Finite Group Databasebeta

← #19133730

Subgroups — #19133730

Order 5504.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583610C211yesmaximal, characteristic
2#14583278C211yesmaximal, characteristic, complemented
3#14583195C211yesmaximal, characteristic, complemented
4#14583190C211yesmaximal, characteristic
5#14582629C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic
7C43×#333C211yesmaximal, characteristic, complemented
8C2×#10621885—22no—
9#13063325C2211yescharacteristic
10#13063316—21no—
11#13063305—21no—
12#13063301—22no—
13C4×Dic86C2211yescharacteristic
14C4×D172C2211yescharacteristic
15#13063287—21no—
16C4⋊C4×D43—21no—
17#13063259—21no—
18#13063257—21no—
19#13063250—21no—
20#13063247—21no—
21C4×C43⋊C8C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4⋊C8×C43C2211yescharacteristic
25C2×Q8×C43D412yes—
26C2×D172D411yescharacteristic
27C2×C4×D43—21no—
28C2×C4×D43—22no—
29C2×Dic86—21no—
30C2×Dic86D411yescharacteristic
31C2×C8×C43—21no—
32C2×C8×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C42×C43C2311yescharacteristic
36#10621885—44no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—21no—
39C4⋊Dic43—22no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43D411yescharacteristic
43C4⋊Dic43D411yescharacteristic
44Dic43⋊C4—22no—
45Dic43⋊C4—21no—
46C4×Dic43—21no—
47C2×C43⋊C8—21no—
48C22×D43—21no—
49Q8×C43—42no—
50C2×C4×C43—22no—
51C2×C4×C43C2×D411yescharacteristic
52C2×C4×C43C2×D411yescharacteristic
53C2×C4×C43C2×D411yescharacteristic
54C2×Dic43—21no—
55C2×Dic43—21no—
56C2×Dic43—21no—
57C2×Dic43—41no—
58D172—21no—
59D172Q1612yescomplemented
60C4×D43—41no—
61C4×D43—41no—
62C4×D43—82no—
63Dic86—21no—
64Dic86—21no—
65Dic86—42no—
66C8×C43—41no—
67C8×C43—41no—
68C43⋊C8—22no—
69C22×C43#12011yescharacteristic
70C2×D43—22no—
71C2×D43—41no—
72C2×D43—41no—
73C4×C43—21no—
74C4×C43—42no—
75C4×C43C2×Q1611yescharacteristic
76C4×C43#13511yescharacteristic
77C4×C43#13711yescharacteristic
78C4×C43#13711yescharacteristic
79Dic43—41no—
80Dic43—41no—
81Dic43—41no—
82Dic43—81no—
83#1632—431nomaximal, Sylow
84C2×C43#45111yescharacteristic
85C2×C43#45211yescharacteristic
86C2×C43#45311yescharacteristic
87D43—42no—
88#554—431no—
89#494—431no—
90#477—431no—
91#476—431no—
92#333D4311yescharacteristic, complemented
93Q8⋊C8—431no—
94D4⋊C8—431no—
95C43#163211yescharacteristic, complemented, Sylow
96C2×Q16—862no—
97C4⋊Q8—431no—
98C4⋊Q8C2×D4311yescharacteristic
99#125—861no—
100C22⋊Q8—861no—
101C22⋊Q8—862no—
102C4×Q8—431no—
103C4×D4—431no—
104C4×D4—861no—
105C2×C4⋊C4—861no—
106#107—861no—
107#106—861no—
108C4⋊C8C2×D4311yescharacteristic
109C4⋊C8C2×D4311yescharacteristic
110#103—861no—
111#102—861no—
112C4×C8—431no—
113C2×Q8—431no—
114C2×Q8—861no—
115C2×Q8D17212yes—
116C2×D4—431no—
117C22×C4—862no—
118C22×C4—861no—
119Q16—1724no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—861no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—431no—
126C4⋊C4—431no—
127C4⋊C4—862no—
128C4⋊C4—862no—
129C4⋊C4—861no—
130C4⋊C4—861no—
131C4⋊C4—861no—
132C22⋊C4—862no—
133C22⋊C4—861no—
134C42—861no—
135C42C22×D4311yescharacteristic
136C23—861no—
137Q8—42no—
138Q8—861no—
139Q8—861no—
140Q8—1722no—
141D4—432no—
142D4—861no—
143C2×C4—22no—
144C2×C4—861no—
145C2×C4—861no—
146C2×C4—861no—
147C2×C4—3442no—
148C2×C4—1721no—
149C2×C4—1721no—
150C2×C4—1721no—
151C2×C4C2×D17211yescharacteristic
152C2×C4D4×D4311yescharacteristic
153C2×C4D4×D4311yescharacteristic
154C8—41no—
155C8—41no—
156C8—862no—
157C22—862no—
158C22—1721no—
159C22—1721no—
160C22#1306329511yescharacteristic
161C4—21no—
162C4—42no—
163C4—3441no—
164C4—1721no—
165C4—1721no—
166C4—1721no—
167C4Q16×D4311yescharacteristic
168C4#1306334611yescharacteristic
169C4#1306335411yescharacteristic
170C4#1306335711yescharacteristic
171C2—1722no—
172C2#1458305611yescharacteristic
173C2#1458306411yescharacteristic
174C2#1458306911yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#333C2
socleC22×C43#120
hypercenter#333D43
hypocenterC43#1632
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14583278C2semidirect
3. #14583195C2semidirect
5. #14582629C2semidirect
7. C43×#333C2semidirect
59. D172Q16semidirect
92. #333D43semidirect
95. C43#1632semidirect