Finite Group Databasebeta

← #20254839

Subgroups — #20254839

Order 6016.

322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689733C212yesmaximal
2#15689433C212yesmaximal, complemented
3#15689428C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic
5#15689362C212yesmaximal
6#15689332C212yesmaximal, complemented
7#15689331C212yesmaximal, complemented
8#15689151C211yesmaximal, characteristic
9C47×#470C211yesmaximal, characteristic
10C2×Dic188C2211yescharacteristic
11C2×#10625337C2212yes—
12C22×C47⋊C8C2211yescharacteristic
13#13094022C2212yes—
14#13094017—22no—
15#13094017—22no—
16#13094015—22no—
17#13094015C2212yes—
18#13094014—22no—
19#13094003C2212yes—
20Q8×Dic47C2212yes—
21#13093989C2212yes—
22#13093983C2211yescharacteristic
23#13093957C2212yes—
24#13093956C2211yescharacteristic
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
37C2×Dic94C2312yes—
38Q16×C47—41no—
39M16×C47—41no—
40C2×C8×C47C2311yescharacteristic
41C2×C8×C47C2311yescharacteristic
42C4⋊C4×C47—22no—
43C4⋊C4×C47C2312yes—
44C22⋊C4×C47—22no—
45C22⋊Dic47—22no—
46C22⋊Dic47D411yescharacteristic
47C22⋊Dic47D411yescharacteristic
48#10625337—42no—
49C4⋊Dic47—22no—
50C4⋊Dic47—22no—
51C4⋊Dic47D412yes—
52C4⋊Dic47C2312yes—
53Dic47⋊C4—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58C4×Dic47—22no—
59C4×Dic47—22no—
60C4×Dic47C2312yes—
61C2×C47⋊C8—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—22no—
74C2×Dic47—22no—
75C2×Dic47C2×D412yes—
76C2×Dic47C2×D412yes—
77Dic94—22no—
78Dic94—22no—
79C8×C47—21no—
80C8×C47—21no—
81C47⋊C8—22no—
82C22×C47—21no—
83C22×C47—22no—
84C22×C47C22×D411yescharacteristic
85C4×C47—21no—
86C4×C47—42no—
87C4×C47—42no—
88C4×C47H(5,𝔽2)11yescharacteristic
89C4×C472−1+411yescharacteristic
90Dic47—22no—
91Dic47—22no—
92Dic47—42no—
93Dic47—42no—
94#3261—471nomaximal, Sylow
95C2×C47—41no—
96C2×C47#53711yescharacteristic
97C2×C47#57812yes—
98#541—472no—
99#479—472no—
100#479—472no—
101#470—471no—
102#470D4711yescharacteristic
103#467—472no—
104#462—472no—
105#462—472no—
106#424—471no—
107C47#326111yescharacteristic, complemented, Sylow
108C2×Q16—472no—
109C2×Q16—471no—
110C2×Q16C2×D4711yescharacteristic
111C2×M16C2×D4711yescharacteristic
112C22×C8—471no—
113C4⋊Q8—472no—
114#126—942no—
115#126—942no—
116#125—472no—
117#125—942no—
118#125—942no—
119C22⋊Q8—472no—
120C22⋊Q8C2×D4712yes—
121C4×Q8—472no—
122C4×Q8—472no—
123#117—471no—
124#107—472no—
125#106—471no—
126#106C2×D4711yescharacteristic
127C4⋊C8—472no—
128C4⋊C8—472no—
129#103—472no—
130#103—472no—
131#103—472no—
132#103C2×D4712yes—
133C2×Q8—472no—
134C2×Q8C22×D4712yes—
135C22×C4C22×D4711yescharacteristic
136Q16—41no—
137Q16—1881no—
138Q16—1882no—
139M16—41no—
140C2×C8—472no—
141C2×C8—1881no—
142C2×C8C22×D4711yescharacteristic
143C2×C8C22×D4711yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—472no—
146C4⋊C4—472no—
147C4⋊C4—942no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4C22×D4712yes—
155C22⋊C4—22no—
156C22⋊C4—471no—
157C22⋊C4—471no—
158C22⋊C4—942no—
159C42—472no—
160C42—942no—
161C42—942no—
162C23D4×D4711yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—942no—
166Q8—942no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—472no—
172C2×C4—472no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4D4×D4711yescharacteristic
176C2×C4C23×D4711yescharacteristic
177C8—21no—
178C8—21no—
179C8—942no—
180C22—22no—
181C22—21no—
182C22C2×D4×D4711yescharacteristic
183C4—21no—
184C4—42no—
185C4—42no—
186C4—942no—
187C4—942no—
188C4—1882no—
189C4—1882no—
190C4#1309406911yescharacteristic
191C4#1309407111yescharacteristic
192C2—41no—
193C2#1568970011yescharacteristic
194C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3261
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. #15689433C2semidirect
3. #15689428C2semidirect
6. #15689332C2semidirect
7. #15689331C2semidirect
107. C47#3261semidirect