Finite Group Databasebeta

← #19135372

Subgroups — #19135372

Order 5504.

196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13063260C211yesmaximal, characteristic
2#14582942C211yesmaximal, characteristic
3C2×#13063256C211yesmaximal, characteristic
4#14582855C211yesmaximal, characteristic
5#14582668C211yesmaximal, characteristic
6#14582667C211yesmaximal, characteristic
7C43×#428C211yesmaximal, characteristic
8C2×#10621877C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C22×C43⋊C8C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12#13063260C414yescomplemented
13#13063258—21no—
14#13063256—21no—
15#13063256—21no—
16#13063256—21no—
17#13063236—21no—
18C4×C43⋊C8—21no—
19C2×M16×C43C2211yescharacteristic
20#117×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22#107×C43—21no—
23#106×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43C2311yescharacteristic
26C22×Dic43—21no—
27M16×C43—21no—
28M16×C43C2×C412yes—
29C2×C8×C43—21no—
30C4⋊C4×C43—21no—
31C4⋊C4×C43—21no—
32C4⋊C4×C43D411yescharacteristic
33C4⋊C4×C43D411yescharacteristic
34C22⋊C4×C43—21no—
35C42×C43—21no—
36C4⋊Dic43—21no—
37C4⋊Dic43—21no—
38#10621877—21no—
39#10621877—21no—
40#10621877C2×C412yes—
41#10621877Q812yes—
42C2×C43⋊C8—21no—
43C2×C43⋊C8—21no—
44C2×C43⋊C8C2×C412yes—
45C2×C43⋊C8D411yescharacteristic
46C2×C43⋊C8D411yescharacteristic
47C2×C43⋊C8Q812yes—
48C23×C43#4111yescharacteristic
49C2×C4×C43—21no—
50C2×C4×C43—21no—
51C2×C4×C43—41no—
52C2×C4×C43—81no—
53C2×C4×C43C22×C411yescharacteristic
54C2×C4×C43C2×D411yescharacteristic
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×Q811yescharacteristic
57C2×C4×C43C2×Q811yescharacteristic
58C2×C4×C43#4111yescharacteristic
59C2×Dic43—41no—
60C2×Dic43—81no—
61C8×C43—22no—
62C43⋊C8—22no—
63C43⋊C8—22no—
64C43⋊C8C4⋊C412yes—
65C43⋊C8C4⋊C412yes—
66C22×C43—21no—
67C22×C43—21no—
68C22×C43C4×Q811yescharacteristic
69C22×C43#12111yescharacteristic
70C22×C43#12511yescharacteristic
71C4×C43—41no—
72C4×C43—41no—
73C4×C43—81no—
74C4×C43C2×C4⋊C411yescharacteristic
75C4×C43C4×D411yescharacteristic
76C4×C43C22⋊Q811yescharacteristic
77C4×C43C4⋊Q811yescharacteristic
78Dic43—81no—
79#1951—431nomaximal, Sylow
80C2×C43—21no—
81C2×C43—21no—
82C2×C43#38911yescharacteristic
83C2×C43#47111yescharacteristic
84C2×C43#47111yescharacteristic
85C2×#108—431no—
86#428—431no—
87#428D4311yescharacteristic
88C2×#106—431no—
89#405—431no—
90#343—431no—
91#343—431no—
92C43#195111yescharacteristic, complemented, Sylow
93C2×M16—431no—
94C2×M16—431no—
95C2×M16C2×D4311yescharacteristic
96C22×C8—431no—
97#117C2×D4311yescharacteristic
98C2×C4⋊C4—431no—
99C2×C4⋊C4C2×D4311yescharacteristic
100#108—434no—
101#107—21no—
102#107—861no—
103#106—21no—
104#106—861no—
105#106—861no—
106#106—861no—
107#97—861no—
108C4×C8—861no—
109C22×C4—21no—
110C22×C4—861no—
111C22×C4C22×D4311yescharacteristic
112M16—21no—
113M16—432no—
114M16—432no—
115M16—861no—
116M16—861no—
117M16C4×D4312yes—
118C2×C8—21no—
119C2×C8—432no—
120C2×C8—431no—
121C2×C8—431no—
122C2×C8—432no—
123C2×C8—861no—
124C2×C8—861no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—861no—
128C4⋊C4—861no—
129C4⋊C4C22⋊D4311yescharacteristic
130C4⋊C4C22⋊D4311yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1062190011yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—3441no—
139C2×C4—1721no—
140C2×C4C2×C4×D4311yescharacteristic
141C2×C4#1062189811yescharacteristic
142C2×C4D4×D4311yescharacteristic
143C2×C4Q8×D4311yescharacteristic
144C2×C4Q8×D4311yescharacteristic
145C2×C4C2×C22⋊D4311yescharacteristic
146C8—22no—
147C8—432no—
148C8—432no—
149C8—862no—
150C8—862no—
151C22—21no—
152C22—21no—
153C22#1306329011yescharacteristic
154C22#1306329711yescharacteristic
155C22#1306331511yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—3441no—
160C4C4⋊C4×D4311yescharacteristic
161C4C4×C22⋊D4311yescharacteristic
162C4#1306330311yescharacteristic
163C4#1306332311yescharacteristic
164C2—21no—
165C2—21no—
166C2#1458279411yescharacteristic
167C2#1458316011yescharacteristic
168C2#1458316411yescharacteristic
subgroupG/H
centerC22#13063297
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#428C2
socleC22×C43#121
hypercenter#428D43
hypocenterC43#1951
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #13063260C4semidirect
92. C43#1951semidirect