Finite Group Databasebeta

← #19133910

Subgroups — #19133910

Order 5504.

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

normal subgroups only

This group has 208 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#14583647C211yesmaximal, characteristic
2#14583291C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14582641C211yesmaximal, characteristic, complemented
5#14582638C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#501C211yesmaximal, characteristic, complemented
8C2×#10621885—21no—
9C2×#10621884—21no—
10#13063313C2211yescharacteristic
11#13063313C2211yescharacteristic
12#13063310—21no—
13#13063310—21no—
14#13063303—21no—
15#13063303—21no—
16#13063300—21no—
17#13063300—21no—
18#13063248—21no—
19#13063245—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×D172—21no—
29C2×D172—21no—
30C2×D172D411yescharacteristic
31C2×D172D411yescharacteristic
32C2×C4×D43—21no—
33C2×C4×D43—21no—
34C2×Dic86D411yescharacteristic
35C2×Dic86D411yescharacteristic
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C4⋊C4×C43D411yescharacteristic
43C42×C43C2311yescharacteristic
44#10621885—42no—
45#10621884—42no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56C22×D43—21no—
57C22×D43—21no—
58Q8×C43—41no—
59Q8×C43—41no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—41no—
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×Dic43—21no—
67C2×Dic43—21no—
68D172—41no—
69D172—41no—
70D172—81no—
71D172—81no—
72C4×D43—81no—
73C4×D43—81no—
74Dic86—41no—
75Dic86—41no—
76C8×C43—22no—
77C43⋊C8—22no—
78C43⋊C8—41no—
79C22×C43#12011yescharacteristic
80C2×D43—41no—
81C2×D43—41no—
82C2×D43—41no—
83C2×D43—41no—
84C2×D43—41no—
85C2×D43—41no—
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C43—41no—
90C4×C43—41no—
91C4×C43—81no—
92Dic43—41no—
93Dic43—41no—
94#1661—431nomaximal, Sylow
95C2×C43#45311yescharacteristic
96C2×C43#45511yescharacteristic
97C2×C43#45611yescharacteristic
98D43—81no—
99D43—81no—
100#562—431no—
101#501D4311yescharacteristic, complemented
102#497—431no—
103#489—431no—
104#330—431no—
105#329—431no—
106#329—431no—
107C43#166111yescharacteristic, complemented, Sylow
108C2×Q16—861no—
109C2×SD16—861no—
110C4⋊Q8C2×D4311yescharacteristic
111#125C2×D4311yescharacteristic
112#124—431no—
113#124—431no—
114#123—861no—
115#123—861no—
116C22⋊Q8—861no—
117C22⋊Q8—861no—
118#121—861no—
119#121—861no—
120#107—21no—
121#106—21no—
122#103—861no—
123#102—861no—
124#97—431no—
125#97—431no—
126#97C2×D4311yescharacteristic
127C2×Q8—21no—
128C2×Q8—431no—
129C2×Q8—431no—
130C2×D4—431no—
131C2×D4—431no—
132C2×D4—861no—
133C2×D4—861no—
134C22×C4—861no—
135C22×C4—861no—
136Q16—1722no—
137SD16—1722no—
138C2×C8—21no—
139C2×C8—861no—
140C2×C8—861no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4C22⋊D4311yescharacteristic
148C4⋊C4C22⋊D4311yescharacteristic
149C22⋊C4—861no—
150C22⋊C4—861no—
151C22⋊C4—861no—
152C22⋊C4—861no—
153C22⋊C4—861no—
154C22⋊C4—861no—
155C42C22×D4311yescharacteristic
156C23—861no—
157C23—861no—
158Q8—41no—
159Q8—41no—
160Q8—1721no—
161Q8—1721no—
162D4—3441no—
163D4—3441no—
164D4—1721no—
165D4—1721no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—861no—
170C2×C4—861no—
171C2×C4—3441no—
172C2×C4—3441no—
173C2×C4D4×D4311yescharacteristic
174C2×C4D4×D4311yescharacteristic
175C2×C4C2×C22⋊D4311yescharacteristic
176C8—22no—
177C8—862no—
178C8—1721no—
179C22—1721no—
180C22—1721no—
181C22—1721no—
182C22—1721no—
183C22—1721no—
184C22—1721no—
185C22#1306329311yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—1721no—
193C4—1721no—
194C2—3441no—
195C2—3441no—
196C2#1458306511yescharacteristic
197C2#1458307511yescharacteristic
198C2#1458308111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#501C2
socleC22×C43#120
hypercenter#501D43
hypocenterC43#1661
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. #14583291C2semidirect
3. #14583261C2semidirect
4. #14582641C2semidirect
5. #14582638C2semidirect
6. #14582638C2semidirect
7. C43×#501C2semidirect
101. #501D43semidirect
107. C43#1661semidirect