Finite Group Databasebeta

← #20254530

Subgroups — #20254530

Order 6016.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689675C211yesmaximal, characteristic
2C2×#13094023C211yesmaximal, characteristic
3#15689520C212yesmaximal, complemented
4#15689472C212yesmaximal, complemented
5#15689454C211yesmaximal, characteristic
6#15689453C211yesmaximal, characteristic
7#15689451C211yesmaximal, characteristic
8#15689407C212yesmaximal, complemented
9#15689406C212yesmaximal, complemented
10#15689173C211yesmaximal, characteristic
11C47×#483C211yesmaximal, characteristic
12C22×Dic94—21no—
13#13094023—21no—
14#13094023—21no—
15#13094023C2212yes—
16#13094023C2211yescharacteristic
17#13094023C2212yes—
18#13094022C2211yescharacteristic
19#13094014—21no—
20#13094003C2211yescharacteristic
21#13094001—21no—
22Q8×Dic47C2211yescharacteristic
23#13093989—21no—
24#13093989C2211yescharacteristic
25#13093980—21no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4—21no—
28C2×C4×Dic47C2211yescharacteristic
29#13093956C2212yes—
30#13093955C2212yes—
31#13093955C2212yes—
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093948C2212yes—
35#13093947C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37C8×Dic47C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×C47C2212yes—
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C22×Dic47—21no—
47C22×Dic47D411yescharacteristic
48C22×Dic47D411yescharacteristic
49C2×Dic94—21no—
50C2×Dic94—22no—
51C2×Dic94—22no—
52C2×Dic94—44no—
53C2×Dic94C2311yescharacteristic
54C2×C8×C47C2312yes—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2312yes—
58C4⋊C4×C47C2311yescharacteristic
59C22⋊C4×C47—21no—
60C22⋊Dic47—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72C4×Dic47—21no—
73C4×Dic47—21no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79C23×C47C2×D411yescharacteristic
80Q8×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—42no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—42no—
93C2×Dic47SD1614yes—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98Dic94—22no—
99Dic94—44no—
100Dic94—44no—
101Dic94—42no—
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47C2×SD1612yes—
107C22×C47C22×D411yescharacteristic
108C4×C47—21no—
109C4×C47—41no—
110C4×C47—42no—
111C4×C47—41no—
112C4×C472−1+412yes—
113Dic47—21no—
114Dic47—41no—
115Dic47—42no—
116Dic47—41no—
117Dic47C2×SD1612yes—
118Dic47C2×SD1612yes—
119Dic47#13712yes—
120#3229—471nomaximal, Sylow
121C2×C47—22no—
122C2×C47#53611yescharacteristic
123C2×C47C22×SD1611yescharacteristic
124C2×C47C2×#13711yescharacteristic
125#533—471no—
126C2×C4⋊Q8—471no—
127#498—472no—
128#487—472no—
129#483—471no—
130#483—471no—
131#483—471no—
132#483D4711yescharacteristic
133#475—472no—
134#475—472no—
135#431—471no—
136C47#322911yescharacteristic, complemented, Sylow
137C22×Q8—941no—
138C4⋊Q8—472no—
139C4⋊Q8—472no—
140C4⋊Q8—471no—
141C4⋊Q8—471no—
142C4⋊Q8—941no—
143C4⋊Q8—941no—
144#125—941no—
145C22⋊Q8—471no—
146C22⋊Q8—941no—
147C22⋊Q8C2×D4711yescharacteristic
148C4×Q8—471no—
149C4×Q8—471no—
150C4×Q8—941no—
151#117—941no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—941no—
154C2×C4⋊C4C2×D4711yescharacteristic
155C2×C42—471no—
156#106—472no—
157#106—472no—
158#106—472no—
159#106C2×D4712yes—
160C4⋊C8—472no—
161#103—472no—
162#103—472no—
163#103—472no—
164#103C2×D4712yes—
165C22⋊C8—471no—
166C22⋊C8C2×D4711yescharacteristic
167C4×C8—472no—
168C2×Q8—471no—
169C2×Q8—941no—
170C2×Q8—942no—
171C2×Q8—942no—
172C2×Q8—1884no—
173C2×Q8C22×D4711yescharacteristic
174C22×C4—21no—
175C22×C4—471no—
176C22×C4—471no—
177C22×C4—941no—
178C22×C4C22×D4711yescharacteristic
179C2×C8—472no—
180C2×C8C22×D4712yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—472no—
184C4⋊C4—471no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4C22×D4712yes—
195C4⋊C4C22×D4711yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—941no—
198C42—471no—
199C42—471no—
200C42—471no—
201C42—471no—
202C42—941no—
203C42—941no—
204C23D4×D4711yescharacteristic
205Q8—22no—
206Q8—942no—
207Q8—1882no—
208Q8—1884no—
209Q8—1884no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—474no—
216C2×C4—471no—
217C2×C4—471no—
218C2×C4—471no—
219C2×C4—471no—
220C2×C4—942no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—1882no—
225C2×C4D4×D4711yescharacteristic
226C2×C4C23×D4711yescharacteristic
227C8—22no—
228C8—942no—
229C22—21no—
230C22—21no—
231C22SD16×D4712yes—
232C22C2×D4×D4711yescharacteristic
233C4—21no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—472no—
238C4—472no—
239C4—472no—
240C4—941no—
241C4—1882no—
242C4—1881no—
243C4—1881no—
244C4#1309407112yes—
245C2—22no—
246C2#1568969511yescharacteristic
247C2C2×SD16×D4711yescharacteristic
248C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3229
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #15689520C2semidirect
4. #15689472C2semidirect
8. #15689407C2semidirect
9. #15689406C2semidirect
136. C47#3229semidirect