Finite Group Databasebeta

← #19136565

Subgroups — #19136565

Order 5504.

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

normal subgroups only

This group has 216 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
2#14583340C211yesmaximal, characteristic, complemented
3#14583171C211yesmaximal, characteristic, complemented
4#14582712C211yesmaximal, characteristic, complemented
5#14582707C211yesmaximal, characteristic, complemented
6#14582682C211yesmaximal, characteristic, complemented
7C2×SD32×C43C211yesmaximal, characteristic, complemented
8#13063370—21no—
9#13063356—21no—
10#13063351—21no—
11#13063349—22no—
12#13063347C2211yescharacteristic
13#13063344—21no—
14D8×D43—21no—
15#13063331C2211yescharacteristic
16#13063271—21no—
17#13063268—21no—
18#13063265C2211yescharacteristic, complemented
19#13063261C2211yescharacteristic, complemented
20#13063244—21no—
21C2×Q16×C43C2211yescharacteristic, complemented
22C2×D8×C43C2211yescharacteristic
23SD32×C43—22no—
24C2×C16×C43C2211yescharacteristic, complemented
25C2×Q8×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
34Q16×C43—21no—
35Q16×C43—21no—
36D8×C43—21no—
37D8×C43D412yes—
38C2×C8×C43C2311yescharacteristic
39#10621885—41no—
40#10621884—41no—
41#10621883—22no—
42#10621882—22no—
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—
53C22×D43—42no—
54Q8×C43—41no—
55Q8×C43—41no—
56D4×C43—22no—
57D4×C43—41no—
58C2×C4×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—161no—
77C22×C43AGL(1,ℤ/8)11yescharacteristic
78C2×D43—21no—
79C2×D43—41no—
80C2×D43—162no—
81C4×C43—81no—
82C4×C43#12011yescharacteristic
83C4×C43C2×D811yescharacteristic
84Dic43—21no—
85Dic43—41no—
86#2194—431nomaximal, Sylow
87C2×C43—21no—
88C2×C43—82no—
89C2×C43#44711yescharacteristic
90D43—41no—
91D43—81no—
92#576—431no—
93#510—431no—
94C2×SD32D4311yescharacteristic, complemented
95#473—431no—
96#361—431no—
97#359—431no—
98#350—431no—
99C43#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—861no—
101#137—861no—
102AGL(1,ℤ/8)—861no—
103AGL(1,ℤ/8)—862no—
104#135—431no—
105#135—861no—
106C2×Q16C2×D4311yescharacteristic, complemented
107C2×D8—861no—
108C2×D8C2×D4311yescharacteristic
109#131—431no—
110Q32—861no—
111SD32—22no—
112SD32—861no—
113M32—431no—
114C2×C16C2×D4311yescharacteristic, complemented
115#108—431no—
116#101—861no—
117#41—431no—
118#41—862no—
119#41—861no—
120#41—1721no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—862no—
124C2×D4—1721no—
125C2×D4—1722no—
126Q16—21no—
127Q16—21no—
128Q16—431no—
129Q16—1721no—
130SD16—862no—
131SD16—861no—
132SD16—1721no—
133D8—21no—
134D8—431no—
135D8—862no—
136D8C22⋊D4312yes—
137M16—431no—
138M16—861no—
139M16—861no—
140C2×C8—861no—
141C2×C8C22×D4311yescharacteristic
142C16—21no—
143C16—861no—
144C23—41no—
145C23—1722no—
146Q8—41no—
147Q8—41no—
148Q8—431no—
149Q8—861no—
150D4—22no—
151D4—41no—
152D4—431no—
153D4—861no—
154D4—861no—
155D4—1722no—
156D4—1722no—
157D4—1721no—
158C2×C4—41no—
159C2×C4—861no—
160C2×C4—1722no—
161C2×C4—1721no—
162C2×C4D4×D4311yescharacteristic
163C8—861no—
164C8—1721no—
165C8D4×D4311yescharacteristic
166C8C2×C22⋊D4311yescharacteristic
167C22—42no—
168C22—161no—
169C22—861no—
170C22—1721no—
171C22—6882no—
172C22#1306334911yescharacteristic
173C4—81no—
174C4—861no—
175C4—1721no—
176C4#1306329311yescharacteristic
177C4D8×D4311yescharacteristic
178C2—21no—
179C2—82no—
180C2—3441no—
181C2—1721no—
182C2#1458303111yescharacteristic
subgroupG/H
centerC2#14583031
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC2×SD32×C43C2
socleC2×C43#447
hypercenterC2×SD32D43
hypocenterC43#2194
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #14583340C2semidirect
3. #14583171C2semidirect
4. #14582712C2semidirect
5. #14582707C2semidirect
6. #14582682C2semidirect
7. C2×SD32×C43C2semidirect
18. #13063265C22semidirect
19. #13063261C22semidirect
21. C2×Q16×C43C22semidirect
24. C2×C16×C43C22semidirect
94. C2×SD32D43semidirect
99. C43#2194semidirect
106. C2×Q16C2×D43semidirect
114. C2×C16C2×D43semidirect