Finite Group Databasebeta

← #19134698

Subgroups — #19134698

Order 5504.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#10621898C211yesmaximal, characteristic
2#14582881C211yesmaximal, characteristic
3#14582872C211yesmaximal, characteristic
4#14582659C211yesmaximal, characteristic, complemented
5#14582656C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C4×Dic86—21no—
11C4×D172—21no—
12C4×C22⋊D43—22no—
13#13063284C2211yescharacteristic
14#13063284C2211yescharacteristic
15#13063282C412yescomplemented
16C42×D43C412yescomplemented
17#13063243—21no—
18#13063241—21no—
19#13063239—22no—
20C2×M16×C43C2211yescharacteristic
21#117×C43C2211yescharacteristic
22C2×C42×C43C2211yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43C2311yescharacteristic
25C2×C22⋊D43D412yes—
26#10621898—21no—
27#10621898—21no—
28#10621898—21no—
29#10621898—21no—
30C2×D172D411yescharacteristic
31C2×C4×D43—22no—
32C2×C4×D43C2×C412yes—
33C2×Dic86D411yescharacteristic
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×C43C2×C411yescharacteristic
42C42×C43C2×C411yescharacteristic
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45(C2×D43)⋊C4—22no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48Dic43⋊C4—22no—
49C4×Dic43—22no—
50C4×Dic43—21no—
51C4×Dic43C2×C412yes—
52#10621877—21no—
53#10621877—21no—
54C2×C43⋊C8—21no—
55C23×C43C2×D411yescharacteristic
56C22×D43C22⋊C412yes—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—42no—
60C2×C4×C43—41no—
61C2×C4×C43C22×C411yescharacteristic
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43#4111yescharacteristic
64C2×C4×C43#4111yescharacteristic
65C2×C4×C43#4111yescharacteristic
66C2×C4×C43#4111yescharacteristic
67C22⋊D43—22no—
68C22⋊D43—22no—
69C2×Dic43—22no—
70C2×Dic43—41no—
71C2×Dic43C22⋊C412yes—
72D172—21no—
73D172—21no—
74C4×D43—22no—
75C4×D43—22no—
76C4×D43—44no—
77Dic86—21no—
78Dic86—21no—
79C8×C43—41no—
80C43⋊C8—41no—
81C22×C43—41no—
82C22×C43C2×C22⋊C411yescharacteristic
83C22×C43#12311yescharacteristic
84C22×C43#12311yescharacteristic
85C2×D43—22no—
86C2×D43—42no—
87C4×C43—22no—
88C4×C43—41no—
89C4×C43—81no—
90C4×C43#11711yescharacteristic
91C4×C43#11711yescharacteristic
92C4×C43#12311yescharacteristic
93C4×C43#12311yescharacteristic
94Dic43—22no—
95Dic43—42no—
96Dic43—81no—
97#1827—431nomaximal, Sylow
98C2×C43—21no—
99C2×C43—21no—
100C2×C43—21no—
101C2×C43#38111yescharacteristic
102D43—42no—
103C4×#41—431no—
104#413—431no—
105#410—431no—
106#339—431no—
107#339D4311yescharacteristic, complemented
108H(3,ℤ/4)—431no—
109H(3,ℤ/4)—431no—
110C43#182711yescharacteristic, complemented, Sylow
111C2×#41—431no—
112C2×M16—431no—
113C2×M16C2×D4311yescharacteristic
114C4×Q8—861no—
115C4×D4—861no—
116C4×D4—862no—
117#117—431no—
118#117—432no—
119#117—431no—
120#117C2×D4311yescharacteristic
121C2×C42—432no—
122C2×C42C2×D4311yescharacteristic
123#101—861no—
124#100—861no—
125#99—862no—
126#41—861no—
127#41—861no—
128#41—861no—
129#41—861no—
130C2×Q8—431no—
131C2×D4—432no—
132C2×D4—431no—
133C22×C4—21no—
134C22×C4—432no—
135C22×C4—862no—
136C22×C4C22×D4311yescharacteristic
137M16—21no—
138M16—21no—
139M16—861no—
140M16—861no—
141C2×C8—21no—
142C2×C8—861no—
143C4⋊C4—21no—
144C4⋊C4—862no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C22⋊C4—21no—
148C22⋊C4—862no—
149C22⋊C4—861no—
150C22⋊C4—861no—
151C42—21no—
152C42—21no—
153C42—432no—
154C42—862no—
155C42—861no—
156C42C4×D4311yescharacteristic
157C42C4×D4311yescharacteristic
158C23—432no—
159C23D4×D4311yescharacteristic
160Q8—861no—
161Q8—861no—
162D4—862no—
163D4—862no—
164D4—861no—
165D4—861no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—432no—
171C2×C4—862no—
172C2×C4—862no—
173C2×C4—862no—
174C2×C4—1724no—
175C2×C4—1721no—
176C2×C4C2×C4×D4311yescharacteristic
177C2×C4#1062189811yescharacteristic
178C2×C4#1062189811yescharacteristic
179C2×C4D4×D4311yescharacteristic
180C2×C4#1062190011yescharacteristic
181C2×C4#1062190211yescharacteristic
182C8—41no—
183C8—1721no—
184C22—41no—
185C22—862no—
186C22—1722no—
187C22C22⋊C4×D4311yescharacteristic
188C22#1306330711yescharacteristic
189C22#1306331011yescharacteristic
190C4—22no—
191C4—41no—
192C4—81no—
193C4—862no—
194C4—3441no—
195C4—1722no—
196C4#1306328211yescharacteristic
197C4#1306328311yescharacteristic
198C4#1306330711yescharacteristic
199C4#1306331011yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—1722no—
204C2#1458276111yescharacteristic
subgroupG/H
centerC4#13063283
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC2×C43#381
hypercenter#339D43
hypocenterC43#1827
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #14582659C2semidirect
5. #14582656C2semidirect
6. #14582655C2semidirect
7. C43×#339C2semidirect
15. #13063282C4semidirect
16. C42×D43C4semidirect
107. #339D43semidirect
110. C43#1827semidirect