Finite Group Databasebeta

← #19145659

Subgroups — #19145659

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#14583469C211yesmaximal, characteristic, complemented
3#14583289C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583269C211yesmaximal, characteristic, complemented
6#14583113C212yesmaximal, complemented
7#14583103C212yesmaximal, complemented
8#14583045C212yesmaximal, complemented
9#14583039C212yesmaximal, complemented
10#14582958C211yesmaximal, characteristic, complemented
11C43×#488C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C2×Q8×D43C2211yescharacteristic
14C2×#10621873C2212yes—
15C2×#10621873C2212yes—
16C2×#10621884C2212yes—
17C2×#10621882C2212yes—
18#13063325C2211yescharacteristic
19#13063323C2211yescharacteristic
20#13063322C2211yescharacteristic
21#13063312C2211yescharacteristic
22#13063310—22no—
23#13063307—22no—
24#13063302—22no—
25#13063300—22no—
26#13063300C2212yes—
27#13063287C2212yes—
28#13063282C2211yescharacteristic
29Dic43⋊C8C2212yes—
30#13063248C2212yes—
31#13063248C2212yes—
32(C2×D43)⋊C8C2212yes—
33#13063236C2211yescharacteristic
34#125×C43C2211yescharacteristic
35#124×C43C2211yescharacteristic
36#103×C43C2212yes—
37#102×C43C2212yes—
38C4×C8×C43C2211yescharacteristic
39C2×Q8×C43C2311yescharacteristic
40C2×D4×C43C2311yescharacteristic
41C2×C22⋊D43—21no—
42C22×Dic43—21no—
43Q8×D43—42no—
44#10621900—42no—
45C2×D172—22no—
46C2×D172—22no—
47C2×D172C2312yes—
48C2×C4×D43—22no—
49C2×C4×D43—21no—
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52C2×Dic86C2311yescharacteristic
53C2×Dic86C2311yescharacteristic
54C2×C8×C43C2312yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43C2312yes—
57C22⋊C4×C43—22no—
58C42×C43C2311yescharacteristic
59C22⋊Dic43—22no—
60#10621884—42no—
61#10621882—42no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4D412yes—
65C4⋊Dic43—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4D412yes—
68C4×Dic43C2311yescharacteristic
69C2×C43⋊C8C2312yes—
70#10621873—42no—
71#10621873—42no—
72C23×C43—21no—
73C22×D43—22no—
74C22×D43C2×D411yescharacteristic
75Q8×C43—22no—
76D4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—42no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—42no—
85C2×Dic43C2×D412yes—
86C2×Dic43C2×D411yescharacteristic
87D172—22no—
88D172—22no—
89D172—82no—
90D172—82no—
91C4×D43—22no—
92C4×D43—42no—
93C4×D43—82no—
94Dic86—22no—
95Dic86—22no—
96Dic86—42no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43C22×D411yescharacteristic
102C2×D43—21no—
103C2×D43—22no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C4×C43—22no—
108C4×C43—41no—
109C4×C43—42no—
110C4×C43H(5,𝔽2)12yes—
111Dic43—21no—
112Dic43—22no—
113Dic43—41no—
114Dic43—41no—
115#3221—431nomaximal, Sylow
116C2×C43—81no—
117C2×C43#53511yescharacteristic
118C2×C43#57712yes—
119D43—41no—
120D43—82no—
121#540—431no—
122#536—431no—
123#496—431no—
124#492—431no—
125#491—431no—
126#488D4311yescharacteristic, complemented
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⋊Q8—431no—
141#127—431no—
142#125C2×D4311yescharacteristic
143#124—431no—
144#124C2×D4311yescharacteristic
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#103C2×D4312yes—
156#102C2×D4312yes—
157C22⋊C8—432no—
158#97—431no—
159C4×C8C2×D4311yescharacteristic
160#41—1722no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×Q8—861no—
164C2×Q8—1722no—
165C2×Q8C22×D4311yescharacteristic
166C2×D4—432no—
167C2×D4—862no—
168C2×D4—861no—
169C2×D4—862no—
170C2×D4C22×D4311yescharacteristic
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—432no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4C22×D4312yes—
186C22⋊C4—22no—
187C22⋊C4—432no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C42—431no—
192C42C22×D4311yescharacteristic
193C23—21no—
194C23—431no—
195C23—862no—
196Q8—22no—
197Q8—862no—
198Q8—862no—
199Q8—1722no—
200D4—22no—
201D4—862no—
202D4—862no—
203D4—3442no—
204D4—3442no—
205D4—1722no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—432no—
209C2×C4—431no—
210C2×C4—862no—
211C2×C4—861no—
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—41no—
222C22—862no—
223C22—861no—
224C22—1722no—
225C22—1722no—
226C22—1722no—
227C22C2×D4×D4311yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—862no—
232C4—861no—
233C4—1721no—
234C4—1721no—
235C4#1306337112yes—
236C2—81no—
237C2—3442no—
238C2—1721no—
239C2#1458346711yescharacteristic
240C2#1458370612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583469C2semidirect
3. #14583289C2semidirect
4. #14583272C2semidirect
5. #14583269C2semidirect
6. #14583113C2semidirect
7. #14583103C2semidirect
8. #14583045C2semidirect
9. #14583039C2semidirect
10. #14582958C2semidirect
11. C43×#488C2semidirect
126. #488D43semidirect
132. C43#3221semidirect