Finite Group Databasebeta

← #19133892

Subgroups — #19133892

Order 5504.

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

normal subgroups only

This group has 206 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, complemented
2#14583286C211yesmaximal, characteristic
3#14583263C211yesmaximal, characteristic, complemented
4#14582641C211yesmaximal, characteristic, complemented
5#14582640C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#490C211yesmaximal, characteristic, complemented
8C2×#10621883—21no—
9C2×#10621882—21no—
10#13063324—21no—
11#13063320—21no—
12#13063320—21no—
13#13063317C2211yescharacteristic
14#13063313C2211yescharacteristic
15#13063310—21no—
16#13063305—21no—
17#13063303—21no—
18#13063246—21no—
19#13063246—21no—
20#13063236C2211yescharacteristic
21#13063236C2211yescharacteristic
22#127×C43C2211yescharacteristic
23#125×C43C2211yescharacteristic
24#102×C43—21no—
25#102×C43—21no—
26#97×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43—21no—
30C2×D172D411yescharacteristic
31C2×C4×D43—21no—
32C2×Dic86—21no—
33C2×Dic86D411yescharacteristic
34C2×C8×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C4⋊C4×C43D411yescharacteristic
39C42×C43C2311yescharacteristic
40#10621883—42no—
41#10621882—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—
56C23×C43—41no—
57C22×D43—21no—
58D4×C43—41no—
59D4×C43—41no—
60D4×C43—42no—
61D4×C43—42no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70D172—41no—
71C4×D43—81no—
72Dic86—41no—
73Dic86—81no—
74C8×C43—41no—
75C43⋊C8—22no—
76C43⋊C8—41no—
77C22×C43—81no—
78C22×C43—81no—
79C22×C43—81no—
80C22×C43#12011yescharacteristic
81C2×D43—41no—
82C2×D43—41no—
83C2×D43—41no—
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—21no—
87C4×C43—41no—
88C4×C43—41no—
89Dic43—41no—
90Dic43—41no—
91Dic43—41no—
92#1657—431nomaximal, Sylow
93C2×C43—161no—
94C2×C43#45311yescharacteristic
95C2×C43#45411yescharacteristic
96C2×C43#45411yescharacteristic
97D43—81no—
98#563—431no—
99#496—431no—
100#490—431no—
101#490D4311yescharacteristic, complemented
102#330—431no—
103#330—431no—
104#329—431no—
105C43#165711yescharacteristic, complemented, Sylow
106C2×SD16—861no—
107C2×D8—861no—
108C4⋊Q8—861no—
109#127C2×D4311yescharacteristic
110#126—861no—
111#126—861no—
112#125—431no—
113#125C2×D4311yescharacteristic
114#124—431no—
115#123—861no—
116C22⋊Q8—861no—
117C22⋊Q8—861no—
118#102—21no—
119#102—21no—
120#102—861no—
121#102—861no—
122#97—431no—
123#97—431no—
124#97C2×D4311yescharacteristic
125C2×Q8—431no—
126C2×Q8—861no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—431no—
131C22×C4—861no—
132SD16—1722no—
133D8—1722no—
134C2×C8—21no—
135C2×C8—861no—
136C2×C8—861no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—431no—
140C4⋊C4—431no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4C22⋊D4311yescharacteristic
146C4⋊C4C22⋊D4311yescharacteristic
147C22⋊C4—861no—
148C22⋊C4—861no—
149C22⋊C4—861no—
150C22⋊C4—861no—
151C22⋊C4—861no—
152C42—861no—
153C42C22×D4311yescharacteristic
154C23—41no—
155C23—861no—
156Q8—3441no—
157Q8—1721no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—1721no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—861no—
166C2×C4—861no—
167C2×C4—861no—
168C2×C4—3441no—
169C2×C4D4×D4311yescharacteristic
170C2×C4D4×D4311yescharacteristic
171C2×C4C2×C22⋊D4311yescharacteristic
172C8—41no—
173C8—862no—
174C8—1721no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—1721no—
179C22—1721no—
180C22—1721no—
181C22#1306329311yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—1721no—
188C4—1721no—
189C4—1721no—
190C2—161no—
191C2—3441no—
192C2#1458306511yescharacteristic
193C2#1458307011yescharacteristic
194C2#1458307111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#490C2
socleC22×C43#120
hypercenter#490D43
hypocenterC43#1657
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583653C2semidirect
3. #14583263C2semidirect
4. #14582641C2semidirect
5. #14582640C2semidirect
6. #14582638C2semidirect
7. C43×#490C2semidirect
101. #490D43semidirect
105. C43#1657semidirect