Finite Group Databasebeta

← #19145339

Subgroups — #19145339

Order 5504.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583454C211yesmaximal, characteristic
2#14583454C211yesmaximal, characteristic
3#14583295C211yesmaximal, characteristic, complemented
4#14583278C211yesmaximal, characteristic, complemented
5#14583250C211yesmaximal, characteristic, complemented
6#14583156C214yesmaximal
7#14583003C214yesmaximal, complemented
8C4×#10621872C211yesmaximal, characteristic
9C43×#487C211yesmaximal, characteristic, complemented
10C2×#10621885C2214yes—
11C2×#10621872C2212yes—
12#13063325C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063316—21no—
15#13063316—21no—
16#13063305—21no—
17#13063305C2212yes—
18#13063301—21no—
19#13063301C2212yes—
20Q8×Dic43—21no—
21Q8×Dic43C2212yes—
22#13063290—21no—
23#13063290C2212yes—
24#13063283—21no—
25#13063283—21no—
26C42×D43C2211yescharacteristic
27#13063256C2214yes—
28#13063250C2214yes—
29#13063235C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#103×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43C2312yes—
37C2×C4×D43D411yescharacteristic
38C2×C4×D43D411yescharacteristic
39C2×C4×D43C2311yescharacteristic
40C2×Dic86—21no—
41C2×Dic86C2312yes—
42C2×C8×C43C2312yes—
43C4⋊C4×C43—21no—
44C4⋊C4×C43—21no—
45C4⋊C4×C43—21no—
46C4⋊C4×C43C2312yes—
47C42×C43C2311yescharacteristic
48#10621885—28no—
49(C2×D43)⋊C4—22no—
50(C2×D43)⋊C4—22no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53C4⋊Dic43—21no—
54C4⋊Dic43—22no—
55C4⋊Dic43—22no—
56C4⋊Dic43C2312yes—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59C4×Dic43—22no—
60C4×Dic43—22no—
61C4×Dic43D411yescharacteristic
62C4×Dic43D411yescharacteristic
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2312yes—
65#10621872—24no—
66C22×D43C2×D411yescharacteristic
67Q8×C43—24no—
68Q8×C43—42no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2411yescharacteristic
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43C2×D411yescharacteristic
77C2×Dic43C2×D411yescharacteristic
78C2×Dic43C2×D411yescharacteristic
79C4×D43—22no—
80C4×D43—22no—
81C4×D43—22no—
82Dic86—24no—
83Dic86—42no—
84C8×C43—22no—
85C43⋊C8#4114yes—
86C22×C43C22×D411yescharacteristic
87C2×D43—21no—
88C2×D43—21no—
89C2×D43—21no—
90C4×C43—42no—
91C4×C43—42no—
92C4×C43#13712yes—
93C4×C43#13712yes—
94C4×C43C2×#4112yes—
95Dic43—21no—
96Dic43—21no—
97Dic43—21no—
98Dic43—42no—
99Dic43—42no—
100#3185—431nomaximal, Sylow
101C2×C43#53211yescharacteristic
102C2×C43C2×#13711yescharacteristic
103C2×C43C2×#13711yescharacteristic
104D43—41no—
105#533—431no—
106#533—431no—
107#498—431no—
108#494—431no—
109#487—431no—
110#487D4311yescharacteristic, complemented
111#470—434no—
112#441—434no—
113C4×M16—431no—
114C43#318511yescharacteristic, complemented, Sylow
115C2×Q16—434no—
116C2×M16—432no—
117C4⋊Q8—431no—
118C4⋊Q8—431no—
119C4⋊Q8C2×D4311yescharacteristic
120C4⋊Q8C2×D4311yescharacteristic
121#125—861no—
122#125—861no—
123C22⋊Q8—432no—
124C22⋊Q8—432no—
125C22⋊Q8—861no—
126C22⋊Q8—861no—
127C4×Q8—432no—
128C4×Q8—432no—
129C4×Q8—861no—
130C4×Q8—861no—
131#117—861no—
132#117—861no—
133C2×C42—431no—
134#106—434no—
135#103—434no—
136#103C2×D4314yes—
137#97—432no—
138C4×C8—431no—
139C4×C8C2×D4311yescharacteristic
140C2×Q8—21no—
141C2×Q8—432no—
142C2×Q8—861no—
143C2×Q8C22×D4312yes—
144C22×C4—431no—
145C22×C4—431no—
146C22×C4—431no—
147Q16—868no—
148M16—864no—
149C2×C8—432no—
150C2×C8C22×D4312yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—432no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—862no—
158C4⋊C4—862no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4C22×D4312yes—
163C22⋊C4—862no—
164C22⋊C4—862no—
165C42—431no—
166C42—431no—
167C42—431no—
168C42—862no—
169C42—862no—
170C42C22×D4311yescharacteristic
171C23—431no—
172Q8—24no—
173Q8—42no—
174Q8—864no—
175Q8—1722no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—431no—
179C2×C4—431no—
180C2×C4—431no—
181C2×C4—862no—
182C2×C4—862no—
183C2×C4—862no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4D4×D4311yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C2×C4C23×D4311yescharacteristic
189C8—22no—
190C8—434no—
191C22—861no—
192C22—861no—
193C22—861no—
194C22C2×D4×D4311yescharacteristic
195C4—42no—
196C4—42no—
197C4—861no—
198C4—861no—
199C4—861no—
200C4—1722no—
201C4—1722no—
202C4#1306335412yes—
203C4#1306335712yes—
204C4#41×D4312yes—
205C2—1721no—
206C2#1458344811yescharacteristic
207C2C2×#1306335411yescharacteristic
208C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3185
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14583295C2semidirect
4. #14583278C2semidirect
5. #14583250C2semidirect
7. #14583003C2semidirect
9. C43×#487C2semidirect
110. #487D43semidirect
114. C43#3185semidirect