Finite Group Databasebeta

← #20254045

Subgroups — #20254045

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#15689731C212yesmaximal
2#15689523C211yesmaximal, characteristic, complemented
3#15689501C211yesmaximal, characteristic, complemented
4#15689490C212yesmaximal, complemented
5#15689382C211yesmaximal, characteristic
6#15689378C211yesmaximal, characteristic
7#15689363C212yesmaximal
8#15689231C211yesmaximal, characteristic, complemented
9C4×#10625337C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic
11C47×#441C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625337C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×C8×D47C2211yescharacteristic
16#13094022C2212yes—
17#13094019—22no—
18#13094018—22no—
19#13094016—22no—
20#13094015C2212yes—
21#13094014—22no—
22#13094004C2212yes—
23#13094000C2212yes—
24C4×Dic94C2212yes—
25#13093981C2211yescharacteristic
26#13093957C2212yes—
27#13093956C2211yescharacteristic
28#13093949C2212yes—
29#13093948C2212yes—
30#13093947C2212yes—
31#13093934C2211yescharacteristic
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C4×Q8×C47C2212yes—
36#106×C47C2211yescharacteristic
37#103×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×C4×D47C2311yescharacteristic
41C2×Dic94C2312yes—
42Q16×C47—22no—
43C2×C8×C47C2311yescharacteristic
44C2×C8×C47C2311yescharacteristic
45C4⋊C4×C47—22no—
46C4⋊C4×C47C2312yes—
47C42×C47—22no—
48C42×C47C2311yescharacteristic
49#10625337—24no—
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4D412yes—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4D412yes—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66Dic188—22no—
67#10625324—22no—
68C8×D47—22no—
69C22×D47C2×D411yescharacteristic
70Q8×C47—22no—
71Q8×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47C2×D412yes—
79C2×Dic47C2×D411yescharacteristic
80C4×D47—21no—
81C4×D47—21no—
82Dic94—22no—
83Dic94—22no—
84C8×C47—21no—
85C8×C47#4112yes—
86C47⋊C8—21no—
87C47⋊C8#4112yes—
88C22×C47C22×D411yescharacteristic
89C2×D47—21no—
90C2×D47—22no—
91C4×C47—22no—
92C4×C47—42no—
93C4×C47—42no—
94C4×C47C2×#4111yescharacteristic
95C4×C47C2×#4111yescharacteristic
96Dic47—21no—
97Dic47—22no—
98Dic47—42no—
99Dic47—42no—
100#3177—471nomaximal, Sylow
101C2×C47#53211yescharacteristic
102C2×C47#57812yes—
103D47—41no—
104#541—472no—
105#499—471no—
106#494—471no—
107#491—472no—
108#470—471no—
109#470—471no—
110#467—472no—
111#441—471no—
112#441D4711yescharacteristic, complemented
113C4×Q16—472no—
114#405—471no—
115C47#317711yescharacteristic, complemented, Sylow
116C2×Q16—472no—
117C2×Q16—471no—
118C2×Q16C2×D4711yescharacteristic
119C2×M16—471no—
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⋊Q8—472no—
129C4×Q8—472no—
130C4×Q8C2×D4712yes—
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#97C2×D4711yescharacteristic
141C4×C8—471no—
142C4×C8—471no—
143C2×Q8—472no—
144C2×Q8C22×D4712yes—
145C22×C4—471no—
146Q16—22no—
147Q16—944no—
148Q16—942no—
149M16—942no—
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—472no—
167C22⋊C4—942no—
168C22⋊C4—942no—
169C42—22no—
170C42—471no—
171C42—942no—
172C42C22×D4711yescharacteristic
173C23—471no—
174Q8—22no—
175Q8—22no—
176Q8—942no—
177Q8—942no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—472no—
181C2×C4—471no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4D4×D4712yes—
187C2×C4C23×D4711yescharacteristic
188C8—21no—
189C8—472no—
190C8—941no—
191C8#1062535012yes—
192C22—941no—
193C22—942no—
194C22C2×D4×D4711yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—941no—
199C4—942no—
200C4—1882no—
201C4—1882no—
202C4#41×D4711yescharacteristic
203C4C2×#1062535011yescharacteristic
204C2—1881no—
205C2#1568967011yescharacteristic
206C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3177
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #15689523C2semidirect
3. #15689501C2semidirect
4. #15689490C2semidirect
8. #15689231C2semidirect
9. C4×#10625337C2semidirect
11. C47×#441C2semidirect
112. #441D47semidirect
115. C47#3177semidirect