Finite Group Databasebeta

← #20248549

Subgroups — #20248549

Order 6016.

532 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094016C211yesmaximal, characteristic, complemented
2C2×C4×D188C211yesmaximal, characteristic
3#15689063C212yesmaximal, complemented
4#15689041C212yesmaximal
5#15689014C214yesmaximal, complemented
6#15688980C212yesmaximal, complemented
7#15688980C212yesmaximal, complemented
8C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C4×D47C2212yes—
11#13094016—24no—
12C4×D188—24no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2214yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C47⋊#95C2214yes—
22C47⋊#95C2214yes—
23C2×C4⋊C4×C47C2212yes—
24C2×C42×C47C2212yes—
25C2×C42×C47C2211yescharacteristic
26#95×C47C2212yes—
27C23×D47C2312yes—
28C22×C4×C47C2314yes—
29C22×C4×C47C2311yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×Dic47C2312yes—
33C22×Dic47C2312yes—
34C22×Dic47C2312yes—
35C2×D188—24no—
36C2×D188—22no—
37C2×C4×D47—24no—
38C2×C4×D47—24no—
39C2×C4×D47—24no—
40C4⋊C4×C47—24no—
41C42×C47—42no—
42C42×C47D414yes—
43(C2×D47)⋊C4—28no—
44(C2×D47)⋊C4—24no—
45(C2×D47)⋊C4—44no—
46C4⋊Dic47—22no—
47C4⋊Dic47—22no—
48C4⋊Dic47—22no—
49Dic47⋊C4—24no—
50Dic47⋊C4—24no—
51C23×C47C2411yescharacteristic
52C22×D47—22no—
53C22×D47—22no—
54C22×D47—22no—
55C22×D47—22no—
56C22×D47—22no—
57C22×D47—22no—
58C22×D47#4114yes—
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—24no—
63C2×C4×C47—24no—
64C2×C4×C47—24no—
65C2×C4×C47C2×D412yes—
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D412yes—
68C2×C4×C47#4114yes—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—24no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77D188—28no—
78C4×D47—48no—
79C22×C47C22×D411yescharacteristic
80C22×C47C2×#4112yes—
81C22×C47C2×#4112yes—
82C22×C47H(5,𝔽2)11yescharacteristic
83C22×C472−1+411yescharacteristic
84C2×D47—24no—
85C2×D47—24no—
86C2×D47—24no—
87C2×D47—42no—
88C2×D47—42no—
89C2×D47—42no—
90C2×D47—42no—
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—44no—
94C4×C47#12414yes—
95Dic47—42no—
96Dic47—42no—
97Dic47—42no—
98#2562—471nomaximal, Sylow
99C2×C47#52511yescharacteristic
100C2×C47C2×#12411yescharacteristic
101C2×C47#53711yescharacteristic
102C2×C47#55212yes—
103C2×C47#55312yes—
104D47—44no—
105C2×#125—471no—
106C2×C4×D4—471no—
107#400—472no—
108#394—472no—
109#388—474no—
110#380—472no—
111#380—472no—
112C4×C4⋊C4D4711yescharacteristic, complemented
113C47#256211yescharacteristic, complemented, Sylow
114C22×D4—471no—
115C23×C4—472no—
116#125—944no—
117C4×D4—944no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4C2×D4712yes—
124C2×C22⋊C4—472no—
125C2×C22⋊C4—474no—
126C2×C22⋊C4—474no—
127C2×C42C2×D4712yes—
128C2×C42C2×D4711yescharacteristic
129#95—474no—
130#95—474no—
131#95C2×D4712yes—
132C24—472no—
133C2×D4—944no—
134C2×D4—942no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4—944no—
139C22×C4—944no—
140C22×C4—944no—
141C22×C4C22×D4714yes—
142C22×C4C22×D4711yescharacteristic
143C22×C4C22×D4711yescharacteristic
144C22×C4C22×D4711yescharacteristic
145C4⋊C4—24no—
146C4⋊C4—944no—
147C4⋊C4—944no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C22⋊C4—948no—
152C22⋊C4—944no—
153C22⋊C4—1884no—
154C42—42no—
155C42D18814yes—
156C23—474no—
157C23—942no—
158C23—942no—
159C23—942no—
160C23—942no—
161C23—942no—
162C23—942no—
163C23C23×D4711yescharacteristic
164D4—948no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—944no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—1888no—
180C2×C4C2×D18812yes—
181C2×C4C2×D18812yes—
182C2×C4C2×D18812yes—
183C2×C4#1062535014yes—
184C22—944no—
185C22—944no—
186C22—944no—
187C22—1882no—
188C22—1882no—
189C22—1882no—
190C22—1882no—
191C22C22×D18811yescharacteristic
192C22#41×D4712yes—
193C22C2×#1062535012yes—
194C22#1309406911yescharacteristic
195C22#1309407211yescharacteristic
196C4—22no—
197C4—22no—
198C4—44no—
199C4—1882no—
200C4—1882no—
201C4—1882no—
202C4#1309401214yes—
203C2—1884no—
204C2#1568963511yescharacteristic
205C2C2×#1309401211yescharacteristic
206C2#1568970411yescharacteristic
207C2#1568981412yes—
208C2#1568982312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C4⋊C4×C47C2
hypercenterC4×C4⋊C4D47
hypocenterC47#2562
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094016C2semidirect
3. #15689063C2semidirect
5. #15689014C2semidirect
6. #15688980C2semidirect
7. #15688980C2semidirect
8. C4×C4⋊C4×C47C2semidirect
112. C4×C4⋊C4D47semidirect
113. C47#2562semidirect