Finite Group Databasebeta

← #20254837

Subgroups — #20254837

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#15689432C212yesmaximal, complemented
3#15689429C212yesmaximal, complemented
4#15689379C212yesmaximal
5#15689364C211yesmaximal, characteristic
6#15689332C212yesmaximal, complemented
7#15689331C212yesmaximal, complemented
8#15689149C211yesmaximal, characteristic
9C47×#467C211yesmaximal, characteristic
10C2×Dic188C2211yescharacteristic
11C2×#10625337C2212yes—
12C2×#10625329C2211yescharacteristic
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#13093958C2211yescharacteristic
24#13093955C2212yes—
25Dic47⋊C8C2212yes—
26Dic47⋊C8C2212yes—
27#13093949C2212yes—
28#13093948C2212yes—
29#13093947C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#107×C47C2211yescharacteristic
34#103×C47C2212yes—
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×Dic94C2312yes—
38Q16×C47—41no—
39C2×C8×C47—41no—
40C2×C8×C47C2311yescharacteristic
41C2×C8×C47C2311yescharacteristic
42C4⋊C4×C47—22no—
43C4⋊C4×C47C2312yes—
44C22⋊C4×C47—22no—
45C22⋊Dic47—22no—
46C22⋊Dic47D412yes—
47#10625337—42no—
48C4⋊Dic47—22no—
49C4⋊Dic47—22no—
50C4⋊Dic47D411yescharacteristic
51C4⋊Dic47D411yescharacteristic
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—
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—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—21no—
84C22×C47—21no—
85C22×C47C22×D411yescharacteristic
86C4×C47—21no—
87C4×C47—42no—
88C4×C47—42no—
89C4×C47H(5,𝔽2)11yescharacteristic
90C4×C472−1+411yescharacteristic
91Dic47—22no—
92Dic47—22no—
93Dic47—42no—
94Dic47—42no—
95#3261—471nomaximal, Sylow
96C2×C47—41no—
97C2×C47#53711yescharacteristic
98C2×C47#57811yescharacteristic
99C2×C47#57811yescharacteristic
100#541—472no—
101#479—472no—
102#479—472no—
103#470—472no—
104#467—471no—
105#467D4711yescharacteristic
106#462—472no—
107#462—472no—
108#424—471no—
109C47#326111yescharacteristic, complemented, Sylow
110C2×Q16—472no—
111C2×Q16—471no—
112C2×Q16C2×D4711yescharacteristic
113C2×M16—471no—
114C22×C8C2×D4711yescharacteristic
115C4⋊Q8—472no—
116#126—942no—
117#126—942no—
118#125—472no—
119#125—942no—
120#125—942no—
121C22⋊Q8—472no—
122C22⋊Q8C2×D4712yes—
123C4×Q8—472no—
124C4×Q8—472no—
125#117—471no—
126#107—471no—
127#107C2×D4711yescharacteristic
128#106—472no—
129C4⋊C8—472no—
130C4⋊C8—472no—
131#103—472no—
132#103—472no—
133#103—472no—
134#103C2×D4712yes—
135C2×Q8—472no—
136C2×Q8C22×D4712yes—
137C22×C4C22×D4711yescharacteristic
138Q16—41no—
139Q16—1881no—
140Q16—1882no—
141M16—1881no—
142C2×C8—41no—
143C2×C8—472no—
144C2×C8C22×D4711yescharacteristic
145C2×C8C22×D4711yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—471no—
148C4⋊C4—471no—
149C4⋊C4—472no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4C22×D4712yes—
158C22⋊C4—22no—
159C22⋊C4—472no—
160C22⋊C4—942no—
161C42—472no—
162C42—942no—
163C42—942no—
164C23D4×D4711yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—942no—
168Q8—942no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—472no—
174C2×C4—472no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4D4×D4711yescharacteristic
178C2×C4C23×D4711yescharacteristic
179C8—21no—
180C8—21no—
181C8—942no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22C2×D4×D4711yescharacteristic
186C4—21no—
187C4—42no—
188C4—42no—
189C4—942no—
190C4—942no—
191C4—1882no—
192C4—1882no—
193C4#1309406911yescharacteristic
194C4#1309407111yescharacteristic
195C2—41no—
196C2#1568970011yescharacteristic
197C2#1568993611yescharacteristic
198C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3261
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #15689432C2semidirect
3. #15689429C2semidirect
6. #15689332C2semidirect
7. #15689331C2semidirect
109. C47#3261semidirect