Finite Group Databasebeta

← #19133739

Subgroups — #19133739

Order 5504.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583614C211yesmaximal, characteristic
2#14583278C211yesmaximal, characteristic, complemented
3#14583186C211yesmaximal, characteristic, complemented
4#14582647C211yesmaximal, characteristic, complemented
5D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic, complemented
7C43×#476C211yesmaximal, characteristic, complemented
8C2×#10621885—22no—
9#13063325C2211yescharacteristic
10#13063311—22no—
11#13063299—21no—
12#13063296—21no—
13C4×D172C2211yescharacteristic
14#13063284—21no—
15#13063283—21no—
16#13063256—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18#13063245—21no—
19C4×C43⋊C8C2211yescharacteristic
20C4⋊Q8×C43C2211yescharacteristic
21C4×D4×C43C2211yescharacteristic
22#106×C43—21no—
23C4⋊C8×C43C2211yescharacteristic
24#102×C43—21no—
25C2×Q8×C43—21no—
26C2×D4×C43D411yescharacteristic
27C22×C4×C43—21no—
28C2×C22⋊D43—22no—
29C2×D172D411yescharacteristic
30C2×C4×D43—21no—
31C2×Dic86D412yes—
32C2×C8×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43D411yescharacteristic
36C22⋊C4×C43—21no—
37C42×C43C2311yescharacteristic
38C22⋊Dic43—22no—
39#10621885—44no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43D411yescharacteristic
45C4×Dic43—22no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C23×C43—21no—
49C22×D43—21no—
50Q8×C43—42no—
51D4×C43—21no—
52D4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C22⋊D43—82no—
61C2×Dic43—21no—
62C2×Dic43—22no—
63D172—21no—
64D172—21no—
65C4×D43—41no—
66C4×D43—41no—
67Dic86—42no—
68C8×C43—41no—
69C43⋊C8—22no—
70C43⋊C8—41no—
71C22×C43—41no—
72C22×C43—41no—
73C22×C43—41no—
74C22×C43#12011yescharacteristic
75C2×D43—41no—
76C2×D43—41no—
77C2×D43—41no—
78C4×C43—21no—
79C4×C43—41no—
80C4×C43—81no—
81C4×C43#13511yescharacteristic
82C4×C43#13511yescharacteristic
83C4×C43#13711yescharacteristic
84C4×C43#13711yescharacteristic
85Dic43—41no—
86Dic43—42no—
87#1634—431nomaximal, Sylow
88C2×C43—81no—
89C2×C43#45211yescharacteristic
90C2×C43#45211yescharacteristic
91C2×C43#45311yescharacteristic
92D43—81no—
93#555—431no—
94#494—431no—
95#476—431no—
96#476D4311yescharacteristic, complemented
97#333—431no—
98D4⋊C8—431no—
99D4⋊C8—431no—
100C43#163411yescharacteristic, complemented, Sylow
101C2×Q16—862no—
102C4⋊Q8—431no—
103C4⋊Q8C2×D4311yescharacteristic
104#124—862no—
105#121—861no—
106#121—861no—
107C4×D4—431no—
108C4×D4C2×D4311yescharacteristic
109#117—861no—
110#117—861no—
111#106—21no—
112#106—861no—
113C4⋊C8—431no—
114C4⋊C8C2×D4311yescharacteristic
115#102—21no—
116#102—861no—
117C4×C8—431no—
118C2×Q8—21no—
119C2×Q8—432no—
120C2×D4—431no—
121C2×D4—862no—
122C2×D4C22⋊D4311yescharacteristic
123C22×C4—21no—
124C22×C4—861no—
125Q16—1724no—
126C2×C8—21no—
127C2×C8—861no—
128C2×C8—861no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—431no—
132C4⋊C4—861no—
133C4⋊C4—861no—
134C4⋊C4C22⋊D4311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—862no—
137C22⋊C4—862no—
138C22⋊C4—861no—
139C42—862no—
140C42C22×D4311yescharacteristic
141C23—21no—
142C23—861no—
143Q8—42no—
144Q8—1722no—
145D4—21no—
146D4—21no—
147D4—861no—
148D4—861no—
149D4—3442no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—861no—
155C2×C4—862no—
156C2×C4—1721no—
157C2×C4—1721no—
158C2×C4D4×D4311yescharacteristic
159C2×C4D4×D4311yescharacteristic
160C2×C4C2×C22⋊D4311yescharacteristic
161C8—41no—
162C8—862no—
163C8—1721no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—1721no—
168C22—1721no—
169C22—1721no—
170C22#1306329311yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—1721no—
175C4—1722no—
176C4#1306334511yescharacteristic
177C4#1306334611yescharacteristic
178C4#1306335411yescharacteristic
179C4#1306335611yescharacteristic
180C2—81no—
181C2—3441no—
182C2#1458305811yescharacteristic
183C2#1458305911yescharacteristic
184C2#1458306511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#476C2
socleC22×C43#120
hypercenter#476D43
hypocenterC43#1634
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14583278C2semidirect
3. #14583186C2semidirect
4. #14582647C2semidirect
5. D4⋊(C43⋊C8)C2semidirect
6. #14582626C2semidirect
7. C43×#476C2semidirect
96. #476D43semidirect
100. C43#1634semidirect