Finite Group Databasebeta

← #20244359

Subgroups — #20244359

Order 6016.

276 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#13094023C211yesmaximal, characteristic
2C2×#13093934C211yesmaximal, characteristic
3#15688988C211yesmaximal, characteristic
4#15688886C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94—21no—
9C22×C47⋊C8C2211yescharacteristic
10#13094023—22no—
11#13094023C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093934—22no—
17C47⋊#95—21no—
18C47⋊#95—21no—
19C22×C8×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47D411yescharacteristic
28C22×Dic47D411yescharacteristic
29C2×Dic94—24no—
30C2×Dic94—42no—
31C2×Dic94—42no—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C2×C8×C47Q812yescomplemented
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C412yes—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47C2×C412yes—
43Dic47⋊C4—24no—
44C4×Dic47C2×C412yes—
45C4×Dic47D412yes—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8Q812yescomplemented
49C23×C47C2×D411yescharacteristic
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C22×C411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×Q811yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—22no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47C22⋊C412yes—
73C2×Dic47C22⋊C412yes—
74Dic94—48no—
75C8×C47—22no—
76C47⋊C8—22no—
77C22×C47C2×C22⋊C411yescharacteristic
78C22×C47#12411yescharacteristic
79C22×C47C4⋊Q811yescharacteristic
80C22×C47AGL(1,ℤ/8)11yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C22×C47#13711yescharacteristic
83C22×C47#13711yescharacteristic
84C4×C47—42no—
85C4×C47—81no—
86C4×C47C4×Q811yescharacteristic
87C4×C47C4×Q811yescharacteristic
88C4×C47C22⋊Q811yescharacteristic
89C4×C47C22⋊Q811yescharacteristic
90Dic47—22no—
91Dic47—22no—
92Dic47—42no—
93Dic47—81no—
94#1993—471nomaximal, Sylow
95C2×C47#39111yescharacteristic
96C2×C47#41811yescharacteristic
97C2×C47#41911yescharacteristic
98C2×C47#48911yescharacteristic
99C2×C47#48911yescharacteristic
100C2×C47#50111yescharacteristic
101C2×C47#50111yescharacteristic
102C2×C4⋊Q8—471no—
103C2×#97—471no—
104#382—471no—
105#340—471no—
106#340—471no—
107#340—471no—
108#340D4711yescharacteristic
109C47#199311yescharacteristic, complemented, Sylow
110C22×Q8—941no—
111C22×C8—471no—
112C22×C8C2×D4711yescharacteristic
113C4⋊Q8—474no—
114C4⋊Q8—942no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—941no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C42—471no—
121#97—942no—
122#95—941no—
123#95—941no—
124C2×Q8—944no—
125C2×Q8—1882no—
126C2×Q8—1882no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—471no—
130C22×C4—471no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—472no—
137C2×C8—941no—
138C2×C8—941no—
139C2×C8Dic9412yescomplemented
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—472no—
144C4⋊C4—944no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4C4×D4712yes—
149C42—472no—
150C42—472no—
151C23D4×D4711yescharacteristic
152Q8—1888no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—472no—
160C2×C4—472no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—941no—
164C2×C4—941no—
165C2×C4—942no—
166C2×C4—1881no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4C2×Dic9411yescharacteristic
172C2×C4C2×C4×D4711yescharacteristic
173C2×C4#1062535011yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C2×C4#1062535211yescharacteristic
176C2×C4Q8×D4711yescharacteristic
177C8—22no—
178C8—942no—
179C22C22⋊C4×D4711yescharacteristic
180C22#1309401011yescharacteristic
181C22#1309402311yescharacteristic
182C22#1309404811yescharacteristic
183C22#1309405111yescharacteristic
184C22#1309405311yescharacteristic
185C22#1309405611yescharacteristic
186C4—42no—
187C4—81no—
188C4—942no—
189C4—942no—
190C4—3761no—
191C4—1882no—
192C4#1309398911yescharacteristic
193C4C4×Dic9411yescharacteristic
194C4#1309400111yescharacteristic
195C4#1309400211yescharacteristic
196C2#1568902711yescharacteristic
197C2#1568912611yescharacteristic
198C2#1568913011yescharacteristic
199C2#1568948111yescharacteristic
200C2#1568948411yescharacteristic
201C2#1568953011yescharacteristic
202C2#1568953111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1993
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #13094023C4semidirect
34. C2×C8×C47Q8semidirect
48. C2×C47⋊C8Q8semidirect
109. C47#1993semidirect
139. C2×C8Dic94semidirect