Finite Group Databasebeta

← #20244836

Subgroups — #20244836

Order 6016.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13093955C211yesmaximal, characteristic, complemented
2#15689124C211yesmaximal, characteristic
3#15689090C211yesmaximal, characteristic
4#15688892C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093955—22no—
13#13093948—21no—
14#13093945—21no—
15C22⋊(C47⋊C8)—22no—
16C2×#41×C47C2211yescharacteristic
17C2×M16×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19#103×C47—21no—
20#102×C47—21no—
21#41×C47—21no—
22#41×C47—21no—
23#41×C47—21no—
24#41×C47—21no—
25C2×Q8×C47D411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32M16×C47—21no—
33M16×C47—21no—
34C2×C8×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊Dic47—21no—
38C4⋊Dic47—21no—
39#10625329—21no—
40#10625329—21no—
41#10625329—21no—
42#10625329—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D412yes—
48C23×C47—21no—
49C23×C47#4111yescharacteristic
50Q8×C47—21no—
51Q8×C47—21no—
52D4×C47—21no—
53D4×C47—21no—
54D4×C47—41no—
55D4×C47—41no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—81no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×Dic47—41no—
68C2×Dic47—81no—
69C8×C47—41no—
70C47⋊C8—22no—
71C47⋊C8—41no—
72C47⋊C8—41no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47#12111yescharacteristic
79C22×C47#12611yescharacteristic
80C22×C47#12611yescharacteristic
81C4×C47—41no—
82C4×C47—81no—
83C4×C47#12311yescharacteristic
84C4×C47#12311yescharacteristic
85C4×C47#12311yescharacteristic
86C4×C47#12411yescharacteristic
87Dic47—81no—
88#2079—471nomaximal, Sylow
89C2×C47—21no—
90C2×C47—21no—
91C2×C47—81no—
92C2×C47#39711yescharacteristic
93C2×C47#47111yescharacteristic
94C2×C47#47111yescharacteristic
95C2×#106—471no—
96#417—471no—
97#417D4711yescharacteristic
98#408—471no—
99#343—471no—
100#343—471no—
101#341—471no—
102C47#207911yescharacteristic, complemented, Sylow
103C2×#41C2×D4711yescharacteristic
104C2×M16—471no—
105C2×M16—471no—
106C2×M16C2×D4711yescharacteristic
107C22×C8—471no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4C2×D4711yescharacteristic
110#106—942no—
111#103—21no—
112#103—941no—
113#102—21no—
114#102—941no—
115C22⋊C8—942no—
116#41—21no—
117#41—21no—
118#41—21no—
119#41—21no—
120C2×Q8C22⋊D4711yescharacteristic
121C2×D4—21no—
122C2×D4C22⋊D4711yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—941no—
126C22×C4C22×D4711yescharacteristic
127M16—21no—
128M16—21no—
129M16—941no—
130M16—941no—
131M16—941no—
132M16—941no—
133C2×C8—21no—
134C2×C8—472no—
135C2×C8—941no—
136C2×C8—941no—
137C2×C8—941no—
138C2×C8—941no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C23—21no—
144C23#1062535211yescharacteristic
145Q8—21no—
146Q8—21no—
147D4—21no—
148D4—21no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—3761no—
157C2×C4—1881no—
158C2×C4#1062535011yescharacteristic
159C2×C4#1062535011yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4#1062535211yescharacteristic
162C2×C4#1062535211yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—41no—
165C8—942no—
166C8—1881no—
167C8—1881no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22#1309399611yescharacteristic
174C22#1309401711yescharacteristic
175C22#1309401711yescharacteristic
176C4—41no—
177C4—81no—
178C4—3761no—
179C4#1309400511yescharacteristic
180C4#1309400611yescharacteristic
181C4#1309400711yescharacteristic
182C4#1309401011yescharacteristic
183C2—21no—
184C2—21no—
185C2—81no—
186C2#1568905111yescharacteristic
187C2#1568938411yescharacteristic
188C2#1568938811yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#121
hypercenter#417D47
hypocenterC47#2079
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#13093955C2semidirect
4. #15688892C2semidirect
5. #15688891C2semidirect
6. #15688887C2semidirect
102. C47#2079semidirect