Finite Group Databasebeta

← #20243749

Subgroups — #20243749

Order 6016.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689923C211yesmaximal, characteristic
2#15689889C211yesmaximal, characteristic, complemented
3#15689141C211yesmaximal, characteristic, complemented
4#15689117C211yesmaximal, characteristic, complemented
5#15689091C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625350C2211yescharacteristic
10#13094057—21no—
11#13094057C412yescomplemented
12#13094052—21no—
13#13094052C412yescomplemented
14#13094046—22no—
15#13094032—22no—
16#13094030—22no—
17C2×#10625329C2211yescharacteristic
18M16×D47—22no—
19C22×C47⋊C8C2211yescharacteristic
20#13093952—22no—
21#13093947—21no—
22#13093944—21no—
23(C2×D47)⋊C8—22no—
24C2×M16×C47C2211yescharacteristic
25C2×M16×C47C2211yescharacteristic
26#117×C47C2211yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—21no—
29C2×C22⋊D47—21no—
30#10625350—21no—
31#10625350—21no—
32#10625350—21no—
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350C2×C412yes—
37#10625350D412yes—
38C2×D188C2×C411yescharacteristic
39C2×D188D411yescharacteristic
40C2×C4×D47—21no—
41C2×C4×D47—21no—
42C2×Dic94C2×C411yescharacteristic
43C2×Dic94D411yescharacteristic
44M16×C47—21no—
45M16×C47—21no—
46M16×C47—21no—
47M16×C47C2×C412yes—
48C2×C8×C47—21no—
49C2×C8×C47D412yes—
50C4⋊C4×C47—21no—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53#10625329—21no—
54#10625329D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59Dic188—22no—
60D376—22no—
61#10625325—22no—
62#10625325—22no—
63#10625324—24no—
64C8×D47—24no—
65C23×C47#4111yescharacteristic
66C22×D47—21no—
67C22×D47—21no—
68C2×C4×C47—41no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C22⋊D47—22no—
76C22⋊D47—22no—
77C22⋊D47—41no—
78C22⋊D47—41no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81D188—21no—
82D188—21no—
83D188—21no—
84D188C22⋊C412yes—
85C4×D47—22no—
86C4×D47—22no—
87C4×D47—41no—
88C4×D47—41no—
89Dic94—21no—
90Dic94—21no—
91Dic94—21no—
92Dic94C22⋊C412yes—
93C8×C47—22no—
94C8×C47—22no—
95C47⋊C8—22no—
96C47⋊C8—41no—
97C22×C47—41no—
98C22×C47C4×D411yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12311yescharacteristic
101C2×D47—22no—
102C2×D47—42no—
103C2×D47—41no—
104C2×D47—81no—
105C4×C47—81no—
106C4×C47C2×C22⋊C411yescharacteristic
107C4×C47C4×D411yescharacteristic
108C4×C47#12011yescharacteristic
109C4×C47#12111yescharacteristic
110Dic47—22no—
111Dic47—41no—
112#1881—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47#38611yescharacteristic
117D47—42no—
118D47—81no—
119#575—471no—
120#568—471no—
121#421—471no—
122#416—471no—
123#408—471no—
124#344D4711yescharacteristic, complemented
125#341—471no—
126C47#188111yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C2×#41—471no—
129#137—472no—
130#137—941no—
131AGL(1,ℤ/8)—472no—
132AGL(1,ℤ/8)—941no—
133#135—942no—
134#131—942no—
135#131—942no—
136C2×M16—471no—
137C2×M16—942no—
138C2×M16C2×D4711yescharacteristic
139C2×M16C2×D4711yescharacteristic
140C22×C8—471no—
141#117C2×D4711yescharacteristic
142#104—942no—
143#103—941no—
144#102—941no—
145C22⋊C8—942no—
146#41—472no—
147#41—472no—
148#41—941no—
149#41—941no—
150#41—941no—
151#41—941no—
152#41—941no—
153#41—941no—
154C2×Q8—471no—
155C2×Q8—471no—
156C2×D4—471no—
157C2×D4—471no—
158C2×D4—941no—
159C2×D4—941no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163Q16—942no—
164SD16—942no—
165SD16—942no—
166D8—942no—
167M16—21no—
168M16—21no—
169M16—21no—
170M16—472no—
171M16—944no—
172M16—941no—
173M16C4×D4712yes—
174C2×C8—21no—
175C2×C8—944no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C2×C8D18812yes—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—941no—
185C23—941no—
186C23#1062535011yescharacteristic
187Q8—472no—
188Q8—941no—
189Q8—941no—
190Q8—941no—
191D4—472no—
192D4—942no—
193D4—942no—
194D4—941no—
195D4—941no—
196D4—941no—
197D4—1881no—
198D4—1881no—
199C2×C4—41no—
200C2×C4—941no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4C2×C4×D4711yescharacteristic
207C2×C4C2×D18811yescharacteristic
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4#1062535411yescharacteristic
212C8—22no—
213C8—22no—
214C8—942no—
215C8—1881no—
216C22—41no—
217C22—942no—
218C22—3761no—
219C22—1882no—
220C22—1881no—
221C22C4×D18811yescharacteristic
222C22#1309399711yescharacteristic
223C22#1309400911yescharacteristic
224C4—81no—
225C4—942no—
226C4—1881no—
227C4C22⋊C4×D4711yescharacteristic
228C4#1309398611yescharacteristic
229C4#1309399411yescharacteristic
230C4#1309399911yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—3761no—
235C2—1882no—
236C2#1568900111yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1881
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #15689889C2semidirect
3. #15689141C2semidirect
4. #15689117C2semidirect
5. #15689091C2semidirect
6. #15688887C2semidirect
7. C47×#344C2semidirect
11. #13094057C4semidirect
13. #13094052C4semidirect
124. #344D47semidirect
126. C47#1881semidirect