Finite Group Databasebeta

← #20254591

Subgroups — #20254591

Order 6016.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13094015C211yesmaximal, characteristic
3#15689530C212yesmaximal, complemented
4#15689490C212yesmaximal, complemented
5#15689459C211yesmaximal, characteristic
6#15689456C211yesmaximal, characteristic
7#15689453C211yesmaximal, characteristic
8#15689433C212yesmaximal, complemented
9#15689432C212yesmaximal, complemented
10#15689177C211yesmaximal, characteristic
11C47×#483C211yesmaximal, characteristic
12#13094023C2211yescharacteristic
13#13094022C2211yescharacteristic
14#13094015—21no—
15#13094015—21no—
16#13094015C2212yes—
17#13094015C2212yes—
18#13094014—21no—
19#13094003C2211yescharacteristic
20#13094001—21no—
21Q8×Dic47C2211yescharacteristic
22#13093989—21no—
23#13093989C2211yescharacteristic
24#13093980—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4—21no—
28C2×C4×Dic47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093955C2212yes—
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093948C2212yes—
35#13093947C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37#13093934C2212yes—
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×Dic94C2311yescharacteristic
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C22⋊C4×C47—21no—
57C22⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63C4⋊Dic47C2311yescharacteristic
64Dic47⋊C4—21no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71C4×Dic47—21no—
72C4×Dic47—21no—
73C4×Dic47D411yescharacteristic
74C4×Dic47D411yescharacteristic
75C4×Dic47C2311yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C23×C47C2×D411yescharacteristic
79Q8×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—42no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—22no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—41no—
92C2×Dic47—42no—
93C2×Dic47C2×D411yescharacteristic
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97Dic94—22no—
98Dic94—42no—
99C8×C47—22no—
100C47⋊C8—22no—
101C22×C47—21no—
102C22×C47—21no—
103C22×C47#13712yes—
104C22×C47C22×D411yescharacteristic
105C4×C47—21no—
106C4×C47—41no—
107C4×C47—42no—
108C4×C47—41no—
109C4×C472−1+412yes—
110Dic47—21no—
111Dic47—21no—
112Dic47—21no—
113Dic47—21no—
114Dic47—41no—
115Dic47—41no—
116Dic47—42no—
117#3236—471nomaximal, Sylow
118C2×C47—22no—
119C2×C47#53611yescharacteristic
120C2×C47C2×#13711yescharacteristic
121C2×C47#57511yescharacteristic
122#533—471no—
123C2×#125—471no—
124#501—472no—
125#491—472no—
126#484—471no—
127#484—471no—
128#483—471no—
129#483D4711yescharacteristic
130#479—472no—
131#479—472no—
132#432—471no—
133C47#323611yescharacteristic, complemented, Sylow
134C4⋊Q8—471no—
135C4⋊Q8—471no—
136#125—472no—
137#125—472no—
138#125—941no—
139#125—941no—
140#125—941no—
141C22⋊Q8—471no—
142C22⋊Q8—941no—
143C22⋊Q8C2×D4711yescharacteristic
144C4×Q8—471no—
145C4×Q8—471no—
146C4×Q8—941no—
147#117—941no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—941no—
150C2×C4⋊C4—941no—
151C2×C4⋊C4C2×D4711yescharacteristic
152C2×C42—471no—
153#107—472no—
154#107—472no—
155#106—472no—
156#106C2×D4712yes—
157C4⋊C8—472no—
158#103—472no—
159#103—472no—
160#103—472no—
161#103C2×D4712yes—
162C22⋊C8—471no—
163C22⋊C8C2×D4711yescharacteristic
164#97—472no—
165C2×Q8—471no—
166C2×Q8—941no—
167C2×Q8C22×D4711yescharacteristic
168C22×C4—21no—
169C22×C4—471no—
170C22×C4—471no—
171C22×C4—941no—
172C22×C4C22×D4711yescharacteristic
173C2×C8—472no—
174C2×C8C22×D4712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—472no—
178C4⋊C4—471no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4C22×D4712yes—
191C4⋊C4C22×D4711yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—941no—
194C42—471no—
195C42—471no—
196C42—471no—
197C42—471no—
198C42—941no—
199C42—941no—
200C23D4×D4711yescharacteristic
201Q8—22no—
202Q8—942no—
203Q8—1882no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—471no—
210C2×C4—471no—
211C2×C4—471no—
212C2×C4—471no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—1881no—
218C2×C4—1882no—
219C2×C4D4×D4711yescharacteristic
220C2×C4C23×D4711yescharacteristic
221C8—22no—
222C8—942no—
223C22—21no—
224C22—21no—
225C22#1309405312yes—
226C22C2×D4×D4711yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—941no—
232C4—941no—
233C4—941no—
234C4—941no—
235C4—1882no—
236C4—1881no—
237C4—1881no—
238C4#1309407112yes—
239C2—22no—
240C2#1568969511yescharacteristic
241C2C2×#1309405311yescharacteristic
242C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3236
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. #15689530C2semidirect
4. #15689490C2semidirect
8. #15689433C2semidirect
9. #15689432C2semidirect
133. C47#3236semidirect