Finite Group Databasebeta

← #19133659

Subgroups — #19133659

Order 5504.

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

normal subgroups only

This group has 278 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#14583570C211yesmaximal, characteristic, complemented
2#14583275C211yesmaximal, characteristic, complemented
3#14583096C211yesmaximal, characteristic, complemented
4#14582642C211yesmaximal, characteristic, complemented
5#14582629C211yesmaximal, characteristic, complemented
6D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
7C43×#459C211yesmaximal, characteristic, complemented
8C2×#10621898—21no—
9C2×#10621883—21no—
10C2×#10621882—22no—
11#13063322C2211yescharacteristic
12#13063321—21no—
13#13063299—21no—
14#13063298—22no—
15C4×Dic86C2211yescharacteristic
16#13063287—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18#13063246—21no—
19C4×C43⋊C8C2211yescharacteristic
20C2×D8×C43—21no—
21#127×C43C2211yescharacteristic
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24#102×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43—21no—
30C2×C22⋊D43—22no—
31C2×C22⋊D43—22no—
32#10621898—42no—
33#10621898—42no—
34C2×D172—21no—
35C2×D172—21no—
36C2×D172D412yes—
37C2×C4×D43—22no—
38C2×Dic86D411yescharacteristic
39D8×C43—42no—
40C2×C8×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C22⋊C4×C43—21no—
43C42×C43C2311yescharacteristic
44#10621883—42no—
45#10621882—44no—
46(C2×D43)⋊C4—22no—
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—21no—
49C4×Dic43—21no—
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C23×C43—21no—
53C23×C43—41no—
54C22×D43—22no—
55D4×C43—21no—
56D4×C43—21no—
57D4×C43—42no—
58D4×C43—41no—
59D4×C43—41no—
60D4×C43—41no—
61D4×C43—41no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—44no—
69C22⋊D43—82no—
70C2×Dic43—21no—
71C2×Dic43—21no—
72D172—42no—
73D172—41no—
74D172—41no—
75D172—41no—
76D172—41no—
77C4×D43—44no—
78Dic86—21no—
79Dic86D812yescomplemented
80C8×C43—41no—
81C43⋊C8—22no—
82C43⋊C8—41no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43—81no—
87C22×C43—81no—
88C22×C43—81no—
89C22×C43#12011yescharacteristic
90C2×D43—42no—
91C2×D43—42no—
92C2×D43—42no—
93C4×C43—21no—
94C4×C43—41no—
95C4×C43C2×D811yescharacteristic
96C4×C43#13511yescharacteristic
97C4×C43AGL(1,ℤ/8)11yescharacteristic
98C4×C43AGL(1,ℤ/8)11yescharacteristic
99Dic43—22no—
100Dic43—41no—
101#1621—431nomaximal, Sylow
102C2×C43—81no—
103C2×C43—161no—
104C2×C43#44711yescharacteristic
105C2×C43#44911yescharacteristic
106C2×C43#45311yescharacteristic
107D43—82no—
108#550—431no—
109#493—431no—
110#460—431no—
111#459D4311yescharacteristic, complemented
112#331—431no—
113Q8⋊C8—431no—
114D4⋊C8—431no—
115C43#162111yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C2×SD16—861no—
118C2×D8—21no—
119C2×D8—862no—
120#127—431no—
121#127—861no—
122#127C2×D4311yescharacteristic
123#121—862no—
124#121—861no—
125C4×Q8—431no—
126C4×D4—861no—
127C4×D4C2×D4311yescharacteristic
128C4⋊C8—431no—
129C4⋊C8C2×D4311yescharacteristic
130#102—21no—
131#102—861no—
132C4×C8—431no—
133#41—1722no—
134#41—1722no—
135C2×Q8—431no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—432no—
140C2×D4—862no—
141C2×D4—862no—
142C2×D4—861no—
143C2×D4—861no—
144C2×D4C22⋊D4311yescharacteristic
145C22×C4—21no—
146C22×C4—862no—
147SD16—1722no—
148D8—42no—
149D8—1724no—
150C2×C8—21no—
151C2×C8—861no—
152C2×C8—861no—
153C4⋊C4—431no—
154C4⋊C4—861no—
155C4⋊C4C22⋊D4311yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—862no—
158C42—861no—
159C42C22×D4311yescharacteristic
160C23—21no—
161C23—41no—
162C23—862no—
163Q8—432no—
164Q8—861no—
165D4—21no—
166D4—21no—
167D4—42no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—3442no—
173D4—1722no—
174D4—1724no—
175D4—1721no—
176D4—1721no—
177D4—1721no—
178D4—1721no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—1724no—
185C2×C4D4×D4311yescharacteristic
186C2×C4D4×D4311yescharacteristic
187C2×C4C2×C22⋊D4311yescharacteristic
188C8—41no—
189C8—862no—
190C8—1721no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—1722no—
198C22—1722no—
199C22—1722no—
200C22#1306329311yescharacteristic
201C4—21no—
202C4—41no—
203C4—862no—
204C4—1721no—
205C4D8×D4311yescharacteristic
206C4#1306334511yescharacteristic
207C4#1306334911yescharacteristic
208C4#1306335111yescharacteristic
209C2—81no—
210C2—161no—
211C2—3442no—
212C2#1458303111yescharacteristic
213C2#1458304211yescharacteristic
214C2#1458306511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#459C2
socleC22×C43#120
hypercenter#459D43
hypocenterC43#1621
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14583570C2semidirect
2. #14583275C2semidirect
3. #14583096C2semidirect
4. #14582642C2semidirect
5. #14582629C2semidirect
6. D4⋊(C43⋊C8)C2semidirect
7. C43×#459C2semidirect
79. Dic86D8semidirect
111. #459D43semidirect
115. C43#1621semidirect