Finite Group Databasebeta

← #20250417

Subgroups — #20250417

Order 6016.

456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094023C212yesmaximal
2#15689053C211yesmaximal, characteristic
3#15689044C212yesmaximal
4#15689043C212yesmaximal
5#15689028C211yesmaximal, characteristic
6#15689018C212yesmaximal
7#15689010C212yesmaximal
8#15689005C212yesmaximal
9C47×#398C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11C22×Dic94C2211yescharacteristic
12#13094023—28no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C4×Dic47C2212yes—
20C2×C4×Dic47C2211yescharacteristic
21C47⋊#95C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
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—41no—
43C2×Dic94—41no—
44C2×Dic94—42no—
45C2×Dic94—42no—
46C2×Dic94D414yes—
47C4⋊C4×C47—24no—
48C4⋊C4×C47—41no—
49C4⋊C4×C47—41no—
50C4⋊Dic47—24no—
51C4⋊Dic47—41no—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54Dic47⋊C4—42no—
55Dic47⋊C4Q818yescomplemented
56C4×Dic47—24no—
57C4×Dic47—41no—
58C23×C47C2411yescharacteristic
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—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×Q814yes—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47C2×D414yes—
82C2×Dic47C2×Q814yes—
83C2×Dic47C2×Q814yes—
84Dic94—44no—
85Dic94—48no—
86C22×C47C22×D411yescharacteristic
87C22×C47C22×Q812yes—
88C22×C47H(5,𝔽2)11yescharacteristic
89C22×C47H(5,𝔽2)11yescharacteristic
90C22×C472−1+412yes—
91C4×C47—22no—
92C4×C47—24no—
93C4×C47—42no—
94C4×C47—41no—
95C4×C47—41no—
96Dic47—24no—
97Dic47—24no—
98Dic47—24no—
99Dic47—42no—
100#2734—471nomaximal, Sylow
101C2×C47#53411yescharacteristic
102C2×C47#54412yes—
103C2×C47D4×Q812yes—
104C2×C47Q8211yescharacteristic
105C2×C47#56311yescharacteristic
106C2×C4⋊Q8—472no—
107#398—471no—
108#398D4711yescharacteristic
109#395—472no—
110#395—472no—
111#391—471no—
112#389—472no—
113#387—472no—
114#387—472no—
115C47#273411yescharacteristic, complemented, Sylow
116C22×Q8—471no—
117C22×Q8—472no—
118C4⋊Q8—948no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4C2×D4712yes—
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C42—472no—
129C2×C42—471no—
130#95—471no—
131#95—472no—
132#95—472no—
133#95—472no—
134#95—472no—
135#95—472no—
136#95C2×D4711yescharacteristic
137#95C2×D4712yes—
138C2×Q8—474no—
139C2×Q8—944no—
140C2×Q8—1881no—
141C2×Q8—1881no—
142C2×Q8—1882no—
143C2×Q8—1882no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4712yes—
151C22×C4C22×D4711yescharacteristic
152C22×C4C22×D4712yes—
153C4⋊C4—24no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—478no—
157C4⋊C4—944no—
158C4⋊C4—944no—
159C4⋊C4—944no—
160C4⋊C4—1882no—
161C4⋊C4—1881no—
162C42—944no—
163C42—1881no—
164C23C23×D4711yescharacteristic
165Q8—1884no—
166Q8—1888no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—474no—
179C2×C4—474no—
180C2×C4—474no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4D4×D4712yes—
191C2×C4Q8×D4714yes—
192C22C2×D4×D4711yescharacteristic
193C22C2×Q8×D4712yes—
194C22#1309406911yescharacteristic
195C22#1309407011yescharacteristic
196C22#1309407112yes—
197C4—24no—
198C4—22no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—944no—
203C4—944no—
204C4—944no—
205C4—1882no—
206C2#1568968111yescharacteristic
207C2#1568975312yes—
208C2#1568978612yes—
209C2#1568985311yescharacteristic
210C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2734
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
55. Dic47⋊C4Q8semidirect
115. C47#2734semidirect