Finite Group Databasebeta

← #20249214

Subgroups — #20249214

Order 6016.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13094023C211yesmaximal, characteristic, complemented
2C2×#13093980C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic, complemented
4#15689061C211yesmaximal, characteristic, complemented
5#15689059C211yesmaximal, characteristic
6#15689043C212yesmaximal, complemented
7#15689035C212yesmaximal
8#15689018C212yesmaximal, complemented
9#15688987C211yesmaximal, characteristic, complemented
10#15688981C212yesmaximal
11C47×#399C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13C23×Dic47C2211yescharacteristic
14#13094023—24no—
15#13093980—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—22no—
43C22×Dic47—22no—
44C22×Dic47Q814yescomplemented
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C2×Dic94—24no—
52C2×Dic94—42no—
53C2×Dic94—42no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—42no—
56C22⋊C4×C47—22no—
57C22⋊C4×C47—42no—
58C22⋊Dic47—22no—
59C22⋊Dic47—42no—
60C4⋊Dic47—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—24no—
65Dic47⋊C4—42no—
66C4×Dic47—22no—
67C4×Dic47D414yes—
68C23×C47—21no—
69C23×C47—21no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47C2×Q812yes—
73C23×C47C2411yescharacteristic
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D412yes—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—28no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47C2×D412yes—
97C2×Dic47C2×D412yes—
98C2×Dic47C2×Q812yes—
99C2×Dic47C2×Q812yes—
100C2×Dic47#4112yes—
101Dic94—48no—
102C22×C47—22no—
103C22×C47—24no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47—42no—
107C22×C47C22×D411yescharacteristic
108C22×C47C22×Q811yescharacteristic
109C22×C47C2×#4111yescharacteristic
110C22×C47H(5,𝔽2)12yes—
111C22×C472−1+412yes—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—42no—
116Dic47—22no—
117Dic47—22no—
118Dic47—42no—
119Dic47—41no—
120Dic47—42no—
121Dic47C22⋊Q814yes—
122#2628—471nomaximal, Sylow
123C2×C47—42no—
124C2×C47C2×C22⋊Q811yescharacteristic
125C2×C47#53511yescharacteristic
126C2×C47#53611yescharacteristic
127C2×C47#54212yes—
128C2×C47#54412yes—
129C2×C4⋊Q8—471no—
130C2×#117—471no—
131#400—471no—
132#400—471no—
133#399—471no—
134#399D4711yescharacteristic
135#395—472no—
136#393—472no—
137#389—472no—
138#382—471no—
139#380—472no—
140C47#262811yescharacteristic, complemented, Sylow
141C22×Q8—472no—
142C23×C4—471no—
143C4⋊Q8—944no—
144#117—944no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—472no—
150C2×C4⋊C4—472no—
151C2×C4⋊C4C2×D4711yescharacteristic
152C2×C4⋊C4C2×D4712yes—
153C2×C22⋊C4—471no—
154C2×C22⋊C4—472no—
155C2×C22⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4C2×D4712yes—
157C2×C42—471no—
158C2×C42—471no—
159#95—472no—
160#95—472no—
161#95—472no—
162#95—471no—
163#95—472no—
164#95—472no—
165#95C2×D4711yescharacteristic
166C24C22×D4711yescharacteristic
167C2×Q8—944no—
168C2×Q8—1882no—
169C2×Q8—1882no—
170C22×C4—471no—
171C22×C4—474no—
172C22×C4—471no—
173C22×C4—471no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—472no—
177C22×C4—942no—
178C22×C4—942no—
179C22×C4C22×D4712yes—
180C22×C4C22×D4712yes—
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—944no—
186C4⋊C4—942no—
187C4⋊C4—944no—
188C4⋊C4—942no—
189C4⋊C4—942no—
190C4⋊C4—1882no—
191C22⋊C4—22no—
192C22⋊C4—42no—
193C22⋊C4—942no—
194C22⋊C4—1882no—
195C42—474no—
196C42—942no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23Q8×D4712yes—
202C23C23×D4711yescharacteristic
203Q8—1888no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—472no—
214C2×C4—472no—
215C2×C4—472no—
216C2×C4—472no—
217C2×C4—472no—
218C2×C4—948no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4D4×D4712yes—
231C22—24no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—41no—
236C22C2×D4×D4711yescharacteristic
237C22C2×Q8×D4711yescharacteristic
238C22#41×D4711yescharacteristic
239C22#1309406912yes—
240C22#1309407112yes—
241C4—22no—
242C4—42no—
243C4—42no—
244C4—41no—
245C4—474no—
246C4—942no—
247C4—942no—
248C4—1882no—
249C4—1882no—
250C4—1881no—
251C2—42no—
252C2C22⋊Q8×D4711yescharacteristic
253C2#1568968611yescharacteristic
254C2#1568969511yescharacteristic
255C2#1568974112yes—
256C2#1568975212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2628
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
3. #15689063C2semidirect
4. #15689061C2semidirect
6. #15689043C2semidirect
8. #15689018C2semidirect
9. #15688987C2semidirect
44. C22×Dic47Q8semidirect
140. C47#2628semidirect