Finite Group Databasebeta

← #20243750

Subgroups — #20243750

Order 6016.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689921C211yesmaximal, characteristic
2#15689139C211yesmaximal, characteristic, complemented
3#15689119C211yesmaximal, characteristic, complemented
4#15689091C211yesmaximal, characteristic, complemented
5#15688894C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#568C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—21no—
10#13094054C412yescomplemented
11#13094050—21no—
12#13094049C412yescomplemented
13#13094044—22no—
14C2×#10625329C2211yescharacteristic
15C22×C47⋊C8C2211yescharacteristic
16#13093983C2211yescharacteristic
17#13093950—22no—
18#13093948—21no—
19#13093945—21no—
20(C2×D47)⋊C8—22no—
21C2×#41×C47C2211yescharacteristic
22#131×C47—22no—
23#131×C47—22no—
24C2×M16×C47—22no—
25C2×M16×C47C2211yescharacteristic
26C2×M16×C47C2211yescharacteristic
27#41×C47—21no—
28#41×C47—21no—
29#41×C47C2×C412yes—
30#41×C47D412yes—
31C2×Q8×C47D411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47D411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—21no—
37#10625350—21no—
38#10625350—21no—
39#10625350—21no—
40#10625350—21no—
41C2×D188C2×C411yescharacteristic
42C2×C4×D47—21no—
43C2×Dic94C2×C411yescharacteristic
44M16×C47—24no—
45M16×C47—21no—
46M16×C47—21no—
47M16×C47—21no—
48M16×C47D412yes—
49C2×C8×C47—24no—
50C2×C8×C47—21no—
51C2×C8×C47D412yes—
52C22⋊Dic47—21no—
53#10625337—22no—
54#10625336—22no—
55#10625335—22no—
56#10625334—22no—
57C4⋊Dic47—21no—
58C4×Dic47—21no—
59#10625329—21no—
60#10625329C2×C412yes—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8—21no—
65C23×C47—21no—
66C23×C47#4111yescharacteristic
67C22×D47—21no—
68Q8×C47—21no—
69Q8×C47C22⋊C412yes—
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—21no—
73D4×C47C22⋊C412yes—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C22⋊D47—41no—
84C22⋊D47—41no—
85C2×Dic47—21no—
86C2×Dic47—41no—
87D188—21no—
88D188—21no—
89C4×D47—41no—
90C4×D47—41no—
91Dic94—21no—
92Dic94—21no—
93C8×C47—22no—
94C8×C47—22no—
95C47⋊C8—22no—
96C47⋊C8—41no—
97C22×C47—22no—
98C22×C47—41no—
99C22×C47—81no—
100C22×C47C4×D411yescharacteristic
101C22×C47#12111yescharacteristic
102C22×C47#12311yescharacteristic
103C2×D47—42no—
104C2×D47—41no—
105C4×C47—22no—
106C4×C47C2×C22⋊C411yescharacteristic
107C4×C47C4×D411yescharacteristic
108C4×C47#12011yescharacteristic
109C4×C47#12111yescharacteristic
110Dic47—41no—
111Dic47—81no—
112#1881—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—42no—
117C2×C47#38611yescharacteristic
118D47—81no—
119#575—471no—
120#568D4711yescharacteristic, complemented
121#421—471no—
122#416—471no—
123#408—471no—
124#344—471no—
125#341—471no—
126C47#188111yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C2×#41C2×D4711yescharacteristic
129#137—472no—
130#137—941no—
131AGL(1,ℤ/8)—472no—
132AGL(1,ℤ/8)—941no—
133#135—942no—
134#131—22no—
135#131—22no—
136C2×M16—22no—
137C2×M16—471no—
138C2×M16C2×D4711yescharacteristic
139C2×M16C2×D4711yescharacteristic
140C22×C8—471no—
141#117—471no—
142#104—942no—
143#103—941no—
144#102—941no—
145C22⋊C8—942no—
146#41—21no—
147#41—21no—
148#41—941no—
149#41—941no—
150#41—941no—
151#41—941no—
152#41C4×D4712yes—
153#41C22⋊D4712yes—
154C2×Q8—471no—
155C2×Q8D18811yescharacteristic
156C2×D4—21no—
157C2×D4—471no—
158C2×D4—941no—
159C2×D4D18811yescharacteristic
160C22×C4—21no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163Q16—942no—
164SD16—942no—
165SD16—942no—
166D8—942no—
167M16—24no—
168M16—21no—
169M16—21no—
170M16—21no—
171M16—472no—
172M16—941no—
173M16C22⋊D4712yes—
174C2×C8—24no—
175C2×C8—21no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C2×C8C22⋊D4712yes—
181C4⋊C4—941no—
182C22⋊C4—941no—
183C42—941no—
184C23—21no—
185C23—941no—
186C23#1062535011yescharacteristic
187Q8—21no—
188Q8—941no—
189Q8—941no—
190Q8(C2×D47)⋊C412yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—941no—
195D4—941no—
196D4—1881no—
197D4—1881no—
198D4(C2×D47)⋊C412yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—941no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4C2×C4×D4711yescharacteristic
207C2×C4C2×D18811yescharacteristic
208C2×C4#1062535011yescharacteristic
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C2×C22⋊D4711yescharacteristic
211C2×C4C2×C22⋊D4711yescharacteristic
212C8—22no—
213C8—22no—
214C8—942no—
215C8—1881no—
216C22—22no—
217C22—41no—
218C22—81no—
219C22—1882no—
220C22—1881no—
221C22C4×C22⋊D4711yescharacteristic
222C22#1309399811yescharacteristic
223C22#1309400711yescharacteristic
224C4—22no—
225C4—3761no—
226C4—1881no—
227C4C2×(C2×D47)⋊C411yescharacteristic
228C4C4×C22⋊D4711yescharacteristic
229C4#1309399311yescharacteristic
230C4#1309399811yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—3761no—
236C2#1568900211yescharacteristic
subgroupG/H
centerC4#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#568C2
socleC2×C47#386
hypercenter#568D47
hypocenterC47#1881
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #15689139C2semidirect
3. #15689119C2semidirect
4. #15689091C2semidirect
5. #15688894C2semidirect
6. #15688887C2semidirect
7. C47×#568C2semidirect
10. #13094054C4semidirect
12. #13094049C4semidirect
120. #568D47semidirect
126. C47#1881semidirect