Finite Group Databasebeta

← #19135698

Subgroups — #19135698

Order 5504.

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

normal subgroups only

This group has 350 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#14583697C212yesmaximal, complemented
2#14582867C211yesmaximal, characteristic, complemented
3#14582866C212yesmaximal, complemented
4C43⋊#338C211yesmaximal, characteristic, complemented
5C43×#575C211yesmaximal, characteristic, complemented
6C2×#10621898C2211yescharacteristic
7#13063356—22no—
8#13063355—22no—
9#13063351—22no—
10#13063350—22no—
11#13063345—24no—
12C2×#10621877C2212yes—
13C22×C43⋊C8C2211yescharacteristic
14C22⋊(C43⋊C8)—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
21#41×C43—22no—
22#41×C43—22no—
23#41×C43—22no—
24#41×C43—22no—
25C2×Q8×C43D412yes—
26C2×D4×C43—22no—
27C2×D4×C43D412yes—
28C22×C4×C43—22no—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31#10621898—22no—
32#10621898—22no—
33C2×D172D411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86D411yescharacteristic
36Q16×C43—22no—
37SD16×C43—24no—
38D8×C43—22no—
39M16×C43—22no—
40C2×C8×C43D412yes—
41#10621885—24no—
42#10621884—24no—
43#10621883—24no—
44#10621882—24no—
45#10621877—22no—
46#10621877—22no—
47C2×C43⋊C8—21no—
48C2×C43⋊C8—22no—
49C2×C43⋊C8D414yes—
50C23×C43—22no—
51C23×C43#4111yescharacteristic
52C22×D43—21no—
53Q8×C43—22no—
54Q8×C43—22no—
55D4×C43—22no—
56D4×C43—22no—
57D4×C43—42no—
58D4×C43—42no—
59C2×C4×C43—22no—
60C2×C4×C43—42no—
61C2×C4×C43—42no—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D412yes—
64C2×C4×C43C2×D412yes—
65C2×C4×C43C2×D411yescharacteristic
66C22⋊D43—42no—
67C2×Dic43—21no—
68D172—22no—
69C4×D43—41no—
70C4×D43—41no—
71Dic86—22no—
72C8×C43—22no—
73C43⋊C8—24no—
74C43⋊C8—41no—
75C22×C43—41no—
76C22×C43—44no—
77C22×C43—42no—
78C22×C43#12111yescharacteristic
79C22×C43#12112yes—
80C2×D43—42no—
81C2×D43—41no—
82C4×C43—42no—
83C4×C43#12012yes—
84C4×C43#12011yescharacteristic
85C4×C43#12711yescharacteristic
86Dic43—41no—
87#2017—431nomaximal, Sylow
88C2×C43—21no—
89C2×C43—22no—
90C2×C43—82no—
91C2×C43#39211yescharacteristic
92D43—81no—
93#575—432no—
94#575D4311yescharacteristic, complemented
95#408—432no—
96#408—431no—
97#338—431no—
98C43#201711yescharacteristic, complemented, Sylow
99C2×#41—431no—
100C2×#41C2×D4312yes—
101#137—22no—
102#137—862no—
103#137—862no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—862no—
106AGL(1,ℤ/8)—862no—
107#135—22no—
108#135—864no—
109C2×M16—432no—
110C2×M16C2×D4311yescharacteristic
111C22×C8—431no—
112C22⋊C8—864no—
113C22⋊C8—862no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—862no—
119#41—862no—
120C2×Q8—431no—
121C2×Q8C22⋊D4312yes—
122C2×D4—22no—
123C2×D4—431no—
124C2×D4—861no—
125C2×D4C22⋊D4312yes—
126C22×C4—22no—
127C22×C4—861no—
128C22×C4C22×D4311yescharacteristic
129Q16—22no—
130Q16—864no—
131SD16—24no—
132SD16—864no—
133SD16—864no—
134D8—22no—
135D8—864no—
136M16—22no—
137M16—862no—
138M16—862no—
139C2×C8—434no—
140C2×C8—862no—
141C2×C8—861no—
142C2×C8C22⋊D4312yes—
143C23—22no—
144C23—861no—
145C23#1062190011yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—862no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—862no—
154D4—1722no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—861no—
159C2×C4—1721no—
160C2×C4—1721no—
161C2×C4D4×D4311yescharacteristic
162C2×C4D4×D4312yes—
163C2×C4C2×C22⋊D4312yes—
164C2×C4C2×C22⋊D4311yescharacteristic
165C8—22no—
166C8—864no—
167C8—1721no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—1722no—
172C22—1721no—
173C22#1306329611yescharacteristic
174C22#1306329712yes—
175C4—42no—
176C4—1721no—
177C4#1306329312yes—
178C4#1306329411yescharacteristic
179C4#1306332111yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—3441no—
184C2#1458280711yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#575C2
socleC2×C43#392
hypercenter#575D43
hypocenterC43#2017
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. #14583697C2semidirect
2. #14582867C2semidirect
3. #14582866C2semidirect
4. C43⋊#338C2semidirect
5. C43×#575C2semidirect
94. #575D43semidirect
98. C43#2017semidirect