Finite Group Databasebeta

← #20254630

Subgroups — #20254630

Order 6016.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689680C211yesmaximal, characteristic, complemented
2#15689657C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689532C211yesmaximal, characteristic, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689483C211yesmaximal, characteristic, complemented
7#15689465C212yesmaximal, complemented
8#15689448C212yesmaximal
9#15689431C212yesmaximal, complemented
10#15689424C212yesmaximal, complemented
11C47×#432C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094018—21no—
15#13094016C2211yescharacteristic
16#13094016C2212yes—
17#13094012C2211yescharacteristic
18#13094007—21no—
19#13094003—21no—
20#13094003—21no—
21#13094003C2211yescharacteristic
22#13093998C2211yescharacteristic
23C4×Dic94—21no—
24C4×Dic94—21no—
25C4×Dic94C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C4×C22⋊D47—21no—
28#13093983C2212yes—
29#13093981—21no—
30#13093958C2212yes—
31#13093958C2212yes—
32#13093956C2212yes—
33#13093956C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36#13093946C2212yes—
37#13093946C2212yes—
38C2×C42×C47C2211yescharacteristic
39C4⋊C8×C47C2212yes—
40C22⋊C8×C47C2212yes—
41#97×C47C2211yescharacteristic
42#97×C47C2211yescharacteristic
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D411yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47C2312yes—
53C2×C8×C47C2312yes—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59C22⋊Dic47—21no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—22no—
74Dic47⋊C4—22no—
75Dic47⋊C4—21no—
76C4×Dic47—21no—
77C4×Dic47—22no—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C22⋊D47—42no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95D188—22no—
96C4×D47—42no—
97Dic94—22no—
98Dic94—42no—
99Dic94—42no—
100C8×C47—22no—
101C8×C47—22no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47—21no—
105C22×C47C22×D411yescharacteristic
106C2×D47—41no—
107C2×D47—41no—
108C2×D47—41no—
109C4×C47—21no—
110C4×C47—21no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47—21no—
114C4×C472−1+412yes—
115Dic47—41no—
116Dic47—42no—
117Dic47—42no—
118Dic47—41no—
119Dic47—41no—
120#3240—471nomaximal, Sylow
121C2×C47—41no—
122C2×C47#53611yescharacteristic
123C2×C47#57511yescharacteristic
124C2×C47#57511yescharacteristic
125D47—81no—
126#533—471no—
127#529—471no—
128#501—471no—
129#501—471no—
130#489—471no—
131#489—471no—
132#485—472no—
133#482—472no—
134#479—472no—
135#478—472no—
136#432D4711yescharacteristic, complemented
137C47#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—471no—
139C4⋊Q8—471no—
140#126—941no—
141#125—471no—
142#125—472no—
143#124—471no—
144#123—941no—
145C22⋊Q8—471no—
146C22⋊Q8—941no—
147C22⋊Q8—941no—
148#121—471no—
149C4×Q8—471no—
150C4×Q8—941no—
151C4×Q8—941no—
152C4×D4—471no—
153C4×D4—941no—
154#117—472no—
155#117—941no—
156C2×C42C2×D4711yescharacteristic
157#107—472no—
158#107—472no—
159#106—472no—
160#106—472no—
161C4⋊C8C2×D4712yes—
162#103—472no—
163#103—472no—
164#102—472no—
165#102—472no—
166C22⋊C8C2×D4712yes—
167#97C2×D4711yescharacteristic
168#97C2×D4711yescharacteristic
169C2×Q8—471no—
170C2×Q8—941no—
171C2×Q8—941no—
172C2×D4—471no—
173C2×D4—941no—
174C22×C4—941no—
175C22×C4D18811yescharacteristic
176C22×C4D18811yescharacteristic
177C22×C4C22×D4711yescharacteristic
178C2×C8C22×D4712yes—
179C2×C8C22×D4712yes—
180C4⋊C4—472no—
181C4⋊C4—472no—
182C4⋊C4—471no—
183C4⋊C4—471no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4—941no—
188C4⋊C4—942no—
189C4⋊C4—942no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C22⋊C4—942no—
193C22⋊C4—941no—
194C22⋊C4—941no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C22⋊C4—941no—
198C42—942no—
199C42—941no—
200C42D18811yescharacteristic
201C42D18811yescharacteristic
202C42C22×D4711yescharacteristic
203C42C22×D4711yescharacteristic
204C23—941no—
205C23C2×D18811yescharacteristic
206Q8—942no—
207Q8—1882no—
208Q8—1882no—
209D4—942no—
210D4—1882no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—1882no—
220C2×C4C2×D18811yescharacteristic
221C2×C4C2×D18811yescharacteristic
222C2×C4C2×D18811yescharacteristic
223C2×C4C2×D18811yescharacteristic
224C2×C4C2×D18811yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—1881no—
232C22—1881no—
233C22—1881no—
234C22C22×D18811yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—1881no—
241C4—1881no—
242C4—1882no—
243C4—1882no—
244C4—1881no—
245C4#1309407112yes—
246C2—41no—
247C2—3761no—
248C2#1568969911yescharacteristic
249C2#1568992311yescharacteristic
250C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3240
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689532C2semidirect
4. #15689532C2semidirect
5. #15689483C2semidirect
6. #15689483C2semidirect
7. #15689465C2semidirect
9. #15689431C2semidirect
10. #15689424C2semidirect
11. C47×#432C2semidirect
136. #432D47semidirect
137. C47#3240semidirect