Finite Group Databasebeta

← #19145660

Subgroups — #19145660

Order 5504.

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

normal subgroups only

This group has 396 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#14583510C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic
3#14583291C211yesmaximal, characteristic, complemented
4#14583263C211yesmaximal, characteristic, complemented
5#14583254C211yesmaximal, characteristic, complemented
6#14583119C212yesmaximal, complemented
7#14583097C212yesmaximal, complemented
8#14583058C212yesmaximal, complemented
9#14583048C212yesmaximal, complemented
10#14582958C211yesmaximal, characteristic, complemented
11C43×#492C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621885C2212yescomplemented
15C2×#10621884C2212yes—
16#13063321C2211yescharacteristic
17#13063320—22no—
18#13063317C2211yescharacteristic, complemented
19#13063315—22no—
20#13063313C2211yescharacteristic
21#13063312C2211yescharacteristic
22#13063301C2212yes—
23#13063297—22no—
24#13063293—22no—
25Q8×Dic43C2212yescomplemented
26#13063282C2211yescharacteristic
27Dic43⋊C8C2212yescomplemented
28#13063250C2212yescomplemented
29#13063247C2212yes—
30#13063246C2212yes—
31#13063246C2212yescomplemented
32(C2×D43)⋊C8C2212yes—
33#13063236C2211yescharacteristic, complemented
34C2×SD16×C43C2212yes—
35C2×SD16×C43C2212yescomplemented
36C4⋊Q8×C43C2211yescharacteristic, complemented
37#127×C43C2211yescharacteristic
38C4×C8×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C2×Q8×C43C2312yes—
41C2×D4×C43—22no—
42C2×D4×C43C2311yescharacteristic
43C2×D4×C43C2311yescharacteristic
44C2×C22⋊D43—21no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48#10621900—42no—
49D4×D43—42no—
50C2×D172C2311yescharacteristic
51C2×C4×D43C2311yescharacteristic
52C2×Dic86C2311yescharacteristic
53SD16×C43—42no—
54SD16×C43—42no—
55C2×C8×C43C2312yes—
56C4⋊C4×C43—22no—
57C42×C43C2311yescharacteristic
58C22⋊Dic43—22no—
59#10621885—42no—
60#10621884—42no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4D412yes—
64C4⋊Dic43—22no—
65C4⋊Dic43C2312yes—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4D412yes—
69C4×Dic43—22no—
70C4×Dic43C2311yescharacteristic
71C2×C43⋊C8C2312yes—
72C23×C43—21no—
73C23×C43—21no—
74C22×D43—21no—
75C22×D43—42no—
76C22×D43—82no—
77C22×D43C2×D411yescharacteristic
78Q8×C43—22no—
79Q8×C43—22no—
80D4×C43—22no—
81D4×C43—22no—
82D4×C43—82no—
83C2×C4×C43—22no—
84C2×C4×C43C2×D412yes—
85C2×C4×C43C2411yescharacteristic
86C22⋊D43—42no—
87C22⋊D43—42no—
88C22⋊D43—82no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—42no—
92C2×Dic43C2×D412yes—
93C2×Dic43C2×D411yescharacteristic
94D172—22no—
95C4×D43—22no—
96Dic86—22no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43C22×D411yescharacteristic
104C2×D43—21no—
105C2×D43—22no—
106C2×D43—41no—
107C2×D43—42no—
108C2×D43—84no—
109C4×C43—22no—
110C4×C43—42no—
111C4×C43H(5,𝔽2)12yes—
112Dic43—21no—
113Dic43—22no—
114Dic43—41no—
115Dic43—42no—
116#3222—431nomaximal, Sylow
117C2×C43—81no—
118C2×C43—81no—
119C2×C43#53511yescharacteristic
120C2×C43#57712yes—
121D43—41no—
122D43—81no—
123#541—431no—
124#535—431no—
125#497—431no—
126#492D4311yescharacteristic, complemented
127#490—431no—
128#488—431no—
129#464—432no—
130#460—432no—
131#452—432no—
132#450—432no—
133#433—431no—
134C43#322211yescharacteristic, complemented, Sylow
135C2×#41—431no—
136C22×D4—431no—
137C2×Q16—432no—
138C2×SD16—432no—
139C2×SD16C2×D4312yes—
140C2×SD16C2×D4312yescomplemented
141C4⋊Q8C2×D4311yescharacteristic, complemented
142#127—431no—
143#127C2×D4311yescharacteristic
144#126—862no—
145#125—431no—
146#125—862no—
147#124—431no—
148#124—431no—
149C22⋊Q8—432no—
150#121—862no—
151#120—862no—
152C4×Q8—432no—
153#117—431no—
154C4⋊C8—432no—
155#103—432no—
156#102—432no—
157#102—432no—
158#102—432no—
159C22⋊C8—432no—
160#97—431no—
161C4×C8C2×D4311yescharacteristic, complemented
162C24—861no—
163#41—1722no—
164C2×Q8—431no—
165C2×Q8C22×D4312yes—
166C2×D4—22no—
167C2×D4—431no—
168C2×D4—862no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—1722no—
172C2×D4C22×D4311yescharacteristic
173C2×D4C22×D4311yescharacteristic
174C22×C4—431no—
175C22×C4—861no—
176Q16—1722no—
177SD16—42no—
178SD16—42no—
179SD16—1722no—
180C2×C8—432no—
181C2×C8C22×D4312yes—
182C4⋊C4—22no—
183C4⋊C4—432no—
184C4⋊C4—432no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4—862no—
188C22⋊C4—432no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C22⋊C4—862no—
192C42—431no—
193C42—862no—
194C42C22×D4311yescharacteristic
195C23—21no—
196C23—21no—
197C23—431no—
198C23—861no—
199C23—3442no—
200C23—1722no—
201Q8—22no—
202Q8—22no—
203Q8—862no—
204D4—22no—
205D4—22no—
206D4—82no—
207D4—862no—
208D4—3442no—
209D4—1722no—
210D4—1722no—
211C2×C4—22no—
212C2×C4—432no—
213C2×C4—431no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—1722no—
218C2×C4D4×D4312yes—
219C2×C4C23×D4311yescharacteristic
220C8—22no—
221C8—862no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22—862no—
227C22—861no—
228C22—3444no—
229C22—1722no—
230C22—1721no—
231C22C2×D4×D4311yescharacteristic
232C4—22no—
233C4—42no—
234C4—862no—
235C4—861no—
236C4—1722no—
237C4—1721no—
238C4#1306337012yes—
239C2—81no—
240C2—81no—
241C2—3441no—
242C2—1721no—
243C2#1458346211yescharacteristic
244C2#1458370512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#492C2
socleC22×C43C22×D4
hypercenter#492D43
hypocenterC43#3222
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. #14583510C2semidirect
3. #14583291C2semidirect
4. #14583263C2semidirect
5. #14583254C2semidirect
6. #14583119C2semidirect
7. #14583097C2semidirect
8. #14583058C2semidirect
9. #14583048C2semidirect
10. #14582958C2semidirect
11. C43×#492C2semidirect
14. C2×#10621885C22semidirect
18. #13063317C22semidirect
25. Q8×Dic43C22semidirect
27. Dic43⋊C8C22semidirect
28. #13063250C22semidirect
31. #13063246C22semidirect
33. #13063236C22semidirect
35. C2×SD16×C43C22semidirect
36. C4⋊Q8×C43C22semidirect
38. C4×C8×C43C22semidirect
126. #492D43semidirect
134. C43#3222semidirect
140. C2×SD16C2×D43semidirect
141. C4⋊Q8C2×D43semidirect
161. C4×C8C2×D43semidirect