Finite Group Databasebeta

← #20244533

Subgroups — #20244533

Order 6016.

294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13093946C211yesmaximal, characteristic
3C2×#13093944C211yesmaximal, characteristic
4#15689024C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094015—22no—
11#13094015—22no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×(C2×D47)⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17C2×C4×Dic47C2211yescharacteristic
18#13093946—22no—
19#13093944—22no—
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C23×D47—21no—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47D411yescharacteristic
29C22×Dic47D411yescharacteristic
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188Q812yes—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47D412yes—
43(C2×D47)⋊C4—42no—
44(C2×D47)⋊C4—42no—
45C4⋊Dic47—24no—
46C4⋊Dic47—21no—
47C4⋊Dic47D412yes—
48Dic47⋊C4—24no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55C22×D47—22no—
56C22×D47—41no—
57C22×D47—41no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47—41no—
61C22×D47—41no—
62C2×C4×C47—22no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×Q811yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83D188—22no—
84D188—22no—
85D188—41no—
86D188—41no—
87C8×C47—41no—
88C47⋊C8—41no—
89C22×C47#12011yescharacteristic
90C22×C47C22⋊Q811yescharacteristic
91C22×C47#12411yescharacteristic
92C22×C47#13511yescharacteristic
93C22×C47#13511yescharacteristic
94C22×C47AGL(1,ℤ/8)11yescharacteristic
95C22×C47AGL(1,ℤ/8)11yescharacteristic
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—81no—
100C2×D47—81no—
101C2×D47—81no—
102C2×D47—81no—
103C4×C47—42no—
104C4×C47—81no—
105C4×C47C22⋊Q811yescharacteristic
106C4×C47C22⋊Q811yescharacteristic
107C4×C47#12411yescharacteristic
108C4×C47#12411yescharacteristic
109Dic47—41no—
110Dic47—41no—
111Dic47—42no—
112#2025—471nomaximal, Sylow
113C2×C47#39311yescharacteristic
114C2×C47#44911yescharacteristic
115C2×C47#44911yescharacteristic
116C2×C47#47811yescharacteristic
117C2×C47#47811yescharacteristic
118C2×C47#48811yescharacteristic
119C2×C47#49011yescharacteristic
120D47—82no—
121C2×#125—471no—
122C2×#102—471no—
123C2×#102—471no—
124#390—471no—
125#340—471no—
126#340D4711yescharacteristic, complemented
127#336—471no—
128C47#202511yescharacteristic, complemented, Sylow
129C22×D4—471no—
130C22×C8—471no—
131C22×C8C2×D4711yescharacteristic
132#125—942no—
133#125—942no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—941no—
136C2×C4⋊C4—941no—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—941no—
140C2×C22⋊C4—941no—
141C2×C42—471no—
142#102—942no—
143#102—942no—
144C24—941no—
145C2×D4—472no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C2×D4—941no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—941no—
156C22×C4C22×D4711yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—941no—
161C2×C8—941no—
162C2×C8—941no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—472no—
167C4⋊C4—944no—
168C4⋊C4—944no—
169C4⋊C4—941no—
170C4⋊C4D18812yes—
171C22⋊C4—1882no—
172C22⋊C4—1882no—
173C42—941no—
174C42—941no—
175C23—942no—
176C23—1881no—
177C23—1881no—
178C23—1881no—
179C23—1881no—
180C23—1881no—
181C23—1881no—
182C23D4×D4711yescharacteristic
183D4—942no—
184D4—942no—
185D4—1881no—
186D4—1881no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—942no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4C2×D18811yescharacteristic
203C2×C4#1062535011yescharacteristic
204C2×C4#1062535011yescharacteristic
205C2×C4D4×D4711yescharacteristic
206C2×C4#1062535211yescharacteristic
207C2×C4Q8×D4711yescharacteristic
208C8—41no—
209C8—1881no—
210C22—3761no—
211C22—3761no—
212C22—3761no—
213C22—3761no—
214C22—1882no—
215C22—1882no—
216C22—1882no—
217C22#1309399411yescharacteristic
218C22#1309400211yescharacteristic
219C22#1309401011yescharacteristic
220C22#1309404511yescharacteristic
221C22#1309404711yescharacteristic
222C22#1309404811yescharacteristic
223C22#1309405111yescharacteristic
224C4—42no—
225C4—81no—
226C4—1881no—
227C4—1881no—
228C4—1882no—
229C4#1309400211yescharacteristic
230C4#1309400411yescharacteristic
231C4#1309401011yescharacteristic
232C4#1309401211yescharacteristic
233C2—3762no—
234C2#1568903611yescharacteristic
235C2#1568926911yescharacteristic
236C2#1568927111yescharacteristic
237C2#1568942211yescharacteristic
238C2#1568942611yescharacteristic
239C2#1568947911yescharacteristic
240C2#1568948611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2025
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
7. C47×#340C2semidirect
126. #340D47semidirect
128. C47#2025semidirect