Finite Group Databasebeta

← #19144172

Subgroups — #19144172

Order 5504.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×C8×D43C211yesmaximal, characteristic, complemented
2#14583406C212yesmaximal, complemented
3#14583137C212yesmaximal, complemented
4#14583132C212yesmaximal, complemented
5#14583125C214yesmaximal, complemented
6#14582937C211yesmaximal, characteristic, complemented
7#14582895C212yesmaximal, complemented
8C2×#135×C43C211yesmaximal, characteristic, complemented
9C22×C4×D43C2211yescharacteristic
10C22×C43⋊C8C2211yescharacteristic
11C2×C8×D43—24no—
12C2×C8×D43C2212yes—
13C2×C8×D43C2212yes—
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—
58C8×D43—24no—
59C8×D43—24no—
60C23×C43—22no—
61C23×C43C2×D411yescharacteristic
62C22×D43—22no—
63C22×D43—24no—
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—28no—
92C2×D43—22no—
93C2×D43—22no—
94C2×D43#13514yescomplemented
95C4×C43—42no—
96C4×C43#12112yes—
97C4×C43C22×D411yescharacteristic
98C4×C43C2×#4111yescharacteristic
99Dic43—22no—
100Dic43—44no—
101#3050—431nomaximal, Sylow
102C2×C43—22no—
103C2×C43—82no—
104C2×C43C2×#12111yescharacteristic
105C2×C43C2×#13512yes—
106D43—24no—
107C2×#135D4311yescharacteristic, complemented
108C23×C8—431no—
109#525—432no—
110#467—432no—
111#466—432no—
112#465—434no—
113#427—431no—
114#416—432no—
115C43#305011yescharacteristic, complemented, Sylow
116C2×#41C2×D4312yes—
117C23×C4—431no—
118#135—24no—
119C2×Q16C2×D4311yescharacteristic, complemented
120C2×SD16C2×D4312yescomplemented
121C2×D8C2×D4311yescharacteristic, complemented
122C22×C8—431no—
123C22×C8—432no—
124C22×C8—432no—
125C22×C8—864no—
126C22×C8C2×D4311yescharacteristic
127#123—862no—
128C22⋊Q8—434no—
129#121—434no—
130#120—862no—
131C4×D4—864no—
132#117—432no—
133#107—432no—
134#106—432no—
135#103—434no—
136#102—434no—
137C24—431no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D4312yes—
141C2×D4—22no—
142C2×D4—864no—
143C2×D4C22×D4312yes—
144C22×C4—22no—
145C22×C4—431no—
146C22×C4—432no—
147C22×C4—432no—
148C22×C4—862no—
149C22×C4—862no—
150C22×C4C22×D4311yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—432no—
155C2×C8—862no—
156C2×C8—864no—
157C2×C8—864no—
158C2×C8C22⋊D4314yescomplemented
159C2×C8C22×D4311yescharacteristic
160C2×C8C22×D4311yescharacteristic
161C4⋊C4—434no—
162C4⋊C4—864no—
163C22⋊C4—864no—
164C22⋊C4—864no—
165C22⋊C4—862no—
166C42—862no—
167C23—22no—
168C23—432no—
169C23—864no—
170C23—862no—
171C23D4×D4311yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—1728no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—432no—
181C2×C4—862no—
182C2×C4—864no—
183C2×C4—862no—
184C2×C4—862no—
185C2×C4—864no—
186C2×C4D4×D4311yescharacteristic
187C2×C4#1062190012yes—
188C2×C4C2×C22⋊D4312yes—
189C2×C4C23×D4311yescharacteristic
190C8—862no—
191C8C2×C22⋊D4312yes—
192C8C2×C22⋊D4312yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—434no—
197C22—868no—
198C22—862no—
199C22—862no—
200C22#1306329612yes—
201C22C2×D4×D4311yescharacteristic
202C4—42no—
203C4—862no—
204C4—1724no—
205C4#1306329612yes—
206C4C22×C22⋊D4311yescharacteristic
207C4C2×#1062190011yescharacteristic
208C2—22no—
209C2—82no—
210C2—864no—
211C2C2×#1306329611yescharacteristic
212C2#135×D4312yes—
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#135×C43C2
socleC22×C43C22×D4
hypercenterC2×#135D43
hypocenterC43#3050
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×C8×D43C2semidirect
2. #14583406C2semidirect
3. #14583137C2semidirect
4. #14583132C2semidirect
5. #14583125C2semidirect
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
94. C2×D43#135semidirect
107. C2×#135D43semidirect
115. C43#3050semidirect
119. C2×Q16C2×D43semidirect
120. C2×SD16C2×D43semidirect
121. C2×D8C2×D43semidirect
158. C2×C8C22⋊D43semidirect