Finite Group Databasebeta

← #19133729

Subgroups — #19133729

Order 5504.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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#14583278C211yesmaximal, characteristic, complemented
2#14583194C211yesmaximal, characteristic, complemented
3#14583189C211yesmaximal, characteristic
4#14582648C211yesmaximal, characteristic, complemented
5Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C43⋊C8)C211yesmaximal, characteristic
7C43×#554C211yesmaximal, characteristic
8C2×#10621885—22no—
9#13063325C2211yescharacteristic
10#13063258—21no—
11#13063256—21no—
12C4⋊(C43⋊C8)C2211yescharacteristic
13C4⋊(C43⋊C8)C2211yescharacteristic
14#13063249—21no—
15#13063246—21no—
16C4×C43⋊C8C2211yescharacteristic
17C4⋊Q8×C43C2211yescharacteristic
18#125×C43—21no—
19C22⋊Q8×C43—21no—
20C22⋊Q8×C43—22no—
21C4×Q8×C43C2211yescharacteristic
22C4×D4×C43—21no—
23C4×D4×C43C2211yescharacteristic
24C2×C4⋊C4×C43—21no—
25C2×Q8×C43D411yescharacteristic
26C2×Q8×C43D412yes—
27C2×D4×C43D411yescharacteristic
28C22×C4×C43—22no—
29C22×C4×C43—21no—
30C2×Dic86—21no—
31C4⋊C4×C43—22no—
32C4⋊C4×C43—22no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43D411yescharacteristic
37C4⋊C4×C43D411yescharacteristic
38C22⋊C4×C43—22no—
39C22⋊C4×C43—21no—
40C42×C43—21no—
41C42×C43C2311yescharacteristic
42#10621885—44no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C2×C43⋊C8—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C23×C43—21no—
49Q8×C43—21no—
50Q8×C43—21no—
51Q8×C43—42no—
52D4×C43—21no—
53D4×C43Q1612yescomplemented
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—22no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—82no—
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×Dic43—41no—
65Dic86—42no—
66C43⋊C8—22no—
67C43⋊C8—41no—
68C43⋊C8—41no—
69C22×C43—22no—
70C22×C43—41no—
71C22×C43—41no—
72C22×C43#12011yescharacteristic
73C4×C43—21no—
74C4×C43—41no—
75C4×C43—41no—
76C4×C43—41no—
77C4×C43—42no—
78C4×C43C2×Q1611yescharacteristic
79C4×C43#13511yescharacteristic
80C4×C43#13711yescharacteristic
81C4×C43#13711yescharacteristic
82Dic43—81no—
83#1632—431nomaximal, Sylow
84C2×C43—42no—
85C2×C43#45111yescharacteristic
86C2×C43#45211yescharacteristic
87C2×C43#45311yescharacteristic
88#554D4311yescharacteristic
89#494—431no—
90#477—431no—
91#476—431no—
92#333—431no—
93Q8⋊C8—431no—
94D4⋊C8—431no—
95C43#163211yescharacteristic, complemented, Sylow
96C2×Q16—862no—
97C4⋊Q8—431no—
98C4⋊Q8C2×D4311yescharacteristic
99#125—21no—
100C22⋊Q8—21no—
101C22⋊Q8—22no—
102C4×Q8C2×D4311yescharacteristic
103C4×D4—21no—
104C4×D4C2×D4311yescharacteristic
105C2×C4⋊C4—21no—
106#107—861no—
107#106—861no—
108C4⋊C8—431no—
109C4⋊C8—431no—
110#103—861no—
111#102—861no—
112C4×C8—431no—
113C2×Q8—861no—
114C2×Q8C22⋊D4311yescharacteristic
115C2×Q8C22⋊D4312yes—
116C2×D4C22⋊D4311yescharacteristic
117C22×C4—22no—
118C22×C4—21no—
119Q16—1724no—
120C2×C8—861no—
121C2×C8—861no—
122C2×C8—861no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—861no—
129C4⋊C4—861no—
130C4⋊C4C22⋊D4311yescharacteristic
131C4⋊C4C22⋊D4311yescharacteristic
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—21no—
135C42C22×D4311yescharacteristic
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—1722no—
141D4—21no—
142D4#1062188512yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—1721no—
151C2×C4C2×C22⋊D4311yescharacteristic
152C2×C4C2×C22⋊D4311yescharacteristic
153C2×C4C2×C22⋊D4311yescharacteristic
154C8—862no—
155C8—1721no—
156C8—1721no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1306329411yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—41no—
165C4—42no—
166C4—3441no—
167C4C2×#1062188511yescharacteristic
168C4#1306334511yescharacteristic
169C4#1306335511yescharacteristic
170C4#1306335611yescharacteristic
171C2—42no—
172C2#1458305511yescharacteristic
173C2#1458306111yescharacteristic
174C2#1458306711yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#554C2
socleC22×C43#120
hypercenter#554D43
hypocenterC43#1632
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #14583278C2semidirect
2. #14583194C2semidirect
4. #14582648C2semidirect
5. Q8⋊(C43⋊C8)C2semidirect
53. D4×C43Q16semidirect
95. C43#1632semidirect
142. D4#10621885semidirect