Finite Group Databasebeta

← #19145733

Subgroups — #19145733

Order 5504.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583449C211yesmaximal, characteristic
3#14583304C211yesmaximal, characteristic, complemented
4#14583297C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583246C211yesmaximal, characteristic, complemented
7#14583224C214yesmaximal, complemented
8#14583200C214yesmaximal, complemented
9C43×#431C211yesmaximal, characteristic, complemented
10C2×#10621898—21no—
11#13063325C2211yescharacteristic
12#13063325C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063322C2211yescharacteristic
15#13063317C2212yes—
16#13063313—21no—
17#13063304—21no—
18#13063304—21no—
19#13063299—21no—
20#13063299C2212yes—
21C4×Dic86—21no—
22C4×Dic86—21no—
23C4×D172—21no—
24C4×D172C2212yes—
25#13063284C2212yes—
26#13063259C2214yes—
27#13063257C2214yes—
28#13063247C2214yes—
29#13063247C2214yes—
30C2×C42×C43C2211yescharacteristic
31C4⋊C8×C43C2212yes—
32C22⋊C8×C43C2212yes—
33C4×C8×C43C2211yescharacteristic
34C4×C8×C43C2211yescharacteristic
35C22×C4×C43D411yescharacteristic
36C22×C4×C43D411yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39#10621898—44no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×Dic86—21no—
45C2×Dic86—21no—
46C2×Dic86—21no—
47C2×C8×C43C2312yes—
48C2×C8×C43C2312yes—
49C42×C43D411yescharacteristic
50C42×C43D411yescharacteristic
51C42×C43C2311yescharacteristic
52C42×C43C2311yescharacteristic
53C22⋊Dic43—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58C4⋊Dic43—21no—
59C4⋊Dic43C2312yes—
60C4⋊Dic43C2312yes—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65C23×C43C2×D411yescharacteristic
66C22×D43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2411yescharacteristic
76C22⋊D43—44no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80D172—24no—
81D172—42no—
82D172—42no—
83C4×D43—44no—
84Dic86—42no—
85Dic86—42no—
86Dic86—42no—
87C8×C43—22no—
88C8×C43—22no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43C22×D411yescharacteristic
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—42no—
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43#13512yes—
100C4×C43AGL(1,ℤ/8)12yes—
101C4×C432−1+412yes—
102Dic43—42no—
103Dic43—42no—
104Dic43—42no—
105#3228—431nomaximal, Sylow
106C2×C43—41no—
107C2×C43#53611yescharacteristic
108C2×C43C2×#13511yescharacteristic
109C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
110D43—82no—
111#533—431no—
112#532—431no—
113#500—431no—
114#498—431no—
115#486—431no—
116#486—431no—
117#482—434no—
118#478—434no—
119#431D4311yescharacteristic, complemented
120C43#322811yescharacteristic, complemented, Sylow
121C2×#41—861no—
122C4⋊Q8—431no—
123C4⋊Q8—431no—
124C4⋊Q8—431no—
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×C42C2×D4311yescharacteristic
138#107—434no—
139#106—434no—
140C4⋊C8C2×D4312yes—
141#102—434no—
142#102—434no—
143C22⋊C8C2×D4312yes—
144C4×C8C2×D4311yescharacteristic
145C4×C8C2×D4311yescharacteristic
146#41—1724no—
147C2×Q8—861no—
148C2×Q8—861no—
149C2×Q8—861no—
150C2×D4—432no—
151C2×D4—862no—
152C2×D4—861no—
153C2×D4—861no—
154C22×C4—862no—
155C22×C4D17211yescharacteristic
156C22×C4D17211yescharacteristic
157C22×C4C22×D4311yescharacteristic
158C2×C8C22×D4312yes—
159C2×C8C22×D4312yes—
160C4⋊C4—432no—
161C4⋊C4—432no—
162C4⋊C4—432no—
163C4⋊C4—861no—
164C4⋊C4—862no—
165C4⋊C4—862no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C22⋊C4—862no—
169C22⋊C4—862no—
170C22⋊C4—862no—
171C42—862no—
172C42D17211yescharacteristic
173C42D17211yescharacteristic
174C42C22×D4311yescharacteristic
175C42C22×D4311yescharacteristic
176C23—862no—
177C23C2×D17211yescharacteristic
178Q8—1722no—
179Q8—1722no—
180Q8—1722no—
181D4—864no—
182D4—1724no—
183D4—1722no—
184D4—1722no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—1724no—
192C2×C4C2×D17211yescharacteristic
193C2×C4C2×D17211yescharacteristic
194C2×C4C2×D17211yescharacteristic
195C2×C4C2×D17211yescharacteristic
196C2×C4C2×D17211yescharacteristic
197C2×C4C23×D4311yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—1722no—
204C22—1722no—
205C22—1722no—
206C22C22×D17211yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—1722no—
211C4—1722no—
212C4—1722no—
213C4#1306334712yes—
214C4#1306335312yes—
215C4#1306337212yes—
216C2—41no—
217C2—3442no—
218C2#1458347511yescharacteristic
219C2C2×#1306334711yescharacteristic
220C2C2×#1306335311yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#431C2
socleC22×C43C22×D4
hypercenter#431D43
hypocenterC43#3228
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #14583456C2semidirect
3. #14583304C2semidirect
4. #14583297C2semidirect
5. #14583246C2semidirect
6. #14583246C2semidirect
7. #14583224C2semidirect
8. #14583200C2semidirect
9. C43×#431C2semidirect
119. #431D43semidirect
120. C43#3228semidirect