Finite Group Databasebeta

← #20245137

Subgroups — #20245137

Order 6016.

220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13093964C211yesmaximal, characteristic, complemented
2C2×#13093960C211yesmaximal, characteristic, complemented
3#15688939C212yesmaximal, complemented
4#15688936C212yesmaximal, complemented
5C2×#135×C47C211yesmaximal, characteristic
6C2×#10625329—21no—
7#13093964—21no—
8#13093964C2212yes—
9C2×C47⋊C16—21no—
10#13093960—21no—
11#13093960C2212yes—
12C2×#41×C47—21no—
13#135×C47—21no—
14#135×C47—21no—
15#135×C47C412yes—
16#135×C47C412yes—
17C2×Q16×C47C2211yescharacteristic
18C2×SD16×C47—21no—
19C2×D8×C47C2211yescharacteristic
20C22×C8×C47C2211yescharacteristic
21#41×C47—22no—
22#41×C47—22no—
23#41×C47—41no—
24#41×C47—41no—
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—41no—
28C22×C4×C47—41no—
29C22×C4×C47D411yescharacteristic
30Q16×C47—21no—
31Q16×C47C2×C412yes—
32SD16×C47—22no—
33SD16×C47—22no—
34D8×C47—21no—
35D8×C47C2×C412yes—
36C2×C8×C47C2×C411yescharacteristic
37C2×C8×C47C2×C411yescharacteristic
38C2×C8×C47D411yescharacteristic
39C2×C8×C47D411yescharacteristic
40C2×C8×C47D411yescharacteristic
41C2×C8×C47C2311yescharacteristic
42#10625329—22no—
43#10625329—41no—
44C2×C47⋊C8—41no—
45C47⋊C16—22no—
46C23×C47—41no—
47C23×C47SD1611yescharacteristic
48Q8×C47—22no—
49Q8×C47—41no—
50D4×C47—22no—
51D4×C47—42no—
52D4×C47—42no—
53D4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—42no—
56C2×C4×C47—42no—
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47D811yescharacteristic
60C2×C4×C47D811yescharacteristic
61C2×C4×C47SD1611yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C8×C47C22⋊C411yescharacteristic
64C8×C47C22⋊C411yescharacteristic
65C8×C47C22×C411yescharacteristic
66C8×C47C2×D411yescharacteristic
67C47⋊C8—42no—
68C22×C47—41no—
69C22×C47—42no—
70C22×C47—82no—
71C22×C47#10211yescharacteristic
72C22×C47#10211yescharacteristic
73C22×C47C2×SD1611yescharacteristic
74C4×C47—42no—
75C4×C47#10211yescharacteristic
76C4×C47#10211yescharacteristic
77C4×C47C2×C22⋊C411yescharacteristic
78C4×C47C2×D811yescharacteristic
79#2148—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—21no—
82C2×C47—21no—
83C2×C47—82no—
84C2×C47C2×#10211yescharacteristic
85C2×#135D4711yescharacteristic
86C2×M32—471no—
87C2×#108—471no—
88#362—472no—
89#361—472no—
90C47#214811yescharacteristic, complemented, Sylow
91C2×#41—21no—
92#135—21no—
93#135—21no—
94#135Dic4712yes—
95#135Dic4712yes—
96C2×Q16C2×D4711yescharacteristic
97C2×SD16—21no—
98C2×D8C2×D4711yescharacteristic
99C2×M16—941no—
100C22×C8C2×D4711yescharacteristic
101M32—472no—
102M32—941no—
103C2×C16—941no—
104#108—472no—
105#108—941no—
106#41—22no—
107#41—22no—
108#41—41no—
109#41—41no—
110C2×Q8—21no—
111C2×D4—21no—
112C2×D4—41no—
113C22×C4—41no—
114C22×C4C22⋊D4711yescharacteristic
115Q16—21no—
116Q16C2×Dic4712yes—
117SD16—22no—
118SD16—22no—
119D8—21no—
120D8C2×Dic4712yes—
121M16—942no—
122M16—1881no—
123C2×C8—1881no—
124C2×C8C2×Dic4711yescharacteristic
125C2×C8C2×Dic4711yescharacteristic
126C2×C8C22⋊D4711yescharacteristic
127C2×C8C22⋊D4711yescharacteristic
128C2×C8C22⋊D4711yescharacteristic
129C2×C8C22×D4711yescharacteristic
130C16—942no—
131C23—41no—
132C23#1062533511yescharacteristic
133Q8—22no—
134Q8—41no—
135D4—22no—
136D4—42no—
137D4—42no—
138D4—41no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4#1062533411yescharacteristic
143C2×C4#1062533411yescharacteristic
144C2×C4#1062533511yescharacteristic
145C2×C4C22⋊Dic4711yescharacteristic
146C2×C4C22⋊Dic4711yescharacteristic
147C2×C4C2×C22⋊D4711yescharacteristic
148C8—1882no—
149C8C22⋊Dic4711yescharacteristic
150C8C22⋊Dic4711yescharacteristic
151C8C22×Dic4711yescharacteristic
152C8C2×C22⋊D4711yescharacteristic
153C22—41no—
154C22—42no—
155C22—82no—
156C22#1309394511yescharacteristic
157C22#1309394511yescharacteristic
158C22C2×#1062533511yescharacteristic
159C4—42no—
160C4#1309394511yescharacteristic
161C4#1309394511yescharacteristic
162C4C2×C22⋊Dic4711yescharacteristic
163C4C2×#1062533411yescharacteristic
164C2—21no—
165C2—21no—
166C2—21no—
167C2—82no—
168C2C2×#1309394511yescharacteristic
subgroupG/H
centerC4#13093945
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC2×#135×C47C2
socleC2×C47C2×#102
hypercenterC2×#135D47
hypocenterC47#2148
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13093964C2semidirect
2. C2×#13093960C2semidirect
3. #15688939C2semidirect
4. #15688936C2semidirect
90. C47#2148semidirect