Finite Group Databasebeta

← #20242618

Subgroups — #20242618

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#15689474C211yesmaximal, characteristic, complemented
3#15689404C211yesmaximal, characteristic, complemented
4#15689328C211yesmaximal, characteristic, complemented
5#15688871C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625335—21no—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094010—22no—
12#13093998—21no—
13#13093995—21no—
14C4×D188C2211yescharacteristic
15#13093983—21no—
16#13093982—21no—
17#13093958—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—22no—
20#13093947—21no—
21#13093946—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C2×C22⋊D47—22no—
28C2×D188D411yescharacteristic
29C2×C4×D47—21no—
30C2×Dic94—21no—
31C2×Dic94D412yes—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C4⋊C4×C47D411yescharacteristic
35C22⋊C4×C47—21no—
36C42×C47C2311yescharacteristic
37C22⋊Dic47—22no—
38#10625335—42no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47D411yescharacteristic
46C4×Dic47—22no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49C22×D47—21no—
50D4×C47—21no—
51D4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C22⋊D47—82no—
59C2×Dic47—21no—
60C2×Dic47—22no—
61C2×Dic47—41no—
62D188—21no—
63D188—21no—
64C4×D47—41no—
65C4×D47—41no—
66Dic94—42no—
67Dic94—41no—
68Dic94—41no—
69C8×C47—41no—
70C8×C47—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#13511yescharacteristic
82C4×C47#13511yescharacteristic
83C4×C47AGL(1,ℤ/8)11yescharacteristic
84C4×C47#13711yescharacteristic
85Dic47—41no—
86Dic47—42no—
87Dic47—81no—
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#461—471no—
98#333—471no—
99D4⋊C8—471no—
100D4⋊C8D4711yescharacteristic, complemented
101C47#164611yescharacteristic, complemented, Sylow
102C2×SD16—941no—
103C4⋊Q8—471no—
104C4⋊Q8—471no—
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—942no—
116#103—941no—
117#102—941no—
118C4×C8C2×D4711yescharacteristic
119C2×Q8—472no—
120C2×Q8—941no—
121C2×D4—471no—
122C2×D4—942no—
123C2×D4D18811yescharacteristic
124C22×C4—21no—
125C22×C4—941no—
126SD16—1882no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—941no—
130C4⋊C4—471no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4D18811yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—942no—
138C22⋊C4—942no—
139C22⋊C4—941no—
140C42—942no—
141C42C22×D4711yescharacteristic
142C23—21no—
143C23—941no—
144Q8—1882no—
145Q8—1881no—
146Q8—1881no—
147D4—21no—
148D4—21no—
149D4—941no—
150D4—941no—
151D4—3762no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—941no—
156C2×C4—942no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4C2×D18811yescharacteristic
161C2×C4D4×D4711yescharacteristic
162C2×C4D4×D4711yescharacteristic
163C8—41no—
164C8—41no—
165C8—1881no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—1881no—
170C22—1881no—
171C22—1881no—
172C22#1309399411yescharacteristic
173C4—21no—
174C4—41no—
175C4—3761no—
176C4—1881no—
177C4—1882no—
178C4#1309404311yescharacteristic
179C4#1309404611yescharacteristic
180C4#1309405211yescharacteristic
181C4#1309405311yescharacteristic
182C2—81no—
183C2—3761no—
184C2#1568927011yescharacteristic
185C2#1568928611yescharacteristic
186C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1646
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. #15689404C2semidirect
4. #15689328C2semidirect
5. #15688871C2semidirect
6. #15688852C2semidirect
7. C47×D4⋊C8C2semidirect
100. D4⋊C8D47semidirect
101. C47#1646semidirect