Finite Group Databasebeta

← #19135769

Subgroups — #19135769

Order 5504.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583452C211yesmaximal, characteristic, complemented
2#14582916C211yesmaximal, characteristic
3C2×#13063252C211yesmaximal, characteristic
4#14582669C211yesmaximal, characteristic, complemented
5#14582658C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#410C211yesmaximal, characteristic
8C2×#10621877C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10#13063324—21no—
11#13063316—21no—
12#13063302—22no—
13C4×Dic86—22no—
14#13063284C2211yescharacteristic
15C2×C4×Dic43C2211yescharacteristic
16#13063252—21no—
17#13063252—21no—
18#13063252—22no—
19C2×#41×C43C2211yescharacteristic
20#117×C43C2211yescharacteristic
21#117×C43C2211yescharacteristic
22#99×C43—22no—
23#41×C43—21no—
24#41×C43—21no—
25#41×C43—21no—
26#41×C43—21no—
27C2×Q8×C43Q811yescharacteristic, complemented
28C2×D4×C43—21no—
29C2×D4×C43Q811yescharacteristic, complemented
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C22×Dic43—21no—
33C2×Dic86—22no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C22⋊C4×C43—21no—
37C22⋊C4×C43D412yes—
38C42×C43—21no—
39C42×C43—21no—
40C22⋊Dic43—21no—
41C4⋊Dic43—22no—
42C4⋊Dic43—21no—
43Dic43⋊C4—22no—
44Dic43⋊C4—22no—
45C4×Dic43—21no—
46C4×Dic43D411yescharacteristic
47C4×Dic43D411yescharacteristic
48C4×Dic43D412yes—
49#10621877—21no—
50#10621877—21no—
51#10621877—21no—
52#10621877—21no—
53C2×C43⋊C8—21no—
54C2×C43⋊C8—21no—
55C23×C43—21no—
56C23×C43C2×D411yescharacteristic
57Q8×C43—21no—
58Q8×C43—21no—
59D4×C43—21no—
60D4×C43—21no—
61D4×C43—41no—
62D4×C43—41no—
63C2×C4×C43—22no—
64C2×C4×C43—21no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×Q811yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×C4×C43#4111yescharacteristic
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—22no—
77C2×Dic43—42no—
78Dic86—44no—
79C43⋊C8—41no—
80C43⋊C8—41no—
81C22×C43—41no—
82C22×C43—41no—
83C22×C43—81no—
84C22×C43#12011yescharacteristic
85C22×C43C22⋊Q811yescharacteristic
86C22×C43#12411yescharacteristic
87C4×C43—42no—
88C4×C43—41no—
89C4×C43—81no—
90C4×C43C22⋊Q811yescharacteristic
91C4×C43C22⋊Q811yescharacteristic
92C4×C43#12411yescharacteristic
93C4×C43#12411yescharacteristic
94Dic43—22no—
95Dic43—42no—
96Dic43—41no—
97#2031—431nomaximal, Sylow
98C2×C43—21no—
99C2×C43—21no—
100C2×C43—21no—
101C2×C43—81no—
102C2×C43#39311yescharacteristic
103#533—431no—
104#421—431no—
105C2×#104—431no—
106#410D4311yescharacteristic
107#344—431no—
108#339—431no—
109H(3,ℤ/4)—431no—
110C43#203111yescharacteristic, complemented, Sylow
111C2×#41C2×D4311yescharacteristic
112C2×M16—431no—
113C2×M16—431no—
114C4⋊Q8—861no—
115#125—861no—
116C22⋊Q8—862no—
117C4×Q8—862no—
118#117—431no—
119#117C2×D4311yescharacteristic
120#117C2×D4311yescharacteristic
121C2×C42—431no—
122#104—861no—
123#104—861no—
124#104—862no—
125#99—22no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—862no—
131C2×Q8Dic8611yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic8611yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—861no—
136C22×C4C22×D4311yescharacteristic
137M16—861no—
138M16—861no—
139M16—861no—
140M16—861no—
141C2×C8—861no—
142C2×C8—861no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—862no—
146C4⋊C4—862no—
147C4⋊C4—862no—
148C4⋊C4—861no—
149C22⋊C4—21no—
150C22⋊C4—861no—
151C22⋊C4C22⋊D4312yes—
152C42—21no—
153C42—21no—
154C42—431no—
155C42—431no—
156C42—432no—
157C42—861no—
158C23—21no—
159C23C2×C22⋊D4311yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—1724no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—861no—
173C2×C4—861no—
174C2×C4—862no—
175C2×C4—1722no—
176C2×C4C2×Dic8611yescharacteristic
177C2×C4#1062189811yescharacteristic
178C2×C4D4×D4311yescharacteristic
179C2×C4D4×D4311yescharacteristic
180C2×C4#1062190011yescharacteristic
181C2×C4#1062190011yescharacteristic
182C8—1721no—
183C8—1721no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#1306329311yescharacteristic
188C22#1306330411yescharacteristic
189C22#1306331211yescharacteristic
190C4—42no—
191C4—41no—
192C4—81no—
193C4—862no—
194C4—1721no—
195C4—1722no—
196C4#1306330211yescharacteristic
197C4#1306330211yescharacteristic
198C4#1306331111yescharacteristic
199C4#1306331111yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1458281111yescharacteristic
subgroupG/H
centerC4#13063311
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#410C2
socleC2×C43#393
hypercenter#410D43
hypocenterC43#2031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14583452C2semidirect
4. #14582669C2semidirect
5. #14582658C2semidirect
6. #14582655C2semidirect
27. C2×Q8×C43Q8semidirect
29. C2×D4×C43Q8semidirect
110. C43#2031semidirect
131. C2×Q8Dic86semidirect
133. C2×D4Dic86semidirect