Finite Group Databasebeta

← #20242616

Subgroups — #20242616

Order 6016.

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

normal subgroups only

This group has 212 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#15689473C211yesmaximal, characteristic, complemented
2#15689403C211yesmaximal, characteristic, complemented
3#15689328C211yesmaximal, characteristic, complemented
4#15688872C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#555C211yesmaximal, characteristic
8C2×#10625335—21no—
9#13094024C2211yescharacteristic
10#13093957—21no—
11C4⋊(C47⋊C8)C2211yescharacteristic
12C4⋊(C47⋊C8)C2211yescharacteristic
13#13093948—22no—
14#13093947—21no—
15#13093945—21no—
16C4×C47⋊C8C2211yescharacteristic
17C4⋊Q8×C47C2211yescharacteristic
18#124×C47—22no—
19#121×C47—21no—
20#121×C47—21no—
21C4×D4×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23#117×C47—21no—
24#117×C47—21no—
25C2×Q8×C47D412yes—
26C2×D4×C47—22no—
27C2×D4×C47D411yescharacteristic
28C2×D4×C47D411yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C2×Dic94—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47D411yescharacteristic
35C4⋊C4×C47D411yescharacteristic
36C22⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C42×C47—22no—
41C42×C47C2311yescharacteristic
42#10625335—42no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49C23×C47—21no—
50Q8×C47—42no—
51D4×C47—21no—
52D4×C47—21no—
53D4×C47—21no—
54D4×C47—21no—
55D4×C47—82no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—22no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×Dic47—41no—
67Dic94—41no—
68Dic94—41no—
69C47⋊C8—41no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47#12011yescharacteristic
79C4×C47—21no—
80C4×C47—41no—
81C4×C47—41no—
82C4×C47—42no—
83C4×C47#13511yescharacteristic
84C4×C47#13511yescharacteristic
85C4×C47AGL(1,ℤ/8)11yescharacteristic
86C4×C47#13711yescharacteristic
87Dic47—81no—
88#1646—471nomaximal, Sylow
89C2×C47—81no—
90C2×C47—81no—
91C2×C47#44911yescharacteristic
92C2×C47#45211yescharacteristic
93C2×C47#45511yescharacteristic
94#555D4711yescharacteristic
95#487—471no—
96#474—471no—
97#461—471no—
98#333—471no—
99D4⋊C8—471no—
100D4⋊C8—471no—
101C47#164611yescharacteristic, complemented, Sylow
102C2×SD16—941no—
103C4⋊Q8—471no—
104C4⋊Q8C2×D4711yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D4711yescharacteristic
109C4×D4C2×D4711yescharacteristic
110#117—21no—
111#117—21no—
112#107—941no—
113C4⋊C8—471no—
114C4⋊C8—471no—
115#103—942no—
116#103—941no—
117#102—941no—
118C4×C8—471no—
119C2×Q8—941no—
120C2×Q8C22⋊D4712yes—
121C2×D4—22no—
122C2×D4C22⋊D4711yescharacteristic
123C2×D4C22⋊D4711yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—1882no—
127C2×C8—941no—
128C2×C8—941no—
129C2×C8—941no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4C22⋊D4711yescharacteristic
135C4⋊C4C22⋊D4711yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D4711yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—1881no—
146Q8—1881no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—1881no—
160C2×C4C2×C22⋊D4711yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C2×C4C2×C22⋊D4711yescharacteristic
163C8—1881no—
164C8—1881no—
165C8—1881no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1309399311yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—3761no—
178C4#1309404411yescharacteristic
179C4#1309404411yescharacteristic
180C4#1309404911yescharacteristic
181C4#1309405411yescharacteristic
182C2—81no—
183C2—81no—
184C2#1568926811yescharacteristic
185C2#1568928511yescharacteristic
186C2#1568930111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#555C2
socleC22×C47#120
hypercenter#555D47
hypocenterC47#1646
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #15689473C2semidirect
2. #15689403C2semidirect
3. #15689328C2semidirect
4. #15688872C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
101. C47#1646semidirect