Finite Group Databasebeta

← #19134571

Subgroups — #19134571

Order 5504.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13063372C211yesmaximal, characteristic
2#14582915C212yesmaximal, complemented
3#14582909C212yesmaximal, complemented
4#14582873C211yesmaximal, characteristic, complemented
5C43×#413C211yesmaximal, characteristic, complemented
6#13063372—24no—
7#13063372—24no—
8C2×#10621898C412yescomplemented
9C2×#10621898C2211yescharacteristic
10C2×#10621900—22no—
11C2×#10621900—21no—
12C22×Dic86C412yescomplemented
13C22×Dic86C2211yescharacteristic
14C2×Q8×D43—21no—
15#13063284C2212yes—
16#13063251—24no—
17#13063250—24no—
18#13063240—22no—
19C2×#41×C43C2211yescharacteristic
20C2×M16×C43C2212yes—
21#101×C43—21no—
22#100×C43—21no—
23#41×C43—22no—
24#41×C43—22no—
25C2×Q8×C43D411yescharacteristic
26C2×D4×C43D411yescharacteristic
27C2×D4×C43D412yes—
28C22×C4×C43C2×C412yes—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—22no—
31C2×C22⋊D43—21no—
32C22×Dic43—22no—
33C22×Dic43—21no—
34Q8×D43—28no—
35#10621900—216no—
36#10621900—28no—
37#10621898—22no—
38#10621898—24no—
39#10621898—24no—
40#10621898D414yes—
41C2×D172C2×C411yescharacteristic
42C2×C4×D43—22no—
43C2×C4×D43—21no—
44C2×Dic86—22no—
45C2×Dic86—21no—
46C2×Dic86—22no—
47C2×Dic86—24no—
48C2×Dic86—24no—
49C2×Dic86C2×C411yescharacteristic
50C2×Dic86C2×C412yes—
51C2×Dic86D414yes—
52M16×C43—22no—
53M16×C43—22no—
54C2×C8×C43—22no—
55C22⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4×Dic43—22no—
58C23×C43C22⋊C412yes—
59C23×C43C2×D411yescharacteristic
60C22×D43—21no—
61Q8×C43—22no—
62D4×C43—24no—
63D4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43C22⋊C412yes—
67C2×C4×C43C22×C411yescharacteristic
68C2×C4×C43C2×D412yes—
69C2×C4×C43C2×D412yes—
70C2×C4×C43C2×D411yescharacteristic
71C22⋊D43—28no—
72C22⋊D43—24no—
73C2×Dic43—28no—
74C2×Dic43—21no—
75C2×Dic43—22no—
76C2×Dic43—24no—
77C2×Dic43—42no—
78D172—21no—
79D172C22⋊C412yes—
80C4×D43—28no—
81C4×D43—24no—
82Dic86—28no—
83Dic86—22no—
84Dic86—21no—
85Dic86—24no—
86Dic86C22⋊C412yes—
87Dic86C22⋊C414yes—
88C8×C43—42no—
89C22×C43—22no—
90C22×C43—41no—
91C22×C43—42no—
92C22×C43C2×C22⋊C411yescharacteristic
93C22×C43#12012yes—
94C2×D43—22no—
95C2×D43—42no—
96C4×C43—22no—
97C4×C43C2×C22⋊C411yescharacteristic
98C4×C43C2×C22⋊C411yescharacteristic
99C4×C43#12012yes—
100Dic43—22no—
101Dic43—24no—
102Dic43—82no—
103#1796—431nomaximal, Sylow
104C2×C43—22no—
105C2×C43—21no—
106C2×C43—42no—
107C2×C43#37911yescharacteristic
108D43—42no—
109C2×2−1+4—431no—
110#421—432no—
111#419—432no—
112#413D4311yescharacteristic, complemented
113#410—431no—
114C43#179611yescharacteristic, complemented, Sylow
1152−1+4—864no—
1162−1+4—864no—
117C2×#41—431no—
118C2×#41—432no—
119C2×#41—862no—
120C2×#41—861no—
121C2×#41C2×D4311yescharacteristic
122C22×Q8—431no—
123C22×Q8—432no—
124C22×Q8—861no—
125C2×M16C2×D4312yes—
126#117—432no—
127#104—864no—
128#103—864no—
129#101—21no—
130#100—21no—
131#99—862no—
132#41—22no—
133#41—22no—
134#41—434no—
135#41—864no—
136#41—864no—
137#41—8616no—
138#41—868no—
139#41—862no—
140C2×Q8—432no—
141C2×Q8—431no—
142C2×Q8—434no—
143C2×Q8—864no—
144C2×Q8—864no—
145C2×Q8—868no—
146C2×Q8—862no—
147C2×Q8—862no—
148C2×Q8—861no—
149C2×Q8C22⋊D4311yescharacteristic
150C2×D4—431no—
151C2×D4—862no—
152C2×D4—861no—
153C2×D4D17212yes—
154C2×D4C22⋊D4311yescharacteristic
155C22×C4—862no—
156C22×C4—861no—
157C22×C4—862no—
158C22×C4—861no—
159C22×C4C4×D4312yes—
160C22×C4C22×D4311yescharacteristic
161M16—22no—
162M16—22no—
163C2×C8—22no—
164C4⋊C4—862no—
165C22⋊C4—862no—
166C42—862no—
167C23—861no—
168C23(C2×D43)⋊C412yes—
169C23C2×D17211yescharacteristic
170Q8—22no—
171Q8—434no—
172Q8—432no—
173Q8—868no—
174Q8—862no—
175Q8—861no—
176Q8—864no—
177D4—24no—
178D4—22no—
179D4—432no—
180D4—868no—
181D4—864no—
182D4—861no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—868no—
186C2×C4—868no—
187C2×C4—861no—
188C2×C4—862no—
189C2×C4—864no—
190C2×C4—864no—
191C2×C4—1722no—
192C2×C4(C2×D43)⋊C412yes—
193C2×C4C2×C4×D4311yescharacteristic
194C2×C4D4×D4312yes—
195C2×C4D4×D4312yes—
196C2×C4C2×C22⋊D4311yescharacteristic
197C8—42no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—862no—
202C22—1722no—
203C22C2×(C2×D43)⋊C411yescharacteristic
204C22#1306329512yes—
205C4—22no—
206C4—864no—
207C4—862no—
208C4—3442no—
209C4C22⋊C4×D4311yescharacteristic
210C4C22⋊C4×D4311yescharacteristic
211C4#1306329312yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—1722no—
216C2#1458275411yescharacteristic
subgroupG/H
centerC2#14582754
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#413C2
socleC2×C43#379
hypercenter#413D43
hypocenterC43#1796
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582915C2semidirect
3. #14582909C2semidirect
4. #14582873C2semidirect
5. C43×#413C2semidirect
8. C2×#10621898C4semidirect
12. C22×Dic86C4semidirect
112. #413D43semidirect
114. C43#1796semidirect