Finite Group Databasebeta

← #19145657

Subgroups — #19145657

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#14583505C211yesmaximal, characteristic, complemented
2#14583474C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583273C211yesmaximal, characteristic, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583117C212yesmaximal, complemented
7#14583103C212yesmaximal, complemented
8#14583047C212yesmaximal, complemented
9#14583039C212yesmaximal, complemented
10#14582961C211yesmaximal, characteristic, complemented
11C43×#491C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×Q8×D43C2211yescharacteristic
14C2×#10621873C2212yes—
15C2×#10621884C2212yes—
16C2×#10621884C2212yes—
17C2×D344C2212yes—
18#13063323C2211yescharacteristic
19#13063322C2211yescharacteristic
20#13063314C2211yescharacteristic
21#13063313C2211yescharacteristic
22#13063310—22no—
23#13063310—22no—
24#13063303—22no—
25#13063300—22no—
26#13063300C2212yes—
27#13063287C2212yes—
28#13063282C2211yescharacteristic
29Dic43⋊C8C2212yes—
30#13063248C2212yes—
31#13063245C2212yes—
32(C2×D43)⋊C8C2212yes—
33C4×C43⋊C8C2211yescharacteristic
34C4⋊Q8×C43C2211yescharacteristic
35#125×C43C2211yescharacteristic
36#103×C43C2212yes—
37#103×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×Q8×C43C2311yescharacteristic
40C2×Q8×C43C2311yescharacteristic
41#10621902—42no—
42Q8×D43—42no—
43C2×D172—22no—
44C2×D172—21no—
45C2×D172—22no—
46C2×D172C2311yescharacteristic
47C2×D172C2312yes—
48C2×C4×D43—21no—
49C2×C4×D43—22no—
50C2×C4×D43—21no—
51C2×C4×D43C2311yescharacteristic
52C2×Dic86—21no—
53C2×Dic86C2311yescharacteristic
54C2×C8×C43C2312yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43C2312yes—
58C42×C43C2311yescharacteristic
59#10621884—42no—
60#10621884—42no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4D412yes—
66Dic43⋊C4—22no—
67Dic43⋊C4D412yes—
68C4×Dic43C2311yescharacteristic
69C2×C43⋊C8C2312yes—
70D344—42no—
71#10621873—42no—
72C22×D43—21no—
73C22×D43—22no—
74C22×D43C2×D411yescharacteristic
75Q8×C43—22no—
76Q8×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43C2×D412yes—
81C2×C4×C43C2411yescharacteristic
82C2×Dic43—21no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D411yescharacteristic
85D172—22no—
86D172—22no—
87D172—22no—
88D172—42no—
89D172—82no—
90D172—82no—
91C4×D43—22no—
92C4×D43—42no—
93C4×D43—42no—
94C4×D43—82no—
95Dic86—22no—
96Dic86—42no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43C22×D411yescharacteristic
100C2×D43—21no—
101C2×D43—22no—
102C2×D43—41no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C4×C43—22no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43—42no—
111C4×C43H(5,𝔽2)12yes—
112Dic43—21no—
113Dic43—22no—
114Dic43—41no—
115#3221—431nomaximal, Sylow
116C2×C43#53511yescharacteristic
117C2×C43#57712yes—
118D43—41no—
119D43—81no—
120D43—82no—
121#540—431no—
122#536—431no—
123#496—431no—
124#492—431no—
125#491D4311yescharacteristic, complemented
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×SD16—432no—
137C2×SD16—432no—
138C2×D8—432no—
139C4⋊Q8—431no—
140C4⋊Q8C2×D4311yescharacteristic
141#127—431no—
142#125C2×D4311yescharacteristic
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#103C2×D4312yes—
155#103C2×D4312yes—
156#102—432no—
157C22⋊C8—432no—
158#97C2×D4311yescharacteristic
159C4×C8—431no—
160#41—1722no—
161C2×Q8—431no—
162C2×Q8—861no—
163C2×Q8—1722no—
164C2×Q8C22×D4311yescharacteristic
165C2×Q8C22×D4311yescharacteristic
166C2×D4—431no—
167C2×D4—432no—
168C2×D4—862no—
169C2×D4—861no—
170C2×D4—862no—
171C22×C4—431no—
172C22×C4—862no—
173C22×C4—861no—
174C22×C4—861no—
175SD16—1722no—
176SD16—1722no—
177SD16—1722no—
178D8—1722no—
179C2×C8—432no—
180C2×C8C22×D4312yes—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—432no—
184C4⋊C4—862no—
185C4⋊C4C22×D4312yes—
186C22⋊C4—432no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C42—431no—
192C42C22×D4311yescharacteristic
193C23—431no—
194C23—861no—
195C23—862no—
196Q8—22no—
197Q8—22no—
198Q8—862no—
199Q8—1722no—
200D4—862no—
201D4—862no—
202D4—862no—
203D4—3442no—
204D4—3442no—
205D4—1722no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—432no—
210C2×C4—431no—
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—862no—
221C22—861no—
222C22—1722no—
223C22—1722no—
224C22—1722no—
225C22—1721no—
226C22—1722no—
227C22C2×D4×D4311yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—862no—
233C4—861no—
234C4—1721no—
235C4#1306337112yes—
236C2—3442no—
237C2—3441no—
238C2—1721no—
239C2#1458346711yescharacteristic
240C2#1458370812yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#491C2
socleC22×C43C22×D4
hypercenter#491D43
hypocenterC43#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583474C2semidirect
3. #14583288C2semidirect
4. #14583273C2semidirect
5. #14583256C2semidirect
6. #14583117C2semidirect
7. #14583103C2semidirect
8. #14583047C2semidirect
9. #14583039C2semidirect
10. #14582961C2semidirect
11. C43×#491C2semidirect
125. #491D43semidirect
132. C43#3221semidirect