Finite Group Databasebeta

← #20248868

Subgroups — #20248868

Order 6016.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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#15689062C212yesmaximal, complemented
3#15689040C212yesmaximal, complemented
4#15689013C214yesmaximal, complemented
5#15689002C212yesmaximal, complemented
6#15689002C212yesmaximal, complemented
7C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C22⋊D47C2212yes—
11#13093998—24no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C22⋊Dic47C2212yes—
14C2×(C2×D47)⋊C4C2214yes—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2214yes—
17C2×C4×Dic47C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21C23×C4×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47—24no—
25C2×C4⋊C4×C47C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C24×C47C2311yescharacteristic
28C23×D47C2312yes—
29C22×C4×C47—22no—
30C22×C4×C47—24no—
31C22×C4×C47—22no—
32C22×C4×C47—42no—
33C22×C4×C47—42no—
34C22×C4×C47D414yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C2×C22⋊D47—24no—
40C2×C22⋊D47—28no—
41C22×Dic47C2312yes—
42C22×Dic47C2314yes—
43C2×D188—22no—
44C2×D188—42no—
45C4⋊C4×C47—24no—
46C4⋊C4×C47—24no—
47C22⋊Dic47—24no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4—28no—
50(C2×D47)⋊C4—44no—
51C4⋊Dic47—22no—
52C4×Dic47—42no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47C2×D412yes—
56C23×C47#4114yes—
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—24no—
60C22×D47—24no—
61C22×D47—24no—
62C2×C4×C47—28no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—24no—
69C2×C4×C47—44no—
70C2×C4×C47—44no—
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—28no—
84C22×C47#12414yes—
85C22×C47C22×D411yescharacteristic
86C22×C47C2×#4112yes—
87C22×C47C2×#4112yes—
88C22×C47H(5,𝔽2)12yes—
89C2×D47—42no—
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—48no—
93C4×C47—24no—
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—42no—
97Dic47—42no—
98Dic47—44no—
99#2591—471nomaximal, Sylow
100C2×C47—24no—
101C2×C47#52511yescharacteristic
102C2×C47C2×#12411yescharacteristic
103C2×C47#53411yescharacteristic
104C2×C47#55314yes—
105D47—82no—
106C2×#121—471no—
107C22×C4⋊C4D4711yescharacteristic, complemented
108#400—472no—
109#394—472no—
110#388—474no—
111#386—472no—
112#386—472no—
113C4×C22⋊C4—471no—
114C47#259111yescharacteristic, complemented, Sylow
115C22×D4—472no—
116C22×D4—471no—
117C23×C4C2×D4711yescharacteristic
118C23×C4C2×D4711yescharacteristic
119C23×C4C2×D4711yescharacteristic
120#121—944no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4C2×D4712yes—
124C2×C4⋊C4C2×D4712yes—
125C2×C22⋊C4—472no—
126C2×C22⋊C4—472no—
127C2×C22⋊C4—474no—
128C2×C22⋊C4—474no—
129C2×C42—472no—
130#95—472no—
131#95—474no—
132#95—474no—
133C24—472no—
134C24C22×D4711yescharacteristic
135C2×D4—948no—
136C2×D4—944no—
137C2×D4—942no—
138C2×D4—1882no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—472no—
145C22×C4—474no—
146C22×C4C22⋊D4714yes—
147C22×C4C22×D4712yes—
148C22×C4C22×D4712yes—
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—942no—
154C22⋊C4—944no—
155C22⋊C4—948no—
156C22⋊C4—944no—
157C22⋊C4—1884no—
158C42—1882no—
159C23—22no—
160C23—22no—
161C23—942no—
162C23—944no—
163C23—944no—
164C23—944no—
165C23#1062535414yes—
166C23C2×C22⋊D4712yes—
167C23C23×D4711yescharacteristic
168D4—1884no—
169D4—1888no—
170C2×C4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—942no—
180C2×C4—944no—
181C2×C4—944no—
182C2×C4—944no—
183C2×C4—944no—
184C2×C4#1062535014yes—
185C2×C4C2×C22⋊D4712yes—
186C2×C4C2×C22⋊D4712yes—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—1888no—
191C22—1882no—
192C22—1882no—
193C22—1882no—
194C22#1309401314yes—
195C22C22×C22⋊D4711yescharacteristic
196C22C2×#1062535012yes—
197C22C2×#1062535412yes—
198C22#1309406912yes—
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—1884no—
204C4—1882no—
205C2—24no—
206C2—3762no—
207C2#1568963411yescharacteristic
208C2C2×#1309401311yescharacteristic
209C2#1568968211yescharacteristic
210C2#1568982114yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C4⋊C4×C47C2
hypercenterC22×C4⋊C4D47
hypocenterC47#2591
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #15689062C2semidirect
3. #15689040C2semidirect
4. #15689013C2semidirect
5. #15689002C2semidirect
6. #15689002C2semidirect
7. C4×C22⋊Dic47C2semidirect
8. C22×C4⋊C4×C47C2semidirect
107. C22×C4⋊C4D47semidirect
114. C47#2591semidirect