Finite Group Databasebeta

← #20253709

Subgroups — #20253709

Order 6016.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689679C211yesmaximal, characteristic, complemented
2#15689672C211yesmaximal, characteristic
3#15689480C211yesmaximal, characteristic, complemented
4#15689478C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689472C212yesmaximal, complemented
7#15689468C212yesmaximal, complemented
8#15689118C212yesmaximal, complemented
9#15689116C212yesmaximal, complemented
10C4×C8×D47C211yesmaximal, characteristic, complemented
11C47×#488C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×#10625352C2211yescharacteristic
14C2×C8×D47C2212yes—
15#13094023C2212yes—
16#13094022C2211yescharacteristic
17#13094020C2211yescharacteristic
18#13094016C2211yescharacteristic
19#13094012C2211yescharacteristic
20#13094002—22no—
21#13093997—22no—
22#13093989—22no—
23(C22⋊D47)⋊C4—22no—
24#13093982C2212yes—
25C42×D47C2211yescharacteristic
26#13093949C2212yes—
27#13093948C2212yes—
28#13093947C2212yes—
29#13093946C2212yes—
30#13093945C2212yes—
31#13093944C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2212yes—
34#125×C47C2211yescharacteristic
35#124×C47C2211yescharacteristic
36#103×C47C2212yes—
37#102×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×Q8×C47C2311yescharacteristic
40C2×D4×C47C2311yescharacteristic
41C2×C22⋊D47—21no—
42C2×C22⋊D47—22no—
43C22×Dic47—21no—
44#10625354—24no—
45#10625352—24no—
46C2×D188—21no—
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×C4×D47D412yes—
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—22no—
52C2×Dic94C2311yescharacteristic
53C2×C8×C47C2312yes—
54C4⋊C4×C47—22no—
55C4⋊C4×C47C2312yes—
56C22⋊C4×C47—22no—
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C4×Dic47D412yes—
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2312yes—
68C8×D47—24no—
69C23×C47—21no—
70C22×D47—21no—
71C22×D47C2×D411yescharacteristic
72Q8×C47—22no—
73D4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—42no—
79C22⋊D47—44no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—42no—
83C2×Dic47C2×D411yescharacteristic
84C2×Dic47C2×D412yes—
85D188—22no—
86D188—42no—
87C4×D47—24no—
88C4×D47—42no—
89C4×D47#4114yes—
90Dic94—22no—
91Dic94—44no—
92C8×C47—22no—
93C47⋊C8—22no—
94C22×C47—41no—
95C22×C47—42no—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—42no—
100C2×D47#12412yes—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47C2×#4112yes—
105Dic47—41no—
106Dic47—42no—
107Dic47#12412yes—
108Dic47#13514yes—
109#3131—471nomaximal, Sylow
110C2×C47—81no—
111C2×C47C2×#12411yescharacteristic
112C2×C47C2×#13512yes—
113D47—22no—
114D47—81no—
115#533—471no—
116#532—471no—
117#488—471no—
118#488—471no—
119#488—471no—
120#488D4711yescharacteristic, complemented
121#487—472no—
122#486—472no—
123#416—472no—
124#416—472no—
125C2×C4×C8—471no—
126C47#313111yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C2×#41—471no—
129C22×C8—472no—
130C4⋊Q8—472no—
131C4⋊Q8—471no—
132#127—471no—
133#125—471no—
134#125C2×D4711yescharacteristic
135#124—471no—
136#124C2×D4711yescharacteristic
137C22⋊Q8—942no—
138#121—942no—
139C4×Q8—942no—
140C4×D4—942no—
141#117—472no—
142C2×C42—471no—
143#103—472no—
144#103—472no—
145#103—472no—
146#103C2×D4712yes—
147#102—472no—
148#102—472no—
149#102—472no—
150#102C2×D4712yes—
151C4×C8—472no—
152C4×C8—471no—
153C4×C8C2×D4711yescharacteristic
154#41—944no—
155#41—944no—
156C2×Q8—471no—
157C2×Q8—942no—
158C2×Q8C22×D4711yescharacteristic
159C2×D4—471no—
160C2×D4—941no—
161C2×D4—942no—
162C2×D4—941no—
163C2×D4C22×D4711yescharacteristic
164C22×C4—471no—
165C22×C4—472no—
166C22×C4—941no—
167C22×C4—941no—
168C2×C8—472no—
169C2×C8—944no—
170C2×C8C22×D4712yes—
171C4⋊C4—22no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4C22×D4712yes—
177C22⋊C4—22no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C42—472no—
181C42—471no—
182C42—942no—
183C42C22×D4711yescharacteristic
184C23—21no—
185C23—471no—
186C23—941no—
187Q8—22no—
188Q8—942no—
189Q8—1884no—
190D4—22no—
191D4—942no—
192D4—1882no—
193D4—1884no—
194D4—1882no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—471no—
198C2×C4—472no—
199C2×C4—474no—
200C2×C4—944no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—1882no—
204C2×C4—1882no—
205C2×C4D4×D4712yes—
206C2×C4C23×D4711yescharacteristic
207C8—22no—
208C8—942no—
209C22—41no—
210C22—42no—
211C22—472no—
212C22—942no—
213C22—1881no—
214C22—1882no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—472no—
220C4—474no—
221C4—1881no—
222C4—1882no—
223C4#41×D4712yes—
224C2—81no—
225C2—942no—
226C2—3761no—
227C2#124×D4711yescharacteristic
228C2#135×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3131
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689480C2semidirect
4. #15689478C2semidirect
5. #15689477C2semidirect
6. #15689472C2semidirect
7. #15689468C2semidirect
8. #15689118C2semidirect
9. #15689116C2semidirect
10. C4×C8×D47C2semidirect
11. C47×#488C2semidirect
120. #488D47semidirect
126. C47#3131semidirect