Finite Group Databasebeta

← #20249177

Subgroups — #20249177

Order 6016.

548 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13093998C211yesmaximal, characteristic
2#15689058C212yesmaximal, complemented
3#15689049C212yesmaximal, complemented
4#15689038C214yesmaximal, complemented
5#15689025C212yesmaximal, complemented
6#15689021C212yesmaximal, complemented
7#15688983C211yesmaximal, characteristic, complemented
8C2×#117×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C22⋊D47C2212yes—
11#13093998—24no—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2214yes—
15C2×C22⋊Dic47C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2214yes—
19C47⋊#95C2212yes—
20C47⋊#95C2214yes—
21C23×C4×C47C2211yescharacteristic
22#117×C47—24no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2212yes—
26C2×C42×C47C2212yes—
27C24×C47C2311yescharacteristic
28C23×D47C2312yes—
29C22×C4×C47—24no—
30C22×C4×C47D414yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—24no—
36C2×C22⋊D47—44no—
37C22×Dic47C2314yes—
38C22×Dic47C2312yes—
39C2×D188—22no—
40C2×D188—24no—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—22no—
43C22⋊C4×C47—24no—
44C42×C47—24no—
45C22⋊Dic47—42no—
46(C2×D47)⋊C4—24no—
47(C2×D47)⋊C4—44no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—22no—
50C4⋊Dic47—24no—
51Dic47⋊C4—44no—
52C23×C47—22no—
53C23×C47—21no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47C2×D412yes—
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—24no—
60C22×D47—22no—
61C22×D47—24no—
62C22×D47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—28no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×D412yes—
73C2×C4×C47#4114yes—
74C22⋊D47—48no—
75C2×Dic47—22no—
76C2×Dic47—24no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80D188—44no—
81C22×C47—22no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47C22×D411yescharacteristic
87C22×C47C2×#4112yes—
88C22×C47H(5,𝔽2)12yes—
89C22×C47H(5,𝔽2)11yescharacteristic
90C22×C472−1+411yescharacteristic
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—42no—
94C2×D47—44no—
95C2×D47—44no—
96C4×C47—22no—
97C4×C47—42no—
98C4×C47—42no—
99C4×C47#12314yes—
100Dic47—42no—
101Dic47—44no—
102#2624—471nomaximal, Sylow
103C2×C47—42no—
104C2×C47C2×#12311yescharacteristic
105C2×C47#53511yescharacteristic
106C2×C47#53711yescharacteristic
107C2×C47#54012yes—
108C2×C47#54212yes—
109D47—82no—
110C2×#121—471no—
111C2×#117D4711yescharacteristic, complemented
112#399—472no—
113#397—472no—
114#394—474no—
115#390—472no—
116#389—472no—
117#380—471no—
118C47#262411yescharacteristic, complemented, Sylow
119C22×D4—472no—
120C22×D4—471no—
121C23×C4C2×D4711yescharacteristic
122#121—944no—
123#117—24no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—474no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C22⋊C4—472no—
130C2×C22⋊C4—472no—
131C2×C22⋊C4—474no—
132C2×C22⋊C4—474no—
133C2×C22⋊C4C2×D4712yes—
134C2×C42C2×D4712yes—
135#95—472no—
136#95—474no—
137C24—472no—
138C24C22×D4711yescharacteristic
139C2×D4—944no—
140C2×D4—944no—
141C2×D4—942no—
142C2×D4—1884no—
143C22×C4—24no—
144C22×C4—474no—
145C22×C4—472no—
146C22×C4C22⋊D4714yes—
147C22×C4C22×D4712yes—
148C22×C4C22×D4712yes—
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—944no—
154C4⋊C4—942no—
155C4⋊C4—1884no—
156C22⋊C4—24no—
157C22⋊C4—944no—
158C22⋊C4—1884no—
159C22⋊C4—1884no—
160C22⋊C4—1882no—
161C42—24no—
162C23—22no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—942no—
167C23—944no—
168C23—942no—
169C23—944no—
170C23—942no—
171C23C2×C22⋊D4712yes—
172C23C23×D4711yescharacteristic
173D4—1888no—
174D4—1884no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—942no—
184C2×C4—944no—
185C2×C4—944no—
186C2×C4—944no—
187C2×C4—944no—
188C2×C4#1062535014yes—
189C2×C4C2×C22⋊D4712yes—
190C2×C4C2×C22⋊D4712yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—1884no—
197C22—1884no—
198C22—1882no—
199C22—1882no—
200C22—1882no—
201C22C22×C22⋊D4711yescharacteristic
202C22C2×#1062535012yes—
203C22#1309407011yescharacteristic
204C22#1309407012yes—
205C22#1309407111yescharacteristic
206C4—22no—
207C4—42no—
208C4—42no—
209C4—1884no—
210C4—1882no—
211C4#1309400714yes—
212C2—42no—
213C2—3762no—
214C2C2×#1309400711yescharacteristic
215C2#1568968711yescharacteristic
216C2#1568970111yescharacteristic
217C2#1568972812yes—
218C2#1568974412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#117×C47C2
hypercenterC2×#117D47
hypocenterC47#2624
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #15689058C2semidirect
3. #15689049C2semidirect
4. #15689038C2semidirect
5. #15689025C2semidirect
6. #15689021C2semidirect
7. #15688983C2semidirect
8. C2×#117×C47C2semidirect
111. C2×#117D47semidirect
118. C47#2624semidirect