Finite Group Databasebeta

← #19136558

Subgroups — #19136558

Order 5504.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#14583712C211yesmaximal, characteristic, complemented
2#14583335C211yesmaximal, characteristic, complemented
3#14583166C211yesmaximal, characteristic, complemented
4#14582715C211yesmaximal, characteristic, complemented
5#14582707C211yesmaximal, characteristic, complemented
6#14582682C211yesmaximal, characteristic, complemented
7C2×SD32×C43C211yesmaximal, characteristic, complemented
8#13063373—21no—
9#13063357—22no—
10#13063356—21no—
11#13063351—21no—
12#13063348—21no—
13#13063347C2211yescharacteristic
14Q16×D43—21no—
15#13063331C2211yescharacteristic
16#13063269—21no—
17#13063266—21no—
18#13063265C2211yescharacteristic
19#13063261C2211yescharacteristic
20#13063242—21no—
21C2×Q16×C43C2211yescharacteristic
22C2×D8×C43C2211yescharacteristic
23SD32×C43—22no—
24C2×C16×C43C2211yescharacteristic
25C2×Q8×C43—21no—
26C2×D4×C43—21no—
27#10621902—22no—
28#10621902—41no—
29Q8×D43—22no—
30Q8×D43—41no—
31#10621898—21no—
32#10621898—42no—
33#10621898D411yescharacteristic
34Q16×C43—21no—
35Q16×C43D412yes—
36D8×C43—21no—
37D8×C43—21no—
38C2×C8×C43C2311yescharacteristic
39#10621885—22no—
40#10621884—22no—
41#10621883—41no—
42#10621882—41no—
43#10621877—21no—
44#10621877D411yescharacteristic
45Dic172D411yescharacteristic
46D344D411yescharacteristic
47#10621873—21no—
48#10621872—21no—
49C8×D43—21no—
50C16×C43—21no—
51C43⋊C16—21no—
52C23×C43—41no—
53Q8×C43—22no—
54Q8×C43—41no—
55D4×C43—41no—
56D4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43C2×D411yescharacteristic
59C22⋊D43—21no—
60C22⋊D43—41no—
61D172—21no—
62D172—42no—
63D172D811yescharacteristic
64C4×D43—21no—
65C4×D43—42no—
66C4×D43—42no—
67C4×D43—41no—
68Dic86—21no—
69Dic86—42no—
70Dic86D811yescharacteristic
71C8×C43C2×D411yescharacteristic
72C8×C43C2×D411yescharacteristic
73C43⋊C8—21no—
74C43⋊C8—41no—
75C22×C43—81no—
76C22×C43—161no—
77C22×C43AGL(1,ℤ/8)11yescharacteristic
78C2×D43—21no—
79C2×D43—41no—
80C4×C43—42no—
81C4×C43#12011yescharacteristic
82C4×C43C2×D811yescharacteristic
83Dic43—21no—
84Dic43—41no—
85#2193—431nomaximal, Sylow
86C2×C43—21no—
87C2×C43—161no—
88C2×C43#44711yescharacteristic
89D43—41no—
90D43—81no—
91#578—431no—
92#509—431no—
93C2×SD32D4311yescharacteristic, complemented
94#472—431no—
95#362—431no—
96#359—431no—
97#350—431no—
98C43#219311yescharacteristic, complemented, Sylow
992−1+4—861no—
100#137—861no—
101#137—862no—
102AGL(1,ℤ/8)—861no—
103#135—431no—
104#135—861no—
105C2×Q16—861no—
106C2×Q16C2×D4311yescharacteristic
107C2×D8C2×D4311yescharacteristic
108#131—431no—
109SD32—22no—
110SD32—861no—
111D16—861no—
112M32—431no—
113C2×C16C2×D4311yescharacteristic
114#108—431no—
115#100—861no—
116#41—431no—
117#41—862no—
118#41—861no—
119#41—1722no—
120#41—1721no—
121C2×Q8—21no—
122C2×Q8—862no—
123C2×Q8—1721no—
124C2×D4—21no—
125Q16—21no—
126Q16—431no—
127Q16—862no—
128Q16C22⋊D4312yes—
129SD16—862no—
130SD16—861no—
131SD16—1721no—
132D8—21no—
133D8—21no—
134D8—431no—
135D8—1721no—
136M16—431no—
137M16—861no—
138M16—861no—
139C2×C8—861no—
140C2×C8C22×D4311yescharacteristic
141C16—21no—
142C16—861no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—431no—
147Q8—861no—
148Q8—1722no—
149D4—41no—
150D4—41no—
151D4—431no—
152D4—861no—
153D4—861no—
154D4—1722no—
155D4—1721no—
156C2×C4—41no—
157C2×C4—861no—
158C2×C4—1722no—
159C2×C4—1722no—
160C2×C4—1721no—
161C2×C4D4×D4311yescharacteristic
162C8—861no—
163C8—1721no—
164C8D4×D4311yescharacteristic
165C8C2×C22⋊D4311yescharacteristic
166C22—81no—
167C22—161no—
168C22—861no—
169C22—1721no—
170C22#1306334911yescharacteristic
171C4—42no—
172C4—861no—
173C4—1721no—
174C4#1306329311yescharacteristic
175C4D8×D4311yescharacteristic
176C2—21no—
177C2—161no—
178C2—3441no—
179C2—1721no—
180C2#1458303111yescharacteristic
subgroupG/H
centerC2#14583031
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC2×SD32×C43C2
socleC2×C43#447
hypercenterC2×SD32D43
hypocenterC43#2193
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14583712C2semidirect
2. #14583335C2semidirect
3. #14583166C2semidirect
4. #14582715C2semidirect
5. #14582707C2semidirect
6. #14582682C2semidirect
7. C2×SD32×C43C2semidirect
93. C2×SD32D43semidirect
98. C43#2193semidirect