Finite Group Databasebeta

← #20243722

Subgroups — #20243722

Order 6016.

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

normal subgroups only

This group has 402 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
1C22×#10625335C211yesmaximal, characteristic
2C2×#13093947C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15689029C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C2×C4×D4×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625335—22no—
10C2×#10625335—22no—
11C2×#10625335C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15#13093947—22no—
16#13093945—22no—
17C47⋊#95—21no—
18C47⋊#95—21no—
19C22×D4×C47C2211yescharacteristic
20C23×C4×C47—21no—
21C4×D4×C47—22no—
22C4×D4×C47—22no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—21no—
25C2×C42×C47C2211yescharacteristic
26C24×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47C2×C412yes—
31C2×D4×C47D412yes—
32C2×D4×C47D412yes—
33C22×C4×C47—24no—
34C22×C4×C47—21no—
35C22×C4×C47—42no—
36C22×C4×C47—42no—
37C22×C4×C47D411yescharacteristic
38C22×C4×C47D411yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×Dic47—21no—
41C22×Dic47—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94C2×C412yescomplemented
48C4⋊C4×C47—21no—
49C4⋊C4×C47D412yes—
50C22⋊C4×C47—24no—
51C42×C47—21no—
52C42×C47—21no—
53#10625335—28no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8C2×C412yescomplemented
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47C2×D411yescharacteristic
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—22no—
73D4×C47C22⋊C414yes—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—48no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47SD1612yescomplemented
84C2×C4×C47C22×C411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96Dic94—22no—
97Dic94—22no—
98Dic94—41no—
99Dic94—41no—
100C47⋊C8—22no—
101C47⋊C8—41no—
102C22×C47—24no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47C4×D411yescharacteristic
110C22×C47#12011yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47C2×SD1611yescharacteristic
113C22×C47#13511yescharacteristic
114C22×C47AGL(1,ℤ/8)11yescharacteristic
115C22×C47#13711yescharacteristic
116C4×C47—22no—
117C4×C47—42no—
118C4×C47—41no—
119C4×C47C2×C22⋊C411yescharacteristic
120C4×C47C4×D411yescharacteristic
121C4×C47#12111yescharacteristic
122C4×C47#12311yescharacteristic
123Dic47—42no—
124Dic47—81no—
125#1877—471nomaximal, Sylow
126C2×C47—44no—
127C2×C47#38611yescharacteristic
128C2×C47C4×SD1611yescharacteristic
129C2×C47#44011yescharacteristic
130C2×C47#45011yescharacteristic
131C2×C47#45211yescharacteristic
132C2×C47#46111yescharacteristic
133C2×C47#46311yescharacteristic
134C22×SD16—471no—
135C2×C4×D4D4711yescharacteristic
136C2×#103—471no—
137C2×#102—471no—
138#391—471no—
139#340—471no—
140#336—471no—
141C47#187711yescharacteristic, complemented, Sylow
142C22×Q8—471no—
143C22×D4C2×D4711yescharacteristic
144C23×C4—21no—
145C2×SD16—474no—
146C2×SD16—942no—
147C2×SD16—942no—
148C22×C8—471no—
149C22×C8—471no—
150C4×D4—22no—
151C4×D4—22no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4C2×D4711yescharacteristic
154C2×C22⋊C4—21no—
155C2×C42C2×D4711yescharacteristic
156#103—942no—
157#102—942no—
158#95—941no—
159#95—941no—
160C24—21no—
161C2×Q8—472no—
162C2×Q8—941no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C4×D4712yes—
171C2×D4D18812yes—
172C2×D4C22⋊D4712yes—
173C22×C4—24no—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—941no—
178C22×C4—941no—
179C22×C4C22⋊D4711yescharacteristic
180C22×C4C22⋊D4711yescharacteristic
181C22×C4C22×D4711yescharacteristic
182SD16—948no—
183C2×C8—472no—
184C2×C8—941no—
185C2×C8—941no—
186C2×C8—941no—
187C2×C8—941no—
188C2×C8—941no—
189C4⋊C4—21no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4C22⋊D4712yes—
193C22⋊C4—24no—
194C42—21no—
195C42—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23C2×C22⋊D4711yescharacteristic
204Q8—942no—
205Q8—942no—
206Q8—1881no—
207Q8—1881no—
208D4—22no—
209D4—22no—
210D4—22no—
211D4(C2×D47)⋊C414yes—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—48no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—942no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4#1062533512yescomplemented
228C2×C4C2×C4×D4711yescharacteristic
229C2×C4C2×D18811yescharacteristic
230C2×C4#1062535011yescharacteristic
231C2×C4#1062535011yescharacteristic
232C2×C4C2×C22⋊D4711yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C8—942no—
235C8—1881no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22C4×C22⋊D4711yescharacteristic
244C22#1309399311yescharacteristic
245C22#1309399811yescharacteristic
246C22C2×#1062533511yescharacteristic
247C22#1309404411yescharacteristic
248C22#1309405011yescharacteristic
249C22#1309405411yescharacteristic
250C4—22no—
251C4—42no—
252C4—41no—
253C4—3761no—
254C4—1882no—
255C4C2×(C2×D47)⋊C411yescharacteristic
256C4C4×C22⋊D4711yescharacteristic
257C4#1309399811yescharacteristic
258C4#1309400711yescharacteristic
259C2—44no—
260C2#1568900211yescharacteristic
261C2C4×#1062533511yescharacteristic
262C2#1568922311yescharacteristic
263C2#1568927411yescharacteristic
264C2#1568928511yescharacteristic
265C2#1568932811yescharacteristic
266C2#1568933811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C4×D4×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×D4D47
hypocenterC47#1877
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#13093947C2semidirect
4. #15689029C2semidirect
5. #15688885C2semidirect
6. #15688878C2semidirect
11. C2×#10625335C4semidirect
47. C2×Dic94C2×C4semidirect
61. C2×C47⋊C8C2×C4semidirect
83. C2×C4×C47SD16semidirect
141. C47#1877semidirect
227. C2×C4#10625335semidirect