Finite Group Databasebeta

← #20244252

Subgroups — #20244252

Order 6016.

384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×D376C211yesmaximal, characteristic
2C2×#13093944C212yesmaximal, complemented
3C2×C8×Dic47C211yesmaximal, characteristic, complemented
4#15689024C212yesmaximal, complemented
5C2×#107×C47C211yesmaximal, characteristic, complemented
6C22×D188C2212yes—
7C2×D376—22no—
8C2×D376—22no—
9C2×D376C414yescomplemented
10C22×C47⋊C8C2211yescharacteristic
11C2×(C2×D47)⋊C4—24no—
12C2×C4×Dic47C2211yescharacteristic
13#13093944—24no—
14C8×Dic47—22no—
15C22×C8×C47C2211yescharacteristic
16C2×C4⋊C4×C47C2212yes—
17#107×C47—22no—
18C23×D47—22no—
19C22×C4×C47—22no—
20C22×C4×C47C2311yescharacteristic
21C22×Dic47D412yes—
22C2×D188—22no—
23C2×D188—22no—
24C2×D188—22no—
25C2×D188—22no—
26C2×D188—22no—
27C2×D188C2×C414yes—
28C2×C8×C47C2×C412yes—
29C2×C8×C47D412yes—
30C2×C8×C47D412yes—
31C4⋊C4×C47—22no—
32C4⋊C4×C47—22no—
33(C2×D47)⋊C4—48no—
34C4×Dic47—21no—
35C4×Dic47—21no—
36C2×C47⋊C8—21no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8D412yes—
39D376—28no—
40C23×C47C2×D411yescharacteristic
41C22×D47—24no—
42C22×D47—42no—
43C22×D47—42no—
44C22×D47—44no—
45C22×D47—44no—
46C2×C4×C47—42no—
47C2×C4×C47—44no—
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47#4111yescharacteristic
53C2×C4×C47#4111yescharacteristic
54C2×Dic47—22no—
55C2×Dic47—22no—
56C2×Dic47D814yescomplemented
57D188—24no—
58D188—24no—
59D188—42no—
60D188—42no—
61C8×C47C22⋊C414yescomplemented
62C47⋊C8—22no—
63C22×C47C4×D411yescharacteristic
64C22×C47#12111yescharacteristic
65C22×C47#12711yescharacteristic
66C22×C47C2×D812yes—
67C22×C47#13512yes—
68C2×D47—44no—
69C2×D47—48no—
70C2×D47—84no—
71C2×D47—82no—
72C2×D47—82no—
73C4×C47—82no—
74C4×C47C2×C22⋊C411yescharacteristic
75C4×C47C4×D411yescharacteristic
76C4×C47#12111yescharacteristic
77C4×C47#12411yescharacteristic
78Dic47—24no—
79#1970—471nomaximal, Sylow
80C2×C47#39011yescharacteristic
81C2×C47C4×D812yes—
82C2×C47#46612yes—
83C2×C47#49311yescharacteristic
84C2×C47#49511yescharacteristic
85D47—84no—
86C22×D8—471no—
87C2×#107D4711yescharacteristic, complemented
88C2×#102—472no—
89C2×C4×C8—471no—
90#390—472no—
91C47#197011yescharacteristic, complemented, Sylow
92C22×D4—472no—
93C2×D8—474no—
94C2×D8—942no—
95C2×D8—942no—
96C22×C8—471no—
97C22×C8C2×D4711yescharacteristic
98C2×C4⋊C4C2×D4712yes—
99C2×C22⋊C4—944no—
100C2×C42—471no—
101#107—22no—
102#102—944no—
103C4×C8—942no—
104C24—942no—
105C2×D4—474no—
106C2×D4—942no—
107C2×D4—942no—
108C2×D4—942no—
109C2×D4—942no—
110C2×D4—942no—
111C22×C4—22no—
112C22×C4—472no—
113C22×C4C22×D4711yescharacteristic
114D8—948no—
115C2×C8—472no—
116C2×C8—941no—
117C2×C8—941no—
118C2×C8C4×D4712yes—
119C2×C8D18812yes—
120C2×C8C22⋊D4712yes—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C22⋊C4—1888no—
124C42—941no—
125C42—941no—
126C23—944no—
127C23—1882no—
128C23—1882no—
129C23—1884no—
130C23—1884no—
131C23D4×D4711yescharacteristic
132D4—944no—
133D4—944no—
134D4—1882no—
135D4—1882no—
136C2×C4—42no—
137C2×C4—44no—
138C2×C4—474no—
139C2×C4—942no—
140C2×C4—942no—
141C2×C4C2×C4×D4711yescharacteristic
142C2×C4C2×D18811yescharacteristic
143C2×C4D4×D4711yescharacteristic
144C2×C4#1062535411yescharacteristic
145C2×C4#1062535411yescharacteristic
146C2×C4C2×C22⋊D4711yescharacteristic
147C8—942no—
148C8(C2×D47)⋊C414yescomplemented
149C22—3762no—
150C22—3762no—
151C22—3764no—
152C22—1884no—
153C22—1888no—
154C22#1309398611yescharacteristic
155C22#1309399911yescharacteristic
156C22#1309402011yescharacteristic
157C22D8×D4712yes—
158C22#1309404712yes—
159C4—82no—
160C4—944no—
161C4C2×(C2×D47)⋊C411yescharacteristic
162C4#1309398611yescharacteristic
163C4#1309399911yescharacteristic
164C4#1309401311yescharacteristic
165C2—3764no—
166C2#1568902411yescharacteristic
167C2#1568920512yes—
168C2#1568936012yes—
169C2#1568949811yescharacteristic
170C2#1568950811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#107×C47C2
socleC23×C47C2×D4
hypercenterC2×#107D47
hypocenterC47#1970
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#13093944C2semidirect
3. C2×C8×Dic47C2semidirect
4. #15689024C2semidirect
5. C2×#107×C47C2semidirect
9. C2×D376C4semidirect
56. C2×Dic47D8semidirect
61. C8×C47C22⋊C4semidirect
87. C2×#107D47semidirect
91. C47#1970semidirect
148. C8(C2×D47)⋊C4semidirect