Finite Group Databasebeta

← #19145649

Subgroups — #19145649

Order 5504.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#14583503C211yesmaximal, characteristic, complemented
2#14583474C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic, complemented
4#14583267C211yesmaximal, characteristic, complemented
5#14583254C211yesmaximal, characteristic, complemented
6#14583116C212yesmaximal, complemented
7#14583102C212yesmaximal, complemented
8#14583043C212yesmaximal, complemented
9#14583036C212yesmaximal, complemented
10#14582958C211yesmaximal, characteristic, complemented
11C43×#492C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×Q8×D43C2211yescharacteristic
14C2×#10621883C2212yes—
15C2×#10621882C2212yes—
16#13063323C2211yescharacteristic
17#13063317C2211yescharacteristic
18#13063314C2211yescharacteristic
19#13063313C2211yescharacteristic
20#13063310—22no—
21#13063306—22no—
22#13063303—22no—
23#13063297—22no—
24#13063296C2212yes—
25D4×Dic43C2212yes—
26#13063282C2211yescharacteristic
27Dic43⋊C8C2212yes—
28#13063250C2212yes—
29#13063249C2212yes—
30#13063249C2212yes—
31#13063247C2212yes—
32(C2×D43)⋊C8C2212yes—
33#13063236C2211yescharacteristic
34C2×SD16×C43C2212yes—
35C2×SD16×C43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37#127×C43C2211yescharacteristic
38C4×C8×C43C2211yescharacteristic
39C2×Q8×C43C2311yescharacteristic
40C2×Q8×C43C2311yescharacteristic
41C2×D4×C43—22no—
42C2×D4×C43C2312yes—
43C2×C22⋊D43—22no—
44C22×Dic43—22no—
45#10621902—42no—
46Q8×D43—42no—
47C2×D172—21no—
48C2×D172C2311yescharacteristic
49C2×C4×D43—21no—
50C2×C4×D43—21no—
51C2×C4×D43C2311yescharacteristic
52C2×Dic86—21no—
53C2×Dic86C2311yescharacteristic
54SD16×C43—42no—
55SD16×C43—42no—
56C2×C8×C43C2312yes—
57C4⋊C4×C43—22no—
58C42×C43C2311yescharacteristic
59C22⋊Dic43—22no—
60C22⋊Dic43—22no—
61#10621883—42no—
62#10621882—42no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4D412yes—
66C4⋊Dic43C2312yes—
67Dic43⋊C4—22no—
68Dic43⋊C4—22no—
69Dic43⋊C4D412yes—
70C4×Dic43C2311yescharacteristic
71C2×C43⋊C8C2312yes—
72C23×C43—22no—
73C22×D43—21no—
74C22×D43C2×D411yescharacteristic
75Q8×C43—22no—
76Q8×C43—22no—
77D4×C43—22no—
78D4×C43—22no—
79D4×C43—82no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2411yescharacteristic
84C22⋊D43—82no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—82no—
88C2×Dic43C2×D412yes—
89C2×Dic43C2×D411yescharacteristic
90D172—22no—
91D172—42no—
92C4×D43—22no—
93C4×D43—42no—
94C4×D43—42no—
95Dic86—22no—
96Dic86—42no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43—42no—
102C22×C43C22×D411yescharacteristic
103C2×D43—21no—
104C2×D43—22no—
105C2×D43—41no—
106C2×D43—42no—
107C4×C43—22no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43H(5,𝔽2)12yes—
111Dic43—21no—
112Dic43—22no—
113Dic43—41no—
114Dic43—42no—
115#3221—431nomaximal, Sylow
116C2×C43—82no—
117C2×C43#53511yescharacteristic
118C2×C43#57712yes—
119D43—41no—
120D43—81no—
121#540—431no—
122#536—431no—
123#496—431no—
124#492D4311yescharacteristic, complemented
125#491—431no—
126#488—431no—
127#463—432no—
128#461—432no—
129#449—432no—
130#448—432no—
131#433—431no—
132C43#322111yescharacteristic, complemented, Sylow
133C2×#41—431no—
134C22×Q8—431no—
135C2×SD16—432no—
136C2×SD16C2×D4312yes—
137C2×SD16C2×D4312yes—
138C2×D8—432no—
139C4⋊Q8—431no—
140C4⋊Q8C2×D4311yescharacteristic
141#127C2×D4311yescharacteristic
142#125—431no—
143#124—431no—
144#124—431no—
145#123—862no—
146#123—862no—
147C22⋊Q8—862no—
148#121—432no—
149#121—862no—
150C4×D4—432no—
151#117—431no—
152C4⋊C8—432no—
153#103—432no—
154#103—432no—
155#103—432no—
156#102—432no—
157C22⋊C8—432no—
158#97—431no—
159C4×C8C2×D4311yescharacteristic
160#41—1722no—
161C2×Q8—431no—
162C2×Q8—861no—
163C2×Q8—1722no—
164C2×Q8C22×D4311yescharacteristic
165C2×Q8C22×D4311yescharacteristic
166C2×D4—22no—
167C2×D4—431no—
168C2×D4—861no—
169C2×D4—862no—
170C2×D4C22×D4312yes—
171C22×C4—431no—
172C22×C4—861no—
173C22×C4—861no—
174C22×C4—862no—
175SD16—42no—
176SD16—42no—
177SD16—1722no—
178D8—1722no—
179C2×C8—432no—
180C2×C8C22×D4312yes—
181C4⋊C4—22no—
182C4⋊C4—432no—
183C4⋊C4—432no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C22⋊C4—432no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C42—431no—
192C42C22×D4311yescharacteristic
193C23—22no—
194C23—431no—
195C23—861no—
196Q8—22no—
197Q8—22no—
198Q8—862no—
199Q8—1722no—
200D4—22no—
201D4—22no—
202D4—82no—
203D4—862no—
204D4—3442no—
205D4—1722no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—432no—
209C2×C4—431no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—861no—
213C2×C4—3442no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4D4×D4312yes—
217C2×C4C23×D4311yescharacteristic
218C8—22no—
219C8—862no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—862no—
224C22—861no—
225C22—1722no—
226C22—1721no—
227C22C2×D4×D4311yescharacteristic
228C4—22no—
229C4—41no—
230C4—41no—
231C4—862no—
232C4—861no—
233C4—1722no—
234C4—1721no—
235C4#1306337012yes—
236C2—82no—
237C2—3441no—
238C2—1721no—
239C2#1458346211yescharacteristic
240C2#1458370512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#492C2
socleC22×C43C22×D4
hypercenter#492D43
hypocenterC43#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #14583503C2semidirect
2. #14583474C2semidirect
3. #14583286C2semidirect
4. #14583267C2semidirect
5. #14583254C2semidirect
6. #14583116C2semidirect
7. #14583102C2semidirect
8. #14583043C2semidirect
9. #14583036C2semidirect
10. #14582958C2semidirect
11. C43×#492C2semidirect
124. #492D43semidirect
132. C43#3221semidirect