Finite Group Databasebeta

← #19134544

Subgroups — #19134544

Order 5504.

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

normal subgroups only

This group has 548 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
1#14583735C211yesmaximal, characteristic
2#14582881C212yesmaximal, complemented
3#14582867C212yesmaximal, complemented
4#14582866C211yesmaximal, characteristic, complemented
5C43×#413C211yesmaximal, characteristic, complemented
6#13063373—21no—
7#13063372—22no—
8#13063371—22no—
9#13063370—21no—
10#13063370C414yes—
11C2×#10621898—22no—
12C2×#10621898C2212yes—
13#41×D43—24no—
14C2×#10621877C2211yescharacteristic, complemented
15C22×C43⋊C8C2211yescharacteristic, complemented
16#13063243—22no—
17#13063241—22no—
18C22⋊(C43⋊C8)—22no—
19(C2×D43)⋊C8—24no—
20C2×#41×C43C2211yescharacteristic
21C2×M16×C43C2212yescomplemented
22#101×C43—21no—
23#100×C43—21no—
24#41×C43—22no—
25#41×C43—22no—
26C2×Q8×C43D411yescharacteristic
27C2×D4×C43C2×C412yes—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43D412yes—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—24no—
32C2×C22⋊D43C2×C414yes—
33#10621902—24no—
34Q8×D43—24no—
35#10621900—24no—
36#10621900—28no—
37D4×D43—24no—
38D4×D43—28no—
39#10621898—24no—
40#10621898—24no—
41#10621898—24no—
42#10621898—22no—
43#10621898—22no—
44#10621898—22no—
45#10621898—22no—
46C2×D172—22no—
47C2×D172D412yes—
48C2×C4×D43—24no—
49C2×C4×D43D414yes—
50C2×Dic86—22no—
51C2×Dic86D412yes—
52M16×C43—22no—
53M16×C43—22no—
54C2×C8×C43—22no—
55#10621877—22no—
56C2×C43⋊C8—22no—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59C23×C43C22⋊C412yes—
60C23×C43C22×C411yescharacteristic
61C22×D43—24no—
62C22×D43C22⋊C414yes—
63Q8×C43—22no—
64D4×C43—24no—
65D4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43C22⋊C412yes—
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D412yes—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—28no—
74C22⋊D43—24no—
75C22⋊D43—24no—
76C2×Dic43—24no—
77C2×Dic43C22⋊C414yes—
78D172—24no—
79D172—22no—
80D172—22no—
81C4×D43—28no—
82C4×D43—24no—
83C4×D43—24no—
84Dic86—24no—
85Dic86—22no—
86Dic86—22no—
87C8×C43—42no—
88C43⋊C8—41no—
89C43⋊C8—41no—
90C22×C43—22no—
91C22×C43—41no—
92C22×C43—42no—
93C22×C43C2×C22⋊C412yes—
94C22×C43C2×C22⋊C411yescharacteristic
95C2×D43—24no—
96C2×D43—44no—
97C2×D43—84no—
98C4×C43—22no—
99C4×C43#12012yes—
100C4×C43#12011yescharacteristic
101C4×C43#12011yescharacteristic
102Dic43—24no—
103#1791—431nomaximal, Sylow
104C2×C43—22no—
105C2×C43—21no—
106C2×C43—42no—
107C2×C43#37911yescharacteristic
108D43—44no—
109#585—431no—
110#413—432no—
111#413D4311yescharacteristic, complemented
112#408—431no—
113#408—432no—
114C43#179111yescharacteristic, complemented, Sylow
1152−1+4—862no—
1162−1+4—861no—
117H(5,𝔽2)—434no—
118H(5,𝔽2)—862no—
119H(5,𝔽2)—861no—
120C2×#41—432no—
121C2×#41—864no—
122C2×#41—862no—
123C2×#41C2×D4311yescharacteristic
124C2×M16—431no—
125C2×M16C2×D4312yescomplemented
126C22×C8—431no—
127#101—21no—
128#101—862no—
129#100—21no—
130#100—862no—
131C22⋊C8—864no—
132C22⋊C8—862no—
133#41—22no—
134#41—22no—
135#41—864no—
136#41—864no—
137#41—868no—
138#41—864no—
139#41—864no—
140#41—864no—
141#41—862no—
142#41—862no—
143#41—862no—
144#41—862no—
145C2×Q8—432no—
146C2×Q8—862no—
147C2×Q8—864no—
148C2×Q8C22⋊D4311yescharacteristic
149C2×D4—434no—
150C2×D4—432no—
151C2×D4—862no—
152C2×D4—868no—
153C2×D4—864no—
154C2×D4—864no—
155C2×D4C4×D4312yes—
156C2×D4C22⋊D4311yescharacteristic
157C22×C4—434no—
158C22×C4—864no—
159C22×C4D17212yes—
160C22×C4C22×D4311yescharacteristic
161M16—22no—
162M16—22no—
163M16—862no—
164C2×C8—22no—
165C2×C8—861no—
166C2×C8—861no—
167C2×C8—862no—
168C23—434no—
169C23—864no—
170C23(C2×D43)⋊C412yes—
171C23C2×C4×D4311yescharacteristic
172Q8—22no—
173Q8—864no—
174Q8—862no—
175Q8—862no—
176D4—24no—
177D4—22no—
178D4—864no—
179D4—868no—
180D4—864no—
181D4—864no—
182D4—862no—
183D4—862no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—434no—
187C2×C4—868no—
188C2×C4—864no—
189C2×C4—864no—
190C2×C4—864no—
191C2×C4(C2×D43)⋊C412yes—
192C2×C4C2×D17211yescharacteristic
193C2×C4D4×D4312yes—
194C2×C4D4×D4312yes—
195C2×C4C2×C22⋊D4311yescharacteristic
196C8—42no—
197C8—1721no—
198C8—1721no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—864no—
203C22—3444no—
204C22—1724no—
205C22C22⋊C4×D4312yes—
206C22C2×(C2×D43)⋊C411yescharacteristic
207C4—22no—
208C4—864no—
209C4#1306329312yes—
210C4#1306329511yescharacteristic
211C4#1306329511yescharacteristic
212C2—21no—
213C2—22no—
214C2—42no—
215C2—1724no—
216C2#1458275411yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#413C2
socleC2×C43#379
hypercenter#413D43
hypocenterC43#1791
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582881C2semidirect
3. #14582867C2semidirect
4. #14582866C2semidirect
5. C43×#413C2semidirect
14. C2×#10621877C22semidirect
15. C22×C43⋊C8C22semidirect
21. C2×M16×C43C22semidirect
111. #413D43semidirect
114. C43#1791semidirect
125. C2×M16C2×D43semidirect