Finite Group Databasebeta

← #20242556

Subgroups — #20242556

Order 6016.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic94C211yesmaximal, characteristic
2#15689474C211yesmaximal, characteristic, complemented
3#15689419C211yesmaximal, characteristic, complemented
4#15689413C211yesmaximal, characteristic
5#15688870C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic
8C22×Dic94—21no—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094023—21no—
12#13094003—21no—
13#13094001—22no—
14C4×Dic94C2211yescharacteristic
15D4×Dic47—21no—
16#13093958—21no—
17#13093955—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—21no—
20#13093949—22no—
21#13093945—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C22×Dic47—22no—
28C2×Dic94—22no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—42no—
32C2×Dic94—42no—
33C2×Dic94D411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D412yes—
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—22no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C23×C47—21no—
50D4×C47—21no—
51D4×C47Q1612yes—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—22no—
61C2×Dic47—44no—
62C2×Dic47—41no—
63Dic94—21no—
64Dic94—44no—
65Dic94—41no—
66Dic94—41no—
67Dic94—42no—
68Dic94SD1612yes—
69C8×C47—41no—
70C8×C47—41no—
71C47⋊C8—41no—
72C22×C47—22no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47#12011yescharacteristic
76C4×C47—21no—
77C4×C47—41no—
78C4×C47C2×SD1611yescharacteristic
79C4×C47C2×Q1611yescharacteristic
80C4×C47AGL(1,ℤ/8)11yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—22no—
83Dic47—42no—
84Dic47—41no—
85Dic47—81no—
86#1637—471nomaximal, Sylow
87C2×C47—42no—
88C2×C47#45011yescharacteristic
89C2×C47#45111yescharacteristic
90C2×C47#45411yescharacteristic
91D4×Q8—471no—
92#487—471no—
93#477—471no—
94#476—471no—
95#332—471no—
96Q8⋊C8—471no—
97D4⋊C8D4711yescharacteristic
98C47#163711yescharacteristic, complemented, Sylow
99C22×Q8—941no—
100C4⋊Q8—471no—
101C4⋊Q8—471no—
102C4⋊Q8—941no—
103C22⋊Q8—942no—
104C22⋊Q8—941no—
105C4×Q8—471no—
106C4×D4—941no—
107C4×D4C2×D4711yescharacteristic
108#107—941no—
109#106—941no—
110C4⋊C8—471no—
111C4⋊C8C2×D4711yescharacteristic
112#103—942no—
113#103—941no—
114#102—941no—
115C4×C8C2×D4711yescharacteristic
116C2×Q8—471no—
117C2×Q8—942no—
118C2×Q8—941no—
119C2×Q8—941no—
120C2×Q8—1882no—
121C2×Q8—1882no—
122C2×D4D18811yescharacteristic
123C22×C4—21no—
124C22×C4—942no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—941no—
128C4⋊C4—472no—
129C4⋊C4—471no—
130C4⋊C4—942no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4D18811yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—942no—
138C42—941no—
139C42C22×D4711yescharacteristic
140C23—21no—
141Q8—472no—
142Q8—941no—
143Q8—1882no—
144Q8—1884no—
145Q8—1881no—
146Q8—1881no—
147D4—21no—
148D4Dic18812yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—942no—
155C2×C4—1884no—
156C2×C4—1881no—
157C2×C4C2×D18811yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C2×C4D4×D4711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1881no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1309399411yescharacteristic
167C4—21no—
168C4—41no—
169C4—942no—
170C4—3761no—
171C4—1882no—
172C4—1881no—
173C4SD16×D4711yescharacteristic
174C4C2×Dic18811yescharacteristic
175C4#1309404811yescharacteristic
176C4#1309405711yescharacteristic
177C2—42no—
178C2#1568927511yescharacteristic
179C2#1568928111yescharacteristic
180C2#1568929711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1637
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. #15689419C2semidirect
5. #15688870C2semidirect
6. #15688855C2semidirect
98. C47#1637semidirect