Finite Group Databasebeta

← #20254625

Subgroups — #20254625

Order 6016.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689678C211yesmaximal, characteristic, complemented
2#15689652C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689529C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689463C212yesmaximal, complemented
7#15689446C212yesmaximal
8#15689428C212yesmaximal, complemented
9#15689421C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094017—21no—
14#13094016C2211yescharacteristic
15#13094015C2212yes—
16#13094006—21no—
17#13094004—21no—
18#13094000—21no—
19#13094000C2211yescharacteristic
20#13093995C2211yescharacteristic
21Q8×Dic47—21no—
22Q8×Dic47C2211yescharacteristic
23#13093989—21no—
24D4×Dic47C2211yescharacteristic
25(C22⋊D47)⋊C4—21no—
26#13093982C2212yes—
27#13093980—21no—
28C42×D47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093956C2212yes—
32#13093955C2212yes—
33Dic47⋊C8C2212yes—
34#13093948C2212yes—
35#13093945C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#124×C47C2211yescharacteristic
40#103×C47C2212yes—
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C2×C4×D47D411yescharacteristic
49C2×C4×D47D411yescharacteristic
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—21no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—21no—
56C22⋊C4×C47—21no—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—21no—
59C22⋊Dic47—21no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2312yes—
66C4⋊Dic47C2311yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—22no—
72C4×Dic47—21no—
73C4×Dic47—22no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C23×C47—21no—
79C22×D47C2×D411yescharacteristic
80Q8×C47—22no—
81Q8×C47—42no—
82D4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—42no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—42no—
93C2×Dic47C2×D411yescharacteristic
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C4×D47—22no—
97C4×D47—41no—
98C4×D47—41no—
99Dic94—42no—
100C8×C47—22no—
101C47⋊C8—22no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47C22×D411yescharacteristic
106C2×D47—21no—
107C2×D47—21no—
108C2×D47—21no—
109C4×C47—21no—
110C4×C47—21no—
111C4×C47—41no—
112C4×C47—42no—
113C4×C472−1+412yes—
114Dic47—21no—
115Dic47—21no—
116Dic47—21no—
117Dic47—42no—
118Dic47—41no—
119Dic47—41no—
120#3240—471nomaximal, Sylow
121C2×C47—81no—
122C2×C47#53611yescharacteristic
123C2×C47#57511yescharacteristic
124C2×C47#57511yescharacteristic
125D47—41no—
126#533—471no—
127#529—471no—
128#501—471no—
129#501—471no—
130#489—471no—
131#489D4711yescharacteristic, complemented
132#485—472no—
133#482—472no—
134#479—472no—
135#478—472no—
136#432—471no—
137C47#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—471no—
139C4⋊Q8C2×D4711yescharacteristic
140#126—941no—
141#125—472no—
142#125—471no—
143#124C2×D4711yescharacteristic
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×C42—471no—
157#107—472no—
158#107—472no—
159#106—472no—
160#106—472no—
161C4⋊C8—472no—
162#103—472no—
163#103C2×D4712yes—
164#102—472no—
165#102C2×D4712yes—
166C22⋊C8—472no—
167#97—471no—
168#97C2×D4711yescharacteristic
169C2×Q8—21no—
170C2×Q8—941no—
171C2×Q8C22×D4711yescharacteristic
172C2×D4—941no—
173C2×D4C22×D4711yescharacteristic
174C22×C4—471no—
175C22×C4—471no—
176C22×C4—471no—
177C22×C4—941no—
178C2×C8—472no—
179C2×C8C22×D4712yes—
180C4⋊C4—21no—
181C4⋊C4—472no—
182C4⋊C4—471no—
183C4⋊C4—471no—
184C4⋊C4—941no—
185C4⋊C4—942no—
186C4⋊C4—941no—
187C4⋊C4—942no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4C22×D4712yes—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—942no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C22⋊C4—941no—
198C42—471no—
199C42—471no—
200C42—471no—
201C42—942no—
202C42—941no—
203C42C22×D4711yescharacteristic
204C23—21no—
205C23—471no—
206Q8—22no—
207Q8—42no—
208Q8—1882no—
209D4—22no—
210D4—1882no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—471no—
214C2×C4—471no—
215C2×C4—471no—
216C2×C4—942no—
217C2×C4—941no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—1881no—
221C2×C4—1881no—
222C2×C4—1882no—
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—22no—
227C8—942no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—941no—
232C22—941no—
233C22—941no—
234C22C2×D4×D4711yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—941no—
240C4—941no—
241C4—941no—
242C4—1881no—
243C4—1881no—
244C4—1882no—
245C4#1309407112yes—
246C2—81no—
247C2—1881no—
248C2#1568969311yescharacteristic
249C2#1568991911yescharacteristic
250C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3240
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689532C2semidirect
4. #15689529C2semidirect
5. #15689482C2semidirect
6. #15689463C2semidirect
8. #15689428C2semidirect
9. #15689421C2semidirect
10. #15689178C2semidirect
11. C47×#489C2semidirect
131. #489D47semidirect
137. C47#3240semidirect