Finite Group Databasebeta

← #20242473

Subgroups — #20242473

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#15689838C211yesmaximal, characteristic, complemented
2#15689496C211yesmaximal, characteristic, complemented
3#15689319C211yesmaximal, characteristic, complemented
4#15689318C211yesmaximal, characteristic, complemented
5#15688871C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625325—22no—
9C2×D376—21no—
10C2×#10625334—21no—
11#13094024C2211yescharacteristic
12#13094021C2211yescharacteristic
13#13094010—22no—
14#13093998—21no—
15#13093995—21no—
16C4×D188C2211yescharacteristic
17#13093983—21no—
18#13093982—21no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093946—21no—
21#13093944—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C2×C22⋊D47—22no—
28C2×D188—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188D411yescharacteristic
32C2×C4×D47—21no—
33C2×Dic94D412yes—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—22no—
40#10625334—42no—
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47D411yescharacteristic
46C4×Dic47—22no—
47C2×C47⋊C8—21no—
48D376—42no—
49#10625325—44no—
50C23×C47—21no—
51C22×D47—21no—
52C22×D47—41no—
53D4×C47—21no—
54D4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C22⋊D47—82no—
62C2×Dic47—21no—
63C2×Dic47—22no—
64D188—21no—
65D188—21no—
66D188—42no—
67D188—41no—
68D188—41no—
69D188—41no—
70D188—41no—
71C4×D47—41no—
72C4×D47—41no—
73Dic94—42no—
74C8×C47—22no—
75C8×C47—41no—
76C47⋊C8—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47#12011yescharacteristic
81C2×D47—41no—
82C2×D47—41no—
83C2×D47—41no—
84C2×D47—81no—
85C2×D47—81no—
86C2×D47—81no—
87C4×C47—21no—
88C4×C47—41no—
89C4×C47#13511yescharacteristic
90C4×C47#13511yescharacteristic
91C4×C47AGL(1,ℤ/8)11yescharacteristic
92C4×C47AGL(1,ℤ/8)11yescharacteristic
93Dic47—41no—
94Dic47—42no—
95#1624—471nomaximal, Sylow
96C2×C47—81no—
97C2×C47#44911yescharacteristic
98C2×C47#44911yescharacteristic
99C2×C47#45311yescharacteristic
100D47—81no—
101D47—161no—
102#555—471no—
103#492—471no—
104#459—471no—
105#459—471no—
106#333—471no—
107D4⋊C8—471no—
108D4⋊C8D4711yescharacteristic, complemented
109C47#162411yescharacteristic, complemented, Sylow
110C2×SD16—942no—
111C2×D8—941no—
112C2×D8—941no—
113C4⋊Q8—471no—
114#127—471no—
115#124—942no—
116#121—941no—
117#121—941no—
118C4×D4—471no—
119C4×D4C2×D4711yescharacteristic
120#117—941no—
121#117—941no—
122C4⋊C8—471no—
123C4⋊C8C2×D4711yescharacteristic
124#102—941no—
125#102—941no—
126C4×C8C2×D4711yescharacteristic
127C2×Q8—472no—
128C2×D4—471no—
129C2×D4—942no—
130C2×D4—941no—
131C2×D4—941no—
132C2×D4—941no—
133C2×D4D18811yescharacteristic
134C22×C4—21no—
135C22×C4—941no—
136SD16—1884no—
137D8—1882no—
138D8—1882no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—941no—
142C4⋊C4—471no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4D18811yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—942no—
148C22⋊C4—942no—
149C22⋊C4—941no—
150C42—942no—
151C42C22×D4711yescharacteristic
152C23—21no—
153C23—941no—
154C23—1881no—
155Q8—1882no—
156D4—21no—
157D4—21no—
158D4—941no—
159D4—941no—
160D4—3762no—
161D4—1882no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165D4—1881no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—941no—
170C2×C4—942no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4C2×D18811yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C2×C4D4×D4711yescharacteristic
176C8—22no—
177C8—41no—
178C8—1881no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—3761no—
183C22—3761no—
184C22—3761no—
185C22—1881no—
186C22—1881no—
187C22—1881no—
188C22#1309399411yescharacteristic
189C4—21no—
190C4—41no—
191C4—1881no—
192C4—1882no—
193C4#1309404511yescharacteristic
194C4#1309404611yescharacteristic
195C4#1309404811yescharacteristic
196C4#1309405211yescharacteristic
197C2—81no—
198C2—3761no—
199C2—7521no—
200C2#1568926911yescharacteristic
201C2#1568927011yescharacteristic
202C2#1568929211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1624
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. #15689496C2semidirect
3. #15689319C2semidirect
4. #15689318C2semidirect
5. #15688871C2semidirect
6. #15688852C2semidirect
7. C47×D4⋊C8C2semidirect
108. D4⋊C8D47semidirect
109. C47#1624semidirect