Finite Group Databasebeta

← #20243649

Subgroups — #20243649

Order 6016.

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

normal subgroups only

This group has 362 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
1C2×#13093955C211yesmaximal, characteristic, complemented
2C2×#13093945C211yesmaximal, characteristic
3C2×#13093945C211yesmaximal, characteristic
4#15689021C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C2×C4×D4×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093955—22no—
14#13093945—22no—
15#13093945C414yescomplemented
16C47⋊#95—21no—
17C22×D4×C47C2211yescharacteristic
18C23×C4×C47—21no—
19C4×D4×C47—22no—
20C4×D4×C47—22no—
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C22⋊C4×C47—21no—
23C2×C42×C47C2211yescharacteristic
24C24×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47C2×C412yes—
29C2×D4×C47D412yes—
30C2×D4×C47Q812yes—
31C22×C4×C47—24no—
32C22×C4×C47—21no—
33C22×C4×C47—42no—
34C22×C4×C47—42no—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—21no—
39C22×Dic47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47D412yes—
42C22⋊C4×C47—24no—
43C42×C47—21no—
44C42×C47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47C2×C412yescomplemented
49Dic47⋊C4—42no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8C2×C412yescomplemented
56C23×C47—22no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—41no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47—41no—
63C23×C47C2×D411yescharacteristic
64D4×C47—22no—
65D4×C47—22no—
66D4×C47—22no—
67D4×C47C4⋊C414yescomplemented
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—48no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47SD1612yes—
78C2×C4×C47C22×C411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×Q811yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×Dic47—22no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C47⋊C8—22no—
91C47⋊C8—41no—
92C22×C47—24no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47C4×D411yescharacteristic
100C22×C47#12011yescharacteristic
101C22×C47C22⋊Q811yescharacteristic
102C22×C47C2×SD1611yescharacteristic
103C22×C47#13511yescharacteristic
104C22×C47AGL(1,ℤ/8)11yescharacteristic
105C22×C47AGL(1,ℤ/8)11yescharacteristic
106C4×C47—22no—
107C4×C47—41no—
108C4×C47—42no—
109C4×C47C2×C4⋊C411yescharacteristic
110C4×C47C4×D411yescharacteristic
111C4×C47C22⋊Q811yescharacteristic
112C4×C47#12311yescharacteristic
113Dic47—42no—
114Dic47—81no—
115#1864—471nomaximal, Sylow
116C2×C47—44no—
117C2×C47#38511yescharacteristic
118C2×C47C4×SD1611yescharacteristic
119C2×C47#44211yescharacteristic
120C2×C47#44911yescharacteristic
121C2×C47#45011yescharacteristic
122C2×C47#47611yescharacteristic
123C2×C47#47811yescharacteristic
124C2×C4×D4D4711yescharacteristic
125C2×#106—471no—
126C2×#102—471no—
127C2×#102—471no—
128#389—471no—
129#340—471no—
130#336—471no—
131C47#186411yescharacteristic, complemented, Sylow
132C22×D4C2×D4711yescharacteristic
133C23×C4—21no—
134C22×C8—471no—
135C22×C8—471no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—471no—
140C2×C4⋊C4—941no—
141C2×C4⋊C4C2×D4711yescharacteristic
142C2×C22⋊C4—21no—
143C2×C42C2×D4711yescharacteristic
144#106—942no—
145#102—474no—
146#102—942no—
147#95—941no—
148C24—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4Dic9412yes—
153C2×D4C4×D4712yes—
154C2×D4C22⋊D4712yes—
155C22×C4—24no—
156C22×C4—21no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—941no—
160C22×C4—941no—
161C22×C4C22⋊D4711yescharacteristic
162C22×C4C22⋊D4711yescharacteristic
163C22×C4C22×D4711yescharacteristic
164C2×C8—472no—
165C2×C8—941no—
166C2×C8—941no—
167C2×C8—941no—
168C2×C8—941no—
169C2×C8—941no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C4⋊C4—1882no—
176C4⋊C4C22⋊D4712yes—
177C22⋊C4—24no—
178C42—21no—
179C42—21no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23C2×C22⋊D4711yescharacteristic
188D4—22no—
189D4—22no—
190D4—22no—
191D4Dic47⋊C414yescomplemented
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—48no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—942no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4#1062533512yes—
208C2×C4C2×Dic9411yescharacteristic
209C2×C4C2×C4×D4711yescharacteristic
210C2×C4#1062535011yescharacteristic
211C2×C4#1062535011yescharacteristic
212C2×C4C2×C22⋊D4711yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C8—942no—
215C8—1881no—
216C22—24no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22C4×C22⋊D4711yescharacteristic
224C22#1309399311yescharacteristic
225C22#1309400311yescharacteristic
226C22C2×#1062533511yescharacteristic
227C22#1309404411yescharacteristic
228C22#1309404911yescharacteristic
229C22#1309405011yescharacteristic
230C4—22no—
231C4—41no—
232C4—42no—
233C4—3761no—
234C4—1882no—
235C4C2×Dic47⋊C411yescharacteristic
236C4C4×C22⋊D4711yescharacteristic
237C4#1309400311yescharacteristic
238C4#1309400711yescharacteristic
239C2—44no—
240C2#1568899611yescharacteristic
241C2C4×#1062533511yescharacteristic
242C2#1568923311yescharacteristic
243C2#1568926811yescharacteristic
244C2#1568927411yescharacteristic
245C2#1568941311yescharacteristic
246C2#1568942311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C4×D4×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×D4D47
hypocenterC47#1864
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
1. C2×#13093955C2semidirect
4. #15689021C2semidirect
5. #15688885C2semidirect
6. #15688878C2semidirect
15. #13093945C4semidirect
48. C4⋊Dic47C2×C4semidirect
55. C2×C47⋊C8C2×C4semidirect
67. D4×C47C4⋊C4semidirect
131. C47#1864semidirect
191. D4Dic47⋊C4semidirect