Finite Group Databasebeta

← #20243728

Subgroups — #20243728

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×Dic188C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic
3C2×#13093949C211yesmaximal, characteristic
4C2×#13093949C211yesmaximal, characteristic
5#15689029C211yesmaximal, characteristic
6#15688886C211yesmaximal, characteristic
7C47×#336C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10C2×Dic188—22no—
11C2×Dic188—22no—
12C2×Dic188C414yescomplemented
13C4×Dic94—22no—
14C4×Dic94—22no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47—21no—
19#13093949—22no—
20#13093949—22no—
21C47⋊#95—21no—
22C47⋊#95—21no—
23C22×C8×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C42×C47C2211yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47C2311yescharacteristic
29C22×Dic47—21no—
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94C2×C412yes—
42C2×Dic94C2×C412yes—
43C2×Dic94D412yes—
44C2×Dic94D412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47—21no—
50C2×C8×C47C2×C412yes—
51C42×C47—21no—
52C42×C47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47D412yes—
57Dic47⋊C4—24no—
58C4×Dic47—24no—
59Dic188—28no—
60C23×C47C2×D411yescharacteristic
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47Q1612yescomplemented
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85Dic94—22no—
86Dic94—22no—
87Dic94—22no—
88Dic94—22no—
89Dic94—22no—
90Dic94—41no—
91Dic94—41no—
92Dic94C22⋊C414yes—
93C8×C47—22no—
94C8×C47—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—41no—
104C4×C47C2×C22⋊C411yescharacteristic
105C4×C47C4×D411yescharacteristic
106C4×C47#12111yescharacteristic
107C4×C47#12311yescharacteristic
108Dic47—24no—
109Dic47—42no—
110Dic47—42no—
111Dic47—81no—
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#391—471no—
125#340—471no—
126#336D4711yescharacteristic
127C47#187811yescharacteristic, complemented, Sylow
128C22×Q8—471no—
129C22×Q8—471no—
130C2×Q16—474no—
131C2×Q16—942no—
132C2×Q16—942no—
133C22×C8C2×D4711yescharacteristic
134C22×C8C2×D4711yescharacteristic
135C4×Q8—942no—
136C4×Q8—942no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—941no—
140C2×C42—941no—
141C2×C42C2×D4711yescharacteristic
142#103—942no—
143#103—942no—
144#95—941no—
145#95—941no—
146C2×Q8—472no—
147C2×Q8—472no—
148C2×Q8—472no—
149C2×Q8—472no—
150C2×Q8—941no—
151C2×Q8—941no—
152C2×Q8—941no—
153C2×Q8—941no—
154C2×Q8—941no—
155C2×Q8—941no—
156C2×Q8—941no—
157C2×Q8—941no—
158C22×C4—941no—
159C22×C4—941no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4D18811yescharacteristic
163C22×C4D18811yescharacteristic
164C22×C4C22×D4711yescharacteristic
165Q16—948no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8C4×D4712yes—
172C4⋊C4—472no—
173C4⋊C4—944no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C42—21no—
178C42—21no—
179C42—944no—
180C23C2×D18811yescharacteristic
181Q8—474no—
182Q8—942no—
183Q8—942no—
184Q8—942no—
185Q8—942no—
186Q8—942no—
187Q8—1881no—
188Q8—1881no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—1881no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4Dic18812yescomplemented
207C2×C4C2×C4×D4711yescharacteristic
208C2×C4#1062535011yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4#1062535411yescharacteristic
213C8—22no—
214C8—41no—
215C22C4×D18811yescharacteristic
216C22#1309399411yescharacteristic
217C22#1309399911yescharacteristic
218C22C2×Dic18811yescharacteristic
219C22#1309404611yescharacteristic
220C22#1309405711yescharacteristic
221C22#1309405711yescharacteristic
222C4—22no—
223C4—41no—
224C4—944no—
225C4—3761no—
226C4—1882no—
227C4—1882no—
228C4C22⋊C4×D4711yescharacteristic
229C4#1309398611yescharacteristic
230C4#1309399711yescharacteristic
231C4#1309400911yescharacteristic
232C2#1568900111yescharacteristic
233C2C4×Dic18811yescharacteristic
234C2#1568923111yescharacteristic
235C2#1568928111yescharacteristic
236C2#1568928711yescharacteristic
237C2#1568933411yescharacteristic
238C2#1568934611yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#1878
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
12. C2×Dic188C4semidirect
66. C2×C4×C47Q16semidirect
127. C47#1878semidirect
206. C2×C4Dic188semidirect