Finite Group Databasebeta

← #20245079

Subgroups — #20245079

Order 6016.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689687C211yesmaximal, characteristic
2#15689107C211yesmaximal, characteristic, complemented
3#15688919C214yesmaximal, complemented
4C47×#413C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic
6C2×#10625329—21no—
7#13094020C412yes—
8#13094013C2212yes—
9#13093998—21no—
10#13093998—21no—
11#13093992—21no—
12#13093992—21no—
13#13093983C411yescharacteristic
14#13093943C2212yescomplemented
15#13093941—21no—
16C2×#41×C47C2211yescharacteristic
17C2×M16×C47—21no—
18#101×C47C2212yescomplemented
19#100×C47—21no—
20C23×D47—21no—
21#41×C47—41no—
22#41×C47—41no—
23C2×Q8×C47C2311yescharacteristic
24C2×D4×C47C2×C411yescharacteristic
25C2×D4×C47D411yescharacteristic
26C2×D4×C47D411yescharacteristic
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32C2×D188—21no—
33C2×D188—41no—
34C2×D188—41no—
35C2×D188C2×C412yes—
36M16×C47—22no—
37M16×C47—41no—
38C2×C8×C47—41no—
39C22⋊Dic47—21no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42C4⋊Dic47—21no—
43C4×Dic47C2×C412yes—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22⋊C411yescharacteristic
49C23×C47C22⋊C411yescharacteristic
50C22×D47—22no—
51C22×D47—42no—
52C22×D47—82no—
53Q8×C47—41no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—41no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C22⋊D47—82no—
68C22⋊D47—82no—
69C2×Dic47—22no—
70D188—42no—
71D188—41no—
72D188—41no—
73C8×C47—42no—
74C47⋊C8—42no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47C2×C22⋊C411yescharacteristic
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47—84no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47#9911yescharacteristic
90C4×C47#9911yescharacteristic
91Dic47—42no—
92#2134—471nomaximal, Sylow
93C2×C47—21no—
94C2×C47—41no—
95C2×C47—41no—
96C2×C47—41no—
97C2×C47C2×#9911yescharacteristic
98D47—82no—
99#535—471no—
100#413—471no—
101#413D4711yescharacteristic, complemented
102#355—474no—
103C47#213411yescharacteristic, complemented, Sylow
104C2×#41C2×D4711yescharacteristic
105C22×D4—471no—
106C2×M16—21no—
107C2×M16—941no—
108#127—472no—
109#124—472no—
110#121—941no—
111#121—941no—
112#120—941no—
113#120—941no—
114#117—471no—
115#101—472no—
116#101C2×D4712yescomplemented
117#100—21no—
118#100—941no—
119C24—941no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D4711yescharacteristic
123C2×D4—472no—
124C2×D4—942no—
125C2×D4—942no—
126C2×D4—941no—
127C2×D4—1881no—
128C2×D4—1881no—
129C2×D4C4×D4711yescharacteristic
130C2×D4D18811yescharacteristic
131C2×D4C22⋊D4711yescharacteristic
132C22×C4C4×D4711yescharacteristic
133C22×C4D18811yescharacteristic
134C22×C4C22⋊D4711yescharacteristic
135M16—22no—
136M16—41no—
137M16—942no—
138M16—1881no—
139C2×C8—41no—
140C2×C8—1881no—
141C4⋊C4—941no—
142C22⋊C4—941no—
143C22⋊C4—942no—
144C22⋊C4—942no—
145C42—472no—
146C23—942no—
147C23—3762no—
148C23—1882no—
149C23(C2×D47)⋊C411yescharacteristic
150C23(C2×D47)⋊C411yescharacteristic
151C23(C2×D47)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—3762no—
157D4—3762no—
158D4—1882no—
159D4—1881no—
160D4—1881no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—942no—
168C2×C4(C2×D47)⋊C411yescharacteristic
169C2×C4C2×C4×D4711yescharacteristic
170C2×C4C2×D18811yescharacteristic
171C2×C4C2×C22⋊D4711yescharacteristic
172C8—42no—
173C8—1882no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—3764no—
181C22—1882no—
182C22—1882no—
183C22—1882no—
184C22C2×(C2×D47)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—1882no—
189C4#1309393811yescharacteristic
190C4#1309393811yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—3762no—
196C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#413C2
socleC2×C47C2×#99
hypercenter#413D47
hypocenterC47#2134
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #15689107C2semidirect
3. #15688919C2semidirect
4. C47×#413C2semidirect
14. #13093943C22semidirect
18. #101×C47C22semidirect
101. #413D47semidirect
103. C47#2134semidirect
116. #101C2×D47semidirect