Finite Group Databasebeta

← #20243757

Subgroups — #20243757

Order 6016.

334 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094054C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic
3#15689131C211yesmaximal, characteristic, complemented
4#15689028C211yesmaximal, characteristic, complemented
5#15688892C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#520C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9#13094054—22no—
10#13094054C414yescomplemented
11C2×#10625337—21no—
12C2×#10625335—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×C4×Dic47C2211yescharacteristic
16#13093951—22no—
17#13093947—21no—
18#13093947—21no—
19C47⋊#95—22no—
20C2×#41×C47C2211yescharacteristic
21C4×Q8×C47—21no—
22C4×D4×C47—21no—
23C4×D4×C47—22no—
24#117×C47—21no—
25#117×C47C2211yescharacteristic
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47C2211yescharacteristic
28#41×C47—21no—
29#41×C47—21no—
30#41×C47C2×C412yes—
31#41×C47D412yes—
32C2×Q8×C47D411yescharacteristic
33C2×D4×C47—21no—
34C2×D4×C47D411yescharacteristic
35C22×C4×C47—21no—
36C22×C4×C47—22no—
37C22×C4×C47D412yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C22×Dic47—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94C2×C412yescomplemented
47C4⋊C4×C47—22no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47D411yescharacteristic
51C4⋊C4×C47D411yescharacteristic
52C22⋊C4×C47—22no—
53C22⋊C4×C47—21no—
54C42×C47—22no—
55C42×C47—21no—
56#10625337—24no—
57#10625335—24no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60#10625329—21no—
61#10625329—21no—
62#10625329—21no—
63#10625329C2×C412yescomplemented
64C2×C47⋊C8—21no—
65C2×C47⋊C8—21no—
66C23×C47—21no—
67C23×C47C2×D411yescharacteristic
68Q8×C47—21no—
69Q8×C47C22⋊C412yes—
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—21no—
73D4×C47C22⋊C412yes—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—42no—
81C2×C4×C47—82no—
82C2×C4×C47C22×C411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94Dic94—22no—
95Dic94—22no—
96Dic94—41no—
97Dic94—41no—
98C47⋊C8—22no—
99C47⋊C8—41no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47—22no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47C4×D411yescharacteristic
106C22×C47#12011yescharacteristic
107C22×C47#12111yescharacteristic
108C4×C47—22no—
109C4×C47—42no—
110C4×C47—41no—
111C4×C47—41no—
112C4×C47C2×C22⋊C411yescharacteristic
113C4×C47C4×D411yescharacteristic
114C4×C47#12111yescharacteristic
115C4×C47#12311yescharacteristic
116Dic47—42no—
117Dic47—42no—
118#1882—471nomaximal, Sylow
119C2×C47—21no—
120C2×C47—21no—
121C2×C47—42no—
122C2×C47#38611yescharacteristic
123C2×C47#45511yescharacteristic
124C2×C47#45611yescharacteristic
125C2×#137—471no—
126#520D4711yescharacteristic
127C2×#104—471no—
128#419—471no—
129#391—471no—
130#343—471no—
131#339—471no—
132C47#188211yescharacteristic, complemented, Sylow
133C2×#41C2×D4711yescharacteristic
134C22×Q8—471no—
135#137—474no—
136#137—942no—
137C2×Q16—941no—
138C2×SD16—941no—
139C2×M16—471no—
140C2×M16—471no—
141C4×Q8—21no—
142C4×D4—21no—
143C4×D4—22no—
144#117—21no—
145#117C2×D4711yescharacteristic
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C42—471no—
149#104—942no—
150#103—941no—
151#103—941no—
152#95—942no—
153#41—21no—
154#41—21no—
155#41C4×D4712yes—
156#41D18812yes—
157C2×Q8—472no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×Q8—941no—
163C2×Q8C22⋊D4711yescharacteristic
164C2×D4—21no—
165C2×D4C22⋊D4711yescharacteristic
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4C22⋊D4712yes—
171C22×C4C22×D4711yescharacteristic
172Q16—944no—
173SD16—944no—
174M16—472no—
175M16—941no—
176M16—941no—
177M16—941no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—22no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4C22⋊D4711yescharacteristic
184C4⋊C4C22⋊D4711yescharacteristic
185C22⋊C4—22no—
186C22⋊C4—21no—
187C42—22no—
188C42—21no—
189C42—941no—
190C42—941no—
191C23—21no—
192C23C2×C22⋊D4711yescharacteristic
193Q8—21no—
194Q8—942no—
195Q8—942no—
196Q8—1881no—
197Q8—1881no—
198Q8(C2×D47)⋊C412yes—
199D4—22no—
200D4—22no—
201D4—21no—
202D4(C2×D47)⋊C412yes—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—1881no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4C2×C4×D4711yescharacteristic
218C2×C4C2×D18811yescharacteristic
219C2×C4#1062535011yescharacteristic
220C2×C4#1062535011yescharacteristic
221C2×C4C2×C22⋊D4711yescharacteristic
222C2×C4C2×C22⋊D4711yescharacteristic
223C8—942no—
224C8—1881no—
225C22—21no—
226C22—21no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22C4×C22⋊D4711yescharacteristic
231C22#1309399311yescharacteristic
232C22#1309399811yescharacteristic
233C4—22no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—1882no—
238C4—1882no—
239C4C2×(C2×D47)⋊C411yescharacteristic
240C4C4×C22⋊D4711yescharacteristic
241C4#1309399811yescharacteristic
242C4#1309400711yescharacteristic
243C2—21no—
244C2—21no—
245C2—42no—
246C2#1568900211yescharacteristic
247C2#1568930111yescharacteristic
248C2#1568930611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#520C2
socleC22×C47#120
hypercenter#520D47
hypocenterC47#1882
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
3. #15689131C2semidirect
4. #15689028C2semidirect
5. #15688892C2semidirect
6. #15688882C2semidirect
10. #13094054C4semidirect
46. C2×Dic94C2×C4semidirect
63. #10625329C2×C4semidirect
132. C47#1882semidirect