Finite Group Databasebeta

← #19145244

Subgroups — #19145244

Order 5504.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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#14583505C211yesmaximal, characteristic, complemented
2#14583503C211yesmaximal, characteristic, complemented
3#14583298C211yesmaximal, characteristic, complemented
4#14583275C211yesmaximal, characteristic, complemented
5#14583264C211yesmaximal, characteristic, complemented
6#14583151C212yesmaximal, complemented
7#14583134C212yesmaximal, complemented
8#14583008C212yesmaximal, complemented
9#14582979C212yesmaximal, complemented
10#14582856C211yesmaximal, characteristic, complemented
11C43×#490C211yesmaximal, characteristic, complemented
12C2×#10621882C2212yes—
13C2×#10621882C2212yes—
14C2×#10621872C2211yescharacteristic
15C2×C8×D43C2211yescharacteristic
16#13063322C2211yescharacteristic
17#13063317C2211yescharacteristic
18#13063310—22no—
19#13063306—22no—
20#13063300—22no—
21#13063300C2212yes—
22#13063297—22no—
23#13063296C2212yes—
24D4×Dic43C2212yes—
25#13063287C2212yes—
26#13063282C2211yescharacteristic
27#13063258C2212yes—
28#13063256C2212yes—
29#13063247C2212yes—
30#13063247C2212yes—
31#13063235C2211yescharacteristic
32C4×C43⋊C8C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34#127×C43C2211yescharacteristic
35#125×C43C2211yescharacteristic
36#102×C43C2212yes—
37#102×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×D4×C43—22no—
40C2×D4×C43C2312yes—
41C2×C22⋊D43—22no—
42C22×Dic43—22no—
43C2×D172—22no—
44C2×D172—22no—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×C4×D43C2311yescharacteristic
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C4⋊C4×C43—22no—
51C4⋊C4×C43C2312yes—
52C42×C43C2311yescharacteristic
53C22⋊Dic43—22no—
54C22⋊Dic43—22no—
55#10621882—24no—
56#10621882—24no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4D412yes—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62Dic43⋊C4D412yes—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66#10621872—22no—
67C8×D43—22no—
68C23×C43—22no—
69C22×D43—22no—
70C22×D43C2×D411yescharacteristic
71D4×C43—22no—
72D4×C43—22no—
73D4×C43—82no—
74C2×C4×C43—22no—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2411yescharacteristic
77C22⋊D43—82no—
78C2×Dic43—22no—
79C2×Dic43—82no—
80C2×Dic43C2×D412yes—
81C2×Dic43C2×D411yescharacteristic
82D172—22no—
83D172—22no—
84D172—82no—
85D172—82no—
86C4×D43—21no—
87C4×D43—21no—
88C4×D43—82no—
89C8×C43—21no—
90C8×C43—21no—
91C43⋊C8#4112yes—
92C43⋊C8#4112yes—
93C22×C43—42no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43C22×D411yescharacteristic
97C2×D43—21no—
98C2×D43—22no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C4×C43—22no—
103C4×C43—42no—
104C4×C43C2×#4111yescharacteristic
105C4×C43C2×#4111yescharacteristic
106Dic43—21no—
107Dic43—22no—
108Dic43—42no—
109#3176—431nomaximal, Sylow
110C2×C43—82no—
111C2×C43#53211yescharacteristic
112C2×C43#57612yes—
113D43—41no—
114D43—82no—
115#540—431no—
116#540—431no—
117#499—431no—
118#493—431no—
119#490—431no—
120#490D4311yescharacteristic, complemented
121#469—432no—
122#466—432no—
123#442—432no—
124C4×D8—432no—
125#405—431no—
126C43#317611yescharacteristic, complemented, Sylow
127C2×D8—432no—
128C2×D8—432no—
129C2×M16—431no—
130C22×C8—431no—
131#127—431no—
132#127C2×D4311yescharacteristic
133#125—431no—
134#125C2×D4311yescharacteristic
135#123—862no—
136#123—862no—
137#121—432no—
138#121—432no—
139#121—862no—
140#121—862no—
141C4×D4—432no—
142C4×D4—432no—
143#117—431no—
144#107—432no—
145#106—432no—
146#102—432no—
147#102—432no—
148#102C2×D4312yes—
149#102C2×D4312yes—
150#97—431no—
151#97C2×D4311yescharacteristic
152C4×C8—431no—
153C4×C8—431no—
154C2×D4—22no—
155C2×D4—432no—
156C2×D4—862no—
157C2×D4—862no—
158C2×D4—862no—
159C2×D4C22×D4312yes—
160C22×C4—431no—
161C22×C4—862no—
162C22×C4—862no—
163D8—864no—
164D8—864no—
165M16—862no—
166C2×C8—431no—
167C2×C8—431no—
168C2×C8—862no—
169C2×C8C22×D4311yescharacteristic
170C2×C8C22×D4311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—432no—
173C4⋊C4—432no—
174C4⋊C4—862no—
175C4⋊C4C22×D4312yes—
176C22⋊C4—432no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C22⋊C4—862no—
180C22⋊C4—862no—
181C42—431no—
182C42C22×D4311yescharacteristic
183C23—22no—
184C23—431no—
185C23—862no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—862no—
190D4—862no—
191D4—3442no—
192D4—3442no—
193D4—3442no—
194C2×C4—22no—
195C2×C4—432no—
196C2×C4—431no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—862no—
200C2×C4—3442no—
201C2×C4—3442no—
202C2×C4D4×D4312yes—
203C2×C4C23×D4311yescharacteristic
204C8—21no—
205C8—21no—
206C8—432no—
207C8—432no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—862no—
212C22—861no—
213C22—1722no—
214C22—1722no—
215C22—1722no—
216C22C2×D4×D4311yescharacteristic
217C4—22no—
218C4—42no—
219C4—862no—
220C4—861no—
221C4—1722no—
222C4#41×D4311yescharacteristic
223C4#41×D4311yescharacteristic
224C2—82no—
225C2—3442no—
226C2—1721no—
227C2#1458344811yescharacteristic
228C2#1458370312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3176
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583503C2semidirect
3. #14583298C2semidirect
4. #14583275C2semidirect
5. #14583264C2semidirect
6. #14583151C2semidirect
7. #14583134C2semidirect
8. #14583008C2semidirect
9. #14582979C2semidirect
10. #14582856C2semidirect
11. C43×#490C2semidirect
120. #490D43semidirect
126. C43#3176semidirect