Finite Group Databasebeta

← #20251423

Subgroups — #20251423

Order 6016.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094003C211yesmaximal, characteristic
2#15689062C212yesmaximal, complemented
3#15689061C212yesmaximal, complemented
4#15689051C214yesmaximal
5#15689043C212yesmaximal, complemented
6#15689042C212yesmaximal, complemented
7#15688986C211yesmaximal, characteristic
8C2×C22⋊Q8×C47C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10#13094003—24no—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2214yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2212yes—
16C47⋊#95C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2214yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21C22×Q8×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23C22⋊Q8×C47—24no—
24C2×C4⋊C4×C47C2212yes—
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2212yes—
27C24×C47C2311yescharacteristic
28C2×Q8×C47—22no—
29C2×Q8×C47—42no—
30C22×C4×C47—42no—
31C22×C4×C47D414yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2314yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C2×Dic94—22no—
40C2×Dic94—42no—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—24no—
43C22⋊C4×C47—24no—
44C22⋊Dic47—24no—
45C22⋊Dic47—42no—
46C4⋊Dic47—22no—
47Dic47⋊C4—24no—
48Dic47⋊C4—44no—
49C23×C47—22no—
50C23×C47—22no—
51C23×C47—22no—
52C23×C47C2×D412yes—
53C23×C47C2411yescharacteristic
54Q8×C47—44no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—24no—
60C2×C4×C47—24no—
61C2×C4×C47—44no—
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D412yes—
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—24no—
67C2×Dic47—24no—
68C2×Dic47—24no—
69C2×Dic47—24no—
70C2×Dic47—24no—
71Dic94—44no—
72C22×C47—22no—
73C22×C47—22no—
74C22×C47—22no—
75C22×C47—44no—
76C22×C47C22×D411yescharacteristic
77C22×C47H(5,𝔽2)12yes—
78C22×C472−1+412yes—
79C22×C472−1+412yes—
80C4×C47—22no—
81C4×C47—22no—
82C4×C47—42no—
83C4×C47—42no—
84Dic47—42no—
85Dic47—42no—
86Dic47—44no—
87#2817—471nomaximal, Sylow
88C2×C47—42no—
89C2×C47#53411yescharacteristic
90C2×C47#53611yescharacteristic
91C2×C47#53611yescharacteristic
92C2×C47#56314yes—
93C2×C22⋊Q8—471no—
94C2×C22⋊Q8D4711yescharacteristic
95#400—472no—
96#400—472no—
97#397—474no—
98#395—472no—
99#395—472no—
100#381—471no—
101C47#281711yescharacteristic, complemented, Sylow
102C22×Q8—471no—
103C22×Q8C2×D4711yescharacteristic
104C23×C4C2×D4711yescharacteristic
105C22⋊Q8—24no—
106C22⋊Q8—944no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—474no—
110C2×C4⋊C4C2×D4712yes—
111C2×C4⋊C4C2×D4711yescharacteristic
112C2×C22⋊C4—472no—
113C2×C22⋊C4—472no—
114C2×C22⋊C4C2×D4712yes—
115#95—472no—
116#95—472no—
117#95—474no—
118#95—474no—
119#95—474no—
120C24C22×D4711yescharacteristic
121C2×Q8—22no—
122C2×Q8—42no—
123C2×Q8—942no—
124C2×Q8—1882no—
125C22×C4—42no—
126C22×C4—474no—
127C22×C4—472no—
128C22×C4—472no—
129C22×C4C22⋊D4714yes—
130C22×C4C22×D4712yes—
131C22×C4C22×D4712yes—
132C22×C4C22×D4711yescharacteristic
133C22×C4C22×D4711yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—24no—
136C4⋊C4—944no—
137C4⋊C4—942no—
138C4⋊C4—1884no—
139C22⋊C4—24no—
140C22⋊C4—944no—
141C22⋊C4—1882no—
142C23—22no—
143C23—22no—
144C23—22no—
145C23C2×C22⋊D4712yes—
146C23C23×D4711yescharacteristic
147Q8—44no—
148Q8—1884no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—44no—
156C2×C4—942no—
157C2×C4—942no—
158C2×C4—944no—
159C2×C4—944no—
160C2×C4—944no—
161C2×C4—944no—
162C2×C4—944no—
163C2×C4C2×C22⋊D4712yes—
164C2×C4C2×C22⋊D4712yes—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22C22×C22⋊D4711yescharacteristic
170C22#1309406912yes—
171C22#1309407112yes—
172C22#1309407212yes—
173C4—22no—
174C4—22no—
175C4—42no—
176C4—42no—
177C4—1884no—
178C4—1882no—
179C4—1882no—
180C2—42no—
181C2#1568968211yescharacteristic
182C2#1568969411yescharacteristic
183C2#1568969711yescharacteristic
184C2#1568987414yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2817
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689062C2semidirect
3. #15689061C2semidirect
5. #15689043C2semidirect
6. #15689042C2semidirect
101. C47#2817semidirect