Finite Group Databasebeta

← #20254042

Subgroups — #20254042

Order 6016.

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

normal subgroups only

This group has 338 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#15689733C212yesmaximal
2#15689523C211yesmaximal, characteristic, complemented
3#15689501C211yesmaximal, characteristic, complemented
4#15689490C212yesmaximal, complemented
5#15689381C211yesmaximal, characteristic
6#15689362C212yesmaximal
7#15689230C211yesmaximal, characteristic, complemented
8#15689229C211yesmaximal, characteristic, complemented
9#15689215C212yesmaximal, complemented
10#15689081C211yesmaximal, characteristic
11C47×#470C211yesmaximal, characteristic
12C2×Dic188C2211yescharacteristic
13C2×#10625337C2212yes—
14C22×C47⋊C8C2211yescharacteristic
15#13094022C2212yes—
16#13094017—22no—
17#13094017—22no—
18#13094015—22no—
19#13094015C2212yes—
20#13094014—22no—
21#13094003C2212yes—
22Q8×Dic47C2212yes—
23#13093989C2212yes—
24#13093983C2211yescharacteristic
25#13093957C2212yes—
26#13093956C2211yescharacteristic
27#13093949C2212yes—
28#13093948C2212yes—
29#13093947C2212yes—
30#13093934C2211yescharacteristic
31#13093934C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C2×M16×C47C2211yescharacteristic
36C22⋊Q8×C47C2212yes—
37#106×C47C2211yescharacteristic
38#103×C47C2212yes—
39C2×Q8×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×Dic94C2312yes—
42Q16×C47—22no—
43M16×C47—22no—
44C2×C8×C47C2311yescharacteristic
45C2×C8×C47C2311yescharacteristic
46C4⋊C4×C47—22no—
47C4⋊C4×C47C2312yes—
48C22⋊C4×C47—22no—
49C22⋊Dic47—22no—
50C22⋊Dic47D412yes—
51#10625337—24no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47D412yes—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8—22no—
66C2×C47⋊C8C2311yescharacteristic
67C2×C47⋊C8C2311yescharacteristic
68Dic188—22no—
69C23×C47C2×D411yescharacteristic
70Q8×C47—22no—
71Q8×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47C2×D412yes—
81C2×Dic47C2×D412yes—
82Dic94—22no—
83Dic94—22no—
84C8×C47—21no—
85C8×C47#4112yes—
86C47⋊C8—21no—
87C47⋊C8#4112yes—
88C22×C47—21no—
89C22×C47—22no—
90C22×C47C22×D411yescharacteristic
91C4×C47—21no—
92C4×C47—42no—
93C4×C47—42no—
94C4×C47C2×#4111yescharacteristic
95C4×C47C2×#4111yescharacteristic
96Dic47—22no—
97Dic47—22no—
98Dic47—42no—
99Dic47—42no—
100#3177—471nomaximal, Sylow
101C2×C47—41no—
102C2×C47#53211yescharacteristic
103C2×C47#57812yes—
104#541—472no—
105#499—471no—
106#494—471no—
107#491—472no—
108#470—471no—
109#470D4711yescharacteristic
110#467—472no—
111#441—471no—
112#441—471no—
113C4×Q16—472no—
114#405—471no—
115C47#317711yescharacteristic, complemented, Sylow
116C2×Q16—472no—
117C2×Q16—471no—
118C2×Q16C2×D4711yescharacteristic
119C2×M16C2×D4711yescharacteristic
120C22×C8—471no—
121C4⋊Q8—472no—
122#126—942no—
123#126—942no—
124#125—472no—
125#125—942no—
126#125—942no—
127C22⋊Q8—472no—
128C22⋊Q8C2×D4712yes—
129C4×Q8—472no—
130C4×Q8—472no—
131#117—471no—
132#107—472no—
133#106—471no—
134#106C2×D4711yescharacteristic
135#103—472no—
136#103—472no—
137#103—472no—
138#103C2×D4712yes—
139#97—471no—
140#97—471no—
141C4×C8—471no—
142C4×C8—471no—
143C2×Q8—472no—
144C2×Q8C22×D4712yes—
145C22×C4C22×D4711yescharacteristic
146Q16—22no—
147Q16—944no—
148Q16—942no—
149M16—22no—
150C2×C8—471no—
151C2×C8—471no—
152C2×C8—942no—
153C2×C8C22×D4711yescharacteristic
154C2×C8C22×D4711yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—472no—
157C4⋊C4—472no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—942no—
161C4⋊C4—942no—
162C4⋊C4—942no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4C22×D4712yes—
166C22⋊C4—22no—
167C22⋊C4—472no—
168C22⋊C4—942no—
169C42—471no—
170C42—471no—
171C42—942no—
172C42—942no—
173C23D4×D4711yescharacteristic
174Q8—22no—
175Q8—22no—
176Q8—942no—
177Q8—942no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—472no—
183C2×C4—472no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4D4×D4711yescharacteristic
187C2×C4C23×D4711yescharacteristic
188C8—21no—
189C8—472no—
190C8—941no—
191C8#1062535212yes—
192C22—21no—
193C22—22no—
194C22C2×D4×D4711yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—942no—
199C4—942no—
200C4—1882no—
201C4—1882no—
202C4#41×D4711yescharacteristic
203C4C2×#1062535211yescharacteristic
204C2—41no—
205C2#1568966811yescharacteristic
206C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3177
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #15689523C2semidirect
3. #15689501C2semidirect
4. #15689490C2semidirect
7. #15689230C2semidirect
8. #15689229C2semidirect
9. #15689215C2semidirect
115. C47#3177semidirect