Finite Group Databasebeta

← #20251564

Subgroups — #20251564

Order 6016.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C47⋊#401C212yesmaximal
2#15689065C212yesmaximal
3#15689064C212yesmaximal
4#15689062C211yesmaximal, characteristic
5#15689057C212yesmaximal
6#15689053C211yesmaximal, characteristic
7#15689042C212yesmaximal
8#15689007C212yesmaximal
9C47×#391C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C47⋊#95C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×Q8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2212yes—
31C2×Q8×C47—22no—
32C2×Q8×C47—41no—
33C2×Q8×C47—41no—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C4⋊C4×C47—41no—
44C42×C47—41no—
45C4⋊Dic47—41no—
46C4⋊Dic47—41no—
47Dic47⋊C4—24no—
48Dic47⋊C4—42no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51C23×C47C2411yescharacteristic
52Q8×C47—44no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47#4112yes—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—24no—
77C22×C47C2×#4111yescharacteristic
78C22×C47H(5,𝔽2)11yescharacteristic
79C22×C47H(5,𝔽2)11yescharacteristic
80C22×C472−1+412yes—
81C22×C472−1+412yes—
82C4×C47—22no—
83C4×C47—42no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47—42no—
87Dic47—42no—
88Dic47—42no—
89Dic47—42no—
90Dic47—42no—
91#2833—471nomaximal, Sylow
92C2×C47#53811yescharacteristic
93C2×C47#54112yes—
94C2×C47#56311yescharacteristic
95C2×C47#56311yescharacteristic
96C2×C47#56312yes—
97#401—472no—
98#400—471no—
99#400—472no—
100#400—472no—
101#398—471no—
102#398—472no—
103#395—472no—
104#391D4711yescharacteristic
105#387—472no—
106C47#283311yescharacteristic, complemented, Sylow
107C22×Q8C2×D4711yescharacteristic
108C2×C4⋊C4—472no—
109C2×C4⋊C4—472no—
110C2×C4⋊C4—472no—
111C2×C4⋊C4—472no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4C2×D4711yescharacteristic
115C2×C42C2×D4711yescharacteristic
116#95—472no—
117#95—472no—
118#95—472no—
119#95—472no—
120#95—472no—
121#95—472no—
122#95—472no—
123#95—472no—
124#95—471no—
125#95—471no—
126#95C2×D4712yes—
127#95C2×D4712yes—
128C2×Q8—22no—
129C2×Q8—41no—
130C2×Q8—41no—
131C22×C4—472no—
132C22×C4—472no—
133C22×C4—472no—
134C22×C4—472no—
135C22×C4C22×D4712yes—
136C22×C4C22×D4711yescharacteristic
137C22×C4C22×D4711yescharacteristic
138C22×C4C22×D4712yes—
139C22×C4C22×D4711yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—944no—
142C4⋊C4—1882no—
143C4⋊C4—1882no—
144C4⋊C4—1882no—
145C4⋊C4—1881no—
146C4⋊C4—1881no—
147C42—41no—
148C23C23×D4711yescharacteristic
149Q8—44no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—944no—
172C2×C4—942no—
173C2×C4#1062535012yes—
174C22C2×#1062535011yescharacteristic
175C22#1309406911yescharacteristic
176C22#1309406911yescharacteristic
177C22#1309407112yes—
178C22#1309407212yes—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—42no—
184C4—1882no—
185C4—1882no—
186C4—1882no—
187C4—1882no—
188C2#1568971111yescharacteristic
189C2#1568973112yes—
190C2#1568987211yescharacteristic
191C2#1568987311yescharacteristic
192C2#1568987412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2833
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
106. C47#2833semidirect