Finite Group Databasebeta

← #19135768

Subgroups — #19135768

Order 5504.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#14583456C211yesmaximal, characteristic, complemented
2#14582915C211yesmaximal, characteristic
3C2×#13063253C211yesmaximal, characteristic
4#14582872C211yesmaximal, characteristic
5#14582670C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10#13063325—21no—
11#13063317—21no—
12#13063304—22no—
13C4×Dic86—22no—
14#13063284C2211yescharacteristic
15#13063284C2211yescharacteristic
16#13063253—21no—
17#13063253—21no—
18#13063251—22no—
19#13063239—22no—
20C2×M16×C43C2211yescharacteristic
21#117×C43C2211yescharacteristic
22C2×C42×C43C2211yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43C2311yescharacteristic
25C2×C22⋊D43—21no—
26#10621898—21no—
27#10621898—21no—
28#10621898—21no—
29#10621898—21no—
30C2×D172Q811yescharacteristic, complemented
31C2×C4×D43—21no—
32C2×Dic86—22no—
33C2×Dic86Q811yescharacteristic, complemented
34M16×C43—21no—
35M16×C43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C22⋊C4×C43—21no—
39C42×C43—21no—
40C42×C43—21no—
41C42×C43D411yescharacteristic
42C42×C43D411yescharacteristic
43C22⋊Dic43—21no—
44C22⋊Dic43D412yes—
45C4⋊Dic43—22no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48Dic43⋊C4—24no—
49C4×Dic43—21no—
50C4×Dic43D412yes—
51#10621877—21no—
52#10621877—21no—
53C2×C43⋊C8—21no—
54C23×C43C2×D411yescharacteristic
55C22×D43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—42no—
59C2×C4×C43—41no—
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×Q811yescharacteristic
63C2×C4×C43#4111yescharacteristic
64C2×C4×C43#4111yescharacteristic
65C2×C4×C43#4111yescharacteristic
66C22⋊D43—41no—
67C22⋊D43—41no—
68C2×Dic43—22no—
69C2×Dic43—22no—
70C2×Dic43—21no—
71D172—21no—
72D172—21no—
73C4×D43—41no—
74C4×D43—41no—
75Dic86—21no—
76Dic86—21no—
77Dic86—44no—
78C8×C43—41no—
79C43⋊C8—41no—
80C22×C43—41no—
81C22×C43#12011yescharacteristic
82C22×C43C22⋊Q811yescharacteristic
83C22×C43#12411yescharacteristic
84C2×D43—41no—
85C2×D43—81no—
86C4×C43—22no—
87C4×C43—41no—
88C4×C43—81no—
89C4×C43C22⋊Q811yescharacteristic
90C4×C43C22⋊Q811yescharacteristic
91C4×C43#12411yescharacteristic
92C4×C43#12411yescharacteristic
93Dic43—42no—
94Dic43—42no—
95Dic43—41no—
96#2031—431nomaximal, Sylow
97C2×C43—21no—
98C2×C43—21no—
99C2×C43—21no—
100C2×C43#39311yescharacteristic
101D43—81no—
102#533—431no—
103#421—431no—
104C2×#104—431no—
105#410—431no—
106#344—431no—
107#339D4311yescharacteristic, complemented
108H(3,ℤ/4)—431no—
109C43#203111yescharacteristic, complemented, Sylow
110C2×#41—431no—
111C2×M16—431no—
112C2×M16C2×D4311yescharacteristic
113C4⋊Q8—861no—
114#125—861no—
115C22⋊Q8—862no—
116C4×Q8—862no—
117#117—431no—
118#117—431no—
119#117C2×D4311yescharacteristic
120C2×C42C2×D4311yescharacteristic
121#104—862no—
122#104—861no—
123#104—861no—
124#99—862no—
125#41—861no—
126#41—861no—
127#41—861no—
128#41—861no—
129C2×Q8—431no—
130C2×Q8—862no—
131C2×D4—431no—
132C2×D4—861no—
133C22×C4—21no—
134C22×C4—861no—
135C22×C4C22×D4311yescharacteristic
136M16—21no—
137M16—21no—
138M16—861no—
139M16—861no—
140C2×C8—21no—
141C2×C8—861no—
142C4⋊C4—21no—
143C4⋊C4—864no—
144C4⋊C4—862no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C22⋊C4—21no—
148C22⋊C4—432no—
149C22⋊C4—861no—
150C42—21no—
151C42—21no—
152C42—432no—
153C42—861no—
154C42D17211yescharacteristic
155C42D17211yescharacteristic
156C23—861no—
157C23D4×D4311yescharacteristic
158Q8—861no—
159Q8—861no—
160Q8—1724no—
161D4—861no—
162D4—861no—
163D4—1721no—
164D4—1721no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—862no—
170C2×C4—862no—
171C2×C4—861no—
172C2×C4—1721no—
173C2×C4—1721no—
174C2×C4C2×D17211yescharacteristic
175C2×C4#1062189811yescharacteristic
176C2×C4#1062189811yescharacteristic
177C2×C4D4×D4311yescharacteristic
178C2×C4#1062190011yescharacteristic
179C2×C4Q8×D4311yescharacteristic
180C8—41no—
181C8—1721no—
182C22—41no—
183C22—3441no—
184C22—1721no—
185C22#1306329511yescharacteristic
186C22#1306330311yescharacteristic
187C22#1306331111yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—1722no—
192C4—1722no—
193C4—1721no—
194C4#1306330311yescharacteristic
195C4#1306330511yescharacteristic
196C4#1306331111yescharacteristic
197C4#1306331311yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—3441no—
202C2#1458281211yescharacteristic
subgroupG/H
centerC4#13063311
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC2×C43#393
hypercenter#339D43
hypocenterC43#2031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #14583456C2semidirect
5. #14582670C2semidirect
6. #14582655C2semidirect
7. C43×#339C2semidirect
30. C2×D172Q8semidirect
33. C2×Dic86Q8semidirect
107. #339D43semidirect
109. C43#2031semidirect