Finite Group Databasebeta

← #19135114

Subgroups — #19135114

Order 5504.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#14583665C211yesmaximal, characteristic
2#14583473C211yesmaximal, characteristic
3#14582908C211yesmaximal, characteristic, complemented
4#14582872C211yesmaximal, characteristic
5#14582656C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#419C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063333—22no—
10#13063331—22no—
11C2×#10621877C2211yescharacteristic
12M16×D43—22no—
13#13063323C412yescomplemented
14#13063314C412yescomplemented
15#13063308—22no—
16#13063301—22no—
17#13063284C2211yescharacteristic
18#13063284C2211yescharacteristic
19#13063249—22no—
20#13063239—22no—
21C22×Q8×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic
23#117×C43C2211yescharacteristic
24#103×C43—22no—
25C2×Q8×C43—21no—
26C2×Q8×C43—21no—
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43C2×C412yes—
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43D412yes—
34#10621898—21no—
35#10621898—21no—
36#10621898—21no—
37#10621898—21no—
38C2×D172C2×C411yescharacteristic
39C2×C4×D43D412yes—
40C2×Dic86C2×C411yescharacteristic
41M16×C43—21no—
42M16×C43—21no—
43C2×C8×C43D412yes—
44C4⋊C4×C43—21no—
45C22⋊C4×C43—21no—
46C42×C43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49(C2×D43)⋊C4—24no—
50C4⋊Dic43—21no—
51C4⋊Dic43—21no—
52Dic43⋊C4—24no—
53C4×Dic43—21no—
54C4×Dic43C2×C412yes—
55#10621877—21no—
56#10621877—21no—
57C2×C43⋊C8D412yes—
58#10621872—24no—
59C8×D43—24no—
60C23×C43C2×D411yescharacteristic
61C22×D43C22⋊C412yes—
62Q8×C43—22no—
63Q8×C43—22no—
64Q8×C43—41no—
65Q8×C43—41no—
66C2×C4×C43—22no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43C22×C411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43#4111yescharacteristic
75C2×C4×C43#4111yescharacteristic
76C22⋊D43—22no—
77C22⋊D43—22no—
78C2×Dic43—22no—
79C2×Dic43—41no—
80C2×Dic43C22⋊C412yes—
81D172—21no—
82D172—21no—
83C4×D43—22no—
84C4×D43—22no—
85Dic86—21no—
86Dic86—21no—
87C8×C43—22no—
88C43⋊C8—22no—
89C22×C43—41no—
90C22×C43C2×C22⋊C411yescharacteristic
91C22×C43#12111yescharacteristic
92C22×C43#12111yescharacteristic
93C2×D43—22no—
94C2×D43—42no—
95C4×C43—42no—
96C4×C43—81no—
97C4×C43C4×D411yescharacteristic
98C4×C43C4×D411yescharacteristic
99C4×C43#12011yescharacteristic
100C4×C43#12311yescharacteristic
101Dic43—22no—
102Dic43—42no—
103Dic43—81no—
104#1909—431nomaximal, Sylow
105C2×C43—21no—
106C2×C43—21no—
107C2×C43—21no—
108C2×C43#38611yescharacteristic
109D43—42no—
110#568—431no—
111#536—431no—
112#419—431no—
113#419D4311yescharacteristic, complemented
114#410—431no—
115H(3,ℤ/4)—431no—
116H(3,ℤ/4)—431no—
117C43#190911yescharacteristic, complemented, Sylow
118C2×#41—431no—
119C22×Q8C2×D4311yescharacteristic
120#131—862no—
121#131—862no—
122C2×M16—431no—
123C2×M16—862no—
124C2×M16C2×D4311yescharacteristic
125C4⋊Q8—432no—
126#124—432no—
127#123—862no—
128C22⋊Q8—862no—
129#117—431no—
130#117—431no—
131#117C2×D4311yescharacteristic
132#103—22no—
133#103—862no—
134#99—862no—
135#41—861no—
136#41—861no—
137#41—861no—
138#41—861no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—431no—
145C2×Q8C4×D4312yes—
146C2×D4—432no—
147C2×D4—431no—
148C22×C4—21no—
149C22×C4—432no—
150C22×C4C22×D4311yescharacteristic
151M16—21no—
152M16—21no—
153M16—864no—
154M16—861no—
155M16—861no—
156C2×C8—432no—
157C2×C8—864no—
158C2×C8C22⋊D4312yes—
159C4⋊C4—21no—
160C4⋊C4—864no—
161C4⋊C4—861no—
162C4⋊C4—861no—
163C22⋊C4—21no—
164C22⋊C4—864no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C42—21no—
168C42—432no—
169C42—861no—
170C23—432no—
171C23D4×D4311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—861no—
177Q8—861no—
178D4—862no—
179D4—862no—
180D4—861no—
181D4—861no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—432no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—1721no—
191C2×C4C2×C4×D4311yescharacteristic
192C2×C4#1062189811yescharacteristic
193C2×C4D4×D4311yescharacteristic
194C2×C4D4×D4311yescharacteristic
195C2×C4#1062190011yescharacteristic
196C2×C4C2×C22⋊D4311yescharacteristic
197C8—22no—
198C8—862no—
199C22—41no—
200C22—862no—
201C22—1722no—
202C22C22⋊C4×D4311yescharacteristic
203C22#1306329611yescharacteristic
204C22#1306329811yescharacteristic
205C4—42no—
206C4—81no—
207C4—862no—
208C4—3441no—
209C4—1722no—
210C4(C22⋊D43)⋊C411yescharacteristic
211C4C4×C22⋊D4311yescharacteristic
212C4#1306329311yescharacteristic
213C4#1306330711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—1722no—
218C2#1458277511yescharacteristic
subgroupG/H
centerC2#14582775
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#419C2
socleC2×C43#386
hypercenter#419D43
hypocenterC43#1909
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #14582908C2semidirect
5. #14582656C2semidirect
6. #14582655C2semidirect
7. C43×#419C2semidirect
13. #13063323C4semidirect
14. #13063314C4semidirect
113. #419D43semidirect
117. C43#1909semidirect