Finite Group Databasebeta

← #20243732

Subgroups — #20243732

Order 6016.

338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#10625337C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C47×#391C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625337—22no—
10C2×#10625337—22no—
11C2×#10625337C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14C4×Dic94—22no—
15C4×Dic94—22no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47—21no—
19#13093948—22no—
20#13093947—22no—
21C22×Q8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C42×C47C2211yescharacteristic
24#95×C47—21no—
25#95×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47C2×C412yes—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C22×Dic47—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94C2×C412yes—
43C2×Dic94D412yes—
44C2×Dic94D412yes—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C42×C47—21no—
48C42×C47—21no—
49#10625337—28no—
50C4⋊Dic47—21no—
51C4⋊Dic47D412yes—
52Dic47⋊C4—24no—
53C4×Dic47—24no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8C2×C412yes—
60C23×C47C2×D411yescharacteristic
61Q8×C47—22no—
62Q8×C47—22no—
63Q8×C47—41no—
64Q8×C47—41no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47Q1612yescomplemented
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89Dic94—22no—
90Dic94—22no—
91Dic94—22no—
92Dic94C22⋊C414yes—
93C47⋊C8—22no—
94C47⋊C8—41no—
95C22×C47C4×D411yescharacteristic
96C22×C47#12011yescharacteristic
97C22×C47#12111yescharacteristic
98C22×C47C2×Q1611yescharacteristic
99C22×C47#13511yescharacteristic
100C22×C47#13711yescharacteristic
101C22×C47#13711yescharacteristic
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47—81no—
106C4×C47C2×C22⋊C411yescharacteristic
107C4×C47C4×D411yescharacteristic
108C4×C47#12111yescharacteristic
109C4×C47#12311yescharacteristic
110Dic47—24no—
111Dic47—42no—
112#1878—471nomaximal, Sylow
113C2×C47#38611yescharacteristic
114C2×C47C4×Q1611yescharacteristic
115C2×C47#44111yescharacteristic
116C2×C47#45111yescharacteristic
117C2×C47#45211yescharacteristic
118C2×C47#46211yescharacteristic
119C2×C47#46411yescharacteristic
120C22×Q16—471no—
121C2×C4×Q8—471no—
122C2×#103—471no—
123C2×#103—471no—
124#391D4711yescharacteristic
125#340—471no—
126#336—471no—
127C47#187811yescharacteristic, complemented, Sylow
128C22×Q8—471no—
129C22×Q8C2×D4711yescharacteristic
130C2×Q16—474no—
131C2×Q16—942no—
132C2×Q16—942no—
133C22×C8—471no—
134C22×C8—471no—
135C4×Q8—942no—
136C4×Q8—942no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—941no—
139C2×C4⋊C4C2×D4711yescharacteristic
140C2×C42—941no—
141C2×C42C2×D4711yescharacteristic
142#103—942no—
143#103—942no—
144#95—21no—
145#95—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—472no—
152C2×Q8—472no—
153C2×Q8—472no—
154C2×Q8—941no—
155C2×Q8—941no—
156C2×Q8—941no—
157C2×Q8C4×D4712yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4C22⋊D4711yescharacteristic
163C22×C4C22⋊D4711yescharacteristic
164C22×C4C22×D4711yescharacteristic
165Q16—948no—
166C2×C8—472no—
167C2×C8—941no—
168C2×C8—941no—
169C2×C8—941no—
170C2×C8—941no—
171C2×C8—941no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—472no—
175C4⋊C4—944no—
176C4⋊C4—941no—
177C42—21no—
178C42—21no—
179C42—944no—
180C23C2×C22⋊D4711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—474no—
186Q8—942no—
187Q8—942no—
188Q8—942no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4#1062533712yescomplemented
207C2×C4C2×C4×D4711yescharacteristic
208C2×C4#1062535011yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4#1062535211yescharacteristic
213C8—942no—
214C8—1881no—
215C22C4×C22⋊D4711yescharacteristic
216C22#1309399211yescharacteristic
217C22#1309399511yescharacteristic
218C22C2×#1062533711yescharacteristic
219C22#1309404411yescharacteristic
220C22#1309405411yescharacteristic
221C22#1309405511yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—944no—
227C4—1882no—
228C4C22⋊C4×D4711yescharacteristic
229C4(C22⋊D47)⋊C411yescharacteristic
230C4#1309399711yescharacteristic
231C4#1309400611yescharacteristic
232C2#1568899911yescharacteristic
233C2C4×#1062533711yescharacteristic
234C2#1568922811yescharacteristic
235C2#1568927811yescharacteristic
236C2#1568928311yescharacteristic
237C2#1568933011yescharacteristic
238C2#1568934211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#391C2
socleC23×C47C2×D4
hypercenter#391D47
hypocenterC47#1878
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
11. C2×#10625337C4semidirect
76. C2×C4×C47Q16semidirect
127. C47#1878semidirect
206. C2×C4#10625337semidirect