Finite Group Databasebeta

← #20244608

Subgroups — #20244608

Order 6016.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#15689699C211yesmaximal, characteristic
2#15689166C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic
4#15689125C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15689029C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094024—21no—
12#13094012—21no—
13#13094008—22no—
14#13094004—21no—
15#13094004—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17#13093957—21no—
18#13093955—21no—
19#13093952—22no—
20#13093949—21no—
21#13093946—21no—
22#13093942—22no—
23C47⋊#95—22no—
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47—21no—
30C22×Dic47—21no—
31C22×Dic47D412yes—
32#10625350—21no—
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36C2×D188D411yescharacteristic
37C2×C4×D47—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94D411yescharacteristic
45M16×C47—21no—
46M16×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47D411yescharacteristic
49C4⋊C4×C47D411yescharacteristic
50C22⋊C4×C47—21no—
51C42×C47—21no—
52C42×C47—21no—
53C42×C47—21no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60#10625329—21no—
61#10625329D412yes—
62C2×C47⋊C8—21no—
63C23×C47C2×D411yescharacteristic
64C22×D47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C22⋊D47—41no—
77C22⋊D47—41no—
78C2×Dic47—21no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—42no—
83C2×Dic47—41no—
84D188—21no—
85D188—21no—
86C4×D47—41no—
87C4×D47—41no—
88Dic94—21no—
89Dic94—21no—
90Dic94—41no—
91Dic94—41no—
92Dic94—41no—
93Dic94—41no—
94C8×C47—41no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47#12011yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12311yescharacteristic
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—41no—
104C4×C47—42no—
105C4×C47—41no—
106C4×C47—41no—
107C4×C47#12111yescharacteristic
108C4×C47#12111yescharacteristic
109C4×C47#12311yescharacteristic
110C4×C47#12411yescharacteristic
111Dic47—41no—
112Dic47—42no—
113Dic47—81no—
114#2038—471nomaximal, Sylow
115C2×C47—21no—
116C2×C47—21no—
117C2×C47#39411yescharacteristic
118C2×C47#45411yescharacteristic
119C2×C47#45611yescharacteristic
120D47—81no—
121#536—471no—
122#428—471no—
123C2×#104—471no—
124#417—471no—
125C2×#101—471no—
126#391—471no—
127#339D4711yescharacteristic, complemented
128C47#203811yescharacteristic, complemented, Sylow
129C2×#41—471no—
130C22×Q8—471no—
131C2×M16—471no—
132C2×M16C2×D4711yescharacteristic
133C4⋊Q8—941no—
134#124—941no—
135#123—942no—
136C22⋊Q8—941no—
137C22⋊Q8—941no—
138#117C2×D4711yescharacteristic
139C2×C4⋊C4—471no—
140C2×C42C2×D4711yescharacteristic
141#107—941no—
142#106—941no—
143#104—942no—
144#103—941no—
145#102—941no—
146#101—942no—
147#95—942no—
148#41—941no—
149#41—941no—
150#41—941no—
151#41—941no—
152C2×Q8—471no—
153C2×Q8—941no—
154C2×Q8—941no—
155C2×Q8—941no—
156C2×Q8—941no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×D4—471no—
160C2×D4—941no—
161C22×C4—21no—
162C22×C4—472no—
163C22×C4—941no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166M16—21no—
167M16—21no—
168M16—472no—
169M16—941no—
170C2×C8—21no—
171C2×C8—941no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4D18811yescharacteristic
177C4⋊C4D18811yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—942no—
180C22⋊C4—942no—
181C42—21no—
182C42—21no—
183C42—21no—
184C23—941no—
185C23D4×D4711yescharacteristic
186Q8—941no—
187Q8—941no—
188Q8—1881no—
189Q8—1881no—
190Q8—1881no—
191Q8—1881no—
192D4—941no—
193D4—941no—
194D4—1881no—
195D4—1881no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—1882no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4C2×D18811yescharacteristic
210C2×C4#1062535011yescharacteristic
211C2×C4#1062535011yescharacteristic
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4#1062535411yescharacteristic
215C8—41no—
216C8—942no—
217C22—21no—
218C22—21no—
219C22—1881no—
220C22—1881no—
221C22—1881no—
222C22#1309399411yescharacteristic
223C22#1309399711yescharacteristic
224C22#1309400911yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—3761no—
229C4—1882no—
230C4—1881no—
231C4#1309399711yescharacteristic
232C4#1309399911yescharacteristic
233C4#1309400911yescharacteristic
234C4#1309401211yescharacteristic
235C2—21no—
236C2—21no—
237C2—3761no—
238C2#1568904111yescharacteristic
239C2#1568929711yescharacteristic
240C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #15689166C2semidirect
5. C2×#13093942C2semidirect
6. #15689029C2semidirect
7. C47×#339C2semidirect
127. #339D47semidirect
128. C47#2038semidirect