Finite Group Databasebeta

← #19144200

Subgroups — #19144200

Order 5504.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#10621872C211yesmaximal, characteristic, complemented
2#14583406C212yesmaximal, complemented
3#14583154C212yesmaximal, complemented
4#14583149C212yesmaximal, complemented
5#14583142C214yesmaximal, complemented
6#14582937C211yesmaximal, characteristic, complemented
7#14582895C212yesmaximal, complemented
8C2×#135×C43C211yesmaximal, characteristic, complemented
9C22×C4×D43C2211yescharacteristic
10C2×#10621872—24no—
11C2×#10621872C2212yes—
12C2×#10621872C2212yes—
13C22×C43⋊C8C2211yescharacteristic
14#13063306—22no—
15#13063301C2214yes—
16#13063296C2214yes—
17#13063293—22no—
18C4×C22⋊D43—24no—
19#13063284C2212yes—
20#13063259C2212yescomplemented
21#13063257C2212yescomplemented
22#13063249C2214yescomplemented
23#13063246C2214yescomplemented
24C2×#41×C43C2212yes—
25#135×C43—24no—
26C2×Q16×C43C2211yescharacteristic, complemented
27C2×SD16×C43C2212yescomplemented
28C2×D8×C43C2211yescharacteristic, complemented
29C22×C8×C43C2211yescharacteristic
30C23×D43D411yescharacteristic
31#41×C43—24no—
32#41×C43—24no—
33C2×Q8×C43C2312yes—
34C2×D4×C43—22no—
35C2×D4×C43C2312yes—
36C22×C4×C43—22no—
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—24no—
39C22×Dic43D411yescharacteristic
40C2×C4×D43—22no—
41C2×C4×D43—22no—
42C2×C4×D43D412yes—
43C2×C4×D43C2312yes—
44Q16×C43—22no—
45SD16×C43—24no—
46D8×C43—22no—
47C2×C8×C43D414yescomplemented
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C22⋊Dic43—24no—
51C22⋊Dic43—22no—
52(C2×D43)⋊C4—24no—
53C4⋊Dic43C2314yes—
54Dic43⋊C4—24no—
55C4×Dic43—22no—
56C2×C43⋊C8—22no—
57C2×C43⋊C8C2312yes—
58#10621872—24no—
59#10621872—24no—
60C23×C43—22no—
61C23×C43C2×D411yescharacteristic
62C22×D43—22no—
63C22×D43—42no—
64C22×D43C2×D412yes—
65Q8×C43—22no—
66Q8×C43—22no—
67D4×C43—22no—
68D4×C43—22no—
69D4×C43—44no—
70C2×C4×C43—22no—
71C2×C4×C43—44no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D412yes—
74C2×C4×C43#4112yes—
75C2×C4×C43C2411yescharacteristic
76C22⋊D43—48no—
77C2×Dic43—22no—
78C2×Dic43—24no—
79C2×Dic43C2×D412yes—
80C4×D43—24no—
81C4×D43—22no—
82C4×D43—22no—
83C8×C43C2×D412yes—
84C8×C43C2×D412yes—
85C43⋊C8—22no—
86C22×C43—22no—
87C22×C43—42no—
88C22×C43—44no—
89C22×C43#12112yes—
90C22×C43C22×D411yescharacteristic
91C2×D43—22no—
92C2×D43—24no—
93C2×D43—44no—
94C4×C43—42no—
95C4×C43#12112yes—
96C4×C43C22×D411yescharacteristic
97C4×C43C2×#4111yescharacteristic
98Dic43—22no—
99Dic43—44no—
100#3054—431nomaximal, Sylow
101C2×C43—22no—
102C2×C43—82no—
103C2×C43C2×#12111yescharacteristic
104C2×C43#57512yes—
105D43—42no—
106C2×#135D4311yescharacteristic, complemented
107C22×M16—431no—
108#525—432no—
109#470—432no—
110#469—432no—
111#468—434no—
112#427—431no—
113#416—432no—
114C43#305411yescharacteristic, complemented, Sylow
115C2×#41C2×D4312yes—
116C23×C4—431no—
117#135—24no—
118C2×Q16C2×D4311yescharacteristic, complemented
119C2×SD16C2×D4312yescomplemented
120C2×D8C2×D4311yescharacteristic, complemented
121C2×M16—432no—
122C2×M16—432no—
123C2×M16—864no—
124C22×C8—431no—
125C22×C8C2×D4311yescharacteristic
126#123—862no—
127C22⋊Q8—434no—
128#121—434no—
129#120—862no—
130C4×D4—864no—
131#117—432no—
132#107—432no—
133#106—432no—
134#103—434no—
135#102—434no—
136C24—431no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D4312yes—
140C2×D4—22no—
141C2×D4—864no—
142C2×D4C22×D4312yes—
143C22×C4—22no—
144C22×C4—431no—
145C22×C4—432no—
146C22×C4—432no—
147C22×C4—862no—
148C22×C4—862no—
149C22×C4C22×D4311yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—864no—
154M16—864no—
155C2×C8—432no—
156C2×C8—862no—
157C2×C8C22⋊D4314yescomplemented
158C2×C8C22×D4311yescharacteristic
159C2×C8C22×D4311yescharacteristic
160C4⋊C4—434no—
161C4⋊C4—864no—
162C22⋊C4—864no—
163C22⋊C4—864no—
164C22⋊C4—862no—
165C42—862no—
166C23—22no—
167C23—432no—
168C23—862no—
169C23—1722no—
170C23D4×D4311yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—1728no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—432no—
180C2×C4—862no—
181C2×C4—864no—
182C2×C4—862no—
183C2×C4—862no—
184C2×C4—864no—
185C2×C4D4×D4311yescharacteristic
186C2×C4#1062190012yes—
187C2×C4C2×C22⋊D4312yes—
188C2×C4C23×D4311yescharacteristic
189C8—862no—
190C8C2×C22⋊D4312yes—
191C8C2×C22⋊D4312yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—862no—
196C22—864no—
197C22—1724no—
198C22#1306329612yes—
199C22C2×D4×D4311yescharacteristic
200C4—42no—
201C4—862no—
202C4—1724no—
203C4#1306329612yes—
204C4C22×C22⋊D4311yescharacteristic
205C4C2×#1062190011yescharacteristic
206C2—22no—
207C2—82no—
208C2—1722no—
209C2C2×#1306329611yescharacteristic
210C2#1458369612yes—
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#135×C43C2
socleC22×C43C22×D4
hypercenterC2×#135D43
hypocenterC43#3054
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#10621872C2semidirect
2. #14583406C2semidirect
3. #14583154C2semidirect
4. #14583149C2semidirect
5. #14583142C2semidirect
6. #14582937C2semidirect
7. #14582895C2semidirect
8. C2×#135×C43C2semidirect
20. #13063259C22semidirect
21. #13063257C22semidirect
22. #13063249C22semidirect
23. #13063246C22semidirect
26. C2×Q16×C43C22semidirect
27. C2×SD16×C43C22semidirect
28. C2×D8×C43C22semidirect
47. C2×C8×C43D4semidirect
106. C2×#135D43semidirect
114. C43#3054semidirect
118. C2×Q16C2×D43semidirect
119. C2×SD16C2×D43semidirect
120. C2×D8C2×D43semidirect
157. C2×C8C22⋊D43semidirect