Finite Group Databasebeta

← #19145209

Subgroups — #19145209

Order 5504.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583518C212yesmaximal, complemented
2#14583297C211yesmaximal, characteristic, complemented
3#14583258C212yesmaximal, complemented
4#14583154C211yesmaximal, characteristic, complemented
5#14583149C211yesmaximal, characteristic
6#14583125C212yesmaximal, complemented
7#14583011C211yesmaximal, characteristic, complemented
8#14583006C211yesmaximal, characteristic, complemented
9SD16×Dic43C212yesmaximal, complemented
10#14582853C211yesmaximal, characteristic, complemented
11C43×#495C211yesmaximal, characteristic, complemented
12C2×#10621872C2211yescharacteristic
13C2×C8×D43C2211yescharacteristic
14#13063325C2212yes—
15#13063318—22no—
16#13063311—22no—
17#13063309—22no—
18#13063302—22no—
19#13063301C2212yes—
20#13063296C2212yes—
21Q8×Dic43C2212yes—
22D4×Dic43C2212yes—
23#13063282C2211yescharacteristic
24#13063257C2212yes—
25#13063257C2211yescharacteristic
26#13063257C2211yescharacteristic
27#13063249C2212yes—
28#13063249C2212yes—
29#13063246C2212yes—
30#13063246C2212yes—
31#13063236C2211yescharacteristic
32#13063235C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34C2×Q16×C43C2211yescharacteristic
35C2×SD16×C43C2212yes—
36C2×D8×C43C2211yescharacteristic
37#124×C43C2212yes—
38C4×C8×C43C2211yescharacteristic
39C2×Q8×C43C2312yes—
40C2×D4×C43C2312yes—
41C2×C22⋊D43—22no—
42C22×Dic43—22no—
43C2×C4×D43C2311yescharacteristic
44C2×Dic86—22no—
45Q16×C43—22no—
46SD16×C43—24no—
47D8×C43—22no—
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C22⋊C4×C43—22no—
51C22⋊C4×C43—22no—
52C42×C43C2311yescharacteristic
53C22⋊Dic43—22no—
54C22⋊Dic43—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4D412yes—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43C2312yes—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62Dic43⋊C4D412yes—
63C4×Dic43—22no—
64C4×Dic43C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66C2×C43⋊C8C2311yescharacteristic
67#10621872—22no—
68C8×D43—22no—
69C23×C43—22no—
70C22×D43C2×D411yescharacteristic
71Q8×C43—22no—
72Q8×C43—22no—
73D4×C43—22no—
74D4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—82no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—82no—
82C2×Dic43C2×D412yes—
83C2×Dic43C2×D411yescharacteristic
84C4×D43—21no—
85C4×D43—21no—
86Dic86—82no—
87C8×C43#4112yes—
88C8×C43#4112yes—
89C43⋊C8—21no—
90C43⋊C8—21no—
91C22×C43—42no—
92C22×C43—42no—
93C22×C43—42no—
94C22×C43C22×D411yescharacteristic
95C2×D43—21no—
96C2×D43—22no—
97C4×C43—22no—
98C4×C43—42no—
99C4×C43C2×#4111yescharacteristic
100C4×C43C2×#4111yescharacteristic
101Dic43—21no—
102Dic43—22no—
103Dic43—42no—
104Dic43—42no—
105#3173—431nomaximal, Sylow
106C2×C43—82no—
107C2×C43#53211yescharacteristic
108C2×C43#57712yes—
109D43—41no—
110#542—432no—
111#498—431no—
112#495D4311yescharacteristic, complemented
113#489—432no—
114#470—431no—
115#469—431no—
116#465—432no—
117#442—431no—
118#441—431no—
119C4×SD16—432no—
120#405—431no—
121C43#317311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4311yescharacteristic
123C2×SD16C2×D4312yes—
124C2×D8C2×D4311yescharacteristic
125C2×M16—431no—
126C22×C8—431no—
127C4⋊Q8—432no—
128#126—862no—
129#124—862no—
130#124C2×D4312yes—
131#123—862no—
132C22⋊Q8—432no—
133C22⋊Q8—862no—
134#121—432no—
135C4×Q8—432no—
136C4×D4—432no—
137#117—431no—
138#106—432no—
139#106—431no—
140#106—431no—
141#103—432no—
142#103—432no—
143#102—432no—
144#102—432no—
145#97—431no—
146#97—431no—
147C4×C8—431no—
148C4×C8C2×D4311yescharacteristic
149C2×Q8—862no—
150C2×Q8C22×D4312yes—
151C2×D4—862no—
152C2×D4C22×D4312yes—
153C22×C4—431no—
154C22×C4—862no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—862no—
159C2×C8—431no—
160C2×C8—431no—
161C2×C8—862no—
162C2×C8C22×D4311yescharacteristic
163C2×C8C22×D4311yescharacteristic
164C4⋊C4—432no—
165C4⋊C4—432no—
166C4⋊C4—432no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—432no—
173C22⋊C4—862no—
174C22⋊C4—862no—
175C22⋊C4—862no—
176C42—431no—
177C42—862no—
178C42C22×D4311yescharacteristic
179C23—22no—
180C23—431no—
181Q8—22no—
182Q8—22no—
183Q8—3442no—
184D4—22no—
185D4—22no—
186D4—3442no—
187C2×C4—22no—
188C2×C4—432no—
189C2×C4—431no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—3442no—
195C2×C4D4×D4312yes—
196C2×C4C23×D4311yescharacteristic
197C8—861no—
198C8—861no—
199C8#1062190012yes—
200C8#1062190012yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—861no—
205C22—862no—
206C22C2×D4×D4311yescharacteristic
207C4—22no—
208C4—42no—
209C4—861no—
210C4—862no—
211C4—1722no—
212C4—1722no—
213C4C2×#1062190011yescharacteristic
214C4C2×#1062190011yescharacteristic
215C2—82no—
216C2—1721no—
217C2#1458344711yescharacteristic
218C2#1458370612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#495C2
socleC22×C43C22×D4
hypercenter#495D43
hypocenterC43#3173
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14583518C2semidirect
2. #14583297C2semidirect
3. #14583258C2semidirect
4. #14583154C2semidirect
6. #14583125C2semidirect
7. #14583011C2semidirect
8. #14583006C2semidirect
9. SD16×Dic43C2semidirect
10. #14582853C2semidirect
11. C43×#495C2semidirect
112. #495D43semidirect
121. C43#3173semidirect