Finite Group Databasebeta

← #20242449

Subgroups — #20242449

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#15689500C211yesmaximal, characteristic
3#15689324C211yesmaximal, characteristic, complemented
4#15689323C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625325—21no—
9C2×#10625336—21no—
10C2×D376—22no—
11#13094021C2211yescharacteristic
12#13094021C2211yescharacteristic
13#13094013—21no—
14#13094012—21no—
15#13094009—22no—
16C4×Dic94C2211yescharacteristic
17C4×D188—21no—
18#13093986—21no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093946—21no—
21#13093944—21no—
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47D411yescharacteristic
26C2×D188—21no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C2×C4×D47—22no—
33C2×Dic94D411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C42×C47—21no—
39C42×C47C2311yescharacteristic
40#10625336—42no—
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—22no—
43(C2×D47)⋊C4—22no—
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48D376—44no—
49#10625325—42no—
50C22×D47—22no—
51C22×D47—41no—
52Q8×C47—21no—
53Q8×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×Dic47—21no—
60C2×Dic47—21no—
61D188—42no—
62D188—42no—
63D188—41no—
64D188—41no—
65D188—41no—
66D188—41no—
67D188—41no—
68D188—41no—
69D188—41no—
70D188—41no—
71C4×D47—82no—
72Dic94—21no—
73Dic94—21no—
74C8×C47—22no—
75C8×C47—41no—
76C47⋊C8—41no—
77C22×C47#12011yescharacteristic
78C2×D47—42no—
79C2×D47—42no—
80C2×D47—42no—
81C2×D47—81no—
82C2×D47—81no—
83C2×D47—81no—
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#44911yescharacteristic
95C2×C47#44911yescharacteristic
96C2×C47#45311yescharacteristic
97D47—82no—
98D47—161no—
99#559—471no—
100#493—471no—
101#460—471no—
102#460—471no—
103#331—471no—
104Q8⋊C8—471no—
105Q8⋊C8D4711yescharacteristic, complemented
106C47#162011yescharacteristic, complemented, Sylow
107C2×SD16—941no—
108C2×SD16—941no—
109C2×D8—942no—
110#127—471no—
111#127—471no—
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—941no—
122#102—941no—
123C4×C8C2×D4711yescharacteristic
124C2×Q8—471no—
125C2×Q8D18811yescharacteristic
126C2×D4—472no—
127C2×D4—941no—
128C2×D4—941no—
129C2×D4—941no—
130C2×D4—941no—
131C2×D4—941no—
132C22×C4—942no—
133SD16—1882no—
134SD16—1882no—
135D8—1884no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—941no—
139C4⋊C4—21no—
140C4⋊C4—471no—
141C4⋊C4—941no—
142C4⋊C4D18811yescharacteristic
143C22⋊C4—942no—
144C22⋊C4—942no—
145C22⋊C4—942no—
146C42—21no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—942no—
150C23—1881no—
151Q8—21no—
152Q8—21no—
153Q8—941no—
154Q8—941no—
155D4—1882no—
156D4—1882no—
157D4—1881no—
158D4—1881no—
159D4—1881no—
160D4—1881no—
161D4—1881no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—3762no—
170C2×C4C2×D18811yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4D4×D4711yescharacteristic
173C8—22no—
174C8—41no—
175C8—1881no—
176C22—3761no—
177C22—3761no—
178C22—3761no—
179C22—1882no—
180C22—1882no—
181C22—1882no—
182C22#1309399411yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1881no—
187C4—1881no—
188C4#1309404611yescharacteristic
189C4#1309404711yescharacteristic
190C4#1309405111yescharacteristic
191C4#1309405211yescharacteristic
192C2—3762no—
193C2—7521no—
194C2#1568927011yescharacteristic
195C2#1568927111yescharacteristic
196C2#1568929211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1620
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
3. #15689324C2semidirect
4. #15689323C2semidirect
5. #15688866C2semidirect
6. #15688855C2semidirect
7. C47×Q8⋊C8C2semidirect
105. Q8⋊C8D47semidirect
106. C47#1620semidirect