Finite Group Databasebeta

← #19133905

Subgroups — #19133905

Order 5504.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14583653C211yesmaximal, characteristic
2#14583305C211yesmaximal, characteristic, complemented
3#14583291C211yesmaximal, characteristic
4#14582641C211yesmaximal, characteristic, complemented
5#14582640C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic
7C43×#501C211yesmaximal, characteristic, complemented
8C2×#10621885—21no—
9C2×#10621884—21no—
10#13063324—21no—
11#13063320—21no—
12#13063320—21no—
13#13063317C2211yescharacteristic
14#13063313C2211yescharacteristic
15#13063310—21no—
16#13063305—21no—
17#13063303—21no—
18#13063258—21no—
19#13063256—21no—
20#13063236C2211yescharacteristic
21#13063236C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23#125×C43C2211yescharacteristic
24#107×C43—21no—
25#106×C43—21no—
26#97×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×D172D411yescharacteristic
29C2×C4×D43—21no—
30C2×Dic86—21no—
31C2×Dic86D411yescharacteristic
32C2×C8×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C4⋊C4×C43D411yescharacteristic
39C42×C43C2311yescharacteristic
40#10621885—42no—
41#10621884—42no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—21no—
47C4⋊Dic43—21no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56C22×D43—21no—
57Q8×C43—41no—
58Q8×C43—41no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—41no—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68D172—41no—
69C4×D43—81no—
70Dic86—41no—
71Dic86—81no—
72C8×C43—22no—
73C43⋊C8—22no—
74C43⋊C8—22no—
75C22×C43#12011yescharacteristic
76C2×D43—41no—
77C2×D43—41no—
78C2×D43—41no—
79C4×C43—21no—
80C4×C43—21no—
81C4×C43—21no—
82C4×C43—41no—
83C4×C43—41no—
84C4×C43—81no—
85Dic43—41no—
86Dic43—41no—
87Dic43—41no—
88#1660—431nomaximal, Sylow
89C2×C43#45311yescharacteristic
90C2×C43#45611yescharacteristic
91C2×C43#45611yescharacteristic
92D43—81no—
93#563—431no—
94#501—431no—
95#501D4311yescharacteristic, complemented
96#497—431no—
97#330—431no—
98#330—431no—
99#329—431no—
100C43#166011yescharacteristic, complemented, Sylow
101C2×Q16—861no—
102C2×SD16—861no—
103C4⋊Q8—861no—
104C4⋊Q8C2×D4311yescharacteristic
105#126—861no—
106#126—861no—
107#125—431no—
108#125C2×D4311yescharacteristic
109#124—431no—
110#123—861no—
111C22⋊Q8—861no—
112C22⋊Q8—861no—
113#107—21no—
114#107—861no—
115#106—21no—
116#106—861no—
117#97—431no—
118#97—431no—
119#97C2×D4311yescharacteristic
120C2×Q8—21no—
121C2×Q8—431no—
122C2×Q8—861no—
123C2×D4—431no—
124C22×C4—861no—
125Q16—1722no—
126SD16—1722no—
127C2×C8—21no—
128C2×C8—861no—
129C2×C8—861no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—431no—
135C4⋊C4—431no—
136C4⋊C4—861no—
137C4⋊C4—861no—
138C4⋊C4—861no—
139C4⋊C4—861no—
140C4⋊C4C22⋊D4311yescharacteristic
141C4⋊C4C22⋊D4311yescharacteristic
142C22⋊C4—861no—
143C22⋊C4—861no—
144C22⋊C4—861no—
145C22⋊C4—861no—
146C22⋊C4—861no—
147C42—861no—
148C42C22×D4311yescharacteristic
149C23—861no—
150Q8—41no—
151Q8—41no—
152Q8—3441no—
153Q8—1721no—
154D4—1721no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—861no—
159C2×C4—861no—
160C2×C4—861no—
161C2×C4—3441no—
162C2×C4D4×D4311yescharacteristic
163C2×C4D4×D4311yescharacteristic
164C2×C4C2×C22⋊D4311yescharacteristic
165C8—22no—
166C8—862no—
167C8—862no—
168C22—1721no—
169C22—1721no—
170C22—1721no—
171C22#1306329311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—1721no—
179C4—1721no—
180C4—1721no—
181C2—3441no—
182C2#1458306511yescharacteristic
183C2#1458308011yescharacteristic
184C2#1458308111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#501C2
socleC22×C43#120
hypercenter#501D43
hypocenterC43#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #14583305C2semidirect
4. #14582641C2semidirect
5. #14582640C2semidirect
7. C43×#501C2semidirect
95. #501D43semidirect
100. C43#1660semidirect