Finite Group Databasebeta

← #20245038

Subgroups — #20245038

Order 6016.

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

normal subgroups only

This group has 266 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#15689107C211yesmaximal, characteristic, complemented
2#15689097C211yesmaximal, characteristic, complemented
3#15688910C214yesmaximal, complemented
4C47×#535C211yesmaximal, characteristic
5C2×#10625329—21no—
6#13093983—21no—
7#13093943—21no—
8#13093941C2212yes—
9#13093939—21no—
10#13093939C2212yes—
11C2×#41×C47C2211yescharacteristic
12C22×D4×C47C411yescharacteristic, complemented
13#127×C47—21no—
14#124×C47—21no—
15#121×C47—21no—
16#121×C47—21no—
17#120×C47C412yescomplemented
18#120×C47C2212yes—
19#117×C47C411yescharacteristic, complemented
20C24×C47C2×C412yes—
21#41×C47—41no—
22#41×C47—41no—
23C2×Q8×C47D411yescharacteristic
24C2×D4×C47—22no—
25C2×D4×C47—22no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—41no—
29C2×D4×C47—41no—
30C2×D4×C47C2×C411yescharacteristic
31C2×D4×C47D411yescharacteristic
32C2×D4×C47C2311yescharacteristic
33C22×C4×C47C2×C411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C4⋊C4×C47—21no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47C2×C412yes—
40C42×C47—21no—
41C22⋊Dic47—22no—
42C4⋊Dic47—41no—
43C4×Dic47—41no—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47—22no—
48C23×C47—42no—
49C23×C47—82no—
50C23×C47C22⋊C411yescharacteristic
51C23×C47C22×C411yescharacteristic
52C23×C47C2×D411yescharacteristic
53Q8×C47—41no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—41no—
57D4×C47—42no—
58D4×C47—41no—
59D4×C47—41no—
60D4×C47—82no—
61D4×C47—82no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47C22⋊C411yescharacteristic
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×Dic47—42no—
74C47⋊C8—42no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47—42no—
82C22×C47—42no—
83C22×C47—42no—
84C22×C47—84no—
85C22×C47C2×C22⋊C411yescharacteristic
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—42no—
90C4×C47#9911yescharacteristic
91C4×C47#9911yescharacteristic
92Dic47—82no—
93#2122—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—41no—
96C2×C47—41no—
97C2×C47—41no—
98C2×C47—82no—
99C2×C47C2×#9911yescharacteristic
100#535D4711yescharacteristic
101#413—471no—
102#410—471no—
103AΣL(1,𝔽16)—474no—
104C47#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D4711yescharacteristic
106C22×D4Dic4711yescharacteristic, complemented
107C2×M16—941no—
108#127—21no—
109#124—21no—
110#121—21no—
111#121—21no—
112#120Dic4712yescomplemented
113#120C2×D4712yes—
114#117—941no—
115#117Dic4711yescharacteristic, complemented
116#101—941no—
117#100—472no—
118#99—472no—
119#99—941no—
120C24C2×Dic4712yes—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D4711yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic4711yescharacteristic
131C2×D4C22⋊D4711yescharacteristic
132C2×D4C22×D4711yescharacteristic
133C22×C4C2×Dic4711yescharacteristic
134C22×C4C22⋊D4711yescharacteristic
135C22×C4C22⋊D4711yescharacteristic
136M16—942no—
137M16—1881no—
138C2×C8—1881no—
139C4⋊C4—21no—
140C4⋊C4—1881no—
141C22⋊C4—22no—
142C22⋊C4—22no—
143C22⋊C4—942no—
144C22⋊C4C2×Dic4712yes—
145C42—21no—
146C42—1881no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23C22⋊Dic4711yescharacteristic
151C23C22×Dic4711yescharacteristic
152C23C2×C22⋊D4711yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—42no—
158D4—41no—
159D4—41no—
160D4—82no—
161D4—82no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—1882no—
170C2×C4C22⋊Dic4711yescharacteristic
171C2×C4C22⋊Dic4711yescharacteristic
172C2×C4C22⋊Dic4711yescharacteristic
173C2×C4C2×C22⋊D4711yescharacteristic
174C8—1882no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—84no—
185C22C2×C22⋊Dic4711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—42no—
190C4—3762no—
191C4#1309393911yescharacteristic
192C4#1309393911yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—82no—
198C2C2×#1309393911yescharacteristic
subgroupG/H
centerC2C2×#13093939
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#535C2
socleC2×C47C2×#99
hypercenter#535D47
hypocenterC47#2122
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689107C2semidirect
2. #15689097C2semidirect
3. #15688910C2semidirect
12. C22×D4×C47C4semidirect
17. #120×C47C4semidirect
19. #117×C47C4semidirect
104. C47#2122semidirect
106. C22×D4Dic47semidirect
112. #120Dic47semidirect
115. #117Dic47semidirect