Finite Group Databasebeta

← #20254601

Subgroups — #20254601

Order 6016.

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

normal subgroups only

This group has 322 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#15689678C211yesmaximal, characteristic
2#15689677C211yesmaximal, characteristic
3#15689530C212yesmaximal, complemented
4#15689490C212yesmaximal, complemented
5#15689467C212yesmaximal
6#15689463C212yesmaximal
7#15689419C211yesmaximal, characteristic, complemented
8#15689418C211yesmaximal, characteristic, complemented
9#15689405C211yesmaximal, characteristic, complemented
10#15689179C211yesmaximal, characteristic
11C47×#475C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094023C2211yescharacteristic
14#13094022C2211yescharacteristic
15#13094015C2212yes—
16#13094014—21no—
17#13094004—21no—
18#13094004C2211yescharacteristic
19#13094002—21no—
20#13094000—21no—
21#13094000C2211yescharacteristic
22Q8×Dic47—21no—
23C4×Dic94—21no—
24C4×Dic94C2211yescharacteristic
25#13093989—21no—
26#13093982C2212yes—
27#13093981—21no—
28C42×D47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093955C2212yes—
32C4⋊(C47⋊C8)C2211yescharacteristic
33#13093949C2212yes—
34#13093948C2212yes—
35#13093947C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093934C2212yes—
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×Dic94—21no—
50C2×Dic94C2311yescharacteristic
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47C2312yes—
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—21no—
67Dic47⋊C4—21no—
68Dic47⋊C4—21no—
69Dic47⋊C4—22no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72C4×Dic47—21no—
73C4×Dic47—22no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C22×D47C2×D411yescharacteristic
79Q8×C47—21no—
80Q8×C47—21no—
81Q8×C47—42no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47C2×D411yescharacteristic
92C2×Dic47C2×D411yescharacteristic
93C2×Dic47C2×D411yescharacteristic
94C4×D47—22no—
95C4×D47—21no—
96C4×D47—21no—
97C4×D47—41no—
98Dic94—21no—
99Dic94—21no—
100Dic94—42no—
101Dic94—42no—
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47C22×D411yescharacteristic
105C2×D47—21no—
106C2×D47—21no—
107C2×D47—21no—
108C4×C47—21no—
109C4×C47—41no—
110C4×C47—42no—
111C4×C47—41no—
112C4×C47#13712yes—
113C4×C472−1+411yescharacteristic
114C4×C472−1+411yescharacteristic
115Dic47—21no—
116Dic47—21no—
117Dic47—21no—
118Dic47—41no—
119Dic47—41no—
120Dic47—42no—
121#3237—471nomaximal, Sylow
122C2×C47#53611yescharacteristic
123C2×C47C2×#13711yescharacteristic
124C2×C47#57511yescharacteristic
125D47—41no—
126#533—471no—
127#533—471no—
128#501—472no—
129#491—472no—
130#485—472no—
131#485—472no—
132#477—471no—
133#477—471no—
134#475—471no—
135#475D4711yescharacteristic, complemented
136#432—471no—
137C47#323711yescharacteristic, complemented, Sylow
138C4⋊Q8—471no—
139C4⋊Q8—471no—
140C4⋊Q8—471no—
141C4⋊Q8C2×D4711yescharacteristic
142#125—472no—
143#125—941no—
144C22⋊Q8—471no—
145C22⋊Q8—471no—
146C22⋊Q8—941no—
147C22⋊Q8—941no—
148C22⋊Q8—941no—
149C4×Q8—471no—
150C4×Q8—941no—
151C4×Q8—941no—
152C4×Q8—941no—
153C4×Q8C2×D4711yescharacteristic
154#117—472no—
155#117—941no—
156C2×C42—471no—
157#107—472no—
158#107—472no—
159#106—472no—
160#106C2×D4712yes—
161C4⋊C8—471no—
162C4⋊C8C2×D4711yescharacteristic
163#103—472no—
164#103—472no—
165#103—472no—
166#103C2×D4712yes—
167C22⋊C8—472no—
168#97—472no—
169C2×Q8—21no—
170C2×Q8—471no—
171C2×Q8—941no—
172C2×Q8—941no—
173C2×Q8C22×D4711yescharacteristic
174C22×C4—471no—
175C22×C4—471no—
176C22×C4—471no—
177C2×C8—472no—
178C2×C8C22×D4712yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—472no—
182C4⋊C4—471no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4—942no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4C22×D4712yes—
193C4⋊C4C22×D4711yescharacteristic
194C22⋊C4—942no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C42—21no—
198C42—471no—
199C42—471no—
200C42—471no—
201C42—942no—
202C42—941no—
203C42C22×D4711yescharacteristic
204C23—471no—
205Q8—21no—
206Q8—21no—
207Q8—42no—
208Q8—941no—
209Q8—941no—
210Q8—1882no—
211Q8—1882no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—471no—
216C2×C4—471no—
217C2×C4—471no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—941no—
224C2×C4—1881no—
225C2×C4D4×D4711yescharacteristic
226C2×C4D4×D4711yescharacteristic
227C2×C4C23×D4711yescharacteristic
228C8—22no—
229C8—942no—
230C22—941no—
231C22—941no—
232C22—941no—
233C22C2×D4×D4711yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—941no—
239C4—941no—
240C4—941no—
241C4—1882no—
242C4—1881no—
243C4—1881no—
244C4#1309405312yes—
245C4#1309407111yescharacteristic
246C4#1309407211yescharacteristic
247C2—1881no—
248C2#1568969611yescharacteristic
249C2C2×#1309405311yescharacteristic
250C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3237
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. #15689530C2semidirect
4. #15689490C2semidirect
7. #15689419C2semidirect
8. #15689418C2semidirect
9. #15689405C2semidirect
11. C47×#475C2semidirect
135. #475D47semidirect
137. C47#3237semidirect