Finite Group Databasebeta

← #19135013

Subgroups — #19135013

Order 5504.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#14583406C211yesmaximal, characteristic
2#14582883C211yesmaximal, characteristic, complemented
3#14582862C212yesmaximal, complemented
4#14582670C212yesmaximal, complemented
5C43×#568C211yesmaximal, characteristic, complemented
6C22×C4×D43C2211yescharacteristic
7C2×#10621877C2212yes—
8#13063306C412yes—
9#13063301—21no—
10#13063296—21no—
11#13063293C412yes—
12C4×C22⋊D43—22no—
13#13063284C2211yescharacteristic
14#13063244—21no—
15#13063242—21no—
16(C2×D43)⋊C8—24no—
17C2×#41×C43C2211yescharacteristic
18#131×C43—24no—
19C2×M16×C43—22no—
20C2×M16×C43C2212yes—
21C23×D43C2×C411yescharacteristic
22#41×C43—22no—
23#41×C43—22no—
24C2×Q8×C43D411yescharacteristic
25C2×D4×C43C2×C412yes—
26C2×D4×C43D411yescharacteristic
27C22×C4×C43D412yes—
28C22×C4×C43C2311yescharacteristic
29C2×C22⋊D43—22no—
30C22×Dic43C2×C411yescharacteristic
31C2×C4×D43—22no—
32C2×C4×D43—21no—
33C2×C4×D43—21no—
34C2×C4×D43—22no—
35M16×C43—24no—
36M16×C43—22no—
37M16×C43—22no—
38C2×C8×C43—24no—
39C2×C8×C43D414yescomplemented
40C22⋊Dic43—22no—
41C22⋊Dic43C2×C412yes—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43—21no—
44Dic43⋊C4—22no—
45C4×Dic43—21no—
46#10621877—22no—
47#10621877—22no—
48C2×C43⋊C8—22no—
49C23×C43C22⋊C412yes—
50C23×C43C22×C411yescharacteristic
51C22×D43—21no—
52C22×D43—22no—
53C22×D43—42no—
54Q8×C43—22no—
55D4×C43—24no—
56D4×C43—22no—
57C2×C4×C43—22no—
58C2×C4×C43—22no—
59C2×C4×C43C22⋊C412yes—
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D412yes—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43#4112yes—
64C22⋊D43—44no—
65C2×Dic43—22no—
66C2×Dic43—21no—
67C2×Dic43—22no—
68C4×D43—41no—
69C4×D43—42no—
70C4×D43—41no—
71C8×C43—24no—
72C43⋊C8—42no—
73C22×C43—22no—
74C22×C43—41no—
75C22×C43—42no—
76C22×C43C2×C22⋊C411yescharacteristic
77C22×C43C4×D412yes—
78C2×D43—24no—
79C2×D43—22no—
80C2×D43—41no—
81C2×D43—42no—
82C2×D43—41no—
83C4×C43—22no—
84C4×C43#12011yescharacteristic
85C4×C43#12112yes—
86C4×C43#12311yescharacteristic
87Dic43—42no—
88Dic43—41no—
89#1891—431nomaximal, Sylow
90C2×C43—21no—
91C2×C43—22no—
92C2×C43—42no—
93C2×C43#38611yescharacteristic
94D43—42no—
95#568D4311yescharacteristic, complemented
96#525—431no—
97#413—431no—
98#407—432no—
99#344—432no—
100C43#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D4311yescharacteristic
102C23×C4—431no—
103#131—24no—
104C2×M16—22no—
105C2×M16—432no—
106C2×M16C2×D4312yes—
107#123—432no—
108C22⋊Q8—861no—
109#121—861no—
110#120—432no—
111C4×D4—862no—
112#117—431no—
113#101—861no—
114#100—861no—
115C22⋊C8—864no—
116C24—431no—
117#41—22no—
118#41—22no—
119C2×Q8D17211yescharacteristic
120C2×D4—862no—
121C2×D4C4×D4312yes—
122C2×D4D17211yescharacteristic
123C22×C4—431no—
124C22×C4—861no—
125C22×C4—862no—
126C22×C4—862no—
127C22×C4—861no—
128C22×C4C22⋊D4312yes—
129C22×C4C22×D4311yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—862no—
134M16—862no—
135C2×C8—24no—
136C2×C8—862no—
137C2×C8C22⋊D4314yescomplemented
138C4⋊C4—862no—
139C4⋊C4—861no—
140C22⋊C4—432no—
141C22⋊C4—862no—
142C22⋊C4—862no—
143C42—861no—
144C23—861no—
145C23—862no—
146C23—1722no—
147C23(C2×D43)⋊C412yes—
148C23C2×C4×D4311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—1724no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—862no—
156C2×C4—861no—
157C2×C4—862no—
158C2×C4—1721no—
159C2×C4—1722no—
160C2×C4—1721no—
161C2×C4(C2×D43)⋊C412yes—
162C2×C4C2×D17211yescharacteristic
163C2×C4#1062189812yes—
164C2×C4C2×C22⋊D4312yes—
165C2×C4C2×C22⋊D4311yescharacteristic
166C8—24no—
167C8—1722no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—862no—
172C22—864no—
173C22—1721no—
174C22—1722no—
175C22—1721no—
176C22C2×(C2×D43)⋊C411yescharacteristic
177C22C4×C22⋊D4312yes—
178C4—22no—
179C4—1722no—
180C4—1721no—
181C4#1306329411yescharacteristic
182C4#1306329912yes—
183C4#1306330811yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—1722no—
188C2#1458277811yescharacteristic
subgroupG/H
centerC4#13063294
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#568C2
socleC2×C43#386
hypercenter#568D43
hypocenterC43#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #14582883C2semidirect
3. #14582862C2semidirect
4. #14582670C2semidirect
5. C43×#568C2semidirect
39. C2×C8×C43D4semidirect
95. #568D43semidirect
100. C43#1891semidirect
137. C2×C8C22⋊D43semidirect