Finite Group Databasebeta

← #19136551

Subgroups — #19136551

Order 5504.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#14583700C211yesmaximal, characteristic, complemented
2#14583335C211yesmaximal, characteristic, complemented
3#14583166C211yesmaximal, characteristic, complemented
4#14582712C211yesmaximal, characteristic, complemented
5#14582707C211yesmaximal, characteristic, complemented
6#14582682C211yesmaximal, characteristic, complemented
7C2×D16×C43C211yesmaximal, characteristic, complemented
8#13063370—21no—
9#13063351—21no—
10#13063351—21no—
11#13063349—22no—
12#13063347C2211yescharacteristic
13#13063344—21no—
14D8×D43—21no—
15#13063331C2211yescharacteristic
16#13063269—21no—
17#13063266—21no—
18#13063265C2211yescharacteristic, complemented
19#13063261C2211yescharacteristic, complemented
20#13063242—21no—
21C2×D8×C43C2211yescharacteristic
22C2×D8×C43C2211yescharacteristic, complemented
23D16×C43—22no—
24C2×C16×C43C2211yescharacteristic, complemented
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×C22⋊D43—42no—
28#10621900—22no—
29#10621900—41no—
30D4×D43—22no—
31D4×D43—41no—
32#10621898—21no—
33#10621898D411yescharacteristic
34D8×C43—21no—
35D8×C43—21no—
36D8×C43—21no—
37D8×C43D412yes—
38C2×C8×C43C2311yescharacteristic
39#10621883—22no—
40#10621883—41no—
41#10621882—22no—
42#10621882—41no—
43#10621877—21no—
44#10621877D411yescharacteristic
45Dic172D411yescharacteristic
46D344D411yescharacteristic
47#10621873—21no—
48#10621872—21no—
49C8×D43—21no—
50C16×C43—21no—
51C43⋊C16—21no—
52C23×C43—41no—
53C23×C43—41no—
54C22×D43—42no—
55D4×C43—22no—
56D4×C43—41no—
57D4×C43—41no—
58D4×C43—41no—
59C2×C4×C43C2×D411yescharacteristic
60C22⋊D43—21no—
61C22⋊D43—42no—
62C22⋊D43—42no—
63C22⋊D43—41no—
64C2×Dic43—42no—
65D172—21no—
66D172D811yescharacteristic
67C4×D43—21no—
68C4×D43—41no—
69Dic86—21no—
70Dic86D811yescharacteristic
71C8×C43C2×D411yescharacteristic
72C8×C43C2×D411yescharacteristic
73C43⋊C8—21no—
74C43⋊C8—41no—
75C22×C43—42no—
76C22×C43—81no—
77C22×C43—161no—
78C22×C43—161no—
79C22×C43AGL(1,ℤ/8)11yescharacteristic
80C2×D43—21no—
81C2×D43—41no—
82C2×D43—162no—
83C4×C43#12011yescharacteristic
84C4×C43C2×D811yescharacteristic
85Dic43—21no—
86Dic43—41no—
87#2192—431nomaximal, Sylow
88C2×C43—21no—
89C2×C43—82no—
90C2×C43—161no—
91C2×C43#44711yescharacteristic
92D43—41no—
93D43—81no—
94#576—431no—
95#509—431no—
96C2×D16D4311yescharacteristic, complemented
97#472—431no—
98#361—431no—
99#359—431no—
100#350—431no—
101C43#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—861no—
103AGL(1,ℤ/8)—861no—
104AGL(1,ℤ/8)—862no—
105AGL(1,ℤ/8)—861no—
106#135—431no—
107#135—861no—
108C2×D8—861no—
109C2×D8C2×D4311yescharacteristic
110C2×D8C2×D4311yescharacteristic, complemented
111#131—431no—
112SD32—861no—
113D16—22no—
114D16—861no—
115M32—431no—
116C2×C16C2×D4311yescharacteristic, complemented
117#108—431no—
118#100—861no—
119#41—431no—
120#41—862no—
121#41—861no—
122#41—1721no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—862no—
126C2×D4—1721no—
127C2×D4—1722no—
128Q16—431no—
129SD16—862no—
130SD16—861no—
131SD16—1721no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—431no—
136D8—862no—
137D8—1721no—
138D8C22⋊D4312yes—
139M16—431no—
140M16—861no—
141M16—861no—
142C2×C8—861no—
143C2×C8C22×D4311yescharacteristic
144C16—21no—
145C16—861no—
146C23—41no—
147C23—41no—
148C23—1722no—
149Q8—431no—
150Q8—861no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—431no—
156D4—861no—
157D4—861no—
158D4—1722no—
159D4—1722no—
160D4—1721no—
161C2×C4—861no—
162C2×C4—1722no—
163C2×C4—1721no—
164C2×C4D4×D4311yescharacteristic
165C8—861no—
166C8—1721no—
167C8D4×D4311yescharacteristic
168C8C2×C22⋊D4311yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—861no—
174C22—1721no—
175C22—6882no—
176C22#1306334911yescharacteristic
177C4—861no—
178C4—1721no—
179C4#1306329311yescharacteristic
180C4D8×D4311yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—3441no—
185C2—1721no—
186C2#1458303111yescharacteristic
subgroupG/H
centerC2#14583031
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC2×D16×C43C2
socleC2×C43#447
hypercenterC2×D16D43
hypocenterC43#2192
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #14583700C2semidirect
2. #14583335C2semidirect
3. #14583166C2semidirect
4. #14582712C2semidirect
5. #14582707C2semidirect
6. #14582682C2semidirect
7. C2×D16×C43C2semidirect
18. #13063265C22semidirect
19. #13063261C22semidirect
22. C2×D8×C43C22semidirect
24. C2×C16×C43C22semidirect
96. C2×D16D43semidirect
101. C43#2192semidirect
110. C2×D8C2×D43semidirect
116. C2×C16C2×D43semidirect