Finite Group Databasebeta

← #19145548

Subgroups — #19145548

Order 5504.

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

normal subgroups only

This group has 394 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#14583273C211yesmaximal, characteristic, complemented
4#14583249C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583123C214yesmaximal, complemented
7#14583060C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic, complemented
9C43×#494C211yesmaximal, characteristic, complemented
10C2×#10621902C2212yes—
11C2×#10621884C2214yes—
12#13063325C2211yescharacteristic
13#13063322C2211yescharacteristic
14#13063316—21no—
15#13063314C2212yes—
16#13063305—21no—
17#13063301C2212yes—
18#13063300—21no—
19#13063300—21no—
20Q8×Dic43C2212yes—
21#13063290—21no—
22#13063287—21no—
23#13063287—21no—
24#13063283—21no—
25C42×D43C2211yescharacteristic
26Dic43⋊C8C2212yes—
27#13063249C2214yes—
28#13063247C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C2×Q16×C43C2214yes—
32C4⋊Q8×C43C2211yescharacteristic
33C4⋊Q8×C43C2211yescharacteristic
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43C2312yes—
36C2×Q8×C43C2312yes—
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—
47Q16×C43—44no—
48C2×C8×C43C2312yes—
49C4⋊C4×C43—21no—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C42×C43C2311yescharacteristic
54#10621884—44no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—21no—
59C4⋊Dic43—22no—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C4×Dic43D411yescharacteristic
64C4×Dic43D411yescharacteristic
65C4×Dic43C2311yescharacteristic
66C2×C43⋊C8C2312yes—
67C22×D43—22no—
68C22×D43C2×D411yescharacteristic
69Q8×C43—24no—
70Q8×C43—24no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2411yescharacteristic
76C2×Dic43—22no—
77C2×Dic43C2×D411yescharacteristic
78C2×Dic43C2×D411yescharacteristic
79C2×Dic43C2×D411yescharacteristic
80D172—24no—
81D172—44no—
82D172—42no—
83D172—42no—
84C4×D43—22no—
85C4×D43—22no—
86C4×D43—22no—
87C4×D43—44no—
88Dic86—42no—
89C8×C43—22no—
90C43⋊C8—22no—
91C22×C43C22×D411yescharacteristic
92C2×D43—21no—
93C2×D43—21no—
94C2×D43—21no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C4×C43—42no—
99C4×C43—42no—
100C4×C43#13512yes—
101C4×C43#13712yes—
102C4×C43H(5,𝔽2)12yes—
103Dic43—21no—
104Dic43—21no—
105Dic43—21no—
106Dic43—42no—
107#3210—431nomaximal, Sylow
108C2×C43#53511yescharacteristic
109C2×C43C2×#13511yescharacteristic
110C2×C43C2×#13711yescharacteristic
111D43—41no—
112D43—82no—
113#533—431no—
114#532—431no—
115#494D4311yescharacteristic, complemented
116#492—431no—
117#487—431no—
118#486—431no—
119#464—434no—
120#452—434no—
121#431—431no—
122C43#321011yescharacteristic, complemented, Sylow
123C2×#41—432no—
124C2×Q16C2×D4314yes—
125C2×SD16—434no—
126C4⋊Q8—431no—
127C4⋊Q8C2×D4311yescharacteristic
128C4⋊Q8C2×D4311yescharacteristic
129#127—431no—
130#125—861no—
131#124—432no—
132C22⋊Q8—432no—
133C22⋊Q8—861no—
134#121—861no—
135#121—861no—
136C4×Q8—432no—
137C4×Q8—861no—
138C4×D4—861no—
139C4×D4—861no—
140#117—861no—
141C2×C42—431no—
142C4⋊C8—432no—
143#103—434no—
144#102—434no—
145C22⋊C8—432no—
146C4×C8—431no—
147C4×C8C2×D4311yescharacteristic
148#41—1724no—
149C2×Q8—861no—
150C2×Q8C22×D4312yes—
151C2×Q8C22×D4312yes—
152C2×D4—432no—
153C2×D4—862no—
154C2×D4—861no—
155C2×D4—861no—
156C22×C4—431no—
157C22×C4—431no—
158C22×C4—431no—
159C22×C4—862no—
160Q16—44no—
161SD16—1724no—
162C2×C8—432no—
163C2×C8C22×D4312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—432no—
169C4⋊C4—862no—
170C4⋊C4—862no—
171C4⋊C4—861no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C22⋊C4—862no—
175C42—431no—
176C42—431no—
177C42—431no—
178C42—862no—
179C42C22×D4311yescharacteristic
180C23—431no—
181C23—862no—
182Q8—24no—
183Q8—24no—
184Q8—1722no—
185D4—864no—
186D4—1724no—
187D4—1722no—
188D4—1722no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—431no—
192C2×C4—431no—
193C2×C4—431no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—1724no—
199C2×C4D4×D4311yescharacteristic
200C2×C4D4×D4311yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—22no—
203C8—862no—
204C22—861no—
205C22—861no—
206C22—861no—
207C22—1722no—
208C22—1722no—
209C22—1722no—
210C22C2×D4×D4311yescharacteristic
211C4—42no—
212C4—42no—
213C4—861no—
214C4—861no—
215C4—861no—
216C4—1722no—
217C4#1306334812yes—
218C4#1306335712yes—
219C4#1306337012yes—
220C2—3442no—
221C2—1721no—
222C2#1458346211yescharacteristic
223C2C2×#1306334811yescharacteristic
224C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#494C2
socleC22×C43C22×D4
hypercenter#494D43
hypocenterC43#3210
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583273C2semidirect
4. #14583249C2semidirect
5. #14583246C2semidirect
6. #14583123C2semidirect
7. #14583060C2semidirect
8. #14582950C2semidirect
9. C43×#494C2semidirect
115. #494D43semidirect
122. C43#3210semidirect