Finite Group Databasebeta

← #19134548

Subgroups — #19134548

Order 5504.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#13063370C211yesmaximal, characteristic
2C2×#13063253C212yesmaximal, complemented
3#14582898C212yesmaximal, complemented
4C2×#13063242C211yesmaximal, characteristic, complemented
5C43×#390C211yesmaximal, characteristic, complemented
6#13063370—22no—
7#13063370—24no—
8#13063370C414yescomplemented
9C2×#10621898C2212yes—
10C2×#10621900—22no—
11C22×C22⋊D43—22no—
12C2×D4×D43—22no—
13C2×#10621877C2212yescomplemented
14#13063253—24no—
15#13063248—22no—
16#13063245—22no—
17#13063242—22no—
18C22×D4×C43C2211yescharacteristic
19C2×C4⋊C4×C43C2211yescharacteristic, complemented
20C2×C22⋊C4×C43—22no—
21C2×C42×C43C2211yescharacteristic, complemented
22C24×C43D412yes—
23C23×D43—22no—
24C2×D4×C43—22no—
25C2×D4×C43—22no—
26C2×D4×C43C2×C412yes—
27C2×D4×C43D412yes—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—24no—
32C2×C22⋊D43—28no—
33C2×C22⋊D43—28no—
34C2×C22⋊D43—22no—
35C22×Dic43—22no—
36#10621900—28no—
37#10621900—28no—
38D4×D43—28no—
39D4×D43—28no—
40#10621898—22no—
41#10621898—22no—
42#10621898C2×C414yes—
43#10621898D414yes—
44C2×D172D412yes—
45C2×C4×D43—22no—
46C2×Dic86D412yes—
47C4⋊C4×C43—22no—
48C22⋊C4×C43—44no—
49C42×C43—22no—
50#10621877—22no—
51#10621877—22no—
52C2×C43⋊C8—22no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43—42no—
56C23×C43—42no—
57C23×C43C22⋊C414yes—
58C23×C43C2×D411yescharacteristic
59C22×D43—22no—
60C22×D43—28no—
61C22×D43—82no—
62C22×D43—82no—
63D4×C43—24no—
64D4×C43—24no—
65C2×C4×C43—22no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—42no—
69C2×C4×C43—41no—
70C2×C4×C43C22×C411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D412yes—
73C2×C4×C43C2×D412yes—
74C22⋊D43—216no—
75C22⋊D43—24no—
76C22⋊D43—24no—
77C2×Dic43—28no—
78C2×Dic43—22no—
79D172—22no—
80D172C22⋊C414yescomplemented
81C4×D43—24no—
82C4×D43—24no—
83Dic86—22no—
84Dic86C22⋊C414yescomplemented
85C43⋊C8—42no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—24no—
89C22×C43—44no—
90C22×C43—42no—
91C22×C43—42no—
92C22×C43—82no—
93C22×C43C2×C22⋊C411yescharacteristic
94C22×C43#12011yescharacteristic
95C22×C43#12011yescharacteristic
96C2×D43—24no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—88no—
100C4×C43—42no—
101C4×C43—81no—
102C4×C43C2×C22⋊C412yes—
103C4×C43#12012yes—
104Dic43—24no—
105#1792—431nomaximal, Sylow
106C2×C43—21no—
107C2×C43—21no—
108C2×C43—44no—
109C2×C43#37911yescharacteristic
110C2×C43#45311yescharacteristic
111C2×C43#45511yescharacteristic
112D43—44no—
113C2×H(5,𝔽2)—431no—
114C2×#104—432no—
115#417—432no—
116C2×#100—431no—
117#390D4311yescharacteristic, complemented
118C43#179211yescharacteristic, complemented, Sylow
119H(5,𝔽2)—434no—
120H(5,𝔽2)—864no—
121H(5,𝔽2)—862no—
122C2×#41—432no—
123C2×#41—862no—
124C22×D4—862no—
125C22×D4—862no—
126C22×D4C2×D4311yescharacteristic
127C2×M16—432no—
128C2×C4⋊C4C2×D4311yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D4311yescharacteristic, complemented
131#104—864no—
132#103—862no—
133#102—862no—
134#100—862no—
135C24—862no—
136C24C22⋊D4312yes—
137#41—434no—
138#41—434no—
139#41—868no—
140#41—868no—
141#41—862no—
142#41—862no—
143C2×Q8—432no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—432no—
147C2×D4—868no—
148C2×D4—868no—
149C2×D4—864no—
150C2×D4—868no—
151C2×D4—868no—
152C2×D4—862no—
153C2×D4C4×D4312yes—
154C2×D4D17212yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—862no—
158C22×C4—862no—
159C22×C4C22×D4311yescharacteristic
160M16—862no—
161M16—862no—
162C2×C8—862no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—868no—
171C23—862no—
172C23—3442no—
173C23—3442no—
174C23(C2×D43)⋊C414yes—
175C23C2×C22⋊D4311yescharacteristic
176Q8—434no—
177Q8—862no—
178D4—24no—
179D4—24no—
180D4—434no—
181D4—8616no—
182D4—864no—
183D4—864no—
184D4—862no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—868no—
191C2×C4—862no—
192C2×C4—864no—
193C2×C4—864no—
194C2×C4C2×C4×D4311yescharacteristic
195C2×C4C2×D17211yescharacteristic
196C2×C4D4×D4312yes—
197C2×C4D4×D4312yes—
198C8—1722no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—864no—
207C22—3448no—
208C22—1722no—
209C22—1722no—
210C22C2×(C2×D43)⋊C411yescharacteristic
211C22#1306329311yescharacteristic
212C22#1306329311yescharacteristic
213C4—42no—
214C4—81no—
215C4—864no—
216C4C22⋊C4×D4312yes—
217C4#1306329512yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—1724no—
222C2#1458275411yescharacteristic
223C2#1458306611yescharacteristic
224C2#1458307611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#390C2
socleC22×C43#120
hypercenter#390D43
hypocenterC43#1792
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13063253C2semidirect
3. #14582898C2semidirect
4. C2×#13063242C2semidirect
5. C43×#390C2semidirect
8. #13063370C4semidirect
13. C2×#10621877C22semidirect
19. C2×C4⋊C4×C43C22semidirect
21. C2×C42×C43C22semidirect
80. D172C22⋊C4semidirect
84. Dic86C22⋊C4semidirect
117. #390D43semidirect
118. C43#1792semidirect
128. C2×C4⋊C4C2×D43semidirect
130. C2×C42C2×D43semidirect