Finite Group Databasebeta

← #20254781

Subgroups — #20254781

Order 6016.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#15689678C211yesmaximal, characteristic
2#15689677C211yesmaximal, characteristic
3#15689407C212yesmaximal, complemented
4#15689405C211yesmaximal, characteristic, complemented
5#15689382C212yesmaximal
6#15689380C212yesmaximal
7#15689334C211yesmaximal, characteristic, complemented
8#15689333C211yesmaximal, characteristic, complemented
9#15689332C212yesmaximal, complemented
10#15689145C211yesmaximal, characteristic
11C47×#475C211yesmaximal, characteristic, complemented
12C2×Dic188C2212yes—
13C2×#10625337C2212yes—
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic
16#13094023C2211yescharacteristic
17#13094022C2211yescharacteristic
18#13094015—21no—
19#13094014—21no—
20#13094004C2212yes—
21#13094004C2211yescharacteristic
22#13094002—21no—
23#13094000—21no—
24#13094000C2211yescharacteristic
25Q8×Dic47—21no—
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic
28#13093989C2212yes—
29#13093982—21no—
30#13093981—21no—
31C42×D47C2211yescharacteristic
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093949C2212yes—
36#13093947C2212yes—
37#13093947C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×Q8×C47C2211yescharacteristic
40#106×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#103×C47C2212yes—
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×C4×D47D411yescharacteristic
47C2×C4×D47C2311yescharacteristic
48C2×Dic94—21no—
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2312yes—
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58#10625337—42no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—22no—
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—21no—
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73C4×Dic47—21no—
74C4×Dic47—22no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79Dic188—42no—
80#10625324—42no—
81C22×D47C2×D411yescharacteristic
82Q8×C47—21no—
83Q8×C47—21no—
84Q8×C47—42no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2411yescharacteristic
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C4×D47—22no—
98C4×D47—21no—
99C4×D47—21no—
100C4×D47—22no—
101Dic94—21no—
102Dic94—22no—
103Dic94—21no—
104Dic94—22no—
105Dic94—42no—
106C8×C47—22no—
107C47⋊C8—22no—
108C22×C47C22×D411yescharacteristic
109C2×D47—21no—
110C2×D47—21no—
111C2×D47—21no—
112C4×C47—21no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47—42no—
116C4×C47#13712yes—
117C4×C47H(5,𝔽2)11yescharacteristic
118C4×C472−1+411yescharacteristic
119Dic47—21no—
120Dic47—21no—
121Dic47—41no—
122Dic47—42no—
123Dic47—41no—
124Dic47#13712yes—
125#3255—471nomaximal, Sylow
126C2×C47#53711yescharacteristic
127C2×C47C2×#13711yescharacteristic
128C2×C47C2×#13711yescharacteristic
129D47—41no—
130#533—471no—
131#533—471no—
132#475—471no—
133#475—472no—
134#475D4711yescharacteristic, complemented
135#470—472no—
136#470—472no—
137#462—471no—
138#462—471no—
139#462—472no—
140#423—471no—
141C47#325511yescharacteristic, complemented, Sylow
142C2×Q16—472no—
143C2×Q16—472no—
144C2×M16—472no—
145C4⋊Q8—471no—
146C4⋊Q8—471no—
147C4⋊Q8—471no—
148C4⋊Q8C2×D4711yescharacteristic
149#125—941no—
150#125—941no—
151C22⋊Q8—471no—
152C22⋊Q8—471no—
153C22⋊Q8—472no—
154C22⋊Q8—941no—
155C22⋊Q8—941no—
156C4×Q8—472no—
157C4×Q8—471no—
158C4×Q8—941no—
159C4×Q8—941no—
160C4×Q8C2×D4711yescharacteristic
161#117—941no—
162#117—941no—
163C2×C42—471no—
164#106—472no—
165#106C2×D4712yes—
166C4⋊C8—472no—
167C4⋊C8—471no—
168C4⋊C8C2×D4711yescharacteristic
169#103—472no—
170#103—472no—
171#103—472no—
172#103C2×D4712yes—
173C2×Q8—21no—
174C2×Q8—471no—
175C2×Q8—472no—
176C2×Q8—941no—
177C2×Q8C22×D4711yescharacteristic
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181Q16—1882no—
182Q16—1882no—
183M16—1882no—
184C2×C8—472no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—471no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—942no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—942no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4C22×D4711yescharacteristic
200C4⋊C4C22×D4712yes—
201C22⋊C4—941no—
202C22⋊C4—941no—
203C22⋊C4—942no—
204C42—21no—
205C42—471no—
206C42—471no—
207C42—471no—
208C42—942no—
209C42—941no—
210C42C22×D4711yescharacteristic
211C23—471no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—941no—
216Q8—942no—
217Q8—941no—
218Q8—942no—
219Q8—1882no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—471no—
224C2×C4—471no—
225C2×C4—471no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4D4×D4711yescharacteristic
234C2×C4D4×D4711yescharacteristic
235C2×C4C23×D4711yescharacteristic
236C8—22no—
237C8—942no—
238C22—941no—
239C22—941no—
240C22—941no—
241C22C2×D4×D4711yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—41no—
246C4—472no—
247C4—941no—
248C4—941no—
249C4—1881no—
250C4—1881no—
251C4—1882no—
252C4#1309405312yes—
253C4#1309407011yescharacteristic
254C4#1309407211yescharacteristic
255C2—1881no—
256C2#1568970311yescharacteristic
257C2#137×D4711yescharacteristic
258C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3255
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #15689407C2semidirect
4. #15689405C2semidirect
7. #15689334C2semidirect
8. #15689333C2semidirect
9. #15689332C2semidirect
11. C47×#475C2semidirect
134. #475D47semidirect
141. C47#3255semidirect