Finite Group Databasebeta

← #20243771

Subgroups — #20243771

Order 6016.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689669C211yesmaximal, characteristic
2#15689139C212yesmaximal, complemented
3#15689097C211yesmaximal, characteristic, complemented
4#15688884C212yesmaximal, complemented
5C47×#568C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7#13094022C411yescharacteristic, complemented
8#13094020C411yescharacteristic, complemented
9#13094013C411yescharacteristic, complemented
10#13094011C411yescharacteristic, complemented
11#13093996—22no—
12C4×C22⋊D47—22no—
13#13093983C2212yes—
14C2×C4×Dic47C2211yescharacteristic
15#13093950—24no—
16#13093939—22no—
17C2×#41×C47C2211yescharacteristic
18#131×C47—24no—
19C2×M16×C47—22no—
20C2×M16×C47C2212yes—
21#41×C47—22no—
22#41×C47—22no—
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47C2×C411yescharacteristic
25C2×D4×C47D412yes—
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—22no—
29C2×C22⋊D47—21no—
30C22×Dic47—21no—
31#10625350—22no—
32#10625350—22no—
33C2×D188C2×C411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94C2×C411yescharacteristic
36M16×C47—24no—
37M16×C47—22no—
38M16×C47D414yescomplemented
39C2×C8×C47—24no—
40C2×C8×C47—22no—
41C22⋊Dic47—22no—
42C22⋊Dic47—22no—
43(C2×D47)⋊C4—22no—
44C4⋊Dic47—22no—
45Dic47⋊C4—22no—
46C4×Dic47—21no—
47C4×Dic47—22no—
48C4×Dic47C2×C411yescharacteristic
49C4×Dic47C2×C411yescharacteristic
50C23×C47C22⋊C412yes—
51C23×C47C2×D411yescharacteristic
52C22×D47—21no—
53Q8×C47—22no—
54D4×C47—24no—
55D4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47C22⋊C412yes—
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47#4112yes—
63C22⋊D47—44no—
64C22⋊D47—42no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70D188—22no—
71C4×D47—41no—
72C4×D47—41no—
73Dic94—22no—
74C8×C47—24no—
75C22×C47—22no—
76C22×C47—41no—
77C22×C47—42no—
78C22×C47C2×C22⋊C411yescharacteristic
79C22×C47#12112yes—
80C2×D47—42no—
81C2×D47—41no—
82C4×C47—22no—
83C4×C47C4×D412yes—
84C4×C47#12011yescharacteristic
85C4×C47#12311yescharacteristic
86Dic47—22no—
87Dic47—41no—
88Dic47—41no—
89Dic47—82no—
90#1884—471nomaximal, Sylow
91C2×C47—21no—
92C2×C47—22no—
93C2×C47—42no—
94C2×C47#38611yescharacteristic
95D47—81no—
96#568D4711yescharacteristic, complemented
97#532—471no—
98#421—472no—
99#410—471no—
100#339—472no—
101C47#188411yescharacteristic, complemented, Sylow
102C2×#41—471no—
103C2×#41C2×D4711yescharacteristic
104#131—24no—
105C2×M16—22no—
106C2×M16C2×D4712yes—
107C4⋊Q8—471no—
108#127—471no—
109#124—471no—
110#124—471no—
111#121—942no—
112C4×D4—942no—
113#117—472no—
114C2×C42—471no—
115#104—944no—
116#99—942no—
117#41—22no—
118#41—22no—
119#41—942no—
120#41—942no—
121C2×Q8—471no—
122C2×Q8C4×D4711yescharacteristic
123C2×D4—471no—
124C2×D4—942no—
125C2×D4—941no—
126C2×D4C4×D4711yescharacteristic
127C2×D4D18812yes—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4C22⋊D4712yes—
131C22×C4C22×D4711yescharacteristic
132M16—24no—
133M16—22no—
134M16C22⋊D4714yescomplemented
135C2×C8—24no—
136C2×C8—22no—
137C4⋊C4—942no—
138C4⋊C4—942no—
139C22⋊C4—942no—
140C22⋊C4—942no—
141C22⋊C4—942no—
142C42—471no—
143C42—471no—
144C42—941no—
145C42—942no—
146C23—941no—
147C23(C2×D47)⋊C412yes—
148C23C2×D18811yescharacteristic
149Q8—22no—
150Q8—942no—
151D4—24no—
152D4—22no—
153D4—942no—
154D4—1884no—
155D4—1882no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—941no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—1882no—
162C2×C4—1882no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4(C2×D47)⋊C412yes—
166C2×C4C2×C4×D4711yescharacteristic
167C2×C4#1062535012yes—
168C2×C4C2×C22⋊D4712yes—
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—24no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—1882no—
175C22—1881no—
176C22C2×(C2×D47)⋊C411yescharacteristic
177C22#1309399812yes—
178C4—22no—
179C4—942no—
180C4—3762no—
181C4—1881no—
182C4—1881no—
183C4C4×C22⋊D4712yes—
184C4#1309399311yescharacteristic
185C4#1309400711yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—3761no—
190C2#1568900211yescharacteristic
subgroupG/H
centerC4#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#568C2
socleC2×C47#386
hypercenter#568D47
hypocenterC47#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #15689139C2semidirect
3. #15689097C2semidirect
4. #15688884C2semidirect
5. C47×#568C2semidirect
7. #13094022C4semidirect
8. #13094020C4semidirect
9. #13094013C4semidirect
10. #13094011C4semidirect
38. M16×C47D4semidirect
96. #568D47semidirect
101. C47#1884semidirect
134. M16C22⋊D47semidirect