Finite Group Databasebeta

← #20242501

Subgroups — #20242501

Order 6016.

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

normal subgroups only

This group has 216 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#15689846C211yesmaximal, characteristic, complemented
2#15689470C211yesmaximal, characteristic, complemented
3#15689323C211yesmaximal, characteristic, complemented
4#15689319C211yesmaximal, characteristic
5#15688870C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625336—21no—
9C2×D376—21no—
10#13094024C2211yescharacteristic
11#13094021C2211yescharacteristic
12#13094019—22no—
13#13094012—21no—
14#13094000—21no—
15C4×Dic94—21no—
16C4×D188C2211yescharacteristic
17#13093982—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093946—21no—
20#13093946—22no—
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×D188D411yescharacteristic
30C2×C4×D47—21no—
31C2×Dic94—21no—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D411yescharacteristic
36C42×C47—21no—
37C42×C47C2311yescharacteristic
38#10625336—42no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D412yes—
45Dic47⋊C4—22no—
46C4×Dic47—22no—
47C2×C47⋊C8—21no—
48D376—42no—
49C22×D47—21no—
50C22×D47—41no—
51Q8×C47—21no—
52Q8×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—22no—
60D188—21no—
61D188—21no—
62D188—42no—
63D188—41no—
64D188—41no—
65D188—41no—
66D188—41no—
67C4×D47—41no—
68C4×D47—41no—
69Dic94—41no—
70Dic94—41no—
71C8×C47—41no—
72C8×C47—41no—
73C47⋊C8—41no—
74C22×C47#12011yescharacteristic
75C2×D47—41no—
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—81no—
79C2×D47—81no—
80C2×D47—81no—
81C4×C47—21no—
82C4×C47—41no—
83C4×C47—41no—
84C4×C47#13511yescharacteristic
85C4×C47#13511yescharacteristic
86C4×C47AGL(1,ℤ/8)11yescharacteristic
87C4×C47AGL(1,ℤ/8)11yescharacteristic
88Dic47—42no—
89Dic47—41no—
90#1628—471nomaximal, Sylow
91C2×C47#44911yescharacteristic
92C2×C47#44911yescharacteristic
93C2×C47#45411yescharacteristic
94D47—81no—
95D47—161no—
96#556—471no—
97#486—471no—
98#460—471no—
99#459—471no—
100#332—471no—
101Q8⋊C8D4711yescharacteristic, complemented
102D4⋊C8—471no—
103C47#162811yescharacteristic, complemented, Sylow
104C2×SD16—941no—
105C2×D8—941no—
106C4⋊Q8—471no—
107#127—471no—
108#126—942no—
109#124—941no—
110C22⋊Q8—941no—
111C4×Q8—941no—
112C4×Q8C2×D4711yescharacteristic
113C4×D4—471no—
114#117—941no—
115C4⋊C8—471no—
116C4⋊C8C2×D4711yescharacteristic
117#102—941no—
118#102—942no—
119#102—941no—
120C4×C8C2×D4711yescharacteristic
121C2×Q8—941no—
122C2×Q8D18811yescharacteristic
123C2×D4—471no—
124C2×D4—941no—
125C2×D4—941no—
126C2×D4—941no—
127C22×C4—941no—
128SD16—1882no—
129D8—1882no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—941no—
133C4⋊C4—21no—
134C4⋊C4—471no—
135C4⋊C4—472no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4D18811yescharacteristic
139C22⋊C4—942no—
140C22⋊C4—942no—
141C22⋊C4—941no—
142C42—21no—
143C42—942no—
144C42C22×D4711yescharacteristic
145C23—941no—
146C23—1881no—
147Q8—21no—
148Q8—21no—
149Q8—1881no—
150Q8—1881no—
151D4—941no—
152D4—941no—
153D4—1882no—
154D4—1881no—
155D4—1881no—
156D4—1881no—
157D4—1881no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—941no—
161C2×C4—942no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4C2×D18811yescharacteristic
165C2×C4D4×D4711yescharacteristic
166C2×C4D4×D4711yescharacteristic
167C8—41no—
168C8—41no—
169C8—1881no—
170C22—3761no—
171C22—3761no—
172C22—3761no—
173C22—1881no—
174C22—1881no—
175C22—1881no—
176C22#1309399411yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—1881no—
181C4—1882no—
182C4#1309404611yescharacteristic
183C4#1309404711yescharacteristic
184C4#1309405111yescharacteristic
185C4#1309405211yescharacteristic
186C2—3761no—
187C2—7521no—
188C2#1568927011yescharacteristic
189C2#1568927111yescharacteristic
190C2#1568929711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1628
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. #15689846C2semidirect
2. #15689470C2semidirect
3. #15689323C2semidirect
5. #15688870C2semidirect
6. #15688852C2semidirect
7. C47×Q8⋊C8C2semidirect
101. Q8⋊C8D47semidirect
103. C47#1628semidirect