Finite Group Databasebeta

← #20244792

Subgroups — #20244792

Order 6016.

274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13093944C212yesmaximal
2#15689025C211yesmaximal, characteristic
3#15688885C212yesmaximal, complemented
4#15688878C211yesmaximal, characteristic, complemented
5C47×#384C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7C22×C47⋊C8C2212yes—
8C2×C4⋊Dic47C2211yescharacteristic
9C2×(C2×D47)⋊C4—21no—
10C2×(C2×D47)⋊C4—21no—
11#13093944—24no—
12C2×C4⋊C4×C47—21no—
13C2×C4⋊C4×C47—21no—
14C2×C4⋊C4×C47C2212yes—
15C2×C42×C47C2211yescharacteristic
16C23×D47—21no—
17C22×C4×C47—22no—
18C22×C4×C47D411yescharacteristic
19C22×C4×C47D411yescharacteristic
20C22×C4×C47C2311yescharacteristic
21C22×Dic47—21no—
22C2×D188—22no—
23C2×D188—22no—
24C2×D188—21no—
25C2×D188D412yes—
26C4⋊C4×C47—22no—
27C4⋊C4×C47—22no—
28C4⋊C4×C47—42no—
29C4⋊C4×C47—42no—
30C42×C47—22no—
31(C2×D47)⋊C4—42no—
32(C2×D47)⋊C4—42no—
33C4⋊Dic47—22no—
34C2×C47⋊C8—22no—
35C2×C47⋊C8—22no—
36C2×C47⋊C8—22no—
37C23×C47C2×D411yescharacteristic
38C22×D47—22no—
39C22×D47—41no—
40C22×D47—41no—
41C22×D47—41no—
42C22×D47—41no—
43C22×D47—41no—
44C22×D47—41no—
45C2×C4×C47—21no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—42no—
50C2×C4×C47—42no—
51C2×C4×C47—42no—
52C2×C4×C47D812yes—
53C2×C4×C47SD1612yes—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47#4112yes—
56C2×C4×C47#4111yescharacteristic
57C2×C4×C47#4112yes—
58C2×Dic47—41no—
59C2×Dic47—41no—
60C2×Dic47—41no—
61D188—24no—
62D188—42no—
63C47⋊C8—42no—
64C22×C47#12111yescharacteristic
65C22×C47#12311yescharacteristic
66C22×C47#12411yescharacteristic
67C22×C47C2×D811yescharacteristic
68C22×C47C2×SD1611yescharacteristic
69C22×C47AGL(1,ℤ/8)11yescharacteristic
70C22×C47#13711yescharacteristic
71C2×D47—42no—
72C2×D47—42no—
73C2×D47—42no—
74C2×D47—81no—
75C2×D47—81no—
76C2×D47—81no—
77C2×D47—81no—
78C4×C47—22no—
79C4×C47—22no—
80C4×C47—82no—
81C4×C47#12312yes—
82C4×C47#12612yes—
83Dic47—81no—
84#2071—471nomaximal, Sylow
85C2×C47#39711yescharacteristic
86C2×C47#45911yescharacteristic
87C2×C47#46111yescharacteristic
88C2×C47#48011yescharacteristic
89C2×C47#48111yescharacteristic
90C2×C47#48611yescharacteristic
91C2×C47#48911yescharacteristic
92D47—82no—
93C2×#102—472no—
94#390—471no—
95#384D4711yescharacteristic, complemented
96#340—472no—
97#336—471no—
98C47#207111yescharacteristic, complemented, Sylow
99C22×D4—471no—
100C22×C8—472no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—471no—
104C2×C4⋊C4C2×D4712yes—
105C2×C22⋊C4—941no—
106C2×C22⋊C4—941no—
107C2×C42C2×D4711yescharacteristic
108#102—944no—
109C24—941no—
110C2×D4—472no—
111C2×D4—942no—
112C2×D4—941no—
113C2×D4—942no—
114C22×C4—22no—
115C22×C4—941no—
116C22×C4C22⋊D4711yescharacteristic
117C22×C4C22⋊D4711yescharacteristic
118C22×C4C22×D4711yescharacteristic
119C2×C8—942no—
120C2×C8—942no—
121C2×C8—942no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—942no—
127C22⋊C4—1882no—
128C22⋊C4—1882no—
129C42—22no—
130C23—942no—
131C23—1881no—
132C23—1881no—
133C23—1881no—
134C23—1881no—
135C23—1881no—
136C23—1881no—
137C23C2×C22⋊D4711yescharacteristic
138D4—944no—
139D4—1882no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—1881no—
148C2×C4—1881no—
149C2×C4—1881no—
150C2×C4#1062533412yes—
151C2×C4#1062533612yes—
152C2×C4#1062535012yes—
153C2×C4D4×D4711yescharacteristic
154C2×C4#1062535211yescharacteristic
155C2×C4#1062535412yes—
156C8—1882no—
157C22—3761no—
158C22—3761no—
159C22—3761no—
160C22—3761no—
161C22—1882no—
162C22—1882no—
163C22—1882no—
164C22#1309399511yescharacteristic
165C22#1309400711yescharacteristic
166C22#1309401311yescharacteristic
167C22C2×#1062533411yescharacteristic
168C22C2×#1062533611yescharacteristic
169C22#1309405011yescharacteristic
170C22#1309405511yescharacteristic
171C4—22no—
172C4—22no—
173C4—82no—
174C4—3761no—
175C4#1309400912yes—
176C4#1309401912yes—
177C2—3762no—
178C2#1568904911yescharacteristic
179C2#1568931511yescharacteristic
180C2#1568932511yescharacteristic
181C2#1568943611yescharacteristic
182C2#1568944111yescharacteristic
183C2#1568947111yescharacteristic
184C2#1568948511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#384C2
socleC23×C47C2×D4
hypercenter#384D47
hypocenterC47#2071
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #15688885C2semidirect
4. #15688878C2semidirect
5. C47×#384C2semidirect
95. #384D47semidirect
98. C47#2071semidirect