Finite Group Databasebeta

← #20244629

Subgroups — #20244629

Order 6016.

318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094012C211yesmaximal, characteristic
2C2×#13093947C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic
5C2×#13093944C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic, complemented
7C47×#389C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×D188C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C22×C47⋊C8C2211yescharacteristic
12#13094012—22no—
13#13094012—22no—
14C2×(C2×D47)⋊C4—21no—
15C2×(C2×D47)⋊C4—21no—
16#13093947—22no—
17#13093947—22no—
18#13093944—22no—
19#13093944—22no—
20C2×C4⋊C4×C47—21no—
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C42×C47C2211yescharacteristic
24#95×C47—21no—
25C23×D47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188D412yes—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94D412yes—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—42no—
48C4⋊C4×C47D412yes—
49C42×C47—21no—
50C42×C47—21no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47C2×D411yescharacteristic
60C22×D47—22no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C2×Dic47—22no—
86C2×Dic47—41no—
87C2×Dic47—41no—
88D188—22no—
89D188—22no—
90D188—41no—
91D188—41no—
92Dic94—22no—
93Dic94—22no—
94Dic94—41no—
95Dic94—41no—
96C47⋊C8—41no—
97C47⋊C8—41no—
98C22×C47#12011yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12411yescharacteristic
101C22×C47#13511yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47AGL(1,ℤ/8)11yescharacteristic
104C22×C47#13711yescharacteristic
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—81no—
109C2×D47—81no—
110C2×D47—81no—
111C2×D47—81no—
112C4×C47—41no—
113C4×C47—41no—
114C4×C47—42no—
115C4×C47—81no—
116C4×C47#12111yescharacteristic
117C4×C47#12111yescharacteristic
118C4×C47#12311yescharacteristic
119C4×C47#12311yescharacteristic
120Dic47—42no—
121#2042—471nomaximal, Sylow
122C2×C47#39411yescharacteristic
123C2×C47#44911yescharacteristic
124C2×C47#45211yescharacteristic
125C2×C47#46311yescharacteristic
126C2×C47#46411yescharacteristic
127C2×C47#48811yescharacteristic
128C2×C47#48911yescharacteristic
129D47—82no—
130C2×#124—471no—
131C2×#103—471no—
132C2×#103—471no—
133C2×#102—471no—
134C2×#102—471no—
135#389D4711yescharacteristic, complemented
136#336—471no—
137C47#204211yescharacteristic, complemented, Sylow
138C22×Q8—471no—
139C22×D4—471no—
140C22×C8—471no—
141C22×C8—471no—
142#124—942no—
143#124—942no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—941no—
148C2×C22⋊C4—941no—
149C2×C42C2×D4711yescharacteristic
150#103—942no—
151#103—942no—
152#102—942no—
153#102—942no—
154#95—21no—
155C24—941no—
156C2×Q8—472no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×D4—472no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4—941no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—941no—
171C22×C4C22⋊D4711yescharacteristic
172C22×C4C22⋊D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C2×C8—941no—
175C2×C8—941no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—42no—
184C4⋊C4D18812yes—
185C22⋊C4—944no—
186C22⋊C4—944no—
187C42—21no—
188C42—21no—
189C23—942no—
190C23—1881no—
191C23—1881no—
192C23—1881no—
193C23—1881no—
194C23—1881no—
195C23—1881no—
196C23C2×C22⋊D4711yescharacteristic
197Q8—942no—
198Q8—942no—
199Q8—1881no—
200Q8—1881no—
201D4—942no—
202D4—942no—
203D4—1881no—
204D4—1881no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—942no—
218C2×C4—1881no—
219C2×C4—1881no—
220C2×C4C2×D18811yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4#1062535411yescharacteristic
225C2×C4#1062535411yescharacteristic
226C8—1881no—
227C8—1881no—
228C22—3761no—
229C22—3761no—
230C22—3761no—
231C22—3761no—
232C22—1882no—
233C22—1882no—
234C22—1882no—
235C22#1309399211yescharacteristic
236C22#1309399811yescharacteristic
237C22#1309401311yescharacteristic
238C22#1309404411yescharacteristic
239C22#1309404411yescharacteristic
240C22#1309405011yescharacteristic
241C22#1309405511yescharacteristic
242C4—41no—
243C4—41no—
244C4—42no—
245C4—81no—
246C4—1882no—
247C4#1309399911yescharacteristic
248C4#1309399911yescharacteristic
249C4#1309400911yescharacteristic
250C4#1309400911yescharacteristic
251C2—3762no—
252C2#1568904011yescharacteristic
253C2#1568926611yescharacteristic
254C2#1568928311yescharacteristic
255C2#1568933811yescharacteristic
256C2#1568934511yescharacteristic
257C2#1568948011yescharacteristic
258C2#1568948511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#389C2
socleC23×C47C2×D4
hypercenter#389D47
hypocenterC47#2042
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#13093947C2semidirect
3. C2×#13093947C2semidirect
6. #15688878C2semidirect
7. C47×#389C2semidirect
135. #389D47semidirect
137. C47#2042semidirect