Finite Group Databasebeta

← #20244022

Subgroups — #20244022

Order 6016.

254 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13093955C211yesmaximal, characteristic
2C2×#13093947C211yesmaximal, characteristic
3C2×#13093947C211yesmaximal, characteristic
4#15689029C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C4×C4⋊C4×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093955—22no—
13#13093947—22no—
14#13093947C414yescomplemented
15C47⋊#95—21no—
16C47⋊#95—21no—
17C2×C4⋊C4×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C42×C47—21no—
20C2×C42×C47C2211yescharacteristic
21#95×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94C2×C412yes—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47C2×C412yes—
38C4⋊C4×C47D412yes—
39C42×C47—21no—
40C42×C47—21no—
41C42×C47—42no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8C2×C412yes—
50C23×C47C2×D411yescharacteristic
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47SD1612yes—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×Dic47—22no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75Dic94—22no—
76Dic94—22no—
77Dic94—41no—
78Dic94—41no—
79C47⋊C8—22no—
80C47⋊C8—41no—
81C22×C47C4×D411yescharacteristic
82C22×C47#12111yescharacteristic
83C22×C47#12311yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47#13511yescharacteristic
86C22×C47#13711yescharacteristic
87C22×C47#13711yescharacteristic
88C4×C47—22no—
89C4×C47—42no—
90C4×C47—42no—
91C4×C47—41no—
92C4×C47#11711yescharacteristic
93C4×C47C4×D411yescharacteristic
94C4×C47#12411yescharacteristic
95C4×C47#12611yescharacteristic
96Dic47—42no—
97Dic47—81no—
98#1927—471nomaximal, Sylow
99C2×C47#38811yescharacteristic
100C2×C47C4×SD1611yescharacteristic
101C2×C47#44111yescharacteristic
102C2×C47#46111yescharacteristic
103C2×C47#46411yescharacteristic
104C2×C47#48311yescharacteristic
105C2×C47#48511yescharacteristic
106C2×#106—471no—
107C2×#103—471no—
108C2×#103—471no—
109#391—471no—
110C4×C4⋊C4D4711yescharacteristic
111#340—471no—
112#336—471no—
113C47#192711yescharacteristic, complemented, Sylow
114C22×Q8—471no—
115C22×C8—471no—
116C22×C8—471no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C42—21no—
121C2×C42C2×D4711yescharacteristic
122#106—942no—
123#103—474no—
124#103—942no—
125#95—21no—
126#95—941no—
127#95—941no—
128C2×Q8—472no—
129C2×Q8—941no—
130C2×Q8—941no—
131C2×Q8—941no—
132C2×Q8—941no—
133C2×Q8—941no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—941no—
137C22×C4—941no—
138C22×C4C22⋊D4711yescharacteristic
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C2×C8—472no—
142C2×C8—941no—
143C2×C8—941no—
144C2×C8—941no—
145C2×C8—941no—
146C2×C8—941no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4C4×D4712yes—
152C4⋊C4D18812yes—
153C42—21no—
154C42—21no—
155C42—42no—
156C23C2×C22⋊D4711yescharacteristic
157Q8—942no—
158Q8—942no—
159Q8—1881no—
160Q8—1881no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—942no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4—1881no—
178C2×C4#1062533512yes—
179C2×C4C2×C4×D4711yescharacteristic
180C2×C4C2×D18811yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4#1062535011yescharacteristic
184C2×C4#1062535011yescharacteristic
185C8—942no—
186C8—1881no—
187C22C4×C22⋊D4711yescharacteristic
188C22#1309399811yescharacteristic
189C22#1309400711yescharacteristic
190C22C2×#1062533511yescharacteristic
191C22#1309404411yescharacteristic
192C22#1309405411yescharacteristic
193C22#1309405511yescharacteristic
194C4—22no—
195C4—42no—
196C4—41no—
197C4—42no—
198C4—3761no—
199C4—1882no—
200C4#1309398111yescharacteristic
201C4C4×D18811yescharacteristic
202C4#1309401211yescharacteristic
203C4#1309401811yescharacteristic
204C2#1568901411yescharacteristic
205C2C4×#1062533511yescharacteristic
206C2#1568922811yescharacteristic
207C2#1568932811yescharacteristic
208C2#1568934511yescharacteristic
209C2#1568945311yescharacteristic
210C2#1568946411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×C4⋊C4×C47C2
socleC23×C47C2×D4
hypercenterC4×C4⋊C4D47
hypocenterC47#1927
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. #13093947C4semidirect
113. C47#1927semidirect