Finite Group Databasebeta

← #20245073

Subgroups — #20245073

Order 6016.

250 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689107C212yesmaximal, complemented
2#15688922C212yesmaximal, complemented
3#15688920C212yesmaximal, complemented
4C47×#532C211yesmaximal, characteristic
5C2×#10625329—22no—
6#13093943C2214yes—
7#13093941—22no—
8C2×#41×C47C411yescharacteristic
9C2×#41×C47C2211yescharacteristic
10C4⋊Q8×C47C2211yescharacteristic
11#127×C47C411yescharacteristic
12#124×C47C411yescharacteristic
13#124×C47C2211yescharacteristic
14#121×C47—22no—
15C4×D4×C47—22no—
16C2×C42×C47C411yescharacteristic
17#41×C47—41no—
18#41×C47—41no—
19#41×C47—41no—
20#41×C47—41no—
21C2×Q8×C47C2×C411yescharacteristic
22C2×Q8×C47C2311yescharacteristic
23C2×D4×C47—22no—
24C2×D4×C47—21no—
25C2×D4×C47C2×C411yescharacteristic
26C2×D4×C47C2×C411yescharacteristic
27C2×D4×C47D412yes—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47C2×C411yescharacteristic
31C22×C4×C47D412yes—
32C4⋊C4×C47—22no—
33C22⋊C4×C47—22no—
34C22⋊C4×C47—22no—
35C42×C47—21no—
36C42×C47C2×C411yescharacteristic
37C42×C47C2×C411yescharacteristic
38#10625329—24no—
39#10625329—42no—
40C2×C47⋊C8—42no—
41C23×C47—21no—
42C23×C47C22⋊C412yes—
43C23×C47C22⋊C411yescharacteristic
44Q8×C47—41no—
45Q8×C47—41no—
46D4×C47—41no—
47D4×C47—42no—
48D4×C47—41no—
49D4×C47—44no—
50D4×C47—42no—
51C2×C4×C47—21no—
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—42no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D412yes—
64C47⋊C8—44no—
65C22×C47—21no—
66C22×C47—22no—
67C22×C47—41no—
68C22×C47—42no—
69C22×C47—42no—
70C22×C47—41no—
71C22×C47C2×C22⋊C411yescharacteristic
72C4×C47—22no—
73C4×C47—22no—
74C4×C47—21no—
75C4×C47—41no—
76C4×C47—41no—
77C4×C47#9911yescharacteristic
78C4×C47#9911yescharacteristic
79#2132—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—41no—
82C2×C47—42no—
83C2×C47—81no—
84C2×C47C2×#9911yescharacteristic
85#532D4711yescharacteristic
86#413—472no—
87#356—472no—
88#355—472no—
89C47#213211yescharacteristic, complemented, Sylow
90C2×#41Dic4711yescharacteristic
91C2×#41C2×D4711yescharacteristic
92C2×M16—942no—
93C4⋊Q8C2×D4711yescharacteristic
94#127Dic4711yescharacteristic
95#124Dic4711yescharacteristic
96#124C2×D4711yescharacteristic
97#121—22no—
98C4×D4—22no—
99C2×C42Dic4711yescharacteristic
100#101—474no—
101#100—942no—
102#41—41no—
103#41—41no—
104#41—41no—
105#41—41no—
106C2×Q8C2×Dic4711yescharacteristic
107C2×Q8C22×D4711yescharacteristic
108C2×D4—22no—
109C2×D4—21no—
110C2×D4C2×Dic4711yescharacteristic
111C2×D4C2×Dic4711yescharacteristic
112C2×D4C22⋊D4712yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4C2×Dic4711yescharacteristic
116C22×C4C22⋊D4712yes—
117M16—944no—
118M16—1882no—
119C2×C8—1882no—
120C4⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C42—21no—
124C42C2×Dic4711yescharacteristic
125C42C2×Dic4711yescharacteristic
126C23—21no—
127C23C22⋊Dic4712yes—
128C23C22⋊Dic4711yescharacteristic
129Q8—41no—
130Q8—41no—
131D4—41no—
132D4—42no—
133D4—41no—
134D4—44no—
135D4—42no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4C22⋊Dic4711yescharacteristic
147C2×C4C22×Dic4711yescharacteristic
148C2×C4C2×C22⋊D4712yes—
149C8—1884no—
150C22—21no—
151C22—22no—
152C22—41no—
153C22—42no—
154C22—42no—
155C22—41no—
156C22C2×C22⋊Dic4711yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4#1309393911yescharacteristic
163C4#1309393911yescharacteristic
164C2—21no—
165C2—41no—
166C2—42no—
167C2—81no—
168C2C2×#1309393911yescharacteristic
subgroupG/H
centerC4#13093939
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#532C2
socleC2×C47C2×#99
hypercenter#532D47
hypocenterC47#2132
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689107C2semidirect
2. #15688922C2semidirect
3. #15688920C2semidirect
89. C47#2132semidirect