Finite Group Databasebeta

← #20249171

Subgroups — #20249171

Order 6016.

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

normal subgroups only

This group has 526 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×#13094007C211yesmaximal, characteristic
2C22×C4⋊Dic47C211yesmaximal, characteristic, complemented
3#15689063C212yesmaximal, complemented
4#15689060C212yesmaximal, complemented
5#15689055C212yesmaximal, complemented
6#15689050C212yesmaximal, complemented
7#15689000C212yesmaximal
8#15688998C212yesmaximal, complemented
9C47×#381C211yesmaximal, characteristic, complemented
10C22×C22⋊D47C2211yescharacteristic
11C23×Dic47C2212yes—
12#13094007—24no—
13C2×C4⋊Dic47—24no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2214yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×C22⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4C2211yescharacteristic
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2214yes—
23C47⋊#95C2214yes—
24C47⋊#95C2214yes—
25C23×C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2212yes—
27#95×C47C2212yes—
28#95×C47C2212yes—
29C24×C47C2311yescharacteristic
30C23×D47C2311yescharacteristic
31C22×C4×C47—24no—
32C22×C4×C47D414yes—
33C22×C4×C47C2314yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C2×C22⋊D47—24no—
38C22×Dic47—24no—
39C22×Dic47—44no—
40C22×Dic47C2311yescharacteristic
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2314yes—
43C22×Dic47C2311yescharacteristic
44C22⋊C4×C47—24no—
45C22⋊Dic47—22no—
46(C2×D47)⋊C4—22no—
47(C2×D47)⋊C4—22no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—24no—
50C4⋊Dic47—24no—
51C4⋊Dic47—44no—
52Dic47⋊C4—22no—
53Dic47⋊C4—22no—
54C23×C47—22no—
55C23×C47—22no—
56C23×C47C2×D412yes—
57C23×C47#4114yes—
58C23×C47C2411yescharacteristic
59C22×D47—21no—
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C2×C4×C47—28no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—24no—
67C2×C4×C47—24no—
68C2×C4×C47—24no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C22⋊D47—44no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—24no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—22no—
81C2×Dic47—48no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—28no—
85C22×C47#12314yes—
86C22×C47C22×D411yescharacteristic
87C22×C47C2×#4112yes—
88C22×C47H(5,𝔽2)12yes—
89C22×C472−1+412yes—
90C2×D47—41no—
91C2×D47—41no—
92C2×D47—41no—
93C2×D47—44no—
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—44no—
97Dic47—41no—
98Dic47—41no—
99Dic47—44no—
100Dic47—41no—
101#2623—471nomaximal, Sylow
102C2×C47—24no—
103C2×C47C2×#12311yescharacteristic
104C2×C47#53511yescharacteristic
105C2×C47#53611yescharacteristic
106C2×C47#53914yes—
107D47—81no—
108C2×#123—471no—
109C22×C4⋊C4—471no—
110#400—472no—
111#399—472no—
112#398—472no—
113#397—472no—
114#386—472no—
115#385—472no—
116#381D4711yescharacteristic, complemented
117C47#262311yescharacteristic, complemented, Sylow
118C22×D4—471no—
119C23×C4—472no—
120C23×C4C2×D4711yescharacteristic
121#123—944no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—474no—
127C2×C4⋊C4—944no—
128C2×C22⋊C4—471no—
129C2×C22⋊C4—471no—
130C2×C22⋊C4—471no—
131C2×C22⋊C4—474no—
132C2×C22⋊C4C2×D4712yes—
133#95—474no—
134#95—474no—
135#95C2×D4712yes—
136#95C2×D4712yes—
137C24—471no—
138C24C22×D4711yescharacteristic
139C2×D4—942no—
140C2×D4—944no—
141C22×C4—24no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—474no—
145C22×C4—471no—
146C22×C4—944no—
147C22×C4—1884no—
148C22×C4D18814yes—
149C22×C4C22×D4714yes—
150C22×C4C22×D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—1884no—
157C22⋊C4—24no—
158C22⋊C4—942no—
159C22⋊C4—942no—
160C22⋊C4—942no—
161C22⋊C4—1884no—
162C23—22no—
163C23—22no—
164C23—941no—
165C23—942no—
166C23—942no—
167C23—942no—
168C23C2×D18812yes—
169C23#1062535214yes—
170C23C23×D4711yescharacteristic
171D4—1884no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—944no—
181C2×C4—941no—
182C2×C4—942no—
183C2×C4—944no—
184C2×C4—942no—
185C2×C4—944no—
186C2×C4—942no—
187C2×C4—1888no—
188C2×C4C2×D18812yes—
189C2×C4C2×D18812yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—1881no—
194C22—1881no—
195C22—1881no—
196C22—1884no—
197C22#1309400814yes—
198C22C22×D18811yescharacteristic
199C22C2×#1062535212yes—
200C22#1309407012yes—
201C22#1309407112yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—1881no—
206C4—1884no—
207C4—1881no—
208C4—1881no—
209C2—24no—
210C2—3761no—
211C2C2×#1309400811yescharacteristic
212C2#1568969211yescharacteristic
213C2#1568969911yescharacteristic
214C2#1568971714yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2623
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic47C2semidirect
3. #15689063C2semidirect
4. #15689060C2semidirect
5. #15689055C2semidirect
6. #15689050C2semidirect
8. #15688998C2semidirect
9. C47×#381C2semidirect
116. #381D47semidirect
117. C47#2623semidirect