Finite Group Databasebeta

← #20243804

Subgroups — #20243804

Order 6016.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#15689890C211yesmaximal, characteristic, complemented
2#15689630C211yesmaximal, characteristic
3#15689086C212yesmaximal, complemented
4#15688895C212yesmaximal, complemented
5C47×#413C211yesmaximal, characteristic, complemented
6C22×C4×D47C2211yescharacteristic
7#13094031—24no—
8C2×#10625329—22no—
9C2×#10625329C2212yes—
10#13094005C412yes—
11#13094000—21no—
12#13093995—21no—
13#13093992C412yes—
14C4×C22⋊D47—22no—
15#13093983C2211yescharacteristic
16(C2×D47)⋊C8—24no—
17C2×#41×C47C2211yescharacteristic
18C2×M16×C47C2212yes—
19#101×C47—21no—
20#100×C47—21no—
21C23×D47C2×C411yescharacteristic
22#41×C47—22no—
23#41×C47—22no—
24C2×Q8×C47D411yescharacteristic
25C2×D4×C47C2×C412yes—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47D412yes—
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47—22no—
30C22×Dic47C2×C411yescharacteristic
31C2×C4×D47—22no—
32C2×C4×D47—21no—
33C2×C4×D47—21no—
34C2×C4×D47—22no—
35M16×C47—22no—
36M16×C47—22no—
37C2×C8×C47—22no—
38C22⋊Dic47—22no—
39C22⋊Dic47C2×C412yes—
40(C2×D47)⋊C4—22no—
41C4⋊Dic47—21no—
42Dic47⋊C4—22no—
43C4×Dic47—21no—
44#10625329—24no—
45#10625329—22no—
46#10625329—22no—
47C2×C47⋊C8—24no—
48C2×C47⋊C8D414yescomplemented
49C23×C47C22⋊C412yes—
50C23×C47C22×C411yescharacteristic
51C22×D47—21no—
52C22×D47—22no—
53C22×D47—42no—
54Q8×C47—22no—
55D4×C47—24no—
56D4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47C22⋊C412yes—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4112yes—
64C22⋊D47—44no—
65C2×Dic47—22no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C4×D47—41no—
69C4×D47—42no—
70C4×D47—41no—
71C8×C47—42no—
72C47⋊C8—24no—
73C22×C47—22no—
74C22×C47—41no—
75C22×C47—42no—
76C22×C47C2×C22⋊C411yescharacteristic
77C22×C47C4×D412yes—
78C2×D47—22no—
79C2×D47—24no—
80C2×D47—41no—
81C2×D47—42no—
82C2×D47—41no—
83C4×C47—22no—
84C4×C47#12011yescharacteristic
85C4×C47#12112yes—
86C4×C47#12311yescharacteristic
87Dic47—42no—
88Dic47—41no—
89#1891—471nomaximal, Sylow
90C2×C47—21no—
91C2×C47—22no—
92C2×C47—42no—
93C2×C47#38611yescharacteristic
94D47—42no—
95#568—471no—
96#525—471no—
97#413D4711yescharacteristic, complemented
98#407—472no—
99#344—472no—
100C47#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D4711yescharacteristic
102C23×C4—471no—
103#131—944no—
104C2×M16—472no—
105C2×M16—942no—
106C2×M16C2×D4712yes—
107#123—472no—
108C22⋊Q8—941no—
109#121—941no—
110#120—472no—
111C4×D4—942no—
112#117—471no—
113#101—21no—
114#100—21no—
115C22⋊C8—944no—
116C24—471no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D4711yescharacteristic
120C2×D4—942no—
121C2×D4C4×D4712yes—
122C2×D4C22⋊D4711yescharacteristic
123C22×C4—471no—
124C22×C4—941no—
125C22×C4—942no—
126C22×C4—942no—
127C22×C4—941no—
128C22×C4D18812yes—
129C22×C4C22×D4711yescharacteristic
130M16—22no—
131M16—22no—
132M16—944no—
133M16—942no—
134M16—942no—
135C2×C8—22no—
136C2×C8—474no—
137C2×C8—944no—
138C4⋊C4—942no—
139C4⋊C4—941no—
140C22⋊C4—472no—
141C22⋊C4—942no—
142C22⋊C4—942no—
143C42—941no—
144C23—941no—
145C23—942no—
146C23—1882no—
147C23(C2×D47)⋊C412yes—
148C23C2×C4×D4711yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—1884no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—942no—
156C2×C4—941no—
157C2×C4—942no—
158C2×C4—1881no—
159C2×C4—1882no—
160C2×C4—1881no—
161C2×C4(C2×D47)⋊C412yes—
162C2×C4C2×D18811yescharacteristic
163C2×C4D4×D4712yes—
164C2×C4#1062535212yes—
165C2×C4C2×C22⋊D4711yescharacteristic
166C8—42no—
167C8—944no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—942no—
172C22—944no—
173C22—1881no—
174C22—1882no—
175C22—1881no—
176C22C2×(C2×D47)⋊C411yescharacteristic
177C22(C22⋊D47)⋊C412yes—
178C4—22no—
179C4—1882no—
180C4—1881no—
181C4#1309399411yescharacteristic
182C4#1309399612yes—
183C4#1309400811yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—1882no—
188C2#1568900011yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#413C2
socleC2×C47#386
hypercenter#413D47
hypocenterC47#1891
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #15689890C2semidirect
3. #15689086C2semidirect
4. #15688895C2semidirect
5. C47×#413C2semidirect
48. C2×C47⋊C8D4semidirect
97. #413D47semidirect
100. C47#1891semidirect