Finite Group Databasebeta

← #19145930

Subgroups — #19145930

Order 5504.

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

normal subgroups only

This group has 354 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#14583454C211yesmaximal, characteristic, complemented
2#14583436C211yesmaximal, characteristic
3#14583208C212yesmaximal, complemented
4#14583184C211yesmaximal, characteristic, complemented
5#14583180C211yesmaximal, characteristic, complemented
6#14583137C212yesmaximal, complemented
7#14583131C212yesmaximal
8#14583123C212yesmaximal, complemented
9#14583101C211yesmaximal, characteristic, complemented
10C4⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#462C211yesmaximal, characteristic, complemented
12C2×#10621884C2212yes—
13C2×C8×D43C2212yes—
14#13063325C2211yescharacteristic
15#13063320—21no—
16#13063316—21no—
17#13063316C2211yescharacteristic
18#13063314C2211yescharacteristic
19#13063310—21no—
20#13063305—21no—
21#13063301C2212yes—
22#13063301C2211yescharacteristic
23#13063300C2211yescharacteristic
24Q8×Dic43C2212yes—
25#13063290—21no—
26C4×D172—21no—
27C4×D172C2211yescharacteristic
28#13063283—21no—
29#13063282—21no—
30C42×D43C2211yescharacteristic
31#13063259C2212yes—
32#13063256C2212yes—
33C4⋊(C43⋊C8)C2211yescharacteristic
34Dic43⋊C8C2212yes—
35#13063249C2212yes—
36#13063249C2212yes—
37#13063247C2212yes—
38C2×Q16×C43C2212yes—
39C4⋊Q8×C43C2211yescharacteristic
40C4×Q8×C43C2211yescharacteristic
41C4⋊C8×C43C2211yescharacteristic
42#103×C43C2212yes—
43C2×Q8×C43C2312yes—
44C2×Q8×C43C2311yescharacteristic
45C2×D172—21no—
46C2×D172C2311yescharacteristic
47C2×C4×D43—21no—
48C2×C4×D43D411yescharacteristic
49C2×C4×D43D411yescharacteristic
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52Q16×C43—42no—
53C2×C8×C43C2312yes—
54C4⋊C4×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—21no—
57C4⋊C4×C43C2311yescharacteristic
58C42×C43—21no—
59C42×C43C2311yescharacteristic
60#10621884—42no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—21no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4—21no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—22no—
70C4⋊Dic43C2312yes—
71C4⋊Dic43C2311yescharacteristic
72Dic43⋊C4—21no—
73Dic43⋊C4—21no—
74Dic43⋊C4—22no—
75C4×Dic43—22no—
76C4×Dic43D411yescharacteristic
77C4×Dic43D411yescharacteristic
78C4×Dic43C2311yescharacteristic
79C2×C43⋊C8C2312yes—
80C8×D43—42no—
81C22×D43—21no—
82C22×D43C2×D411yescharacteristic
83Q8×C43—22no—
84Q8×C43—21no—
85Q8×C43—22no—
86Q8×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43C2411yescharacteristic
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43C2×D411yescharacteristic
96C2×Dic43C2×D411yescharacteristic
97C2×Dic43C2×D411yescharacteristic
98D172—21no—
99D172—21no—
100D172—42no—
101C4×D43—22no—
102C4×D43—22no—
103C4×D43—21no—
104C4×D43—21no—
105C4×D43—42no—
106Dic86—42no—
107C8×C43—22no—
108C43⋊C8—22no—
109C22×C43C22×D411yescharacteristic
110C2×D43—21no—
111C2×D43—21no—
112C2×D43—41no—
113C2×D43—41no—
114C2×D43—41no—
115C2×D43#13712yes—
116C4×C43—21no—
117C4×C43—42no—
118C4×C43—41no—
119C4×C43—41no—
120C4×C43#13512yes—
121C4×C43H(5,𝔽2)11yescharacteristic
122C4×C432−1+411yescharacteristic
123Dic43—21no—
124Dic43—21no—
125Dic43—21no—
126Dic43—42no—
127Dic43—41no—
128#3248—431nomaximal, Sylow
129C2×C43#53711yescharacteristic
130C2×C43C2×#13511yescharacteristic
131C2×C43C2×#13711yescharacteristic
132D43—22no—
133D43—81no—
134#533—431no—
135#529—431no—
136#479—432no—
137#475—431no—
138#474—431no—
139#467—432no—
140#465—432no—
141#464—432no—
142#462D4311yescharacteristic, complemented
143#461—431no—
144C2×C4⋊C8—431no—
145C43#324811yescharacteristic, complemented, Sylow
146C2×Q16C2×D4312yes—
147C2×SD16—432no—
148C22×C8—432no—
149C4⋊Q8—431no—
150C4⋊Q8C2×D4311yescharacteristic
151#126—861no—
152#125—431no—
153#125—861no—
154#124—431no—
155#123—861no—
156C22⋊Q8—431no—
157C22⋊Q8—432no—
158C22⋊Q8—861no—
159#121—431no—
160C4×Q8—432no—
161C4×Q8—861no—
162C4×Q8C2×D4311yescharacteristic
163C4×D4—431no—
164C4×D4—861no—
165#117—861no—
166#117—861no—
167C2×C42—431no—
168#107—432no—
169#106—432no—
170C4⋊C8—432no—
171C4⋊C8—431no—
172C4⋊C8C2×D4311yescharacteristic
173#103—432no—
174#103—432no—
175#103C2×D4312yes—
176#102—432no—
177C2×Q8—861no—
178C2×Q8C22×D4311yescharacteristic
179C2×Q8C22×D4312yes—
180C2×D4—431no—
181C2×D4—861no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—861no—
186Q16—42no—
187SD16—1722no—
188C2×C8—432no—
189C2×C8—1722no—
190C2×C8C22×D4312yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—432no—
195C4⋊C4—431no—
196C4⋊C4—861no—
197C4⋊C4—861no—
198C4⋊C4—861no—
199C4⋊C4—862no—
200C4⋊C4—862no—
201C4⋊C4—861no—
202C4⋊C4C22×D4311yescharacteristic
203C22⋊C4—861no—
204C22⋊C4—861no—
205C22⋊C4—861no—
206C22⋊C4—862no—
207C22⋊C4—861no—
208C22⋊C4—861no—
209C42—21no—
210C42—431no—
211C42—431no—
212C42—431no—
213C42—862no—
214C42C22×D4311yescharacteristic
215C23—431no—
216C23—861no—
217Q8—22no—
218Q8—21no—
219Q8—21no—
220Q8—22no—
221Q8—1722no—
222D4—861no—
223D4—861no—
224D4—1722no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—431no—
229C2×C4—431no—
230C2×C4—431no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—861no—
234C2×C4—861no—
235C2×C4—862no—
236C2×C4—861no—
237C2×C4—1722no—
238C2×C4D4×D4311yescharacteristic
239C2×C4D4×D4311yescharacteristic
240C2×C4C23×D4311yescharacteristic
241C8—22no—
242C8—862no—
243C22—432no—
244C22—861no—
245C22—861no—
246C22—1721no—
247C22—1721no—
248C22—1721no—
249C22C2×D4×D4311yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—861no—
255C4—861no—
256C4—861no—
257C4—1721no—
258C4—1722no—
259C4#1306334812yes—
260C4#1306337011yescharacteristic
261C4#1306337211yescharacteristic
262C2—862no—
263C2—3441no—
264C2#1458347811yescharacteristic
265C2C2×#1306334811yescharacteristic
266C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#462C2
socleC22×C43C22×D4
hypercenter#462D43
hypocenterC43#3248
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583208C2semidirect
4. #14583184C2semidirect
5. #14583180C2semidirect
6. #14583137C2semidirect
8. #14583123C2semidirect
9. #14583101C2semidirect
10. C4⋊C8×D43C2semidirect
11. C43×#462C2semidirect
142. #462D43semidirect
145. C43#3248semidirect