Finite Group Databasebeta

← #20244397

Subgroups — #20244397

Order 6016.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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×#10625337C211yesmaximal, characteristic, complemented
2C2×#13094004C211yesmaximal, characteristic
3C2×#13094000C211yesmaximal, characteristic
4C2×#13093949C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×C4×D47C2211yescharacteristic
10C2×#10625337—22no—
11C2×#10625337—22no—
12C2×#10625337—22no—
13C22×C47⋊C8C2211yescharacteristic
14#13094004—22no—
15#13094004—22no—
16#13094000—22no—
17#13094000—22no—
18C2×C4⋊Dic47—21no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4—21no—
21C2×(C2×D47)⋊C4—21no—
22C2×(C2×D47)⋊C4—21no—
23#13093949—22no—
24(C2×D47)⋊C8—22no—
25C22×Q8×C47C2211yescharacteristic
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#103×C47—22no—
29C23×D47D411yescharacteristic
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47D412yes—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C22×Dic47—21no—
41C22×Dic47D411yescharacteristic
42C2×C4×D47—21no—
43C2×C4×D47—21no—
44C2×C4×D47—21no—
45C2×C4×D47—21no—
46C2×C4×D47—21no—
47C2×C4×D47—21no—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94—21no—
52C2×Dic94—21no—
53C2×Dic94D412yes—
54C2×C8×C47—21no—
55C2×C8×C47—21no—
56C2×C8×C47—21no—
57C4⋊C4×C47—21no—
58C4⋊C4×C47D412yes—
59#10625337—28no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—24no—
62C4⋊Dic47—24no—
63C4⋊Dic47—21no—
64C4⋊Dic47D412yes—
65Dic47⋊C4—24no—
66C2×C47⋊C8—21no—
67C2×C47⋊C8—21no—
68C2×C47⋊C8D412yes—
69C23×C47C2×D411yescharacteristic
70C22×D47—21no—
71C22×D47—21no—
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—21no—
76C22×D47Q1612yescomplemented
77Q8×C47—22no—
78Q8×C47—22no—
79Q8×C47—41no—
80Q8×C47—41no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—41no—
99C2×Dic47—41no—
100C2×Dic47—41no—
101C2×Dic47—41no—
102C4×D47—41no—
103C4×D47—41no—
104C4×D47—41no—
105C4×D47—41no—
106Dic94—22no—
107Dic94—22no—
108Dic94—41no—
109Dic94—41no—
110C8×C47—41no—
111C47⋊C8—22no—
112C22×C47#12011yescharacteristic
113C22×C47#12011yescharacteristic
114C22×C47#12111yescharacteristic
115C22×C47C2×Q1611yescharacteristic
116C22×C47#13511yescharacteristic
117C22×C47#13711yescharacteristic
118C22×C47#13711yescharacteristic
119C2×D47—22no—
120C2×D47—22no—
121C2×D47—22no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—41no—
125C2×D47—41no—
126C4×C47—42no—
127C4×C47—42no—
128C4×C47#12011yescharacteristic
129C4×C47#12111yescharacteristic
130C4×C47#12111yescharacteristic
131C4×C47#12711yescharacteristic
132Dic47—42no—
133Dic47—41no—
134Dic47—42no—
135#2001—471nomaximal, Sylow
136C2×C47#39211yescharacteristic
137C2×C47#45111yescharacteristic
138C2×C47#45111yescharacteristic
139C2×C47#45211yescharacteristic
140C2×C47#45211yescharacteristic
141C2×C47#46711yescharacteristic
142C2×C47#47011yescharacteristic
143D47—42no—
144C22×Q16—471no—
145C2×C22⋊Q8—471no—
146C2×C22⋊Q8—471no—
147C2×#103—471no—
148C2×#103D4711yescharacteristic, complemented
149C2×C22⋊C8—471no—
150#340—471no—
151C47#200111yescharacteristic, complemented, Sylow
152C22×Q8—471no—
153C22×Q8C2×D4711yescharacteristic
154C23×C4—471no—
155C2×Q16—942no—
156C2×Q16—942no—
157C2×Q16—942no—
158C22×C8—471no—
159C22×C8C2×D4711yescharacteristic
160C22⋊Q8—942no—
161C22⋊Q8—942no—
162C22⋊Q8—942no—
163C22⋊Q8—942no—
164C2×C4⋊C4—471no—
165C2×C4⋊C4—941no—
166C2×C4⋊C4—941no—
167C2×C4⋊C4C2×D4711yescharacteristic
168C2×C22⋊C4—941no—
169C2×C22⋊C4—941no—
170#103—22no—
171#103—942no—
172C22⋊C8—942no—
173C24—471no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—472no—
180C2×Q8—941no—
181C2×Q8—941no—
182C2×Q8—941no—
183C2×Q8—941no—
184C2×Q8—941no—
185C2×Q8D18812yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—471no—
189C22×C4—941no—
190C22×C4—941no—
191C22×C4—941no—
192C22×C4—941no—
193C22×C4—941no—
194C22×C4—941no—
195C22×C4—941no—
196C22×C4—941no—
197C22×C4C22×D4711yescharacteristic
198Q16—948no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—472no—
203C2×C8—941no—
204C2×C8—941no—
205C4⋊C4—21no—
206C4⋊C4—472no—
207C4⋊C4—944no—
208C4⋊C4—944no—
209C4⋊C4—941no—
210C4⋊C4C22⋊D4712yes—
211C22⋊C4—944no—
212C22⋊C4—944no—
213C23—472no—
214C23—941no—
215C23—941no—
216C23—941no—
217C23—941no—
218C23—941no—
219C23—941no—
220C23D4×D4711yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—41no—
224Q8—41no—
225Q8—942no—
226Q8—942no—
227Q8—1881no—
228Q8—1881no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—942no—
236C2×C4—941no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—1881no—
241C2×C4—1881no—
242C2×C4—1881no—
243C2×C4—1881no—
244C2×C4—1881no—
245C2×C4—1881no—
246C2×C4—1881no—
247C2×C4—1881no—
248C2×C4C2×D18811yescharacteristic
249C2×C4#1062535011yescharacteristic
250C2×C4D4×D4711yescharacteristic
251C2×C4D4×D4711yescharacteristic
252C2×C4D4×D4711yescharacteristic
253C2×C4C2×C22⋊D4711yescharacteristic
254C8—41no—
255C8—942no—
256C22—942no—
257C22—942no—
258C22—942no—
259C22—1881no—
260C22—1881no—
261C22—1881no—
262C22—1881no—
263C22#1309399211yescharacteristic
264C22#1309399411yescharacteristic
265C22#1309399711yescharacteristic
266C22Q16×D4711yescharacteristic
267C22#1309404511yescharacteristic
268C22#1309405311yescharacteristic
269C22#1309405611yescharacteristic
270C4—42no—
271C4—42no—
272C4—1881no—
273C4—1882no—
274C4—1882no—
275C4#1309399411yescharacteristic
276C4#1309399711yescharacteristic
277C4#1309399811yescharacteristic
278C4#1309402011yescharacteristic
279C2—1882no—
280C2#1568903211yescharacteristic
281C2#1568927711yescharacteristic
282C2#1568928011yescharacteristic
283C2#1568928211yescharacteristic
284C2#1568928811yescharacteristic
285C2#1568936311yescharacteristic
286C2#1568938011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2001
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#10625337C2semidirect
4. C2×#13093949C2semidirect
6. #15688885C2semidirect
7. C2×#103×C47C2semidirect
76. C22×D47Q16semidirect
148. C2×#103D47semidirect
151. C47#2001semidirect