Finite Group Databasebeta

← #19133723

Subgroups — #19133723

Order 5504.

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

normal subgroups only

This group has 256 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#14583569C211yesmaximal, characteristic
2#14583271C211yesmaximal, characteristic, complemented
3#14583195C211yesmaximal, characteristic, complemented
4#14583190C211yesmaximal, characteristic, complemented
5#14582629C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic, complemented
7C43×#331C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9C2×#10621883—22no—
10#13063325C2211yescharacteristic
11#13063321—21no—
12#13063297—22no—
13#13063296—21no—
14C4×Dic86C2211yescharacteristic
15C4×D172C2211yescharacteristic
16D4×Dic43—21no—
17#13063259—21no—
18#13063257—21no—
19#13063250—21no—
20#13063247—21no—
21C4×C43⋊C8C2211yescharacteristic
22#127×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4⋊C8×C43C2211yescharacteristic
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43D412yes—
28C2×C22⋊D43—22no—
29C2×C22⋊D43—22no—
30C22×Dic43—22no—
31#10621900—42no—
32#10621900—42no—
33C2×D172D411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86—21no—
36C2×Dic86D411yescharacteristic
37C2×C8×C43—21no—
38C2×C8×C43—21no—
39C42×C43C2311yescharacteristic
40C22⋊Dic43—22no—
41#10621883—44no—
42(C2×D43)⋊C4—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43D411yescharacteristic
46C4⋊Dic43D411yescharacteristic
47Dic43⋊C4—21no—
48C4×Dic43—21no—
49C2×C43⋊C8—21no—
50C23×C43—22no—
51C22×D43—21no—
52D4×C43—42no—
53D4×C43—41no—
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—41no—
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C22⋊D43—44no—
61C22⋊D43—82no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65C2×Dic43—44no—
66C2×Dic43—41no—
67D172—21no—
68D172—21no—
69C4×D43—41no—
70C4×D43—41no—
71Dic86—21no—
72Dic86—42no—
73Dic86SD1612yescomplemented
74C8×C43—41no—
75C8×C43—41no—
76C43⋊C8—22no—
77C22×C43—42no—
78C22×C43—42no—
79C22×C43—42no—
80C22×C43#12011yescharacteristic
81C2×D43—41no—
82C2×D43—41no—
83C2×D43—41no—
84C4×C43—21no—
85C4×C43C2×SD1611yescharacteristic
86C4×C43#13511yescharacteristic
87C4×C43AGL(1,ℤ/8)11yescharacteristic
88C4×C43#13711yescharacteristic
89Dic43—22no—
90Dic43—41no—
91Dic43—41no—
92Dic43—81no—
93#1631—431nomaximal, Sylow
94C2×C43—82no—
95C2×C43#45011yescharacteristic
96C2×C43#45211yescharacteristic
97C2×C43#45311yescharacteristic
98D43—81no—
99#550—431no—
100#492—431no—
101#477—431no—
102#476—431no—
103#331D4311yescharacteristic, complemented
104Q8⋊C8—431no—
105D4⋊C8—431no—
106C43#163111yescharacteristic, complemented, Sylow
107C2×#41—861no—
108C2×SD16—862no—
109C4⋊Q8—431no—
110#127—861no—
111#127C2×D4311yescharacteristic
112#121—861no—
113#121—862no—
114C4×Q8—431no—
115C4×D4—431no—
116C4×D4—861no—
117#107—861no—
118#106—861no—
119C4⋊C8C2×D4311yescharacteristic
120C4⋊C8C2×D4311yescharacteristic
121#103—861no—
122#102—861no—
123C4×C8—431no—
124#41—1722no—
125#41—1722no—
126C2×Q8—431no—
127C2×Q8—861no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—431no—
131C2×D4—862no—
132C2×D4—862no—
133C2×D4D17212yes—
134C22×C4—862no—
135C22×C4—861no—
136SD16—1724no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—861no—
140C4⋊C4—431no—
141C4⋊C4—431no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C22⋊C4—862no—
146C22⋊C4—861no—
147C42—861no—
148C42C22×D4311yescharacteristic
149C23—22no—
150C23—861no—
151Q8—432no—
152Q8—861no—
153Q8—1722no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—861no—
160D4—861no—
161D4—3442no—
162D4—1724no—
163C2×C4—861no—
164C2×C4—861no—
165C2×C4—861no—
166C2×C4—1724no—
167C2×C4—1721no—
168C2×C4—1721no—
169C2×C4—1721no—
170C2×C4C2×D17211yescharacteristic
171C2×C4D4×D4311yescharacteristic
172C2×C4D4×D4311yescharacteristic
173C8—41no—
174C8—41no—
175C8—862no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1721no—
180C22—1721no—
181C22—1721no—
182C22#1306329511yescharacteristic
183C4—21no—
184C4—862no—
185C4—3441no—
186C4—1721no—
187C4—1721no—
188C4SD16×D4311yescharacteristic
189C4#1306334411yescharacteristic
190C4#1306334911yescharacteristic
191C4#1306335411yescharacteristic
192C2—82no—
193C2—3441no—
194C2#1458305111yescharacteristic
195C2#1458306211yescharacteristic
196C2#1458306911yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#331C2
socleC22×C43#120
hypercenter#331D43
hypocenterC43#1631
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14583271C2semidirect
3. #14583195C2semidirect
4. #14583190C2semidirect
5. #14582629C2semidirect
6. #14582626C2semidirect
7. C43×#331C2semidirect
73. Dic86SD16semidirect
103. #331D43semidirect
106. C43#1631semidirect