Finite Group Databasebeta

← #20242373

Subgroups — #20242373

Order 6016.

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

normal subgroups only

This group has 280 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#15689436C212yesmaximal, complemented
3#15688856C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic, complemented
5C47×#397C211yesmaximal, characteristic, complemented
6C22×C22⋊D47—21no—
7#13094008—22no—
8#13093998—21no—
9#13093998C2212yes—
10#13093994—22no—
11#13093957—22no—
12#13093944—22no—
13C22⋊(C47⋊C8)C2212yescomplemented
14C2×C4⋊C4×C47C2211yescharacteristic, complemented
15C2×C22⋊C4×C47—21no—
16C2×C22⋊C4×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47C2211yescharacteristic, complemented
19C24×C47D411yescharacteristic
20C23×D47—21no—
21C22×C4×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C2×C22⋊D47—22no—
26C2×C22⋊D47—22no—
27C2×C22⋊D47—42no—
28C2×C22⋊D47—42no—
29C22×Dic47—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C4⋊C4×C47—22no—
33C22⋊C4×C47—22no—
34C22⋊C4×C47—42no—
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4⋊Dic47—21no—
38C4⋊Dic47D412yes—
39C2×C47⋊C8—22no—
40C23×C47—21no—
41C23×C47—21no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47D812yes—
45C23×C47C2×D411yescharacteristic
46C22×D47—22no—
47C22×D47—42no—
48C22×D47—81no—
49C22×D47—81no—
50C2×C4×C47—21no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D412yes—
60C22⋊D47—44no—
61C22⋊D47—42no—
62C22⋊D47—42no—
63C2×Dic47—22no—
64C2×Dic47—42no—
65D188—42no—
66D188—81no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—22no—
71C22×C47—42no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—81no—
75C22×C47#12011yescharacteristic
76C22×C47C2×D811yescharacteristic
77C22×C47AGL(1,ℤ/8)11yescharacteristic
78C2×D47—42no—
79C2×D47—42no—
80C2×D47—42no—
81C2×D47—84no—
82C4×C47—22no—
83C4×C47—41no—
84C4×C47—81no—
85C4×C47—81no—
86Dic47—42no—
87#1607—471nomaximal, Sylow
88C2×C47—21no—
89C2×C47—21no—
90C2×C47—42no—
91C2×C47#44711yescharacteristic
92C2×C47#45511yescharacteristic
93C2×C47#45811yescharacteristic
94D47—82no—
95#534—471no—
96#480—472no—
97#397D4711yescharacteristic, complemented
98#327—472no—
99#323—471no—
100C47#160711yescharacteristic, complemented, Sylow
101C22×D4—941no—
102#123—942no—
103#121—472no—
104#121—941no—
105#120—942no—
106C2×C4⋊C4C2×D4711yescharacteristic, complemented
107C2×C22⋊C4—21no—
108C2×C22⋊C4C2×D4711yescharacteristic
109#107—942no—
110#102—942no—
111C22⋊C8—472no—
112#95—21no—
113#95C2×D4711yescharacteristic, complemented
114C24—941no—
115C24C22⋊D4711yescharacteristic
116C2×D4—472no—
117C2×D4—941no—
118C2×D4—942no—
119C2×D4—942no—
120C2×D4—1882no—
121C2×D4—1882no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—941no—
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22×D4711yescharacteristic
127C2×C8—942no—
128C4⋊C4—22no—
129C4⋊C4—472no—
130C4⋊C4—941no—
131C22⋊C4—22no—
132C22⋊C4—42no—
133C22⋊C4—942no—
134C22⋊C4—942no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—942no—
140C23—3761no—
141C23—3761no—
142C23—1882no—
143C23#1062533412yes—
144C23C2×C22⋊D4711yescharacteristic
145D4—3761no—
146D4—1882no—
147D4—1884no—
148D4—1882no—
149D4—1882no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—942no—
160C2×C4—1882no—
161C2×C4D4×D4712yes—
162C8—1882no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—3764no—
171C22—1882no—
172C22—1882no—
173C22—1882no—
174C22#1309399211yescharacteristic
175C22C2×#1062533411yescharacteristic
176C22#1309404911yescharacteristic
177C4—22no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—1882no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—3762no—
186C2#1568925611yescharacteristic
187C2#1568930011yescharacteristic
188C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#397C2
socleC22×C47#120
hypercenter#397D47
hypocenterC47#1607
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #15689436C2semidirect
3. #15688856C2semidirect
4. #15688847C2semidirect
5. C47×#397C2semidirect
13. C22⋊(C47⋊C8)C22semidirect
14. C2×C4⋊C4×C47C22semidirect
18. #95×C47C22semidirect
97. #397D47semidirect
100. C47#1607semidirect
106. C2×C4⋊C4C2×D47semidirect
113. #95C2×D47semidirect