Finite Group Databasebeta

← #20254729

Subgroups — #20254729

Order 6016.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689417C212yesmaximal, complemented
3#15689416C212yesmaximal, complemented
4#15689364C211yesmaximal, characteristic
5#15689362C212yesmaximal
6#15689332C212yesmaximal, complemented
7#15689331C212yesmaximal, complemented
8C2×Dic47⋊C8C211yesmaximal, characteristic
9C47×#467C211yesmaximal, characteristic
10C2×Dic188C2211yescharacteristic
11C2×#10625337C2212yes—
12C22×C47⋊C8C2211yescharacteristic
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#13093958C2211yescharacteristic
24#13093957C2212yes—
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
37C22×Dic47D411yescharacteristic
38C22×Dic47D411yescharacteristic
39C2×Dic94—22no—
40C2×Dic94C2312yes—
41Q16×C47—41no—
42C2×C8×C47—41no—
43C2×C8×C47C2311yescharacteristic
44C2×C8×C47C2311yescharacteristic
45C4⋊C4×C47—22no—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—22no—
48C22⋊Dic47—22no—
49#10625337—42no—
50C4⋊Dic47—22no—
51C4⋊Dic47C2312yes—
52Dic47⋊C4—22no—
53Dic47⋊C4—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57C4×Dic47—22no—
58C4×Dic47—22no—
59C4×Dic47D412yes—
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×Dic47—41no—
76C2×Dic47Q1614yescomplemented
77C2×Dic47C2×D412yes—
78C2×Dic47C2×D412yes—
79Dic94—22no—
80Dic94—22no—
81Dic94—44no—
82C8×C47—21no—
83C8×C47—21no—
84C47⋊C8—22no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47C2×Q1612yes—
88C22×C47C22×D411yescharacteristic
89C4×C47—21no—
90C4×C47—42no—
91C4×C47—42no—
92C4×C47H(5,𝔽2)11yescharacteristic
93C4×C472−1+411yescharacteristic
94Dic47—22no—
95Dic47—42no—
96Dic47—42no—
97Dic47C2×Q1614yes—
98#3249—471nomaximal, Sylow
99C2×C47—22no—
100C2×C47#53711yescharacteristic
101C2×C47C22×Q1611yescharacteristic
102C2×C47#57511yescharacteristic
103#533—472no—
104#477—472no—
105#477—472no—
106#467—471no—
107#467—472no—
108#467D4711yescharacteristic
109#462—472no—
110#462—472no—
111C2×C4⋊C8—471no—
112C47#324911yescharacteristic, complemented, Sylow
113C2×Q16—472no—
114C2×Q16—471no—
115C2×Q16C2×D4711yescharacteristic
116C22×C8—471no—
117C22×C8C2×D4711yescharacteristic
118C4⋊Q8—472no—
119C4⋊Q8—472no—
120#125—942no—
121C22⋊Q8—472no—
122C22⋊Q8—942no—
123C22⋊Q8C2×D4712yes—
124C4×Q8—472no—
125C4×Q8—472no—
126C4×Q8—942no—
127#117—942no—
128C2×C42—471no—
129#107—471no—
130#107—472no—
131#107C2×D4711yescharacteristic
132C4⋊C8—472no—
133C4⋊C8—472no—
134#103—472no—
135#103—472no—
136#103—472no—
137#103C2×D4712yes—
138C2×Q8—472no—
139C2×Q8—942no—
140C2×Q8C22×D4712yes—
141C22×C4—471no—
142C22×C4—471no—
143C22×C4C22×D4711yescharacteristic
144Q16—41no—
145Q16—1881no—
146Q16—1882no—
147C2×C8—41no—
148C2×C8—472no—
149C2×C8—1881no—
150C2×C8C22×D4711yescharacteristic
151C2×C8C22×D4711yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—472no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4C22×D4712yes—
161C22⋊C4—22no—
162C22⋊C4—942no—
163C42—472no—
164C42—472no—
165C42—942no—
166C42—942no—
167C23D4×D4711yescharacteristic
168Q8—22no—
169Q8—22no—
170Q8—942no—
171Q8—942no—
172Q8—1884no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—474no—
178C2×C4—472no—
179C2×C4—472no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—1881no—
183C2×C4D4×D4711yescharacteristic
184C2×C4C23×D4711yescharacteristic
185C8—21no—
186C8—21no—
187C8—942no—
188C22—21no—
189C22—21no—
190C22Q16×D4712yes—
191C22C2×D4×D4711yescharacteristic
192C4—21no—
193C4—42no—
194C4—42no—
195C4—474no—
196C4—942no—
197C4—1882no—
198C4—1882no—
199C4#1309406911yescharacteristic
200C4#1309407111yescharacteristic
201C2—22no—
202C2#1568970011yescharacteristic
203C2C2×Q16×D4711yescharacteristic
204C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3249
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. #15689417C2semidirect
3. #15689416C2semidirect
6. #15689332C2semidirect
7. #15689331C2semidirect
76. C2×Dic47Q16semidirect
112. C47#3249semidirect