Finite Group Databasebeta

← #20244460

Subgroups — #20244460

Order 6016.

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

normal subgroups only

This group has 510 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
1C22×D376C211yesmaximal, characteristic, complemented
2C22×#10625334C211yesmaximal, characteristic, complemented
3C2×#13094020C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic, complemented
5#15689024C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×D188C2211yescharacteristic
10C22×C22⋊D47—22no—
11C2×D376—22no—
12C2×D376—22no—
13C2×D376—22no—
14C2×#10625334—22no—
15C2×#10625334—22no—
16C2×#10625334—22no—
17C22×C47⋊C8C2211yescharacteristic
18#13094020—22no—
19#13094020—22no—
20C2×(C2×D47)⋊C4—22no—
21C2×C4×Dic47C2211yescharacteristic
22#13093944—22no—
23C22×D4×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26#102×C47—22no—
27C24×C47—21no—
28C23×D47—21no—
29C23×D47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47D412yes—
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—28no—
39C2×C22⋊D47—44no—
40C2×C22⋊D47—44no—
41C22×Dic47D412yes—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—21no—
52C2×D188D412yes—
53C2×D188D412yescomplemented
54C2×C8×C47—21no—
55C2×C8×C47—21no—
56C2×C8×C47D412yescomplemented
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59#10625334—28no—
60(C2×D47)⋊C4—44no—
61C4×Dic47—21no—
62C4×Dic47—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8—21no—
65C2×C47⋊C8D412yescomplemented
66D376—28no—
67C23×C47—22no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—42no—
71C23×C47—42no—
72C23×C47C2×D411yescharacteristic
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—41no—
76C22×D47—41no—
77C22×D47—41no—
78C22×D47—41no—
79C22×D47—42no—
80C22×D47—42no—
81C22×D47—42no—
82C22×D47—42no—
83D4×C47—22no—
84D4×C47—22no—
85D4×C47—41no—
86D4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—42no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47#4111yescharacteristic
95C22⋊D47—416no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47D814yescomplemented
99D188—22no—
100D188—22no—
101D188—22no—
102D188—22no—
103D188—41no—
104D188—41no—
105D188—41no—
106D188—41no—
107C8×C47—22no—
108C47⋊C8—22no—
109C22×C47—42no—
110C22×C47—44no—
111C22×C47—82no—
112C22×C47—81no—
113C22×C47—81no—
114C22×C47#12011yescharacteristic
115C22×C47#12111yescharacteristic
116C22×C47#12711yescharacteristic
117C22×C47C2×D812yes—
118C22×C47AGL(1,ℤ/8)12yes—
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—44no—
122C2×D47—44no—
123C2×D47—82no—
124C2×D47—82no—
125C2×D47—81no—
126C2×D47—81no—
127C2×D47—81no—
128C2×D47—81no—
129C4×C47—81no—
130C4×C47#12011yescharacteristic
131C4×C47#12011yescharacteristic
132C4×C47#12111yescharacteristic
133C4×C47#12111yescharacteristic
134Dic47—24no—
135#2011—471nomaximal, Sylow
136C2×C47—82no—
137C2×C47#39211yescharacteristic
138C2×C47#44712yes—
139C2×C47#45912yes—
140C2×C47#49311yescharacteristic
141C2×C47#49611yescharacteristic
142D47—82no—
143D47—82no—
144C22×D8—471no—
145C22×D8—471no—
146C2×#127—471no—
147C2×#102—471no—
148C2×#102D4711yescharacteristic, complemented
149#390—471no—
150#336—471no—
151C47#201111yescharacteristic, complemented, Sylow
152C22×D4—471no—
153C22×D4—471no—
154C22×D4—942no—
155C22×D4C2×D4711yescharacteristic
156C2×D8—942no—
157C2×D8—942no—
158C2×D8—942no—
159C2×D8—942no—
160C2×D8—942no—
161C2×D8—942no—
162C22×C8—471no—
163C22×C8C2×D4711yescharacteristic
164#127—942no—
165#127—942no—
166C2×C4⋊C4C2×D4711yescharacteristic
167C2×C22⋊C4—942no—
168C2×C42—471no—
169#102—22no—
170#102—942no—
171C24—21no—
172C24—941no—
173C24—941no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—472no—
180C2×D4—472no—
181C2×D4—948no—
182C2×D4—941no—
183C2×D4—941no—
184C2×D4—941no—
185C2×D4—941no—
186C2×D4—941no—
187C2×D4—941no—
188C2×D4—941no—
189C2×D4—941no—
190C2×D4—941no—
191C2×D4—941no—
192C2×D4—1884no—
193C2×D4—1884no—
194C2×D4D18812yes—
195C22×C4—21no—
196C22×C4—472no—
197C22×C4C22×D4711yescharacteristic
198D8—948no—
199D8—948no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—472no—
203C2×C8—941no—
204C2×C8—941no—
205C2×C8C22⋊D4712yescomplemented
206C4⋊C4—21no—
207C4⋊C4—21no—
208C22⋊C4—1884no—
209C42—941no—
210C42—941no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—42no—
215C23—42no—
216C23—942no—
217C23—942no—
218C23—1881no—
219C23—1881no—
220C23—1881no—
221C23—1881no—
222C23—1882no—
223C23—1882no—
224C23—1882no—
225C23—1882no—
226C23D4×D4711yescharacteristic
227D4—22no—
228D4—22no—
229D4—41no—
230D4—41no—
231D4—942no—
232D4—942no—
233D4—942no—
234D4—942no—
235D4—18816no—
236D4—1881no—
237D4—1881no—
238D4—1881no—
239D4—1881no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—474no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4C2×D18811yescharacteristic
246C2×C4#1062535011yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4D4×D4711yescharacteristic
249C2×C4D4×D4711yescharacteristic
250C2×C4C2×C22⋊D4711yescharacteristic
251C8—22no—
252C8—942no—
253C22—44no—
254C22—42no—
255C22—81no—
256C22—81no—
257C22—82no—
258C22—3761no—
259C22—3761no—
260C22—3761no—
261C22—3761no—
262C22—3762no—
263C22—3762no—
264C22—1884no—
265C22—1882no—
266C22—1882no—
267C22—1884no—
268C22#1309399411yescharacteristic
269C22#1309399711yescharacteristic
270C22#1309402011yescharacteristic
271C22D8×D4712yes—
272C22#1309405112yes—
273C4—81no—
274C4—944no—
275C4#1309399211yescharacteristic
276C4#1309399411yescharacteristic
277C4#1309399711yescharacteristic
278C4#1309399811yescharacteristic
279C2—82no—
280C2—3762no—
281C2—3762no—
282C2#1568903211yescharacteristic
283C2#1568925812yes—
284C2#1568931712yes—
285C2#1568949811yescharacteristic
286C2#1568950911yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2011
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×D376C2semidirect
2. C22×#10625334C2semidirect
3. C2×#13094020C2semidirect
4. C2×#13093944C2semidirect
5. #15689024C2semidirect
6. #15688877C2semidirect
7. C2×#102×C47C2semidirect
53. C2×D188D4semidirect
56. C2×C8×C47D4semidirect
65. C2×C47⋊C8D4semidirect
98. C2×Dic47D8semidirect
148. C2×#102D47semidirect
151. C47#2011semidirect
205. C2×C8C22⋊D47semidirect