Finite Group Databasebeta

← #20242541

Subgroups — #20242541

Order 6016.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689777C211yesmaximal, characteristic
2#15689474C211yesmaximal, characteristic, complemented
3#15689414C211yesmaximal, characteristic, complemented
4#15689413C211yesmaximal, characteristic, complemented
5#15688868C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094008—22no—
12#13094004—21no—
13#13093998—21no—
14C4×D188C2211yescharacteristic
15C2×C4⋊Dic47—21no—
16#13093956—21no—
17#13093955—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—22no—
20#13093946—21no—
21#13093945—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C2×C22⋊D47—22no—
28C22×Dic47—22no—
29#10625352—42no—
30#10625352—42no—
31C2×D188D411yescharacteristic
32C2×C4×D47—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47—21no—
39C42×C47C2311yescharacteristic
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42C4⋊Dic47—22no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47D412yes—
47C4⋊Dic47D411yescharacteristic
48C2×C47⋊C8—21no—
49C23×C47—21no—
50C22×D47—21no—
51D4×C47—21no—
52D4×C47SD1612yes—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C22⋊D47—44no—
60C2×Dic47—22no—
61C2×Dic47—21no—
62C2×Dic47—44no—
63C2×Dic47—41no—
64D188—21no—
65D188—21no—
66C4×D47—41no—
67C4×D47—41no—
68Dic94—41no—
69Dic94—41no—
70Dic94—42no—
71C8×C47—41no—
72C8×C47—41no—
73C47⋊C8—41no—
74C22×C47—22no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47#12011yescharacteristic
78C2×D47—41no—
79C2×D47—41no—
80C2×D47—41no—
81C4×C47—21no—
82C4×C47—41no—
83C4×C47C2×SD1611yescharacteristic
84C4×C47#13511yescharacteristic
85C4×C47AGL(1,ℤ/8)11yescharacteristic
86C4×C47#13711yescharacteristic
87Dic47—42no—
88Dic47—41no—
89Dic47—81no—
90#1635—471nomaximal, Sylow
91C2×C47—42no—
92C2×C47#45011yescharacteristic
93C2×C47#45211yescharacteristic
94C2×C47#45411yescharacteristic
95D47—81no—
96#547—471no—
97#487—471no—
98#476—471no—
99#476—471no—
100#332—471no—
101D4⋊C8—471no—
102D4⋊C8D4711yescharacteristic, complemented
103C47#163511yescharacteristic, complemented, Sylow
104C2×#41—941no—
105C4⋊Q8—471no—
106C4⋊Q8—471no—
107#123—942no—
108C22⋊Q8—941no—
109#121—941no—
110C4×D4—471no—
111C4×D4C2×D4711yescharacteristic
112C2×C4⋊C4—941no—
113#106—941no—
114#106—941no—
115C4⋊C8—471no—
116C4⋊C8C2×D4711yescharacteristic
117#103—942no—
118#102—941no—
119#102—941no—
120C4×C8C2×D4711yescharacteristic
121#41—1882no—
122#41—1882no—
123C2×Q8—941no—
124C2×Q8—941no—
125C2×D4—471no—
126C2×D4—942no—
127C2×D4D18811yescharacteristic
128C22×C4—21no—
129C22×C4—942no—
130C22×C4—941no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—941no—
134C4⋊C4—472no—
135C4⋊C4—471no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4D18811yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—942no—
143C22⋊C4—941no—
144C42C22×D4711yescharacteristic
145C23—21no—
146C23—941no—
147Q8—1882no—
148Q8—1881no—
149Q8—1881no—
150D4—21no—
151D4—941no—
152D4—941no—
153D4—1884no—
154D4#1062532512yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—941no—
159C2×C4—942no—
160C2×C4—1881no—
161C2×C4—1884no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4C2×D18811yescharacteristic
165C2×C4D4×D4711yescharacteristic
166C2×C4D4×D4711yescharacteristic
167C8—41no—
168C8—41no—
169C8—1881no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—1881no—
174C22—1881no—
175C22—1881no—
176C22#1309399411yescharacteristic
177C4—21no—
178C4—41no—
179C4—3761no—
180C4—1881no—
181C4—1882no—
182C4C2×#1062532511yescharacteristic
183C4#1309404311yescharacteristic
184C4#1309405211yescharacteristic
185C4#1309405311yescharacteristic
186C2—42no—
187C2—3761no—
188C2#1568927611yescharacteristic
189C2#1568928611yescharacteristic
190C2#1568929711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1635
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
2. #15689474C2semidirect
3. #15689414C2semidirect
4. #15689413C2semidirect
5. #15688868C2semidirect
6. #15688852C2semidirect
7. C47×D4⋊C8C2semidirect
102. D4⋊C8D47semidirect
103. C47#1635semidirect