Finite Group Databasebeta

← #19145243

Subgroups — #19145243

Order 5504.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583500C212yesmaximal, complemented
2#14583299C211yesmaximal, characteristic, complemented
3#14583274C211yesmaximal, characteristic, complemented
4#14583262C212yesmaximal, complemented
5#14583153C211yesmaximal, characteristic, complemented
6#14583149C211yesmaximal, characteristic, complemented
7#14583134C212yesmaximal, complemented
8#14583012C211yesmaximal, characteristic, complemented
9C4×#10621882C212yesmaximal, complemented
10#14582856C211yesmaximal, characteristic, complemented
11C43×#442C211yesmaximal, characteristic, complemented
12C2×D344C2211yescharacteristic
13C2×#10621882C2212yes—
14C2×#10621872C2211yescharacteristic
15C2×C8×D43C2211yescharacteristic
16#13063321C2212yes—
17#13063316C2212yes—
18#13063308—22no—
19#13063307—22no—
20#13063300C2212yes—
21#13063299—22no—
22#13063298—22no—
23#13063296C2212yes—
24C4×D172C2212yes—
25#13063282C2211yescharacteristic
26#13063258C2212yes—
27#13063257C2211yescharacteristic
28#13063247C2212yes—
29#13063246C2212yes—
30#13063245C2212yes—
31#13063235C2211yescharacteristic
32C4×C43⋊C8C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34C2×D8×C43C2211yescharacteristic
35C4×D4×C43C2212yes—
36#106×C43C2211yescharacteristic
37#102×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×D4×C43C2312yes—
40C22×C4×C43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43C2×C22⋊D43—22no—
44C2×D172—22no—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×C4×D43C2311yescharacteristic
48D8×C43—22no—
49C2×C8×C43C2311yescharacteristic
50C2×C8×C43C2311yescharacteristic
51C4⋊C4×C43C2312yes—
52C22⋊C4×C43—22no—
53C42×C43C2311yescharacteristic
54C22⋊Dic43—22no—
55#10621882—24no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4D412yes—
59C4⋊Dic43—22no—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62Dic43⋊C4D412yes—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66D344—22no—
67#10621872—22no—
68C8×D43—22no—
69C23×C43—22no—
70C22×D43—22no—
71C22×D43C2×D411yescharacteristic
72D4×C43—22no—
73D4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—82no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—82no—
79C22⋊D43—82no—
80C22⋊D43—82no—
81C2×Dic43—22no—
82C2×Dic43C2×D412yes—
83C2×Dic43C2×D411yescharacteristic
84D172—22no—
85D172—22no—
86D172—82no—
87C4×D43—21no—
88C4×D43—21no—
89C4×D43—82no—
90C8×C43—21no—
91C8×C43#4112yes—
92C43⋊C8—21no—
93C43⋊C8#4112yes—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43—42no—
97C22×C43C22×D411yescharacteristic
98C2×D43—21no—
99C2×D43—22no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C4×C43—22no—
104C4×C43—42no—
105C4×C43C2×#4111yescharacteristic
106C4×C43C2×#4111yescharacteristic
107Dic43—21no—
108Dic43—22no—
109Dic43—42no—
110#3176—431nomaximal, Sylow
111C2×C43—82no—
112C2×C43#53211yescharacteristic
113C2×C43#57612yes—
114D43—41no—
115D43—82no—
116#540—432no—
117#499—431no—
118#493—431no—
119#490—432no—
120#469—431no—
121#469—431no—
122#466—432no—
123#442—431no—
124#442D4311yescharacteristic, complemented
125C4×D8—432no—
126#405—431no—
127C43#317611yescharacteristic, complemented, Sylow
128C2×D8—432no—
129C2×D8—431no—
130C2×D8C2×D4311yescharacteristic
131C2×M16—431no—
132C22×C8—431no—
133#127—432no—
134#125—432no—
135#123—862no—
136#123—862no—
137#121—432no—
138#121—432no—
139#121—862no—
140#121—862no—
141C4×D4—432no—
142C4×D4C2×D4312yes—
143#117—431no—
144#107—432no—
145#106—431no—
146#106C2×D4311yescharacteristic
147#102—432no—
148#102—432no—
149#102—432no—
150#102C2×D4312yes—
151#97—431no—
152#97C2×D4311yescharacteristic
153C4×C8—431no—
154C4×C8—431no—
155C2×D4—432no—
156C2×D4—862no—
157C2×D4—862no—
158C2×D4—862no—
159C2×D4—862no—
160C2×D4C22×D4312yes—
161C22×C4—22no—
162C22×C4—431no—
163C22×C4—862no—
164D8—22no—
165D8—864no—
166D8—862no—
167M16—862no—
168C2×C8—431no—
169C2×C8—431no—
170C2×C8—862no—
171C2×C8C22×D4311yescharacteristic
172C2×C8C22×D4311yescharacteristic
173C4⋊C4—432no—
174C4⋊C4—432no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4C22×D4312yes—
178C22⋊C4—22no—
179C22⋊C4—432no—
180C22⋊C4—862no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C42—431no—
184C42C22×D4311yescharacteristic
185C23—22no—
186C23—431no—
187C23—862no—
188D4—22no—
189D4—22no—
190D4—862no—
191D4—862no—
192D4—3442no—
193D4—3442no—
194D4—3442no—
195D4—3442no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—432no—
199C2×C4—431no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—862no—
203C2×C4—3442no—
204C2×C4D4×D4312yes—
205C2×C4C23×D4311yescharacteristic
206C8—21no—
207C8—432no—
208C8—861no—
209C8#1062189812yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—861no—
214C22—862no—
215C22—1722no—
216C22—1722no—
217C22—1722no—
218C22C2×D4×D4311yescharacteristic
219C4—22no—
220C4—42no—
221C4—861no—
222C4—862no—
223C4—1722no—
224C4#41×D4311yescharacteristic
225C4C2×#1062189811yescharacteristic
226C2—82no—
227C2—3442no—
228C2—1721no—
229C2#1458344611yescharacteristic
230C2#1458370312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3176
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583500C2semidirect
2. #14583299C2semidirect
3. #14583274C2semidirect
4. #14583262C2semidirect
5. #14583153C2semidirect
6. #14583149C2semidirect
7. #14583134C2semidirect
8. #14583012C2semidirect
9. C4×#10621882C2semidirect
10. #14582856C2semidirect
11. C43×#442C2semidirect
124. #442D43semidirect
127. C43#3176semidirect