Finite Group Databasebeta

← #20243886

Subgroups — #20243886

Order 6016.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689921C211yesmaximal, characteristic
2#15689591C211yesmaximal, characteristic, complemented
3#15689141C211yesmaximal, characteristic, complemented
4C2×#13093951C211yesmaximal, characteristic, complemented
5#15688893C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#410C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055C412yescomplemented
10#13094054—21no—
11#13094050C412yescomplemented
12#13094049—21no—
13#13094044—22no—
14C2×#10625329C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13093989—21no—
17#13093986—21no—
18(C22⋊D47)⋊C4—22no—
19#13093981—21no—
20C2×C4×Dic47C2211yescharacteristic
21C42×D47—21no—
22#13093952—22no—
23#13093951—21no—
24#13093951—21no—
25C2×#41×C47C2211yescharacteristic
26#117×C47C2211yescharacteristic
27#117×C47C2211yescharacteristic
28#99×C47—22no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32#41×C47—21no—
33C2×Q8×C47C2×C411yescharacteristic, complemented
34C2×D4×C47—21no—
35C2×D4×C47C2×C411yescharacteristic, complemented
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—21no—
39C22×Dic47—21no—
40#10625350—21no—
41#10625350—21no—
42#10625350C2×C412yes—
43#10625350D412yes—
44C2×D188D411yescharacteristic
45C2×C4×D47—21no—
46C2×C4×D47—22no—
47C2×Dic94D411yescharacteristic
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C22⋊C4×C47D412yes—
52C42×C47—21no—
53C42×C47—21no—
54#10625337—22no—
55#10625336—22no—
56#10625335—22no—
57#10625334—22no—
58(C2×D47)⋊C4—22no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C4×Dic47—21no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64#10625329—21no—
65#10625329—21no—
66#10625329—21no—
67#10625329C2×C412yescomplemented
68C2×C47⋊C8—21no—
69C2×C47⋊C8—21no—
70C23×C47—21no—
71C23×C47C2×D411yescharacteristic
72C22×D47—21no—
73Q8×C47—21no—
74Q8×C47—21no—
75D4×C47—21no—
76D4×C47—21no—
77D4×C47—41no—
78D4×C47—41no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47C22×C411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C22⋊D47—22no—
91C22⋊D47—22no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—42no—
96D188—21no—
97D188C22⋊C412yes—
98C4×D47—22no—
99C4×D47—22no—
100C4×D47—44no—
101Dic94—21no—
102Dic94C22⋊C412yes—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47—81no—
108C22×C47C4×D411yescharacteristic
109C22×C47#12011yescharacteristic
110C22×C47#12111yescharacteristic
111C2×D47—22no—
112C2×D47—42no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—81no—
116C4×C47C2×C22⋊C411yescharacteristic
117C4×C47C4×D411yescharacteristic
118C4×C47#12111yescharacteristic
119C4×C47#12311yescharacteristic
120Dic47—22no—
121Dic47—22no—
122Dic47—41no—
123#1906—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—21no—
127C2×C47—81no—
128C2×C47#38611yescharacteristic
129D47—42no—
130#575—471no—
131C4×#41—471no—
132#421—471no—
133C2×#104—471no—
134#410D4711yescharacteristic, complemented
135#344—471no—
136#339—471no—
137C47#190611yescharacteristic, complemented, Sylow
138C2×#41—471no—
139C2×#41C2×D4711yescharacteristic
140#137—472no—
141#137—941no—
142AGL(1,ℤ/8)—472no—
143AGL(1,ℤ/8)—941no—
144#135—942no—
145C2×M16—471no—
146C2×M16—471no—
147C4×Q8—941no—
148C4×D4—941no—
149C4×D4—942no—
150#117—941no—
151#117C2×D4711yescharacteristic
152#117C2×D4711yescharacteristic
153C2×C42—471no—
154C2×C42—941no—
155#104—942no—
156#104—941no—
157#104—941no—
158#99—22no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—472no—
164#41—472no—
165#41—941no—
166#41—941no—
167C2×Q8—471no—
168C2×Q8C4×D4711yescharacteristic, complemented
169C2×D4—21no—
170C2×D4—471no—
171C2×D4—941no—
172C2×D4C4×D4711yescharacteristic, complemented
173C22×C4—21no—
174C22×C4—942no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—472no—
183M16—941no—
184M16—941no—
185M16—941no—
186C2×C8—941no—
187C2×C8—941no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—942no—
191C22⋊C4—21no—
192C22⋊C4—942no—
193C22⋊C4C22⋊D4712yes—
194C42—21no—
195C42—21no—
196C42—471no—
197C42—471no—
198C42—942no—
199C42—941no—
200C23—21no—
201C23—941no—
202C23C2×C22⋊D4711yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—472no—
206Q8—941no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—472no—
212D4—942no—
213D4—942no—
214D4—941no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—1884no—
226C2×C4—1882no—
227C2×C4C2×C4×D4711yescharacteristic
228C2×C4#1062535011yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4#1062535211yescharacteristic
233C8—942no—
234C8—1881no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—942no—
239C22—1882no—
240C22C4×C22⋊D4711yescharacteristic
241C22#1309399211yescharacteristic
242C22#1309399511yescharacteristic
243C4—42no—
244C4—41no—
245C4—81no—
246C4—942no—
247C4—942no—
248C4—1881no—
249C4C22⋊C4×D4711yescharacteristic
250C4(C22⋊D47)⋊C411yescharacteristic
251C4#1309399711yescharacteristic
252C4#1309400611yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—81no—
257C2—1882no—
258C2#1568899911yescharacteristic
subgroupG/H
centerC4#13093997
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#410C2
socleC2×C47#386
hypercenter#410D47
hypocenterC47#1906
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689591C2semidirect
3. #15689141C2semidirect
4. C2×#13093951C2semidirect
5. #15688893C2semidirect
6. #15688882C2semidirect
7. C47×#410C2semidirect
9. #13094055C4semidirect
11. #13094050C4semidirect
33. C2×Q8×C47C2×C4semidirect
35. C2×D4×C47C2×C4semidirect
67. #10625329C2×C4semidirect
134. #410D47semidirect
137. C47#1906semidirect
168. C2×Q8C4×D47semidirect
172. C2×D4C4×D47semidirect