Finite Group Databasebeta

← #20243421

Subgroups — #20243421

Order 6016.

316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13093958C211yesmaximal, characteristic, complemented
2C2×#13093956C211yesmaximal, characteristic, complemented
3#15688983C212yesmaximal
4#15688886C212yesmaximal, complemented
5C22×M16×C47C211yesmaximal, characteristic
6C2×C4⋊Dic47C2212yes—
7C2×C4⋊Dic47C2212yes—
8C2×C22⋊Dic47—22no—
9#13093958—22no—
10#13093956—22no—
11C47⋊#95—22no—
12C23×C4×C47C2211yescharacteristic
13C2×M16×C47—22no—
14C2×M16×C47—22no—
15C2×M16×C47C414yescomplemented
16C22×C8×C47C2211yescharacteristic
17C22×C8×C47C2211yescharacteristic
18C24×C47D411yescharacteristic
19C22×C4×C47—21no—
20C22×C4×C47—21no—
21C22×C4×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47C2×C412yes—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47Q812yes—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—22no—
28C22×Dic47—22no—
29M16×C47—28no—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C2×C8×C47C2×C412yes—
33C2×C8×C47C2×C412yes—
34C2×C8×C47D412yes—
35C2×C8×C47D412yes—
36C22⋊Dic47—44no—
37C4⋊Dic47—22no—
38C4⋊Dic47—22no—
39C4⋊Dic47—22no—
40C4⋊Dic47—22no—
41C23×C47—21no—
42C23×C47—21no—
43C23×C47—22no—
44C23×C47—22no—
45C23×C47C4⋊C412yes—
46C23×C47C2×D411yescharacteristic
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47C4⋊C412yes—
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×Q811yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×Dic47—42no—
61C2×Dic47—42no—
62C2×Dic47—42no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66C8×C47—22no—
67C8×C47C22⋊C414yescomplemented
68C22×C47—22no—
69C22×C47—24no—
70C22×C47—42no—
71C22×C47—41no—
72C22×C47—41no—
73C22×C47C2×C4⋊C411yescharacteristic
74C22×C47#12111yescharacteristic
75C22×C47#12111yescharacteristic
76C22×C47AGL(1,ℤ/8)12yes—
77C22×C47#13712yes—
78C4×C47—22no—
79C4×C47C2×C22⋊C411yescharacteristic
80C4×C47#11711yescharacteristic
81C4×C47C22⋊Q811yescharacteristic
82C4×C47C22⋊Q811yescharacteristic
83Dic47—82no—
84Dic47—82no—
85#1809—471nomaximal, Sylow
86C2×C47—42no—
87C2×C47#38011yescharacteristic
88C2×C47#42812yes—
89C2×C47#46812yes—
90C2×C47#46911yescharacteristic
91C2×C47#47011yescharacteristic
92C22×M16D4711yescharacteristic
93C2×#107—471no—
94C2×#106—471no—
95#380—472no—
96#340—472no—
97C47#180911yescharacteristic, complemented, Sylow
98C23×C4C2×D4711yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16Dic4714yescomplemented
102C22×C8C2×D4711yescharacteristic
103C22×C8C2×D4711yescharacteristic
104C2×C4⋊C4—472no—
105C2×C4⋊C4—472no—
106C2×C22⋊C4—942no—
107#107—942no—
108#106—942no—
109#95—942no—
110C24D18811yescharacteristic
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—942no—
116C22×C4—942no—
117C22×C4Dic9412yes—
118C22×C4D18811yescharacteristic
119C22×C4C2×Dic4712yes—
120C22×C4C22×D4711yescharacteristic
121M16—28no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8C2×Dic4712yes—
125C2×C8C2×Dic4712yes—
126C2×C8C22⋊D4712yes—
127C2×C8C22⋊D4712yes—
128C4⋊C4—942no—
129C4⋊C4—942no—
130C4⋊C4—942no—
131C4⋊C4—942no—
132C22⋊C4—1884no—
133C23—21no—
134C23—21no—
135C23—22no—
136C23—22no—
137C23C4⋊Dic4712yes—
138C23C2×D18811yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—1882no—
146C2×C4—1882no—
147C2×C4—1882no—
148C2×C4—1882no—
149C2×C4—1882no—
150C2×C4—1882no—
151C2×C4C4⋊Dic4712yes—
152C2×C4C2×Dic9411yescharacteristic
153C2×C4#1062535011yescharacteristic
154C2×C4#1062535011yescharacteristic
155C2×C4C22×Dic4711yescharacteristic
156C2×C4C2×C22⋊D4711yescharacteristic
157C2×C4C2×C22⋊D4711yescharacteristic
158C8—22no—
159C8C22⋊Dic4714yescomplemented
160C22—22no—
161C22—24no—
162C22—42no—
163C22—41no—
164C22—41no—
165C22C2×C4⋊Dic4711yescharacteristic
166C22#1309399811yescharacteristic
167C22#1309399811yescharacteristic
168C22#1309405212yes—
169C22#1309405712yes—
170C4—22no—
171C4—3762no—
172C4—3762no—
173C4C2×C22⋊Dic4711yescharacteristic
174C4#1309398311yescharacteristic
175C4#1309400311yescharacteristic
176C4#1309400311yescharacteristic
177C2—42no—
178C2#1568898311yescharacteristic
179C2#1568916512yes—
180C2#1568936912yes—
181C2#1568937611yescharacteristic
182C2#1568938111yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×M16×C47C2
socleC23×C47C2×D4
hypercenterC22×M16D47
hypocenterC47#1809
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#13093958C2semidirect
2. C2×#13093956C2semidirect
4. #15688886C2semidirect
15. C2×M16×C47C4semidirect
67. C8×C47C22⋊C4semidirect
97. C47#1809semidirect
101. C2×M16Dic47semidirect
159. C8C22⋊Dic47semidirect