Finite Group Databasebeta

← #19135662

Subgroups — #19135662

Order 5504.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583699C211yesmaximal, characteristic, complemented
2#14583410C212yesmaximal, complemented
3#14582915C212yesmaximal, complemented
4#14582656C211yesmaximal, characteristic, complemented
5C43×#407C211yesmaximal, characteristic, complemented
6C2×#10621898C2212yes—
7#13063358—22no—
8#13063353—22no—
9#13063347—22no—
10#13063308—22no—
11#13063304—22no—
12#13063299—22no—
13#13063294—22no—
14C4×C22⋊D43—24no—
15#13063284C2212yes—
16#13063251—24no—
17C23×C4×C43C2211yescharacteristic
18C2×M16×C43C2211yescharacteristic
19C2×M16×C43C2211yescharacteristic
20C22⋊C8×C43—22no—
21C24×C43D411yescharacteristic
22C22×C4×C43—21no—
23C22×C4×C43—22no—
24C22×C4×C43—22no—
25C22×C4×C43—21no—
26C22×C4×C43D411yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—24no—
29C2×C22⋊D43—22no—
30#10621898—22no—
31#10621898—22no—
32#10621898—22no—
33#10621898—22no—
34C2×D172D412yescomplemented
35C2×C4×D43—22no—
36C2×Dic86D412yescomplemented
37M16×C43—22no—
38M16×C43—22no—
39C2×C8×C43—21no—
40C2×C8×C43D412yescomplemented
41C22⋊Dic43—24no—
42C22⋊Dic43—22no—
43(C2×D43)⋊C4—24no—
44C4⋊Dic43—22no—
45Dic43⋊C4—24no—
46C4×Dic43D414yescomplemented
47Dic172—22no—
48D344—22no—
49#10621873—24no—
50C23×C43—22no—
51C23×C43—21no—
52C23×C43—42no—
53C23×C43C2×D411yescharacteristic
54C22×D43—22no—
55C2×C4×C43—22no—
56C2×C4×C43—21no—
57C2×C4×C43—41no—
58C2×C4×C43—42no—
59C2×C4×C43—41no—
60C2×C4×C43C2×D412yes—
61C2×C4×C43C2×D412yes—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43#4111yescharacteristic
64C22⋊D43—48no—
65C22⋊D43—42no—
66C22⋊D43—42no—
67C2×Dic43—24no—
68C2×Dic43—22no—
69D172—22no—
70D172—22no—
71C4×D43—42no—
72C4×D43—42no—
73Dic86—22no—
74Dic86—22no—
75C8×C43—22no—
76C8×C43—41no—
77C22×C43—22no—
78C22×C43—24no—
79C22×C43—41no—
80C22×C43—42no—
81C22×C43—41no—
82C22×C43—41no—
83C22×C43#12012yes—
84C22×C43#12111yescharacteristic
85C2×D43—44no—
86C2×D43—42no—
87C4×C43—41no—
88C4×C43#12011yescharacteristic
89C4×C43#12112yes—
90C4×C43#12711yescharacteristic
91Dic43—44no—
92Dic43—42no—
93#2010—431nomaximal, Sylow
94C2×C43—22no—
95C2×C43—21no—
96C2×C43—42no—
97C2×C43#39211yescharacteristic
98D43—82no—
99#575—431no—
100#525—432no—
101#421—432no—
102#407D4311yescharacteristic, complemented
103H(3,ℤ/4)—431no—
104C43#201011yescharacteristic, complemented, Sylow
105C2×#41—432no—
106C23×C4C2×D4311yescharacteristic
107#137—862no—
108AGL(1,ℤ/8)—862no—
109#135—862no—
110C2×M16C2×D4311yescharacteristic
111C2×M16C2×D4311yescharacteristic
112#123—862no—
113C22⋊Q8—862no—
114#121—862no—
115#120—862no—
116C4×D4—864no—
117#117—432no—
118#104—864no—
119C22⋊C8—22no—
120C24D17211yescharacteristic
121#41—862no—
122#41—862no—
123#41—862no—
124#41—862no—
125C2×Q8—432no—
126C2×D4—432no—
127C2×D4—864no—
128C2×D4—862no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—862no—
134C22×C4D17211yescharacteristic
135C22×C4C22×D4311yescharacteristic
136Q16—862no—
137SD16—864no—
138D8—862no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D4312yescomplemented
143C4⋊C4—864no—
144C4⋊C4—862no—
145C22⋊C4—864no—
146C22⋊C4—864no—
147C22⋊C4—862no—
148C42—434no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—862no—
153C23C2×D17211yescharacteristic
154Q8—862no—
155Q8—862no—
156D4—862no—
157D4—862no—
158D4—1728no—
159D4—1722no—
160D4—1722no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—864no—
167C2×C4—862no—
168C2×C4—1722no—
169C2×C4—1722no—
170C2×C4#1062189811yescharacteristic
171C2×C4D4×D4312yes—
172C2×C4D4×D4312yes—
173C2×C4C2×C22⋊D4311yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1724no—
183C22—1722no—
184C22#1306329512yes—
185C22#1306329911yescharacteristic
186C4—41no—
187C4—1724no—
188C4—1722no—
189C4#1306329311yescharacteristic
190C4#1306329812yes—
191C4#1306332111yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—3442no—
196C2#1458280811yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#407C2
socleC2×C43#392
hypercenter#407D43
hypocenterC43#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14583699C2semidirect
2. #14583410C2semidirect
3. #14582915C2semidirect
4. #14582656C2semidirect
5. C43×#407C2semidirect
34. C2×D172D4semidirect
36. C2×Dic86D4semidirect
40. C2×C8×C43D4semidirect
46. C4×Dic43D4semidirect
102. #407D43semidirect
104. C43#2010semidirect
142. C2×C8C22⋊D43semidirect