Finite Group Databasebeta

← #20243846

Subgroups — #20243846

Order 6016.

378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#13094007C211yesmaximal, characteristic
2C2×#13093938C212yesmaximal
3#15688986C211yesmaximal, characteristic, complemented
4#15688889C212yesmaximal, complemented
5C2×#117×C47C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C2211yescharacteristic
7#13094007—22no—
8#13094007—21no—
9#13094007—21no—
10C2×Dic47⋊C4C412yescomplemented
11C2×C22⋊Dic47C2212yes—
12C2×C22⋊Dic47C2211yescharacteristic
13C2×(C2×D47)⋊C4C412yescomplemented
14#13093938—24no—
15C47⋊#95—22no—
16C23×C4×C47C2211yescharacteristic
17#117×C47—24no—
18C2×C4⋊C4×C47—21no—
19C2×C22⋊C4×C47C2212yes—
20C2×C42×C47—21no—
21C24×C47C2311yescharacteristic
22C23×D47C2×C411yescharacteristic
23C22×C4×C47—22no—
24C22×C4×C47—22no—
25C22×C4×C47—22no—
26C22×C4×C47C2×C412yes—
27C22×C4×C47D412yes—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C2×C22⋊D47—22no—
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33C2×C22⋊D47—22no—
34C22×Dic47—22no—
35C22×Dic47C2×C411yescharacteristic
36C22×Dic47C2×C412yes—
37C4⋊C4×C47—24no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47D414yes—
40C42×C47—24no—
41C22⋊Dic47—21no—
42C22⋊Dic47—21no—
43C22⋊Dic47—22no—
44C22⋊Dic47—22no—
45(C2×D47)⋊C4—22no—
46(C2×D47)⋊C4—22no—
47Dic47⋊C4—22no—
48Dic47⋊C4—22no—
49C23×C47—42no—
50C23×C47C22×C411yescharacteristic
51C23×C47C2×D411yescharacteristic
52C23×C47C2×D411yescharacteristic
53C23×C47C2×D412yes—
54C23×C47#4112yes—
55C22×D47—21no—
56C22×D47—22no—
57C22×D47—42no—
58C2×C4×C47—24no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—24no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—24no—
65C2×C4×C47—44no—
66C2×C4×C47C22⋊C412yes—
67C2×C4×C47C22⋊C412yes—
68C22⋊D47—41no—
69C22⋊D47—42no—
70C22⋊D47—41no—
71C2×Dic47—21no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—42no—
75C2×Dic47—44no—
76C2×Dic47—42no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—42no—
81C22×C47—42no—
82C22×C47C2×C22⋊C411yescharacteristic
83C22×C47C4×D412yes—
84C22×C47#12011yescharacteristic
85C22×C47#12112yes—
86C22×C47#12311yescharacteristic
87C2×D47—41no—
88C2×D47—42no—
89C2×D47—82no—
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—44no—
93Dic47—41no—
94Dic47—42no—
95Dic47—82no—
96#1899—471nomaximal, Sylow
97C2×C47—22no—
98C2×C47—21no—
99C2×C47—22no—
100C2×C47—21no—
101C2×C47#38611yescharacteristic
102C2×C47#41012yes—
103D47—81no—
104C2×#123—471no—
105C2×#117D4711yescharacteristic, complemented
106C2×#99—472no—
107#381—471no—
108#342—472no—
109C47#189911yescharacteristic, complemented, Sylow
110C22×D4—471no—
111C23×C4C2×D4711yescharacteristic
112#123—942no—
113#123—941no—
114#123—941no—
115#117—24no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—472no—
118C2×C22⋊C4—471no—
119C2×C22⋊C4—472no—
120C2×C22⋊C4—472no—
121C2×C22⋊C4C2×D4712yes—
122C2×C42—21no—
123#99—944no—
124#95—942no—
125C24—471no—
126C24C22×D4711yescharacteristic
127C2×D4—941no—
128C2×D4—942no—
129C2×D4—942no—
130C2×D4—941no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—471no—
135C22×C4—472no—
136C22×C4—942no—
137C22×C4C4×D4712yes—
138C22×C4D18812yes—
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22⋊D4711yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—942no—
143C4⋊C4—942no—
144C22⋊C4—22no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C22⋊C4—942no—
148C22⋊C4—942no—
149C22⋊C4—942no—
150C22⋊C4—942no—
151C22⋊C4C22⋊D4714yes—
152C42—24no—
153C23—42no—
154C23—942no—
155C23—941no—
156C23—1882no—
157C23C2×C4×D4711yescharacteristic
158C23C2×D18811yescharacteristic
159C23#1062535012yes—
160C23C2×C22⋊D4711yescharacteristic
161C23C2×C22⋊D4712yes—
162D4—1881no—
163D4—1882no—
164D4—1881no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—942no—
174C2×C4—941no—
175C2×C4—942no—
176C2×C4—1884no—
177C2×C4—1882no—
178C2×C4—1882no—
179C2×C4(C2×D47)⋊C412yes—
180C2×C4(C2×D47)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—3762no—
187C22—1881no—
188C22—1882no—
189C22C2×(C2×D47)⋊C411yescharacteristic
190C22C4×C22⋊D4712yes—
191C22#1309399311yescharacteristic
192C22#1309399812yes—
193C22#1309400711yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—3762no—
198C4—1881no—
199C4—1882no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—3761no—
205C2#1568900211yescharacteristic
206C2#1568909612yes—
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC2×#117×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#117D47
hypocenterC47#1899
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #15688986C2semidirect
4. #15688889C2semidirect
5. C2×#117×C47C2semidirect
10. C2×Dic47⋊C4C4semidirect
13. C2×(C2×D47)⋊C4C4semidirect
105. C2×#117D47semidirect
109. C47#1899semidirect