Finite Group Databasebeta

← #19145734

Subgroups — #19145734

Order 5504.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583454C211yesmaximal, characteristic, complemented
2#14583450C211yesmaximal, characteristic
3#14583295C211yesmaximal, characteristic, complemented
4#14583247C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583226C214yesmaximal, complemented
7#14583202C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic, complemented
9C43×#500C211yesmaximal, characteristic, complemented
10C2×#10621902—21no—
11#13063325C2211yescharacteristic
12#13063322C2211yescharacteristic
13#13063316C2212yes—
14#13063314—21no—
15#13063305—21no—
16#13063301—21no—
17#13063300—21no—
18#13063300C2212yes—
19Q8×Dic43—21no—
20#13063290—21no—
21#13063287—21no—
22#13063287C2212yes—
23#13063283C2212yes—
24C42×D43C2211yescharacteristic
25#13063256C2214yes—
26Dic43⋊C8C2212yes—
27#13063247C2214yes—
28#13063245C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#107×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43—21no—
37#10621902—44no—
38C2×D172—21no—
39C2×D172—21no—
40C2×D172—22no—
41C2×D172C2312yes—
42C2×C4×D43—22no—
43C2×C4×D43D411yescharacteristic
44C2×C4×D43D411yescharacteristic
45C2×C4×D43C2311yescharacteristic
46C2×Dic86—21no—
47C2×C8×C43C2312yes—
48C4⋊C4×C43—21no—
49C4⋊C4×C43—21no—
50C4⋊C4×C43C2312yes—
51C4⋊C4×C43C2312yes—
52C42×C43C2311yescharacteristic
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43—21no—
57C4⋊Dic43—22no—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60C4×Dic43—22no—
61C4×Dic43D411yescharacteristic
62C4×Dic43D411yescharacteristic
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2312yes—
65C22×D43—22no—
66C22×D43C2×D411yescharacteristic
67Q8×C43—42no—
68Q8×C43—42no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2411yescharacteristic
74C2×Dic43—22no—
75C2×Dic43C2×D411yescharacteristic
76C2×Dic43C2×D411yescharacteristic
77C2×Dic43C2×D411yescharacteristic
78D172—24no—
79D172—44no—
80D172—42no—
81D172—42no—
82C4×D43—22no—
83C4×D43—22no—
84C4×D43—22no—
85C4×D43—44no—
86Dic86—42no—
87C8×C43—22no—
88C43⋊C8—22no—
89C22×C43C22×D411yescharacteristic
90C2×D43—21no—
91C2×D43—21no—
92C2×D43—21no—
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—42no—
96C4×C43—42no—
97C4×C43—42no—
98C4×C43#13512yes—
99C4×C43AGL(1,ℤ/8)12yes—
100C4×C432−1+412yes—
101Dic43—21no—
102Dic43—21no—
103Dic43—21no—
104Dic43—42no—
105#3228—431nomaximal, Sylow
106C2×C43#53611yescharacteristic
107C2×C43C2×#13511yescharacteristic
108C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
109D43—41no—
110D43—82no—
111#533—431no—
112#532—431no—
113#500D4311yescharacteristic, complemented
114#498—431no—
115#486—431no—
116#486—431no—
117#482—434no—
118#478—434no—
119#431—431no—
120C43#322811yescharacteristic, complemented, Sylow
121C2×#41—861no—
122C4⋊Q8—431no—
123C4⋊Q8C2×D4311yescharacteristic
124C4⋊Q8C2×D4311yescharacteristic
125#127—431no—
126#125—432no—
127#124—861no—
128C22⋊Q8—861no—
129C22⋊Q8—861no—
130#121—432no—
131#121—861no—
132C4×Q8—861no—
133C4×Q8—861no—
134C4×D4—432no—
135C4×D4—861no—
136#117—432no—
137C2×C42—431no—
138#107C2×D4314yes—
139#106—434no—
140C4⋊C8—432no—
141#102—434no—
142#102—434no—
143C22⋊C8—432no—
144C4×C8—431no—
145C4×C8C2×D4311yescharacteristic
146#41—1724no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—861no—
150C2×D4—432no—
151C2×D4—862no—
152C2×D4—861no—
153C2×D4—861no—
154C22×C4—431no—
155C22×C4—431no—
156C22×C4—431no—
157C22×C4—862no—
158C2×C8—432no—
159C2×C8C22×D4312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—432no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C4⋊C4—861no—
166C4⋊C4C22×D4312yes—
167C4⋊C4C22×D4312yes—
168C22⋊C4—862no—
169C22⋊C4—862no—
170C22⋊C4—862no—
171C42—431no—
172C42—431no—
173C42—431no—
174C42—862no—
175C42C22×D4311yescharacteristic
176C23—431no—
177C23—862no—
178Q8—42no—
179Q8—42no—
180Q8—1722no—
181D4—864no—
182D4—1724no—
183D4—1722no—
184D4—1722no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—431no—
188C2×C4—431no—
189C2×C4—431no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—1724no—
195C2×C4D4×D4311yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C2×C4C23×D4311yescharacteristic
198C8—22no—
199C8—862no—
200C22—861no—
201C22—861no—
202C22—861no—
203C22—1722no—
204C22—1722no—
205C22—1722no—
206C22C2×D4×D4311yescharacteristic
207C4—42no—
208C4—42no—
209C4—861no—
210C4—861no—
211C4—861no—
212C4—1722no—
213C4#1306334812yes—
214C4#1306334912yes—
215C4#1306337312yes—
216C2—3442no—
217C2—1721no—
218C2#1458347411yescharacteristic
219C2C2×#1306334811yescharacteristic
220C2C2×#1306334911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#500C2
socleC22×C43C22×D4
hypercenter#500D43
hypocenterC43#3228
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583295C2semidirect
4. #14583247C2semidirect
5. #14583246C2semidirect
6. #14583226C2semidirect
7. #14583202C2semidirect
8. #14582950C2semidirect
9. C43×#500C2semidirect
113. #500D43semidirect
120. C43#3228semidirect