Finite Group Databasebeta

← #19135097

Subgroups — #19135097

Order 5504.

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

normal subgroups only

This group has 332 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#14583699C211yesmaximal, characteristic
2#14583367C211yesmaximal, characteristic, complemented
3#14582915C211yesmaximal, characteristic, complemented
4C2×#13063251C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582660C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621898C2211yescharacteristic
10#13063358—21no—
11#13063358C412yescomplemented
12#13063353—21no—
13#13063353C412yescomplemented
14#13063347—22no—
15#13063290—21no—
16#13063287—21no—
17(C22⋊D43)⋊C4—22no—
18#13063284C2211yescharacteristic
19#13063282—21no—
20C2×C4×Dic43C2211yescharacteristic
21C42×D43—21no—
22#13063251—22no—
23#13063251—21no—
24#13063251—21no—
25#13063239—22no—
26C2×M16×C43C2211yescharacteristic
27C2×M16×C43C2211yescharacteristic
28#117×C43C2211yescharacteristic
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C2×C22⋊D43—21no—
32C22×Dic43—21no—
33#10621898—21no—
34#10621898—21no—
35#10621898—21no—
36#10621898—21no—
37#10621898—21no—
38#10621898—21no—
39#10621898C2×C412yes—
40#10621898D412yes—
41C2×D172C2×C411yescharacteristic, complemented
42C2×D172D411yescharacteristic
43C2×C4×D43—21no—
44C2×C4×D43—22no—
45C2×C4×D43—21no—
46C2×Dic86C2×C411yescharacteristic, complemented
47C2×Dic86D411yescharacteristic
48M16×C43—21no—
49M16×C43—21no—
50M16×C43—21no—
51M16×C43C2×C412yescomplemented
52C2×C8×C43—21no—
53C2×C8×C43—21no—
54C4⋊C4×C43—21no—
55C22⋊C4×C43D412yes—
56C42×C43—21no—
57C22⋊Dic43—21no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—21no—
60Dic43⋊C4—22no—
61C4×Dic43—22no—
62C4×Dic43—21no—
63C4×Dic43—21no—
64C4×Dic43D411yescharacteristic
65C4×Dic43D411yescharacteristic
66Dic172—22no—
67D344—22no—
68#10621873—22no—
69#10621873—22no—
70C23×C43C2×D411yescharacteristic
71C22×D43—21no—
72C22×D43—21no—
73C2×C4×C43—22no—
74C2×C4×C43C22×C411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43#4111yescharacteristic
79C2×C4×C43#4111yescharacteristic
80C22⋊D43—22no—
81C22⋊D43—22no—
82C22⋊D43—41no—
83C22⋊D43—41no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—42no—
89C2×Dic43—41no—
90D172—21no—
91D172—21no—
92D172—21no—
93D172C22⋊C412yes—
94C4×D43—22no—
95C4×D43—22no—
96C4×D43—44no—
97C4×D43—41no—
98C4×D43—41no—
99Dic86—21no—
100Dic86—21no—
101Dic86—21no—
102Dic86C22⋊C412yes—
103C8×C43—22no—
104C8×C43—41no—
105C22×C43—41no—
106C22×C43C4×D411yescharacteristic
107C22×C43#12011yescharacteristic
108C22×C43#12111yescharacteristic
109C2×D43—22no—
110C2×D43—42no—
111C2×D43—41no—
112C2×D43—81no—
113C4×C43—42no—
114C4×C43C2×C22⋊C411yescharacteristic
115C4×C43C4×D411yescharacteristic
116C4×C43#12111yescharacteristic
117C4×C43#12311yescharacteristic
118Dic43—22no—
119Dic43—22no—
120Dic43—41no—
121Dic43—41no—
122Dic43—81no—
123#1906—431nomaximal, Sylow
124C2×C43—21no—
125C2×C43—21no—
126C2×C43—21no—
127C2×C43#38611yescharacteristic
128D43—42no—
129D43—81no—
130#575—431no—
131C4×#41—431no—
132#421—431no—
133C2×#104—431no—
134#410—431no—
135#344D4311yescharacteristic, complemented
136#339—431no—
137C43#190611yescharacteristic, complemented, Sylow
138C2×#41—431no—
139C2×#41—431no—
140#137—432no—
141#137—861no—
142AGL(1,ℤ/8)—432no—
143AGL(1,ℤ/8)—861no—
144#135—862no—
145C2×M16C2×D4311yescharacteristic
146C2×M16C2×D4311yescharacteristic
147C4×Q8—861no—
148C4×D4—861no—
149C4×D4—862no—
150#117—431no—
151#117—861no—
152#117C2×D4311yescharacteristic
153C2×C42—431no—
154C2×C42—861no—
155#104—861no—
156#104—861no—
157#104—862no—
158#99—862no—
159#41—432no—
160#41—432no—
161#41—861no—
162#41—861no—
163#41—861no—
164#41—861no—
165#41—861no—
166#41—861no—
167C2×Q8—431no—
168C2×Q8—431no—
169C2×D4—431no—
170C2×D4—431no—
171C2×D4—861no—
172C2×D4—861no—
173C22×C4—862no—
174C22×C4—861no—
175C22×C4—861no—
176C22×C4—861no—
177C22×C4C22×D4311yescharacteristic
178Q16—862no—
179SD16—862no—
180SD16—862no—
181D8—862no—
182M16—21no—
183M16—21no—
184M16—21no—
185M16C4×D4312yescomplemented
186C2×C8—21no—
187C2×C8—21no—
188C4⋊C4—21no—
189C4⋊C4—862no—
190C4⋊C4—861no—
191C22⋊C4—862no—
192C22⋊C4—861no—
193C22⋊C4D17212yes—
194C42—21no—
195C42—431no—
196C42—431no—
197C42—862no—
198C42—861no—
199C42—861no—
200C23—861no—
201C23—861no—
202C23C2×D17211yescharacteristic
203Q8—432no—
204Q8—861no—
205Q8—861no—
206Q8—861no—
207D4—432no—
208D4—862no—
209D4—862no—
210D4—861no—
211D4—861no—
212D4—861no—
213D4—1721no—
214D4—1721no—
215C2×C4—22no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—1724no—
223C2×C4—1722no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4C2×C4×D4311yescharacteristic
228C2×C4#1062189811yescharacteristic
229C2×C4D4×D4311yescharacteristic
230C2×C4D4×D4311yescharacteristic
231C2×C4D4×D4311yescharacteristic
232C2×C4#1062190211yescharacteristic
233C8—22no—
234C8—41no—
235C22—41no—
236C22—862no—
237C22—3441no—
238C22—1722no—
239C22—1721no—
240C22C4×D17211yescharacteristic
241C22#1306329511yescharacteristic
242C22#1306330011yescharacteristic
243C4—42no—
244C4—862no—
245C4—862no—
246C4—3441no—
247C4—1721no—
248C4—1721no—
249C4C22⋊C4×D4311yescharacteristic
250C4#1306328711yescharacteristic
251C4#1306329811yescharacteristic
252C4#1306331011yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—3441no—
257C2—1722no—
258C2#1458277711yescharacteristic
subgroupG/H
centerC4#13063298
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1906
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #14583367C2semidirect
3. #14582915C2semidirect
4. C2×#13063251C2semidirect
5. #14582872C2semidirect
6. #14582660C2semidirect
7. C43×#344C2semidirect
11. #13063358C4semidirect
13. #13063353C4semidirect
41. C2×D172C2×C4semidirect
46. C2×Dic86C2×C4semidirect
51. M16×C43C2×C4semidirect
135. #344D43semidirect
137. C43#1906semidirect
185. M16C4×D43semidirect