Finite Group Databasebeta

← #19146910

Subgroups — #19146910

Order 5504.

388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583610C211yesmaximal, characteristic, complemented
2#14583552C211yesmaximal, characteristic
3#14583228C212yesmaximal, complemented
4#14583186C211yesmaximal, characteristic, complemented
5#14583156C212yesmaximal, complemented
6#14583106C211yesmaximal, characteristic, complemented
7#14583064C212yesmaximal, complemented
8C4×#10621873C211yesmaximal, characteristic, complemented
9#14582978C211yesmaximal, characteristic, complemented
10#14582899C212yesmaximal, complemented
11C43×#487C211yesmaximal, characteristic, complemented
12C2×#10621902C2212yes—
13C2×#10621885C2212yes—
14C2×#10621873C2211yescharacteristic
15C2×#10621872C2212yes—
16#13063316—21no—
17#13063310—22no—
18#13063305C2212yes—
19#13063301—22no—
20#13063301C2212yes—
21#13063300—21no—
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25#13063287—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43C2212yes—
28#13063257C2211yescharacteristic
29#13063256C2212yes—
30C4⋊(C43⋊C8)C2211yescharacteristic
31#13063250C2211yescharacteristic
32#13063249C2212yes—
33#13063247C2211yescharacteristic
34#13063245C2212yes—
35(C2×D43)⋊C8C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#103×C43C2212yes—
39#103×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43C2312yes—
43#10621902—24no—
44#10621902—42no—
45C2×D172—22no—
46C2×D172D411yescharacteristic
47C2×D172C2311yescharacteristic
48C2×C4×D43—21no—
49C2×C4×D43—22no—
50C2×C4×D43—22no—
51C2×C4×D43C2312yes—
52C2×Dic86C2311yescharacteristic
53C2×C8×C43C2311yescharacteristic
54C2×C8×C43C2311yescharacteristic
55C4⋊C4×C43—21no—
56C4⋊C4×C43—21no—
57C4⋊C4×C43—21no—
58C4⋊C4×C43C2312yes—
59C42×C43C2311yescharacteristic
60#10621885—42no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4D412yes—
65C4⋊Dic43—22no—
66C4⋊Dic43D411yescharacteristic
67C4⋊Dic43C2311yescharacteristic
68C4⋊Dic43C2311yescharacteristic
69Dic43⋊C4—21no—
70Dic43⋊C4—22no—
71Dic43⋊C4—22no—
72C4×Dic43—21no—
73C2×C43⋊C8C2312yes—
74#10621873—22no—
75#10621872—42no—
76C22×D43—21no—
77C22×D43C2×D412yes—
78Q8×C43—22no—
79Q8×C43—22no—
80Q8×C43—81no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2411yescharacteristic
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43C2×D412yes—
90D172—22no—
91D172—21no—
92D172—44no—
93D172#4112yes—
94C4×D43—22no—
95C4×D43—22no—
96C4×D43—44no—
97C4×D43—42no—
98C4×D43—82no—
99Dic86—21no—
100Dic86—21no—
101C8×C43—21no—
102C8×C43—21no—
103C43⋊C8—22no—
104C22×C43C22×D411yescharacteristic
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—22no—
108C2×D43—22no—
109C2×D43—41no—
110C2×D43—41no—
111C4×C43—21no—
112C4×C43—42no—
113C4×C43—42no—
114C4×C43#13712yes—
115C4×C43C2×#4111yescharacteristic
116C4×C43H(5,𝔽2)11yescharacteristic
117Dic43—22no—
118Dic43—41no—
119Dic43—41no—
120Dic43—41no—
121#3331—431nomaximal, Sylow
122C2×C43#54611yescharacteristic
123C2×C43C2×#13711yescharacteristic
124C2×C43#57711yescharacteristic
125D43—42no—
126D43—42no—
127#554—431no—
128#547—431no—
129#487D4311yescharacteristic, complemented
130#483—432no—
131#476—431no—
132#470—432no—
133#462—431no—
134#452—432no—
135C4×SD16—431no—
136#436—431no—
137#417—432no—
138C43#333111yescharacteristic, complemented, Sylow
139C2×#41—432no—
140C2×Q16—432no—
141C2×SD16—431no—
142C2×M16—432no—
143C4⋊Q8C2×D4311yescharacteristic
144C4⋊Q8C2×D4311yescharacteristic
145#125—861no—
146#123—862no—
147C22⋊Q8—432no—
148C22⋊Q8—432no—
149C22⋊Q8—862no—
150#121—861no—
151C4×Q8—431no—
152C4×D4—431no—
153C4×D4—431no—
154C4×D4—861no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—861no—
157#106—431no—
158#106—432no—
159C4⋊C8—431no—
160#103—432no—
161#103—431no—
162#103C2×D4312yes—
163#103C2×D4312yes—
164#102—431no—
165#102—432no—
166C22⋊C8—432no—
167C4×C8C2×D4311yescharacteristic
168#41—864no—
169#41—1722no—
170C2×Q8—21no—
171C2×Q8—431no—
172C2×Q8C22×D4312yes—
173C2×D4—431no—
174C2×D4—431no—
175C2×D4—862no—
176C22×C4—432no—
177C22×C4—862no—
178C22×C4—862no—
179C22×C4—861no—
180Q16—1722no—
181SD16—862no—
182M16—1722no—
183C2×C8—432no—
184C2×C8C22×D4311yescharacteristic
185C2×C8C22×D4311yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—431no—
190C4⋊C4—431no—
191C4⋊C4—431no—
192C4⋊C4—862no—
193C4⋊C4—862no—
194C4⋊C4—862no—
195C4⋊C4—861no—
196C4⋊C4C22×D4312yes—
197C22⋊C4—432no—
198C22⋊C4—862no—
199C22⋊C4—862no—
200C22⋊C4—861no—
201C42—861no—
202C42C22×D4311yescharacteristic
203C23—432no—
204C23—861no—
205Q8—22no—
206Q8—22no—
207Q8—81no—
208Q8—861no—
209Q8—861no—
210D4—432no—
211D4—862no—
212D4—861no—
213D4—1724no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—432no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—3442no—
223C2×C4—1724no—
224C2×C4—1722no—
225C2×C4D4×D4311yescharacteristic
226C2×C4D4×D4311yescharacteristic
227C2×C4C23×D4311yescharacteristic
228C8—21no—
229C8—21no—
230C8—862no—
231C22—862no—
232C22—862no—
233C22—862no—
234C22—862no—
235C22—1721no—
236C22—1721no—
237C22C2×D4×D4311yescharacteristic
238C4—21no—
239C4—42no—
240C4—42no—
241C4—862no—
242C4—1721no—
243C4—1721no—
244C4—1721no—
245C4#1306335712yes—
246C4#41×D4311yescharacteristic
247C4#1306337111yescharacteristic
248C2—1722no—
249C2—1722no—
250C2#1458354211yescharacteristic
251C2C2×#1306335711yescharacteristic
252C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3331
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
3. #14583228C2semidirect
4. #14583186C2semidirect
5. #14583156C2semidirect
6. #14583106C2semidirect
7. #14583064C2semidirect
8. C4×#10621873C2semidirect
9. #14582978C2semidirect
10. #14582899C2semidirect
11. C43×#487C2semidirect
129. #487D43semidirect
138. C43#3331semidirect