Finite Group Databasebeta

← #20253192

Subgroups — #20253192

Order 6016.

376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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#15689676C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689433C212yesmaximal, complemented
4#15689429C212yesmaximal, complemented
5#15689417C212yesmaximal, complemented
6#15689407C212yesmaximal, complemented
7#15689163C211yesmaximal, characteristic
8#15689146C211yesmaximal, characteristic
9#15689133C211yesmaximal, characteristic
10#15689131C211yesmaximal, characteristic
11C47×#428C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14#13094023C2211yescharacteristic
15#13094023C2211yescharacteristic
16#13094015C2211yescharacteristic
17#13094015C2211yescharacteristic
18#13094001—21no—
19#13094001—21no—
20C4×Dic94—21no—
21C4×Dic94—21no—
22#13093989—21no—
23#13093989—21no—
24#13093989C2212yes—
25#13093989C2212yes—
26#13093983C2211yescharacteristic
27C2×Dic47⋊C4—21no—
28C2×C4×Dic47—21no—
29C2×C4×Dic47C2211yescharacteristic
30#13093957C2212yes—
31#13093955C2212yes—
32Dic47⋊C8C2212yes—
33Dic47⋊C8C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36#13093947C2212yes—
37#13093947C2212yes—
38C2×M16×C47C2211yescharacteristic
39#117×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41#107×C47C2212yes—
42#106×C47C2212yes—
43C22×C4×C47—21no—
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47D411yescharacteristic
47C22×Dic47D411yescharacteristic
48C2×Dic94—21no—
49C2×Dic94—22no—
50C2×Dic94—21no—
51C2×Dic94—21no—
52C2×Dic94Q814yescomplemented
53C2×Dic94C2312yes—
54M16×C47—22no—
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2311yescharacteristic
58C4⋊C4×C47C2312yes—
59C4⋊C4×C47C2311yescharacteristic
60C22⋊C4×C47—21no—
61C42×C47—21no—
62C22⋊Dic47—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73C4×Dic47—21no—
74C4×Dic47—22no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C4×Dic47C2311yescharacteristic
80#10625329—22no—
81C2×C47⋊C8C2312yes—
82C23×C47C2×D411yescharacteristic
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—42no—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×Q812yes—
89C2×C4×C47#4112yes—
90C2×C4×C47C2411yescharacteristic
91C2×Dic47—24no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—41no—
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101Dic94—24no—
102Dic94—22no—
103Dic94—42no—
104Dic94—42no—
105Dic94C2×Q814yes—
106C8×C47—22no—
107C47⋊C8—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47C22⋊Q812yes—
111C22×C47C22×D411yescharacteristic
112C4×C47—41no—
113C4×C47—41no—
114C4×C47—42no—
115C4×C47C22⋊Q812yes—
116C4×C47C22×Q811yescharacteristic
117C4×C47C2×#4111yescharacteristic
118Dic47—24no—
119Dic47—21no—
120Dic47—21no—
121Dic47—21no—
122Dic47—41no—
123Dic47—41no—
124Dic47#13712yes—
125#3078—471nomaximal, Sylow
126C2×C47—22no—
127C2×C47C2×C22⋊Q811yescharacteristic
128C2×C47C2×#13711yescharacteristic
129C2×C47#57511yescharacteristic
130#533—471no—
131C2×C4×Q8—471no—
132#479—472no—
133#479—472no—
134#477—472no—
135#475—472no—
136#428—471no—
137#428D4711yescharacteristic
138#423—471no—
139#419—471no—
140#419—471no—
141C47#307811yescharacteristic, complemented, Sylow
142C22×Q8—471no—
143C2×M16—471no—
144C2×M16C2×D4711yescharacteristic
145C4⋊Q8—471no—
146C4⋊Q8—471no—
147#125—471no—
148#125—471no—
149C22⋊Q8—941no—
150C22⋊Q8—941no—
151C4×Q8—472no—
152C4×Q8—472no—
153C4×Q8—941no—
154C4×Q8—941no—
155C4×Q8—941no—
156C4×Q8—941no—
157#117—471no—
158#117C2×D4711yescharacteristic
159C2×C4⋊C4—941no—
160C2×C4⋊C4C2×D4711yescharacteristic
161C2×C42—471no—
162C2×C42—941no—
163#107—472no—
164#107C2×D4712yes—
165#106—472no—
166#106C2×D4712yes—
167C4⋊C8—472no—
168C4⋊C8—472no—
169#103—472no—
170#103—472no—
171#103—472no—
172#103—472no—
173C2×Q8—474no—
174C2×Q8—472no—
175C2×Q8—941no—
176C2×Q8—941no—
177C2×Q8—942no—
178C2×Q8—941no—
179C22×C4—21no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—941no—
183C22×C4C22×D4711yescharacteristic
184M16—22no—
185M16—942no—
186C2×C8—472no—
187C2×C8C22×D4712yes—
188C4⋊C4—21no—
189C4⋊C4—471no—
190C4⋊C4—471no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4C22×D4711yescharacteristic
200C4⋊C4C22×D4711yescharacteristic
201C4⋊C4C22×D4712yes—
202C22⋊C4—21no—
203C22⋊C4—941no—
204C42—21no—
205C42—471no—
206C42—471no—
207C42—471no—
208C42—471no—
209C42—942no—
210C42—942no—
211C42—941no—
212C23D4×D4711yescharacteristic
213Q8—474no—
214Q8—944no—
215Q8—942no—
216Q8—1882no—
217Q8—1882no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—471no—
223C2×C4—471no—
224C2×C4—471no—
225C2×C4—471no—
226C2×C4—942no—
227C2×C4—944no—
228C2×C4—942no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—1881no—
232C2×C4#1062535012yes—
233C2×C4D4×D4711yescharacteristic
234C2×C4Q8×D4712yes—
235C2×C4C23×D4711yescharacteristic
236C8—22no—
237C8—942no—
238C22—21no—
239C22—21no—
240C22#1309400212yes—
241C22C2×D4×D4711yescharacteristic
242C4—41no—
243C4—42no—
244C4—41no—
245C4—472no—
246C4—944no—
247C4—941no—
248C4—941no—
249C4—941no—
250C4—1881no—
251C4—1881no—
252C4#1309400212yes—
253C4C2×Q8×D4711yescharacteristic
254C4C2×#1062535011yescharacteristic
255C2—22no—
256C2C2×#1309400211yescharacteristic
257C2#137×D4711yescharacteristic
258C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3078
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #15689433C2semidirect
4. #15689429C2semidirect
5. #15689417C2semidirect
6. #15689407C2semidirect
52. C2×Dic94Q8semidirect
141. C47#3078semidirect