Finite Group Databasebeta

← #19133710

Subgroups — #19133710

Order 5504.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D172C211yesmaximal, characteristic
2#14583273C211yesmaximal, characteristic, complemented
3#14583186C211yesmaximal, characteristic, complemented
4#14582642C211yesmaximal, characteristic, complemented
5D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic, complemented
7C43×#476C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C2×D4×D43—21no—
10C2×#10621884—22no—
11#13063322C2211yescharacteristic
12#13063300—21no—
13#13063299—21no—
14#13063295—22no—
15C4×D172C2211yescharacteristic
16#13063256—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic, complemented
18#13063245—21no—
19C4×C43⋊C8C2211yescharacteristic, complemented
20C4⋊Q8×C43C2211yescharacteristic, complemented
21C4×D4×C43C2211yescharacteristic
22#106×C43—21no—
23C4⋊C8×C43C2211yescharacteristic, complemented
24#102×C43—21no—
25C23×D43—22no—
26C2×Q8×C43—21no—
27C2×D4×C43D411yescharacteristic
28C22×C4×C43—21no—
29C2×C22⋊D43—22no—
30D4×D43—42no—
31D4×D43—42no—
32C2×D172—22no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—42no—
36C2×D172—42no—
37C2×D172D411yescharacteristic
38C2×D172D412yes—
39C2×C4×D43—21no—
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43—21no—
43C4⋊C4×C43D411yescharacteristic
44C22⋊C4×C43—21no—
45C42×C43C2311yescharacteristic
46#10621884—44no—
47(C2×D43)⋊C4—22no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43D411yescharacteristic
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C23×C43—21no—
53C22×D43—21no—
54C22×D43—22no—
55C22×D43—44no—
56C22×D43—44no—
57C22×D43—82no—
58Q8×C43—42no—
59D4×C43—21no—
60D4×C43SD1612yescomplemented
61C2×C4×C43—21no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—44no—
69C2×Dic43—21no—
70D172—21no—
71D172—42no—
72D172—44no—
73D172—41no—
74D172—41no—
75D172—41no—
76D172—41no—
77D172SD1612yescomplemented
78C4×D43—41no—
79C4×D43—41no—
80C8×C43—41no—
81C43⋊C8—22no—
82C43⋊C8—41no—
83C22×C43—22no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43#12011yescharacteristic
87C2×D43—22no—
88C2×D43—41no—
89C2×D43—41no—
90C2×D43—42no—
91C2×D43—42no—
92C2×D43—42no—
93C2×D43—88no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43—81no—
97C4×C43C2×SD1611yescharacteristic
98C4×C43C2×SD1611yescharacteristic
99C4×C43AGL(1,ℤ/8)11yescharacteristic
100C4×C43AGL(1,ℤ/8)11yescharacteristic
101Dic43—41no—
102#1629—431nomaximal, Sylow
103C2×C43—42no—
104C2×C43#45011yescharacteristic
105C2×C43#45011yescharacteristic
106C2×C43#45311yescharacteristic
107D43—42no—
108D43—82no—
109D42—431no—
110#492—431no—
111#476—431no—
112#476D4311yescharacteristic, complemented
113#331—431no—
114D4⋊C8—431no—
115D4⋊C8—431no—
116C43#162911yescharacteristic, complemented, Sylow
117C22×D4—861no—
118C22×D4—861no—
119C2×SD16—862no—
120C4⋊Q8C2×D4311yescharacteristic, complemented
121#127—431no—
122#121—861no—
123#121—861no—
124#120—862no—
125C4×D4—431no—
126C4×D4C2×D4311yescharacteristic
127#106—21no—
128#106—861no—
129C4⋊C8—431no—
130C4⋊C8C2×D4311yescharacteristic, complemented
131#102—21no—
132#102—861no—
133C4×C8—431no—
134C24—862no—
135C2×Q8—21no—
136C2×D4—431no—
137C2×D4—432no—
138C2×D4—862no—
139C2×D4—862no—
140C2×D4—861no—
141C2×D4—861no—
142C2×D4—1722no—
143C2×D4—1722no—
144C2×D4—1722no—
145C2×D4—1722no—
146C2×D4C22⋊D4311yescharacteristic
147C22×C4—21no—
148C22×C4—861no—
149SD16—1724no—
150C2×C8—21no—
151C2×C8—861no—
152C2×C8—861no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—431no—
156C4⋊C4C22⋊D4311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—862no—
159C22⋊C4—861no—
160C42C22×D4311yescharacteristic
161C23—21no—
162C23—861no—
163C23—862no—
164C23—3442no—
165C23—1724no—
166C23—1724no—
167Q8—42no—
168D4—21no—
169D4—432no—
170D4—861no—
171D4—1722no—
172D4—1724no—
173D4—1724no—
174D4—1721no—
175D4—1721no—
176D4—1721no—
177D4—1721no—
178D4#1062188412yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—861no—
184C2×C4—1721no—
185C2×C4—1721no—
186C2×C4D4×D4311yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C2×C4C2×C22⋊D4311yescharacteristic
189C8—41no—
190C8—862no—
191C8—1721no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—862no—
196C22—3448no—
197C22—1722no—
198C22—1722no—
199C22—1722no—
200C22—1721no—
201C22—1721no—
202C22#1306329311yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—1721no—
207C4SD16×D4311yescharacteristic
208C4C2×#1062188411yescharacteristic
209C4#1306335011yescharacteristic
210C4#1306335211yescharacteristic
211C2—42no—
212C2—3442no—
213C2—1722no—
214C2#1458304811yescharacteristic
215C2#1458304911yescharacteristic
216C2#1458306511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#476C2
socleC22×C43#120
hypercenter#476D43
hypocenterC43#1629
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14583273C2semidirect
3. #14583186C2semidirect
4. #14582642C2semidirect
5. D4⋊(C43⋊C8)C2semidirect
6. #14582626C2semidirect
7. C43×#476C2semidirect
17. C4⋊(C43⋊C8)C22semidirect
19. C4×C43⋊C8C22semidirect
20. C4⋊Q8×C43C22semidirect
23. C4⋊C8×C43C22semidirect
60. D4×C43SD16semidirect
77. D172SD16semidirect
112. #476D43semidirect
116. C43#1629semidirect
120. C4⋊Q8C2×D43semidirect
130. C4⋊C8C2×D43semidirect
178. D4#10621884semidirect