Finite Group Databasebeta

← #19133731

Subgroups — #19133731

Order 5504.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#14583606C211yesmaximal, characteristic
2#14583279C211yesmaximal, characteristic, complemented
3#14583195C211yesmaximal, characteristic, complemented
4#14583189C211yesmaximal, characteristic
5#14582647C211yesmaximal, characteristic, complemented
6#14582631C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic
8C2×Dic172—22no—
9#13063325C2211yescharacteristic
10#13063325C2211yescharacteristic
11#13063316—21no—
12#13063304—21no—
13#13063302—22no—
14C4×Dic86C2211yescharacteristic
15D4×Dic43—21no—
16C2×C4⋊Dic43—21no—
17#13063259—21no—
18#13063256—21no—
19C4⋊(C43⋊C8)C2211yescharacteristic
20#13063250—21no—
21#13063246—21no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×D4×C43D411yescharacteristic
26C22×C4×C43—21no—
27C22×Dic43—22no—
28C2×Dic86—21no—
29C2×Dic86D411yescharacteristic
30C2×Dic86D412yes—
31C2×C8×C43—21no—
32C2×C8×C43—21no—
33C4⋊C4×C43D411yescharacteristic
34C22⋊C4×C43—21no—
35C42×C43C2311yescharacteristic
36C22⋊Dic43—22no—
37C4⋊Dic43—22no—
38C4⋊Dic43—21no—
39C4⋊Dic43—21no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43D411yescharacteristic
43Dic43⋊C4—22no—
44Dic43⋊C4—21no—
45C4×Dic43—21no—
46C2×C43⋊C8—21no—
47Dic172—44no—
48C23×C43—21no—
49D4×C43—21no—
50D4×C43Q1612yescomplemented
51C2×C4×C43—21no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43C2×D411yescharacteristic
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—21no—
58C2×Dic43—21no—
59C2×Dic43—22no—
60C2×Dic43—41no—
61C2×Dic43—82no—
62Dic86—21no—
63Dic86—21no—
64Dic86—42no—
65Dic86—42no—
66C8×C43—22no—
67C8×C43—41no—
68C43⋊C8—41no—
69C22×C43—22no—
70C22×C43—41no—
71C22×C43—41no—
72C22×C43#12011yescharacteristic
73C4×C43—21no—
74C4×C43—41no—
75C4×C43C2×Q1611yescharacteristic
76C4×C43#13511yescharacteristic
77C4×C43#13711yescharacteristic
78C4×C43#13711yescharacteristic
79Dic43—41no—
80Dic43—42no—
81Dic43—41no—
82Dic43—81no—
83#1632—431nomaximal, Sylow
84C2×C43—42no—
85C2×C43#45111yescharacteristic
86C2×C43#45211yescharacteristic
87C2×C43#45311yescharacteristic
88#554—431no—
89#494—431no—
90#477—431no—
91#476—431no—
92#333—431no—
93Q8⋊C8—431no—
94D4⋊C8D4311yescharacteristic
95C43#163211yescharacteristic, complemented, Sylow
96C2×Q16—862no—
97C4⋊Q8—431no—
98C4⋊Q8—431no—
99#125—861no—
100C22⋊Q8—862no—
101C22⋊Q8—861no—
102C4×Q8—431no—
103C4×D4—861no—
104C4×D4C2×D4311yescharacteristic
105C2×C4⋊C4—861no—
106#107—861no—
107#106—861no—
108C4⋊C8—431no—
109C4⋊C8C2×D4311yescharacteristic
110#103—861no—
111#102—861no—
112C4×C8C2×D4311yescharacteristic
113C2×Q8—431no—
114C2×Q8—432no—
115C2×Q8—861no—
116C2×D4D17211yescharacteristic
117C22×C4—21no—
118C22×C4—862no—
119Q16—1724no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—861no—
123C4⋊C4—431no—
124C4⋊C4—862no—
125C4⋊C4—862no—
126C4⋊C4—861no—
127C4⋊C4—861no—
128C4⋊C4—861no—
129C4⋊C4—861no—
130C4⋊C4—861no—
131C4⋊C4D17211yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—862no—
134C42—861no—
135C42C22×D4311yescharacteristic
136C23—21no—
137Q8—861no—
138Q8—861no—
139Q8—1722no—
140Q8—1722no—
141D4—21no—
142D4Dic17212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—861no—
147C2×C4—861no—
148C2×C4—862no—
149C2×C4—3442no—
150C2×C4—1721no—
151C2×C4C2×D17211yescharacteristic
152C2×C4D4×D4311yescharacteristic
153C2×C4D4×D4311yescharacteristic
154C8—22no—
155C8—41no—
156C8—1721no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1306329511yescharacteristic
161C4—21no—
162C4—41no—
163C4—3441no—
164C4—1721no—
165C4—1721no—
166C4—1722no—
167C4C2×Dic17211yescharacteristic
168C4#1306334411yescharacteristic
169C4#1306335411yescharacteristic
170C4#1306335811yescharacteristic
171C2—42no—
172C2#1458305711yescharacteristic
173C2#1458306211yescharacteristic
174C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1632
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14583279C2semidirect
3. #14583195C2semidirect
5. #14582647C2semidirect
6. #14582631C2semidirect
50. D4×C43Q16semidirect
95. C43#1632semidirect
142. D4Dic172semidirect