Finite Group Databasebeta

← #20244523

Subgroups — #20244523

Order 6016.

326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13094023C211yesmaximal, characteristic, complemented
2C2×#13093946C211yesmaximal, characteristic
3C2×#13093944C211yesmaximal, characteristic
4#15689024C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×Dic94—21no—
9C22×D188C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13094023—22no—
12#13094023—22no—
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×D188Q812yescomplemented
36C2×Dic94—24no—
37C2×Dic94—42no—
38C2×Dic94—42no—
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47D412yes—
46(C2×D47)⋊C4—42no—
47(C2×D47)⋊C4—42no—
48C4⋊Dic47—21no—
49C4⋊Dic47D412yes—
50Dic47⋊C4—24no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47C2×D411yescharacteristic
57C22×D47—22no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47—41no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×Q811yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47D812yes—
84C2×Dic47SD1612yes—
85D188—22no—
86D188—22no—
87D188—41no—
88D188—41no—
89Dic94—48no—
90C8×C47—41no—
91C47⋊C8—41no—
92C22×C47#12011yescharacteristic
93C22×C47C22⋊Q811yescharacteristic
94C22×C47#12411yescharacteristic
95C22×C47C2×D811yescharacteristic
96C22×C47C2×SD1611yescharacteristic
97C22×C47AGL(1,ℤ/8)11yescharacteristic
98C22×C47#13711yescharacteristic
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—81no—
103C2×D47—81no—
104C2×D47—81no—
105C2×D47—81no—
106C4×C47—42no—
107C4×C47—81no—
108C4×C47C22⋊Q811yescharacteristic
109C4×C47C22⋊Q811yescharacteristic
110C4×C47#12411yescharacteristic
111C4×C47#12411yescharacteristic
112Dic47—22no—
113Dic47—22no—
114Dic47—42no—
115#2023—471nomaximal, Sylow
116C2×C47#39311yescharacteristic
117C2×C47#44711yescharacteristic
118C2×C47#44811yescharacteristic
119C2×C47#47411yescharacteristic
120C2×C47#47611yescharacteristic
121C2×C47#48611yescharacteristic
122C2×C47#48911yescharacteristic
123D47—82no—
124C2×C4⋊Q8—471no—
125C2×#102—471no—
126C2×#102—471no—
127#390—471no—
128#340—471no—
129#340D4711yescharacteristic, complemented
130#336—471no—
131C47#202311yescharacteristic, complemented, Sylow
132C22×Q8—941no—
133C22×D4—471no—
134C22×C8—471no—
135C22×C8C2×D4711yescharacteristic
136C4⋊Q8—942no—
137C4⋊Q8—942no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—941no—
140C2×C4⋊C4C2×D4711yescharacteristic
141C2×C4⋊C4C2×D4711yescharacteristic
142C2×C22⋊C4—941no—
143C2×C22⋊C4—941no—
144C2×C42—471no—
145#102—942no—
146#102—942no—
147C24—941no—
148C2×Q8—944no—
149C2×Q8—1882no—
150C2×Q8—1882no—
151C2×D4—472no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4—941no—
156C2×D4—941no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—471no—
160C22×C4—471no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—941no—
167C2×C8—941no—
168C2×C8—941no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—472no—
173C4⋊C4—944no—
174C4⋊C4—941no—
175C4⋊C4D18812yes—
176C22⋊C4—1882no—
177C22⋊C4—1882no—
178C42—941no—
179C42—941no—
180C23—942no—
181C23—1881no—
182C23—1881no—
183C23—1881no—
184C23—1881no—
185C23—1881no—
186C23—1881no—
187C23D4×D4711yescharacteristic
188Q8—1888no—
189D4—942no—
190D4—942no—
191D4—1881no—
192D4—1881no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4C2×D18811yescharacteristic
209C2×C4#1062535011yescharacteristic
210C2×C4#1062535011yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4#1062535211yescharacteristic
213C2×C4Q8×D4711yescharacteristic
214C8—41no—
215C8—1881no—
216C22—3761no—
217C22—3761no—
218C22—3761no—
219C22—3761no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22#1309399411yescharacteristic
224C22#1309400211yescharacteristic
225C22#1309401011yescharacteristic
226C22D8×D4711yescharacteristic
227C22SD16×D4711yescharacteristic
228C22#1309405111yescharacteristic
229C22#1309405611yescharacteristic
230C4—42no—
231C4—81no—
232C4—942no—
233C4—942no—
234C4—1882no—
235C4#1309400211yescharacteristic
236C4#1309400411yescharacteristic
237C4#1309401011yescharacteristic
238C4#1309401211yescharacteristic
239C2—3762no—
240C2#1568903611yescharacteristic
241C2#1568925811yescharacteristic
242C2#1568926311yescharacteristic
243C2#1568940211yescharacteristic
244C2#1568941211yescharacteristic
245C2#1568946811yescharacteristic
246C2#1568948411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2023
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×#13094023C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
7. C47×#340C2semidirect
35. C2×D188Q8semidirect
129. #340D47semidirect
131. C47#2023semidirect