Finite Group Databasebeta

← #20242614

Subgroups — #20242614

Order 6016.

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

normal subgroups only

This group has 212 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
2#15689475C211yesmaximal, characteristic, complemented
3#15689400C211yesmaximal, characteristic, complemented
4#15688871C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#461C211yesmaximal, characteristic, complemented
8#13094024C2211yescharacteristic
9#13094010—22no—
10#13093998—21no—
11#13093995—21no—
12C4×D188C2211yescharacteristic
13#13093983—21no—
14#13093982—21no—
15#13093957—21no—
16C4⋊(C47⋊C8)C2211yescharacteristic
17#13093947—22no—
18#13093944—21no—
19C4×C47⋊C8C2211yescharacteristic
20C2×SD16×C47—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#103×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C2×C22⋊D47—22no—
29C2×D188D411yescharacteristic
30C2×C4×D47—21no—
31C2×Dic94D412yes—
32SD16×C47—42no—
33C2×C8×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—22no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47D411yescharacteristic
45C4×Dic47—22no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49C22×D47—21no—
50Q8×C47—41no—
51Q8×C47—41no—
52D4×C47—21no—
53D4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—41no—
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—
66C4×D47—41no—
67C4×D47—41no—
68Dic94—42no—
69C8×C47—41no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47#12011yescharacteristic
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—41no—
79C4×C47—21no—
80C4×C47—41no—
81C4×C47—81no—
82C4×C47#13511yescharacteristic
83C4×C47#13511yescharacteristic
84C4×C47AGL(1,ℤ/8)11yescharacteristic
85C4×C47#13711yescharacteristic
86Dic47—41no—
87Dic47—42no—
88#1646—471nomaximal, Sylow
89C2×C47—81no—
90C2×C47#44911yescharacteristic
91C2×C47#45211yescharacteristic
92C2×C47#45511yescharacteristic
93D47—81no—
94#555—471no—
95#487—471no—
96#474—471no—
97#461D4711yescharacteristic, complemented
98#333—471no—
99D4⋊C8—471no—
100D4⋊C8—471no—
101C47#164611yescharacteristic, complemented, Sylow
102C2×SD16—21no—
103C4⋊Q8—471no—
104C4⋊Q8C2×D4711yescharacteristic
105#124—942no—
106#121—941no—
107#121—941no—
108C4×D4—471no—
109C4×D4C2×D4711yescharacteristic
110#117—941no—
111#117—941no—
112#107—941no—
113C4⋊C8—471no—
114C4⋊C8C2×D4711yescharacteristic
115#103—21no—
116#103—942no—
117#102—941no—
118C4×C8—471no—
119C2×Q8—21no—
120C2×Q8—472no—
121C2×D4—471no—
122C2×D4—942no—
123C2×D4C22⋊D4711yescharacteristic
124C22×C4—21no—
125C22×C4—941no—
126SD16—42no—
127C2×C8—21no—
128C2×C8—941no—
129C2×C8—941no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—471no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4C22⋊D4711yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—942no—
138C22⋊C4—942no—
139C22⋊C4—941no—
140C42—942no—
141C42C22×D4711yescharacteristic
142C23—21no—
143C23—941no—
144Q8—41no—
145Q8—41no—
146Q8—1882no—
147D4—21no—
148D4—21no—
149D4—941no—
150D4—941no—
151D4—3762no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—941no—
157C2×C4—942no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4D4×D4711yescharacteristic
161C2×C4D4×D4711yescharacteristic
162C2×C4C2×C22⋊D4711yescharacteristic
163C8—41no—
164C8—1881no—
165C8—1881no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—1881no—
170C22—1881no—
171C22—1881no—
172C22#1309399211yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—1881no—
177C4—1882no—
178C4#1309404411yescharacteristic
179C4#1309404511yescharacteristic
180C4#1309405011yescharacteristic
181C4#1309405311yescharacteristic
182C2—81no—
183C2—3761no—
184C2#1568926611yescharacteristic
185C2#1568928211yescharacteristic
186C2#1568929911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#461C2
socleC22×C47#120
hypercenter#461D47
hypocenterC47#1646
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #15689475C2semidirect
3. #15689400C2semidirect
4. #15688871C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#461C2semidirect
97. #461D47semidirect
101. C47#1646semidirect