Finite Group Databasebeta

← #19134977

Subgroups — #19134977

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#14583665C211yesmaximal, characteristic, complemented
2#14583449C211yesmaximal, characteristic
3#14582917C211yesmaximal, characteristic, complemented
4#14582915C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621898C2211yescharacteristic
10#13063333—22no—
11#13063331—22no—
12C2×#10621877C2211yescharacteristic
13M16×D43—22no—
14#13063325C411yescharacteristic, complemented
15#13063322C411yescharacteristic, complemented
16#13063313C411yescharacteristic, complemented
17#13063313C411yescharacteristic, complemented
18#13063299—22no—
19C4×D172—22no—
20#13063284C2211yescharacteristic
21#13063253—22no—
22#13063251—22no—
23#13063239—22no—
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26C2×C42×C43C2211yescharacteristic
27C22×C4×C43—21no—
28C22×C4×C43C2311yescharacteristic
29C2×C22⋊D43—21no—
30C2×C22⋊D43D412yes—
31#10621898—21no—
32#10621898—21no—
33#10621898—21no—
34#10621898—21no—
35#10621898—21no—
36#10621898—21no—
37#10621898—21no—
38#10621898—21no—
39C2×D172—22no—
40C2×D172C2×C411yescharacteristic
41C2×D172C2×C411yescharacteristic
42C2×C4×D43—21no—
43C2×C4×D43D412yes—
44C2×Dic86C2×C411yescharacteristic
45C2×Dic86C2×C411yescharacteristic
46M16×C43—21no—
47M16×C43D412yescomplemented
48C2×C8×C43—21no—
49C4⋊C4×C43—21no—
50C22⋊C4×C43—21no—
51C42×C43—21no—
52C42×C43—21no—
53C42×C43C2×C411yescharacteristic
54C42×C43C2×C411yescharacteristic
55C22⋊Dic43—21no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—21no—
60C4×Dic43—21no—
61#10621877—21no—
62#10621877D412yescomplemented
63C2×C43⋊C8—21no—
64#10621872—24no—
65C8×D43—24no—
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68C22×D43C22⋊C412yes—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—42no—
72C2×C4×C43—41no—
73C2×C4×C43C22×C411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43#4111yescharacteristic
78C2×C4×C43#4111yescharacteristic
79C22⋊D43—22no—
80C22⋊D43—22no—
81C22⋊D43—41no—
82C22⋊D43—41no—
83C2×Dic43—21no—
84C2×Dic43—41no—
85C2×Dic43C22⋊C412yes—
86D172—21no—
87D172—21no—
88D172—21no—
89D172—21no—
90D172—44no—
91C4×D43—22no—
92C4×D43—22no—
93C4×D43—41no—
94C4×D43—41no—
95Dic86—21no—
96Dic86—21no—
97Dic86—21no—
98Dic86—21no—
99C8×C43—22no—
100C43⋊C8—22no—
101C22×C43—41no—
102C22×C43C2×C22⋊C411yescharacteristic
103C22×C43#12111yescharacteristic
104C22×C43#12111yescharacteristic
105C2×D43—22no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—41no—
109C4×C43—22no—
110C4×C43—41no—
111C4×C43—81no—
112C4×C43C4×D411yescharacteristic
113C4×C43C4×D411yescharacteristic
114C4×C43#12011yescharacteristic
115C4×C43#12311yescharacteristic
116Dic43—22no—
117Dic43—41no—
118Dic43—81no—
119#1884—431nomaximal, Sylow
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43#38611yescharacteristic
124D43—42no—
125D43—81no—
126#568—431no—
127#532—431no—
128#421—431no—
129#421—431no—
130#410—431no—
131#339—431no—
132#339D4311yescharacteristic, complemented
133C43#188411yescharacteristic, complemented, Sylow
134C2×#41—431no—
135C2×#41—431no—
136#131—862no—
137#131—862no—
138C2×M16—431no—
139C2×M16—862no—
140C2×M16C2×D4311yescharacteristic
141C4⋊Q8—431no—
142#127—431no—
143#124—431no—
144#124—431no—
145#121—862no—
146C4×D4—862no—
147#117—431no—
148#117C2×D4311yescharacteristic
149C2×C42C2×D4311yescharacteristic
150#104—862no—
151#104—862no—
152#99—862no—
153#41—861no—
154#41—861no—
155#41—861no—
156#41—861no—
157#41—861no—
158#41—861no—
159#41—861no—
160#41—861no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×D4—432no—
164C2×D4—431no—
165C2×D4—431no—
166C2×D4—862no—
167C2×D4—861no—
168C22×C4—21no—
169C22×C4—432no—
170C22×C4—861no—
171C22×C4C22×D4311yescharacteristic
172M16—21no—
173M16—432no—
174M16—864no—
175M16—861no—
176M16D17212yescomplemented
177C2×C8—21no—
178C2×C8—864no—
179C2×C8—861no—
180C4⋊C4—21no—
181C4⋊C4—862no—
182C4⋊C4—861no—
183C22⋊C4—21no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—861no—
187C42—21no—
188C42—21no—
189C42—861no—
190C42C4×D4311yescharacteristic
191C42C4×D4311yescharacteristic
192C23—432no—
193C23—861no—
194C23D4×D4311yescharacteristic
195Q8—861no—
196Q8—861no—
197Q8—861no—
198Q8—861no—
199D4—862no—
200D4—862no—
201D4—861no—
202D4—861no—
203D4—861no—
204D4—861no—
205D4—1724no—
206D4—1721no—
207D4—1721no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—432no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—861no—
216C2×C4—1721no—
217C2×C4—1721no—
218C2×C4—1721no—
219C2×C4C2×C4×D4311yescharacteristic
220C2×C4C2×D17211yescharacteristic
221C2×C4#1062189811yescharacteristic
222C2×C4D4×D4311yescharacteristic
223C2×C4D4×D4311yescharacteristic
224C2×C4#1062190211yescharacteristic
225C8—22no—
226C8—862no—
227C22—41no—
228C22—862no—
229C22—1722no—
230C22—1722no—
231C22—1721no—
232C22C22⋊C4×D4311yescharacteristic
233C22#1306329811yescharacteristic
234C22#1306330011yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—862no—
239C4—3441no—
240C4—1721no—
241C4#1306328711yescharacteristic
242C4C4×D17211yescharacteristic
243C4#1306329511yescharacteristic
244C4#1306331011yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—3441no—
249C2—1722no—
250C2#1458277711yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC2×C43#386
hypercenter#339D43
hypocenterC43#1884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #14583665C2semidirect
3. #14582917C2semidirect
4. #14582915C2semidirect
5. #14582872C2semidirect
6. #14582659C2semidirect
7. C43×#339C2semidirect
14. #13063325C4semidirect
15. #13063322C4semidirect
16. #13063313C4semidirect
17. #13063313C4semidirect
47. M16×C43D4semidirect
62. #10621877D4semidirect
132. #339D43semidirect
133. C43#1884semidirect
176. M16D172semidirect