Finite Group Databasebeta

← #20254778

Subgroups — #20254778

Order 6016.

342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689675C212yesmaximal
2#15689407C212yesmaximal, complemented
3#15689406C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic
5#15689379C212yesmaximal
6#15689332C212yesmaximal, complemented
7#15689331C212yesmaximal, complemented
8#15689146C211yesmaximal, characteristic
9C47×#470C211yesmaximal, characteristic
10C2×Dic188C2211yescharacteristic
11C2×#10625337C2212yes—
12C2×#10625329C2211yescharacteristic
13#13094023C2212yes—
14#13094022C2212yes—
15#13094014—22no—
16#13094003C2212yes—
17#13094001—22no—
18Q8×Dic47C2212yes—
19#13093989—22no—
20#13093989C2212yes—
21#13093980—22no—
22C2×C4×Dic47C2211yescharacteristic
23#13093956C2211yescharacteristic
24#13093955C2212yes—
25Dic47⋊C8C2212yes—
26Dic47⋊C8C2212yes—
27#13093949C2212yes—
28#13093948C2212yes—
29#13093947C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#106×C47C2211yescharacteristic
34#103×C47C2212yes—
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47D412yes—
38C2×Dic94—22no—
39C2×Dic94C2312yes—
40Q16×C47—41no—
41M16×C47—41no—
42C2×C8×C47C2311yescharacteristic
43C2×C8×C47C2311yescharacteristic
44C4⋊C4×C47—22no—
45C4⋊C4×C47C2312yes—
46C22⋊C4×C47—22no—
47C22⋊Dic47—22no—
48#10625337—42no—
49C4⋊Dic47—22no—
50C4⋊Dic47C2312yes—
51Dic47⋊C4—22no—
52Dic47⋊C4—22no—
53Dic47⋊C4—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56C4×Dic47—22no—
57C4×Dic47—22no—
58C4×Dic47D411yescharacteristic
59C4×Dic47D411yescharacteristic
60C4×Dic47C2312yes—
61#10625329—41no—
62C2×C47⋊C8C2312yes—
63Dic188—41no—
64C23×C47C2×D411yescharacteristic
65Q8×C47—22no—
66Q8×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—24no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47C2×D412yes—
77C2×Dic47C2×D412yes—
78Dic94—22no—
79Dic94—22no—
80Dic94—44no—
81C8×C47—21no—
82C8×C47—21no—
83C47⋊C8—22no—
84C22×C47—21no—
85C22×C47—22no—
86C22×C47C22×D411yescharacteristic
87C4×C47—21no—
88C4×C47—42no—
89C4×C47—42no—
90C4×C47H(5,𝔽2)11yescharacteristic
91C4×C472−1+411yescharacteristic
92Dic47—22no—
93Dic47—42no—
94Dic47—42no—
95Dic47#13714yes—
96#3255—471nomaximal, Sylow
97C2×C47—41no—
98C2×C47#53711yescharacteristic
99C2×C47C2×#13712yes—
100#533—472no—
101#475—472no—
102#475—472no—
103#470—471no—
104#470—472no—
105#470D4711yescharacteristic
106#462—472no—
107#462—472no—
108#423—471no—
109C47#325511yescharacteristic, complemented, Sylow
110C2×Q16—472no—
111C2×Q16—471no—
112C2×Q16C2×D4711yescharacteristic
113C2×M16—471no—
114C2×M16C2×D4711yescharacteristic
115C4⋊Q8—472no—
116C4⋊Q8—472no—
117#125—942no—
118C22⋊Q8—472no—
119C22⋊Q8—942no—
120C22⋊Q8C2×D4712yes—
121C4×Q8—472no—
122C4×Q8—472no—
123C4×Q8—942no—
124#117—942no—
125C2×C42—471no—
126#106—471no—
127#106—472no—
128#106C2×D4711yescharacteristic
129C4⋊C8—472no—
130C4⋊C8—472no—
131#103—472no—
132#103—472no—
133#103—472no—
134#103C2×D4712yes—
135C2×Q8—472no—
136C2×Q8—942no—
137C2×Q8C22×D4712yes—
138C22×C4—472no—
139C22×C4C22×D4711yescharacteristic
140Q16—41no—
141Q16—1881no—
142Q16—1882no—
143M16—41no—
144M16—1881no—
145C2×C8—472no—
146C2×C8C22×D4711yescharacteristic
147C2×C8C22×D4711yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—472no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4C22×D4712yes—
157C22⋊C4—22no—
158C22⋊C4—942no—
159C42—471no—
160C42—471no—
161C42—472no—
162C42—942no—
163C42—942no—
164C23D4×D4711yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—942no—
168Q8—942no—
169Q8—1884no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—472no—
175C2×C4—472no—
176C2×C4—944no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4D4×D4711yescharacteristic
180C2×C4C23×D4711yescharacteristic
181C8—21no—
182C8—21no—
183C8—942no—
184C22—22no—
185C22—21no—
186C22C2×D4×D4711yescharacteristic
187C4—21no—
188C4—42no—
189C4—42no—
190C4—474no—
191C4—942no—
192C4—1882no—
193C4—1882no—
194C4#1309406911yescharacteristic
195C4#1309407111yescharacteristic
196C2—41no—
197C2#1568970011yescharacteristic
198C2#137×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3255
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #15689407C2semidirect
3. #15689406C2semidirect
6. #15689332C2semidirect
7. #15689331C2semidirect
109. C47#3255semidirect