Finite Group Databasebeta

← #20242653

Subgroups — #20242653

Order 6016.

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

normal subgroups only

This group has 234 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#15689521C211yesmaximal, characteristic, complemented
3#15689409C211yesmaximal, characteristic, complemented
4#15689328C211yesmaximal, characteristic
5#15688870C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic
8C22×Dic94—21no—
9C2×#10625335—21no—
10#13094024C2211yescharacteristic
11#13094024C2211yescharacteristic
12#13094023—21no—
13#13094003—21no—
14#13094001—22no—
15C4×Dic94C2211yescharacteristic
16D4×Dic47—21no—
17#13093956—22no—
18#13093956—21no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093949—21no—
21#13093947—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—
40#10625335—42no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47D411yescharacteristic
45C4⋊Dic47D412yes—
46Dic47⋊C4—22no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—21no—
50C23×C47—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
59C2×Dic47—21no—
60C2×Dic47—21no—
61C2×Dic47—22no—
62C2×Dic47—44no—
63C2×Dic47—41no—
64Dic94—21no—
65Dic94—44no—
66Dic94—41no—
67Dic94—41no—
68Dic94—41no—
69Dic94—41no—
70Dic94SD1612yescomplemented
71C8×C47—22no—
72C8×C47—41no—
73C47⋊C8—41no—
74C22×C47—22no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47#12011yescharacteristic
78C4×C47—21no—
79C4×C47—41no—
80C4×C47C2×SD1611yescharacteristic
81C4×C47C2×SD1611yescharacteristic
82C4×C47AGL(1,ℤ/8)11yescharacteristic
83C4×C47#13711yescharacteristic
84Dic47—22no—
85Dic47—42no—
86Dic47—41no—
87Dic47—81no—
88#1651—471nomaximal, Sylow
89C2×C47—42no—
90C2×C47#44811yescharacteristic
91C2×C47#45011yescharacteristic
92C2×C47#45611yescharacteristic
93D4×Q8—471no—
94#498—471no—
95#475—471no—
96#461—471no—
97#332—471no—
98Q8⋊C8—471no—
99D4⋊C8D4711yescharacteristic
100C47#165111yescharacteristic, complemented, Sylow
101C22×Q8—941no—
102C2×SD16—941no—
103C4⋊Q8—471no—
104C4⋊Q8—471no—
105C4⋊Q8—941no—
106C22⋊Q8—942no—
107C22⋊Q8—941no—
108C4×Q8—471no—
109C4×D4—941no—
110C4×D4C2×D4711yescharacteristic
111#106—941no—
112#106—942no—
113C4⋊C8—471no—
114C4⋊C8C2×D4711yescharacteristic
115#103—941no—
116#103—941no—
117C4×C8C2×D4711yescharacteristic
118C2×Q8—471no—
119C2×Q8—942no—
120C2×Q8—941no—
121C2×Q8—941no—
122C2×Q8—1882no—
123C2×Q8—1882no—
124C2×D4D18811yescharacteristic
125C22×C4—21no—
126C22×C4—942no—
127SD16—1882no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—941no—
131C4⋊C4—471no—
132C4⋊C4—472no—
133C4⋊C4—942no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4D18811yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—942no—
141C42—941no—
142C42C22×D4711yescharacteristic
143C23—21no—
144Q8—472no—
145Q8—941no—
146Q8—1884no—
147Q8—1881no—
148Q8—1881no—
149Q8—1881no—
150Q8—1881no—
151D4—21no—
152D4#1062532512yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4—942no—
159C2×C4—1884no—
160C2×C4—1881no—
161C2×C4C2×D18811yescharacteristic
162C2×C4D4×D4711yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C8—22no—
165C8—41no—
166C8—1881no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1309399411yescharacteristic
171C4—21no—
172C4—41no—
173C4—942no—
174C4—3761no—
175C4—1882no—
176C4—1881no—
177C4SD16×D4711yescharacteristic
178C4C2×#1062532511yescharacteristic
179C4#1309404811yescharacteristic
180C4#1309405711yescharacteristic
181C2—42no—
182C2#1568926411yescharacteristic
183C2#1568927511yescharacteristic
184C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1651
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. #15689521C2semidirect
3. #15689409C2semidirect
5. #15688870C2semidirect
6. #15688855C2semidirect
70. Dic94SD16semidirect
100. C47#1651semidirect