D47C2312yes—
34C2×D4×C47—41no—
35C2×D4×C47—41no—
36C2×D4×C47D414yescomplemented
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—24no—
42C2×C22⋊D47—24no—
43C2×C22⋊D47—24no—
44C2×C22⋊D47—42no—
45C2×C22⋊D47—42no—
46C2×C22⋊D47—42no—
47C22×Dic47—24no—
48C22×Dic47—24no—
49C22×Dic47—42no—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C22×Dic47C2312yes—
53C2×D188—42no—
54C2×D188—41no—
55C4⋊C4×C47—41no—
56C22⋊C4×C47—42no—
57C22⋊C4×C47—42no—
58C42×C47—41no—
59C22⋊Dic47—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—42no—
63(C2×D47)⋊C4—42no—
64C4⋊Dic47—41no—
65Dic47⋊C4—24no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47C2×D414yes—
73C23×C47C2411yescharacteristic
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—22no—
81D4×C47—44no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47C2×D412yes—
92C22⋊D47—48no—
93C22⋊D47—48no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—48no—
103C2×Dic47#4114yes—
104D188—44no—
105C22×C47—24no—
106C22×C47—24no—
107C22×C47—24no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47C22×D411yescharacteristic
113C22×C47C2×#4112yes—
114C22×C47H(5,𝔽2)11yescharacteristic
115C22×C47H(5,𝔽2)11yescharacteristic
116C22×C47H(5,𝔽2)12yes—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—42no—
123C2×D47—42no—
124C4×C47—22no—
125C4×C47—42no—
126C4×C47—41no—
127C4×C47—41no—
128Dic47—24no—
129Dic47—42no—
130Dic47—42no—
131#2699—471nomaximal, Sylow
132C2×C47—44no—
133C2×C47#53411yescharacteristic
134C2×C47#54012yes—
135C2×C47#54612yes—
136C2×C47#55511yescharacteristic
137C2×C47#56011yescharacteristic
138D47—82no—
139C2×#121—472no—
140#398—471no—
141#394—471no—
142#394—472no—
143#392—472no—
144#390D4711yescharacteristic, complemented
145#388—472no—
146#386—472no—
147#381—472no—
148C47#269911yescharacteristic, complemented, Sylow
149C22×D4—472no—
150C22×D4—472no—
151C22×D4—471no—
152C22×D4C2×D4711yescharacteristic
153C23×C4—472no—
154#121—948no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4C2×D4711yescharacteristic
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4C2×D4712yes—
164C2×C22⋊C4C2×D4712yes—
165C2×C42C2×D4711yescharacteristic
166#95—471no—
167#95—472no—
168#95—472no—
169#95—472no—
170#95—471no—
171C24—472no—
172C24C22×D4712yes—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4—944no—
176C2×D4—944no—
177C2×D4—944no—
178C2×D4—1882no—
179C2×D4—1881no—
180C2×D4—1882no—
181C2×D4—1882no—
182C2×D4—1882no—
183C2×D4D18814yescomplemented
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—472no—
187C22×C4—944no—
188C22×C4—944no—
189C22×C4—1882no—
190C22×C4C22×D4711yescharacteristic
191C22×C4C22×D4712yes—
192C22×C4C22×D4711yescharacteristic
193C22×C4C22×D4711yescharacteristic
194C4⋊C4—41no—
195C4⋊C4—944no—
196C4⋊C4—1881no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—944no—
200C22⋊C4—944no—
201C22⋊C4—944no—
202C22⋊C4—1882no—
203C22⋊C4—1882no—
204C42—41no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23—942no—
212C23—942no—
213C23—942no—
214C23—942no—
215C23—942no—
216C23—942no—
217C23—942no—
218C23C2×D18814yes—
219C23C23×D4711yescharacteristic
220D4—44no—
221D4—1884no—
222D4—1888no—
223D4—1888no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—474no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—1888no—
243C2×C4C2×D18812yes—
244C22—24no—
245C22—24no—
246C22—24no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—1882no—
252C22—1882no—
253C22—1882no—
254C22—1882no—
255C22—1882no—
256C22—1882no—
257C22—1882no—
258C22C22×D18811yescharacteristic
259C22#41×D4712yes—
260C22#1309406912yes—
261C22#1309406911yescharacteristic
262C22#1309406911yescharacteristic
263C4—22no—
264C4—41no—
265C4—41no—
266C4—42no—
267C4—944no—
268C4—1882no—
269C4—1882no—
270C2—44no—
271C2—3762no—
272C2#1568968511yescharacteristic
273C2#1568972312yes—
274C2#1568976812yes—
275C2#1568983511yescharacteristic
276C2#1568986011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2699
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13093996C2semidirect
2. #15689053C2semidirect
3. #15689040C2semidirect
4. #15689039C2semidirect
5. #15689032C2semidirect
6. #15689014C2semidirect
7. #15689000C2semidirect
8. #15688984C2semidirect
9. C47×#390C2semidirect
36. C2×D4×C47D4semidirect
144. #390D47semidirect
148. C47#2699semidirect
183. C2×D4D188semidirect