Finite Group Databasebeta

← #19135659

Subgroups — #19135659

Order 5504.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#14583406C212yesmaximal, complemented
2#14582916C212yesmaximal, complemented
3#14582862C211yesmaximal, characteristic, complemented
4#14582656C211yesmaximal, characteristic, complemented
5C43×#575C211yesmaximal, characteristic, complemented
6C22×C4×D43C2211yescharacteristic
7C2×#10621877C2211yescharacteristic
8#13063306—22no—
9#13063301—22no—
10#13063296—22no—
11#13063293—22no—
12C4×C22⋊D43—24no—
13#13063284C2212yes—
14#13063252—24no—
15(C2×D43)⋊C8—22no—
16C2×#41×C43C2212yes—
17#137×C43—22no—
18AGL(1,ℤ/8)×C43—22no—
19#135×C43—22no—
20C2×M16×C43C2211yescharacteristic
21C23×D43D411yescharacteristic
22#41×C43—22no—
23#41×C43—22no—
24#41×C43—22no—
25#41×C43—22no—
26C2×Q8×C43D412yescomplemented
27C2×D4×C43—22no—
28C2×D4×C43D412yescomplemented
29C22×C4×C43—22no—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—24no—
32C22×Dic43D411yescharacteristic
33C2×C4×D43—21no—
34C2×C4×D43—22no—
35C2×C4×D43—22no—
36C2×C4×D43—21no—
37Q16×C43—22no—
38SD16×C43—24no—
39D8×C43—22no—
40M16×C43—22no—
41C2×C8×C43D412yescomplemented
42C22⋊Dic43—24no—
43C22⋊Dic43—22no—
44(C2×D43)⋊C4—24no—
45C4⋊Dic43—22no—
46Dic43⋊C4—24no—
47C4×Dic43D414yescomplemented
48#10621877—22no—
49C2×C43⋊C8—21no—
50C23×C43—22no—
51C23×C43C2×D411yescharacteristic
52C22×D43—22no—
53C22×D43—21no—
54C22×D43—42no—
55Q8×C43—22no—
56Q8×C43—22no—
57D4×C43—22no—
58D4×C43—22no—
59D4×C43—42no—
60D4×C43—42no—
61C2×C4×C43—22no—
62C2×C4×C43—42no—
63C2×C4×C43—42no—
64C2×C4×C43C2×D412yes—
65C2×C4×C43C2×D412yes—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43#4111yescharacteristic
68C22⋊D43—48no—
69C2×Dic43—24no—
70C2×Dic43—22no—
71C2×Dic43—21no—
72C4×D43—41no—
73C4×D43—42no—
74C4×D43—41no—
75C8×C43—22no—
76C43⋊C8—41no—
77C22×C43—41no—
78C22×C43—44no—
79C22×C43—42no—
80C22×C43#12012yes—
81C22×C43#12111yescharacteristic
82C2×D43—22no—
83C2×D43—24no—
84C2×D43—42no—
85C2×D43—41no—
86C2×D43—41no—
87C4×C43—42no—
88C4×C43#12011yescharacteristic
89C4×C43#12112yes—
90C4×C43#12711yescharacteristic
91Dic43—44no—
92Dic43—41no—
93#2010—431nomaximal, Sylow
94C2×C43—22no—
95C2×C43—21no—
96C2×C43—82no—
97C2×C43#39211yescharacteristic
98D43—42no—
99#575D4311yescharacteristic, complemented
100#525—432no—
101#421—432no—
102#407—431no—
103H(3,ℤ/4)—431no—
104C43#201011yescharacteristic, complemented, Sylow
105C2×#41C2×D4312yes—
106C23×C4—431no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—431no—
111C2×M16C2×D4311yescharacteristic
112#123—862no—
113C22⋊Q8—862no—
114#121—862no—
115#120—862no—
116C4×D4—864no—
117#117—432no—
118#104—864no—
119C22⋊C8—862no—
120C24—431no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D4312yescomplemented
126C2×D4—22no—
127C2×D4—864no—
128C2×D4C22⋊D4312yescomplemented
129C22×C4—22no—
130C22×C4—431no—
131C22×C4—862no—
132C22×C4—861no—
133C22×C4—861no—
134C22×C4—862no—
135C22×C4C22×D4311yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—862no—
141C2×C8—861no—
142C2×C8C22⋊D4312yescomplemented
143C4⋊C4—864no—
144C4⋊C4—862no—
145C22⋊C4—864no—
146C22⋊C4—864no—
147C22⋊C4—862no—
148C42—434no—
149C23—22no—
150C23—862no—
151C23—861no—
152C23—1722no—
153C23D4×D4311yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—1728no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—864no—
165C2×C4—862no—
166C2×C4—861no—
167C2×C4—1721no—
168C2×C4—1722no—
169C2×C4—1721no—
170C2×C4D4×D4312yes—
171C2×C4#1062190011yescharacteristic
172C2×C4C2×C22⋊D4312yes—
173C2×C4C2×C22⋊D4311yescharacteristic
174C8—22no—
175C8—1721no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—864no—
180C22—862no—
181C22—1722no—
182C22—1721no—
183C22—1721no—
184C22#1306329312yes—
185C22#1306329611yescharacteristic
186C4—42no—
187C4—1724no—
188C4—1721no—
189C4#1306329411yescharacteristic
190C4#1306329712yes—
191C4#1306332111yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—1722no—
196C2#1458280711yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#575C2
socleC2×C43#392
hypercenter#575D43
hypocenterC43#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14583406C2semidirect
2. #14582916C2semidirect
3. #14582862C2semidirect
4. #14582656C2semidirect
5. C43×#575C2semidirect
26. C2×Q8×C43D4semidirect
28. C2×D4×C43D4semidirect
41. C2×C8×C43D4semidirect
47. C4×Dic43D4semidirect
99. #575D43semidirect
104. C43#2010semidirect
125. C2×Q8C22⋊D43semidirect
128. C2×D4C22⋊D43semidirect
142. C2×C8C22⋊D43semidirect