Finite Group Databasebeta

← #20247868

Subgroups — #20247868

Order 6016.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094002C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic, complemented
4#15689062C211yesmaximal, characteristic, complemented
5#15689061C211yesmaximal, characteristic, complemented
6#15689027C212yesmaximal, complemented
7#15688987C212yesmaximal, complemented
8#15688985C212yesmaximal
9#15688985C212yesmaximal
10#15688970C211yesmaximal, characteristic
11C47×#400C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C4×D47C2212yes—
14C22×C4×D47C2211yescharacteristic
15#13094002—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C4⋊C4×D47—24no—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×C4×Dic47C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C2×C4×D47—24no—
49C2×C4×D47—24no—
50C2×C4×D47—28no—
51C2×C4×D47D414yes—
52C2×Dic94—22no—
53C2×Dic94—24no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—24no—
59C4⋊Dic47—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—24no—
62Dic47⋊C4—22no—
63C4×Dic47—24no—
64C23×C47C2411yescharacteristic
65C22×D47—22no—
66C22×D47—21no—
67C22×D47—21no—
68C22×D47C2×D412yes—
69C22×D47#4114yes—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—24no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47C2×D412yes—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—24no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47C2×D412yes—
93C2×Dic47#4114yes—
94C4×D47—28no—
95C4×D47—48no—
96Dic94—44no—
97C22×C47C22×D411yescharacteristic
98C22×C47C2×#4112yes—
99C22×C47C2×#4112yes—
100C22×C472−1+411yescharacteristic
101C22×C472−1+411yescharacteristic
102C2×D47—22no—
103C2×D47—22no—
104C2×D47—24no—
105C2×D47—24no—
106C2×D47#12414yes—
107C4×C47—22no—
108C4×C47—41no—
109C4×C47—42no—
110C4×C47—41no—
111C4×C47—42no—
112Dic47—41no—
113Dic47—42no—
114Dic47—41no—
115Dic47—42no—
116Dic47#12314yes—
117#2503—471nomaximal, Sylow
118C2×C47C2×#12311yescharacteristic
119C2×C47C2×#12411yescharacteristic
120C2×C47#53611yescharacteristic
121C2×C47#55212yes—
122C2×C47#55212yes—
123D47—24no—
124C2×C22⋊Q8—471no—
125C22×C4⋊C4—471no—
126#400—471no—
127#400—471no—
128#400—471no—
129#400D4711yescharacteristic, complemented
130#391—472no—
131#382—472no—
132#381—472no—
133#381—472no—
134C4×C22⋊C4—471no—
135C47#250311yescharacteristic, complemented, Sylow
136C22×Q8—471no—
137C23×C4—471no—
138C23×C4—472no—
139C22⋊Q8—944no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—944no—
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—471no—
148C2×C22⋊C4—471no—
149C2×C22⋊C4—472no—
150C2×C42—472no—
151#95—471no—
152#95—472no—
153#95—472no—
154#95—472no—
155#95—472no—
156#95—472no—
157#95—472no—
158#95C2×D4711yescharacteristic
159#95C2×D4712yes—
160#95C2×D4712yes—
161C24—471no—
162C2×Q8—942no—
163C2×Q8—944no—
164C22×C4—471no—
165C22×C4—474no—
166C22×C4—472no—
167C22×C4—471no—
168C22×C4—471no—
169C22×C4—472no—
170C22×C4—944no—
171C22×C4—944no—
172C22×C4—948no—
173C22×C4C22×D4712yes—
174C22×C4C22×D4711yescharacteristic
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4712yes—
177C22×C4C22×D4711yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—944no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C22⋊C4—944no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C42—944no—
188C23—472no—
189C23—474no—
190C23—942no—
191C23—941no—
192C23—941no—
193C23C23×D4711yescharacteristic
194Q8—1884no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—472no—
207C2×C4—474no—
208C2×C4—948no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—944no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—1888no—
220C2×C4D4×D4712yes—
221C22—474no—
222C22—944no—
223C22—944no—
224C22—942no—
225C22—942no—
226C22C2×D4×D4711yescharacteristic
227C22#41×D4712yes—
228C22#41×D4712yes—
229C22#1309407111yescharacteristic
230C22#1309407211yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—42no—
235C4—41no—
236C4—474no—
237C4—1882no—
238C4—1881no—
239C4—1882no—
240C4—1881no—
241C2—944no—
242C2#123×D4711yescharacteristic
243C2#124×D4711yescharacteristic
244C2#1568969611yescharacteristic
245C2#1568980512yes—
246C2#1568980912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2503
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #15689063C2semidirect
4. #15689062C2semidirect
5. #15689061C2semidirect
6. #15689027C2semidirect
7. #15688987C2semidirect
11. C47×#400C2semidirect
129. #400D47semidirect
135. C47#2503semidirect