Finite Group Databasebeta

← #20254036

Subgroups — #20254036

Order 6016.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689724C212yesmaximal, complemented
2#15689523C211yesmaximal, characteristic, complemented
3#15689498C211yesmaximal, characteristic, complemented
4#15689486C212yesmaximal, complemented
5#15689377C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic, complemented
7#15689358C212yesmaximal, complemented
8#15689236C211yesmaximal, characteristic, complemented
9C4×#10625334C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×D376C2211yescharacteristic
13C2×#10625334C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×C8×D47C2211yescharacteristic
16#13094020C2212yes—
17#13094015C2212yes—
18#13094007—22no—
19#13094006—22no—
20#13093999C2212yes—
21#13093998—22no—
22#13093997—22no—
23#13093995C2212yes—
24C4×D188C2212yes—
25#13093981C2211yescharacteristic
26#13093957C2212yes—
27#13093956C2211yescharacteristic
28#13093946C2212yes—
29#13093945C2212yes—
30#13093944C2212yes—
31#13093934C2211yescharacteristic
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×D8×C47C2211yescharacteristic
35C4×D4×C47C2212yes—
36#106×C47C2211yescharacteristic
37#102×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×D4×C47C2312yes—
40C22×C4×C47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44C2×D188—22no—
45C2×D188C2312yes—
46C2×C4×D47—22no—
47C2×C4×D47C2311yescharacteristic
48D8×C47—22no—
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C4⋊C4×C47C2312yes—
52C22⋊C4×C47—22no—
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55#10625334—24no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4D412yes—
59C4⋊Dic47—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62Dic47⋊C4D412yes—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66D376—22no—
67#10625324—22no—
68C8×D47—22no—
69C23×C47—22no—
70C22×D47—22no—
71C22×D47C2×D411yescharacteristic
72D4×C47—22no—
73D4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—82no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—82no—
79C22⋊D47—82no—
80C22⋊D47—82no—
81C2×Dic47—22no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D411yescharacteristic
84D188—22no—
85D188—22no—
86D188—82no—
87C4×D47—21no—
88C4×D47—21no—
89C4×D47—82no—
90C8×C47—21no—
91C8×C47#4112yes—
92C47⋊C8—21no—
93C47⋊C8#4112yes—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47C22×D411yescharacteristic
98C2×D47—21no—
99C2×D47—22no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C4×C47—22no—
104C4×C47—42no—
105C4×C47C2×#4111yescharacteristic
106C4×C47C2×#4111yescharacteristic
107Dic47—21no—
108Dic47—22no—
109Dic47—42no—
110#3176—471nomaximal, Sylow
111C2×C47—82no—
112C2×C47#53211yescharacteristic
113C2×C47#57612yes—
114D47—41no—
115D47—82no—
116#540—472no—
117#499—471no—
118#493—471no—
119#490—472no—
120#469—471no—
121#469—471no—
122#466—472no—
123#442—471no—
124#442D4711yescharacteristic, complemented
125C4×D8—472no—
126#405—471no—
127C47#317611yescharacteristic, complemented, Sylow
128C2×D8—472no—
129C2×D8—471no—
130C2×D8C2×D4711yescharacteristic
131C2×M16—471no—
132C22×C8—471no—
133#127—472no—
134#125—472no—
135#123—942no—
136#123—942no—
137#121—472no—
138#121—472no—
139#121—942no—
140#121—942no—
141C4×D4—472no—
142C4×D4C2×D4712yes—
143#117—471no—
144#107—472no—
145#106—471no—
146#106C2×D4711yescharacteristic
147#102—472no—
148#102—472no—
149#102—472no—
150#102C2×D4712yes—
151#97—471no—
152#97C2×D4711yescharacteristic
153C4×C8—471no—
154C4×C8—471no—
155C2×D4—472no—
156C2×D4—942no—
157C2×D4—942no—
158C2×D4—942no—
159C2×D4—942no—
160C2×D4C22×D4712yes—
161C22×C4—22no—
162C22×C4—471no—
163C22×C4—942no—
164D8—22no—
165D8—944no—
166D8—942no—
167M16—942no—
168C2×C8—471no—
169C2×C8—471no—
170C2×C8—942no—
171C2×C8C22×D4711yescharacteristic
172C2×C8C22×D4711yescharacteristic
173C4⋊C4—472no—
174C4⋊C4—472no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4C22×D4712yes—
178C22⋊C4—22no—
179C22⋊C4—472no—
180C22⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C42—471no—
184C42C22×D4711yescharacteristic
185C23—22no—
186C23—471no—
187C23—942no—
188D4—22no—
189D4—22no—
190D4—942no—
191D4—942no—
192D4—3762no—
193D4—3762no—
194D4—3762no—
195D4—3762no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—472no—
199C2×C4—471no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—942no—
203C2×C4—3762no—
204C2×C4D4×D4712yes—
205C2×C4C23×D4711yescharacteristic
206C8—21no—
207C8—472no—
208C8—941no—
209C8#1062535012yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—941no—
214C22—942no—
215C22—1882no—
216C22—1882no—
217C22—1882no—
218C22C2×D4×D4711yescharacteristic
219C4—22no—
220C4—42no—
221C4—941no—
222C4—942no—
223C4—1882no—
224C4#41×D4711yescharacteristic
225C4C2×#1062535011yescharacteristic
226C2—82no—
227C2—3762no—
228C2—1881no—
229C2#1568967011yescharacteristic
230C2#1568992712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3176
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689724C2semidirect
2. #15689523C2semidirect
3. #15689498C2semidirect
4. #15689486C2semidirect
5. #15689377C2semidirect
6. #15689373C2semidirect
7. #15689358C2semidirect
8. #15689236C2semidirect
9. C4×#10625334C2semidirect
10. #15689080C2semidirect
11. C47×#442C2semidirect
124. #442D47semidirect
127. C47#3176semidirect