Finite Group Databasebeta

← #19133908

Subgroups — #19133908

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#14583309C211yesmaximal, characteristic, complemented
3#14583308C211yesmaximal, characteristic, complemented
4#14583293C211yesmaximal, characteristic
5#14582640C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic
7C43×#330C211yesmaximal, characteristic, complemented
8C2×Dic172—21no—
9C2×#10621873—21no—
10#13063325C2211yescharacteristic
11#13063324—21no—
12#13063320—21no—
13#13063320—21no—
14#13063317C2211yescharacteristic
15#13063313C2211yescharacteristic
16#13063310—21no—
17#13063305—21no—
18#13063303—21no—
19#13063259—21no—
20#13063258—21no—
21#13063257—21no—
22#13063256—21no—
23#13063236C2211yescharacteristic
24#125×C43C2211yescharacteristic
25#97×C43C2211yescharacteristic
26#97×C43C2211yescharacteristic
27C2×D172D411yescharacteristic
28C2×C4×D43—21no—
29C2×Dic86—21no—
30C2×Dic86—21no—
31C2×Dic86D411yescharacteristic
32C2×C8×C43—21no—
33C2×C8×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43D411yescharacteristic
37C4⋊C4×C43D411yescharacteristic
38C42×C43C2311yescharacteristic
39(C2×D43)⋊C4—21no—
40(C2×D43)⋊C4—21no—
41(C2×D43)⋊C4—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43—21no—
47C4⋊Dic43D411yescharacteristic
48C4⋊Dic43D411yescharacteristic
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C2×C43⋊C8—21no—
54Dic172—42no—
55#10621873—42no—
56C22×D43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65C2×Dic43—41no—
66D172—41no—
67C4×D43—81no—
68Dic86—41no—
69Dic86—41no—
70Dic86—41no—
71Dic86—81no—
72C8×C43—22no—
73C8×C43—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—
84Dic43—41no—
85Dic43—41no—
86Dic43—41no—
87Dic43—81no—
88#1660—431nomaximal, Sylow
89C2×C43#45311yescharacteristic
90C2×C43#45611yescharacteristic
91C2×C43#45611yescharacteristic
92D43—81no—
93#563—431no—
94#501—431no—
95#501—431no—
96#497—431no—
97#330—431no—
98#330D4311yescharacteristic, complemented
99#329—431no—
100C43#166011yescharacteristic, complemented, Sylow
101C2×Q16—861no—
102C2×SD16—861no—
103C4⋊Q8—431no—
104C4⋊Q8—861no—
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—861no—
114#107—861no—
115#106—861no—
116#106—861no—
117#97—431no—
118#97C2×D4311yescharacteristic
119#97C2×D4311yescharacteristic
120C2×Q8—431no—
121C2×Q8—861no—
122C2×Q8—861no—
123C2×D4—431no—
124C22×C4—861no—
125Q16—1722no—
126SD16—1722no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—861no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—431no—
133C4⋊C4—431no—
134C4⋊C4—861no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C4⋊C4—861no—
138C4⋊C4—861no—
139C4⋊C4—861no—
140C4⋊C4D17211yescharacteristic
141C4⋊C4D17211yescharacteristic
142C22⋊C4—861no—
143C22⋊C4—861no—
144C22⋊C4—861no—
145C22⋊C4—861no—
146C22⋊C4—861no—
147C42—861no—
148C42C22×D4311yescharacteristic
149C23—861no—
150Q8—3441no—
151Q8—1721no—
152Q8—1721no—
153Q8—1721no—
154D4—1721no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—861no—
158C2×C4—861no—
159C2×C4—861no—
160C2×C4—3441no—
161C2×C4—1721no—
162C2×C4C2×D17211yescharacteristic
163C2×C4D4×D4311yescharacteristic
164C2×C4D4×D4311yescharacteristic
165C8—22no—
166C8—22no—
167C8—862no—
168C22—1721no—
169C22—1721no—
170C22—1721no—
171C22#1306329511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—3441no—
178C4—1721no—
179C4—1721no—
180C4—1721no—
181C2—3441no—
182C2#1458306811yescharacteristic
183C2#1458308311yescharacteristic
184C2#1458308411yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#330C2
socleC22×C43#120
hypercenter#330D43
hypocenterC43#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14583309C2semidirect
3. #14583308C2semidirect
5. #14582640C2semidirect
7. C43×#330C2semidirect
98. #330D43semidirect
100. C43#1660semidirect