Finite Group Databasebeta

← #20242446

Subgroups — #20242446

Order 6016.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689858C211yesmaximal, characteristic, complemented
2#15689499C211yesmaximal, characteristic
3#15689320C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688853C211yesmaximal, characteristic, complemented
7C47×#460C211yesmaximal, characteristic, complemented
8C2×#10625335—21no—
9C2×#10625334—22no—
10#13094021C2211yescharacteristic
11#13094013—21no—
12#13094012—21no—
13#13094009—22no—
14C4×Dic94C2211yescharacteristic
15C4×D188—21no—
16#13093986—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093945—21no—
19C4×C47⋊C8C2211yescharacteristic
20C2×SD16×C47—21no—
21#127×C47C2211yescharacteristic
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×Q8×C47D411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C2×C4×D47—22no—
33C2×Dic94D411yescharacteristic
34SD16×C47—42no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C42×C47—21no—
39C42×C47C2311yescharacteristic
40#10625335—42no—
41#10625334—44no—
42(C2×D47)⋊C4—22no—
43(C2×D47)⋊C4—22no—
44(C2×D47)⋊C4—22no—
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—41no—
51C22×D47—22no—
52Q8×C47—21no—
53Q8×C47—21no—
54D4×C47—42no—
55D4×C47—41no—
56D4×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—21no—
65C2×Dic47—21no—
66D188—42no—
67D188—41no—
68D188—41no—
69D188—41no—
70D188—41no—
71C4×D47—82no—
72Dic94—21no—
73Dic94—21no—
74C8×C47—41no—
75C47⋊C8—22no—
76C47⋊C8—41no—
77C22×C47—81no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47#12011yescharacteristic
81C2×D47—42no—
82C2×D47—42no—
83C2×D47—42no—
84C4×C47—21no—
85C4×C47—41no—
86C4×C47—41no—
87C4×C47#13511yescharacteristic
88C4×C47#13511yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47AGL(1,ℤ/8)11yescharacteristic
91Dic47—41no—
92Dic47—41no—
93#1620—471nomaximal, Sylow
94C2×C47—161no—
95C2×C47#44911yescharacteristic
96C2×C47#44911yescharacteristic
97C2×C47#45311yescharacteristic
98D47—82no—
99#559—471no—
100#493—471no—
101#460—471no—
102#460D4711yescharacteristic, complemented
103#331—471no—
104Q8⋊C8—471no—
105Q8⋊C8—471no—
106C47#162011yescharacteristic, complemented, Sylow
107C2×SD16—21no—
108C2×SD16—941no—
109C2×D8—942no—
110#127—471no—
111#127C2×D4711yescharacteristic
112#124—941no—
113#124—941no—
114#123—942no—
115C4×Q8—471no—
116C4×Q8C2×D4711yescharacteristic
117C4×D4—941no—
118C4×D4—941no—
119C4⋊C8—471no—
120C4⋊C8C2×D4711yescharacteristic
121#102—21no—
122#102—941no—
123C4×C8—471no—
124C2×Q8—471no—
125C2×Q8C22⋊D4711yescharacteristic
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—472no—
130C2×D4—941no—
131C2×D4—941no—
132C22×C4—942no—
133SD16—42no—
134SD16—1882no—
135D8—1884no—
136C2×C8—21no—
137C2×C8—941no—
138C2×C8—941no—
139C4⋊C4—21no—
140C4⋊C4—471no—
141C4⋊C4—941no—
142C4⋊C4C22⋊D4711yescharacteristic
143C22⋊C4—942no—
144C22⋊C4—942no—
145C22⋊C4—942no—
146C42—21no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—41no—
150C23—942no—
151Q8—21no—
152Q8—21no—
153Q8—941no—
154Q8—941no—
155D4—42no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—1882no—
161D4—1881no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—3762no—
170C2×C4D4×D4711yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—41no—
174C8—942no—
175C8—1881no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—1882no—
180C22—1882no—
181C22—1882no—
182C22#1309399211yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1881no—
187C4—1881no—
188C4#1309404411yescharacteristic
189C4#1309404511yescharacteristic
190C4#1309405011yescharacteristic
191C4#1309405111yescharacteristic
192C2—161no—
193C2—3762no—
194C2#1568926611yescharacteristic
195C2#1568926711yescharacteristic
196C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#460C2
socleC22×C47#120
hypercenter#460D47
hypocenterC47#1620
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
3. #15689320C2semidirect
4. #15688866C2semidirect
5. Q8⋊(C47⋊C8)C2semidirect
6. #15688853C2semidirect
7. C47×#460C2semidirect
102. #460D47semidirect
106. C47#1620semidirect