Finite Group Databasebeta

← #20245074

Subgroups — #20245074

Order 6016.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689693C211yesmaximal, characteristic
2#101×D47C212yesmaximal, complemented
3#15688921C212yesmaximal, complemented
4#15688920C211yesmaximal, characteristic, complemented
5C47×#355C211yesmaximal, characteristic, complemented
6C2×#10625352C411yescharacteristic
7C2×Q8×D47C2211yescharacteristic
8M16×D47—22no—
9#13094024C411yescharacteristic
10#13094022C2211yescharacteristic
11#13094011C411yescharacteristic
12#13094006—22no—
13#13094001—22no—
14#13093981C411yescharacteristic
15#13093943C2212yes—
16#13093942—22no—
17#124×C47C2211yescharacteristic
18#101×C47C2212yes—
19C2×Q8×C47C2311yescharacteristic
20C2×D4×C47C2×C411yescharacteristic
21C2×C22⋊D47—21no—
22C22×Dic47—21no—
23Q8×D47—42no—
24#10625352—42no—
25C2×C4×D47C2×C411yescharacteristic
26C2×C4×D47D412yes—
27C2×Dic94C2×C411yescharacteristic
28C2×Dic94C2×C411yescharacteristic
29C2×Dic94D412yes—
30M16×C47—22no—
31C22⋊C4×C47—22no—
32C42×C47C2×C411yescharacteristic
33C22⋊Dic47—22no—
34(C2×D47)⋊C4—21no—
35C4⋊Dic47—22no—
36Dic47⋊C4—22no—
37Dic47⋊C4—21no—
38C4×Dic47C2×C411yescharacteristic
39#10625329—22no—
40#10625324—42no—
41C8×D47—42no—
42C23×C47—21no—
43C22×D47C22⋊C411yescharacteristic
44Q8×C47—41no—
45D4×C47—41no—
46C2×C4×C47—21no—
47C2×C4×C47C22×C411yescharacteristic
48C2×C4×C47C2×D412yes—
49C22⋊D47—42no—
50C2×Dic47—21no—
51C2×Dic47—21no—
52C2×Dic47—42no—
53C2×Dic47C22⋊C411yescharacteristic
54C2×Dic47C22⋊C412yes—
55C4×D47—22no—
56C4×D47—22no—
57C4×D47—22no—
58Dic94—41no—
59Dic94—42no—
60Dic94—41no—
61C8×C47—42no—
62C47⋊C8—42no—
63C22×C47—42no—
64C22×C47—41no—
65C22×C47C2×C22⋊C411yescharacteristic
66C2×D47—41no—
67C2×D47#9912yes—
68C4×C47—22no—
69C4×C47—21no—
70C4×C47—41no—
71Dic47—21no—
72Dic47—22no—
73Dic47—41no—
74Dic47—41no—
75#2133—471nomaximal, Sylow
76C2×C47—21no—
77C2×C47—81no—
78C2×C47C2×#9911yescharacteristic
79D47—22no—
80#536—471no—
81C2×#101—472no—
82#356—472no—
83#355—471no—
84#355D4711yescharacteristic, complemented
85C47#213311yescharacteristic, complemented, Sylow
86C2×#41—471no—
87C22×Q8—471no—
88C2×M16—942no—
89C4⋊Q8—471no—
90C4⋊Q8—471no—
91#124—471no—
92#124C2×D4711yescharacteristic
93#123—942no—
94C22⋊Q8—942no—
95#117—471no—
96#101—472no—
97#101—942no—
98#101C2×D4712yes—
99#41—1882no—
100C2×Q8—471no—
101C2×Q8—472no—
102C2×Q8—471no—
103C2×Q8—1882no—
104C2×Q8C22×D4711yescharacteristic
105C2×D4—941no—
106C2×D4C4×D4711yescharacteristic
107C22×C4—471no—
108C22×C4—472no—
109C22×C4—941no—
110M16—22no—
111M16—942no—
112M16—1882no—
113C2×C8—1882no—
114C4⋊C4—941no—
115C4⋊C4—942no—
116C4⋊C4—942no—
117C22⋊C4—22no—
118C22⋊C4—941no—
119C22⋊C4—942no—
120C42—471no—
121C42C4×D4711yescharacteristic
122C23—21no—
123C23—471no—
124Q8—41no—
125Q8—1882no—
126Q8—1881no—
127Q8—1881no—
128D4—41no—
129D4—1882no—
130C2×C4—21no—
131C2×C4—472no—
132C2×C4—471no—
133C2×C4—942no—
134C2×C4—942no—
135C2×C4—942no—
136C2×C4—941no—
137C2×C4—941no—
138C2×C4—1882no—
139C2×C4C2×C4×D4711yescharacteristic
140C2×C4D4×D4712yes—
141C8—42no—
142C8—1882no—
143C22—42no—
144C22—41no—
145C22—472no—
146C22—1881no—
147C22C22⋊C4×D4711yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—941no—
152C4—942no—
153C4—1881no—
154C4—1881no—
155C2—21no—
156C2—81no—
157C2—942no—
158C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#355C2
socleC2×C47C2×#99
hypercenter#355D47
hypocenterC47#2133
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D47C2semidirect
3. #15688921C2semidirect
4. #15688920C2semidirect
5. C47×#355C2semidirect
84. #355D47semidirect
85. C47#2133semidirect