Finite Group Databasebeta

← #20248757

Subgroups — #20248757

Order 6016.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13093989C212yesmaximal
2#15689056C212yesmaximal
3#15689053C211yesmaximal, characteristic
4#15689027C212yesmaximal
5#15689027C212yesmaximal
6#15689020C212yesmaximal
7#15689018C212yesmaximal
8#15688992C211yesmaximal, characteristic
9C47×#398C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11#13093989—28no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C4×Dic47C2212yes—
20C2×C4×Dic47C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2211yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×Dic94—24no—
42C2×Dic94—24no—
43C2×Dic94Q818yescomplemented
44C4⋊C4×C47—24no—
45C4⋊C4×C47—41no—
46C4⋊C4×C47—41no—
47C4⋊Dic47—41no—
48C4⋊Dic47—41no—
49Dic47⋊C4—24no—
50Dic47⋊C4—24no—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—42no—
54C4×Dic47—24no—
55C4×Dic47—24no—
56C4×Dic47D414yes—
57C23×C47C2411yescharacteristic
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×Q814yes—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47C2×D414yes—
80C2×Dic47C2×Q814yes—
81C2×Dic47C2×Q814yes—
82C2×Dic47#4114yes—
83Dic94—216no—
84C22×C47C22×D411yescharacteristic
85C22×C47C22×Q812yes—
86C22×C47C2×#4112yes—
87C22×C47H(5,𝔽2)11yescharacteristic
88C22×C472−1+411yescharacteristic
89C4×C47—24no—
90C4×C47—22no—
91C4×C47—42no—
92C4×C47—41no—
93C4×C47—41no—
94Dic47—24no—
95Dic47—42no—
96Dic47—42no—
97Dic47C22⋊Q818yes—
98#2582—471nomaximal, Sylow
99C2×C47C2×C22⋊Q812yes—
100C2×C47#53711yescharacteristic
101C2×C47#55712yes—
102C2×C47Q8211yescharacteristic
103C2×C47#55911yescharacteristic
104C2×C4×Q8—472no—
105#398—471no—
106#398—472no—
107#398D4711yescharacteristic
108#391—472no—
109#391—472no—
110#389—472no—
111#389—472no—
112#384—471no—
113C47#258211yescharacteristic, complemented, Sylow
114C22×Q8—472no—
115C4×Q8—948no—
116C2×C4⋊C4—472no—
117C2×C4⋊C4—472no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4C2×D4712yes—
124C2×C4⋊C4C2×D4711yescharacteristic
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C42—471no—
127C2×C42—472no—
128C2×C42—472no—
129#95—472no—
130#95—472no—
131#95—472no—
132#95—471no—
133#95—472no—
134#95C2×D4712yes—
135#95C2×D4711yescharacteristic
136C2×Q8—478no—
137C2×Q8—944no—
138C2×Q8—944no—
139C22×C4—472no—
140C22×C4—472no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4C22×D4711yescharacteristic
144C22×C4C22×D4711yescharacteristic
145C22×C4C22×D4712yes—
146C22×C4C22×D4711yescharacteristic
147C22×C4C22×D4712yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—944no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—1882no—
156C4⋊C4—1881no—
157C4⋊C4—1881no—
158C42—474no—
159C42—944no—
160C42—944no—
161C23C23×D4711yescharacteristic
162Q8—9416no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—474no—
175C2×C4—474no—
176C2×C4—474no—
177C2×C4—474no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4D4×D4712yes—
187C2×C4Q8×D4714yes—
188C22C2×D4×D4711yescharacteristic
189C22C2×Q8×D4712yes—
190C22#41×D4712yes—
191C22#1309406911yescharacteristic
192C22#1309407111yescharacteristic
193C4—24no—
194C4—22no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—478no—
199C4—944no—
200C4—1882no—
201C4—1882no—
202C2C22⋊Q8×D4712yes—
203C2#1568970011yescharacteristic
204C2#1568985012yes—
205C2#1568985311yescharacteristic
206C2#1568985711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2582
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic94Q8semidirect
113. C47#2582semidirect