Finite Group Databasebeta

← #19145222

Subgroups — #19145222

Order 5504.

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

normal subgroups only

This group has 362 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#14583512C211yesmaximal, characteristic, complemented
2#14583503C211yesmaximal, characteristic
3#14583298C211yesmaximal, characteristic, complemented
4#14583271C211yesmaximal, characteristic, complemented
5#14583268C211yesmaximal, characteristic, complemented
6#14583144C212yesmaximal, complemented
7#14583127C212yesmaximal, complemented
8#14582996C212yesmaximal, complemented
9#14582990C212yesmaximal, complemented
10#14582856C211yesmaximal, characteristic, complemented
11C43×#490C211yesmaximal, characteristic, complemented
12C2×#10621883C2212yes—
13C2×#10621883C2212yes—
14C2×#10621872C2211yescharacteristic
15C2×C8×D43C2211yescharacteristic
16#13063325C2211yescharacteristic
17#13063320—22no—
18#13063317C2211yescharacteristic
19#13063316—22no—
20#13063306—22no—
21#13063305C2212yes—
22#13063297—22no—
23#13063296C2212yes—
24#13063290C2212yes—
25D4×Dic43C2212yes—
26#13063282C2211yescharacteristic
27#13063258C2212yes—
28#13063256C2212yes—
29#13063250C2212yes—
30#13063250C2212yes—
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×C4×D43C2311yescharacteristic
44C2×Dic86C2312yes—
45C2×C8×C43C2311yescharacteristic
46C2×C8×C43C2311yescharacteristic
47C4⋊C4×C43—22no—
48C4⋊C4×C43C2312yes—
49C42×C43C2311yescharacteristic
50C22⋊Dic43—22no—
51C22⋊Dic43—22no—
52#10621883—24no—
53#10621883—24no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4D412yes—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4D412yes—
62C4×Dic43—22no—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66#10621872—22no—
67C8×D43—22no—
68C23×C43—22no—
69C22×D43C2×D411yescharacteristic
70D4×C43—22no—
71D4×C43—22no—
72D4×C43—82no—
73C2×C4×C43—22no—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2411yescharacteristic
76C22⋊D43—82no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—82no—
80C2×Dic43C2×D412yes—
81C2×Dic43C2×D411yescharacteristic
82C4×D43—21no—
83C4×D43—21no—
84Dic86—22no—
85Dic86—22no—
86C8×C43—21no—
87C8×C43—21no—
88C43⋊C8#4112yes—
89C43⋊C8#4112yes—
90C22×C43—42no—
91C22×C43—42no—
92C22×C43—42no—
93C22×C43C22×D411yescharacteristic
94C2×D43—21no—
95C2×D43—22no—
96C4×C43—22no—
97C4×C43—42no—
98C4×C43C2×#4111yescharacteristic
99C4×C43C2×#4111yescharacteristic
100Dic43—21no—
101Dic43—22no—
102Dic43—42no—
103Dic43—42no—
104#3174—431nomaximal, Sylow
105C2×C43—82no—
106C2×C43#53211yescharacteristic
107C2×C43#57712yes—
108D43—41no—
109#541—431no—
110#540—431no—
111#499—431no—
112#492—431no—
113#491—431no—
114#490D4311yescharacteristic, complemented
115#468—432no—
116#465—432no—
117#440—432no—
118C4×SD16—432no—
119#405—431no—
120C43#317411yescharacteristic, complemented, Sylow
121C2×SD16—432no—
122C2×SD16—432no—
123C2×M16—431no—
124C22×C8—431no—
125C4⋊Q8—431no—
126#127C2×D4311yescharacteristic
127#126—862no—
128#125—431no—
129#125—862no—
130#125C2×D4311yescharacteristic
131#123—862no—
132C22⋊Q8—432no—
133#121—432no—
134#121—862no—
135C4×Q8—432no—
136C4×D4—432no—
137#117—431no—
138#107—432no—
139#106—432no—
140#103—432no—
141#103—432no—
142#102C2×D4312yes—
143#102C2×D4312yes—
144#97—431no—
145#97C2×D4311yescharacteristic
146C4×C8—431no—
147C4×C8—431no—
148C2×Q8—432no—
149C2×D4—22no—
150C2×D4—862no—
151C2×D4C22×D4312yes—
152C22×C4—431no—
153C22×C4—862no—
154SD16—864no—
155SD16—864no—
156M16—862no—
157C2×C8—431no—
158C2×C8—431no—
159C2×C8—862no—
160C2×C8C22×D4311yescharacteristic
161C2×C8C22×D4311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—432no—
164C4⋊C4—432no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4C22×D4312yes—
170C22⋊C4—432no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C42—431no—
175C42—862no—
176C42C22×D4311yescharacteristic
177C23—22no—
178C23—431no—
179Q8—862no—
180Q8—862no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—3442no—
185C2×C4—22no—
186C2×C4—432no—
187C2×C4—431no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—3442no—
193C2×C4D4×D4312yes—
194C2×C4C23×D4311yescharacteristic
195C8—21no—
196C8—21no—
197C8—432no—
198C8—432no—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—861no—
203C22—862no—
204C22C2×D4×D4311yescharacteristic
205C4—22no—
206C4—42no—
207C4—861no—
208C4—862no—
209C4—1722no—
210C4—1722no—
211C4#41×D4311yescharacteristic
212C4#41×D4311yescharacteristic
213C2—82no—
214C2—1721no—
215C2#1458344811yescharacteristic
216C2#1458370912yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3174
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. #14583512C2semidirect
3. #14583298C2semidirect
4. #14583271C2semidirect
5. #14583268C2semidirect
6. #14583144C2semidirect
7. #14583127C2semidirect
8. #14582996C2semidirect
9. #14582990C2semidirect
10. #14582856C2semidirect
11. C43×#490C2semidirect
114. #490D43semidirect
120. C43#3174semidirect