Finite Group Databasebeta

← #20242410

Subgroups — #20242410

Order 6016.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#15689685C211yesmaximal, characteristic
2#15689442C212yesmaximal, complemented
3#15689059C211yesmaximal, characteristic, complemented
4#15688858C212yesmaximal, complemented
5C47×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D47—21no—
7#13094008—22no—
8#13093998—21no—
9#13093998C2212yes—
10#13093994—22no—
11C2×C4⋊Dic47C2211yescharacteristic, complemented
12C2×Dic47⋊C4—21no—
13C2×C22⋊Dic47—21no—
14#13093956—22no—
15#13093946—22no—
16C47⋊#95C2211yescharacteristic, complemented
17C2×C22⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yescomplemented
19C24×C47D411yescharacteristic
20C23×D47—21no—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C2×C22⋊D47—22no—
25C2×C22⋊D47—42no—
26C2×C22⋊D47—42no—
27C22×Dic47—21no—
28C22×Dic47—21no—
29C22×Dic47—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C2×C8×C47—22no—
33C22⋊C4×C47—22no—
34C22⋊Dic47—42no—
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4⋊Dic47—21no—
38C4⋊Dic47—22no—
39C4⋊Dic47D412yes—
40Dic47⋊C4—42no—
41C23×C47—21no—
42C23×C47—21no—
43C23×C47—41no—
44C23×C47—41no—
45C23×C47SD1612yes—
46C23×C47C2×D411yescharacteristic
47C22×D47—22no—
48C22×D47—42no—
49C22×D47—81no—
50C22×D47—81no—
51C2×C4×C47—21no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47C2×D412yes—
55C22⋊D47—44no—
56C22⋊D47—42no—
57C22⋊D47—42no—
58C2×Dic47—22no—
59C2×Dic47—22no—
60C2×Dic47—41no—
61C2×Dic47—42no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66D188—42no—
67D188—81no—
68C8×C47—42no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47—22no—
72C22×C47—42no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47—81no—
76C22×C47#12011yescharacteristic
77C22×C47C2×SD1611yescharacteristic
78C22×C47AGL(1,ℤ/8)11yescharacteristic
79C2×D47—42no—
80C2×D47—42no—
81C2×D47—42no—
82C2×D47—84no—
83C4×C47—22no—
84C4×C47—41no—
85Dic47—42no—
86Dic47—42no—
87Dic47—81no—
88#1613—471nomaximal, Sylow
89C2×C47—21no—
90C2×C47—21no—
91C2×C47—42no—
92C2×C47#45011yescharacteristic
93C2×C47#45311yescharacteristic
94C2×C47#45811yescharacteristic
95D47—82no—
96#534—471no—
97#481—472no—
98#399—471no—
99#327—472no—
100#323D4711yescharacteristic, complemented
101C47#161311yescharacteristic, complemented, Sylow
102C22×D4—941no—
103#123—942no—
104#121—472no—
105#121—941no—
106#120—942no—
107C2×C4⋊C4—471no—
108C2×C4⋊C4—941no—
109C2×C22⋊C4—941no—
110C2×C22⋊C4C2×D4711yescharacteristic
111#106—942no—
112#102—942no—
113C22⋊C8C2×D4712yescomplemented
114#95—471no—
115C24—941no—
116C24D18811yescharacteristic
117C2×D4—472no—
118C2×D4—941no—
119C2×D4—942no—
120C2×D4—942no—
121C2×D4—1882no—
122C2×D4—1882no—
123C22×C4—941no—
124C22×C4—941no—
125C22×C4—941no—
126C22×C4D18811yescharacteristic
127C22×C4C22×D4711yescharacteristic
128C2×C8—22no—
129C4⋊C4—472no—
130C4⋊C4—941no—
131C4⋊C4—942no—
132C4⋊C4—1882no—
133C22⋊C4—22no—
134C22⋊C4—942no—
135C22⋊C4—942no—
136C22⋊C4—1882no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—942no—
142C23—3761no—
143C23—3761no—
144C23—1882no—
145C23#1062532512yes—
146C23C2×D18811yescharacteristic
147D4—3761no—
148D4—1882no—
149D4—1884no—
150D4—1882no—
151D4—1882no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4—1882no—
162C2×C4—1881no—
163C2×C4D4×D4712yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—3764no—
173C22—1882no—
174C22—1882no—
175C22—1882no—
176C22#1309399411yescharacteristic
177C22C2×#1062532511yescharacteristic
178C22#1309405211yescharacteristic
179C4—22no—
180C4—41no—
181C4—3761no—
182C4—1882no—
183C4—1882no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—3762no—
188C2#1568927611yescharacteristic
189C2#1568929311yescharacteristic
190C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#323C2
socleC22×C47#120
hypercenter#323D47
hypocenterC47#1613
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #15689442C2semidirect
3. #15689059C2semidirect
4. #15688858C2semidirect
5. C47×#323C2semidirect
11. C2×C4⋊Dic47C22semidirect
16. C47⋊#95C22semidirect
18. C22⋊C8×C47C22semidirect
100. #323D47semidirect
101. C47#1613semidirect
113. C22⋊C8C2×D47semidirect