Finite Group Databasebeta

← #19145829

Subgroups — #19145829

Order 5504.

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

normal subgroups only

This group has 362 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
1C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2#14583436C211yesmaximal, characteristic
3#14583306C212yesmaximal, complemented
4#14583260C212yesmaximal, complemented
5#14583233C212yesmaximal, complemented
6#14583219C212yesmaximal
7#14583184C211yesmaximal, characteristic, complemented
8#14583180C211yesmaximal, characteristic, complemented
9#14583176C211yesmaximal, characteristic, complemented
10#14582955C211yesmaximal, characteristic, complemented
11C43×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13#13063325C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063323—21no—
17#13063320—21no—
18#13063316C2211yescharacteristic
19#13063314C2211yescharacteristic
20#13063310—21no—
21#13063301C2211yescharacteristic
22#13063300C2211yescharacteristic
23C4×D172—21no—
24C4×D172C2211yescharacteristic
25#13063282—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43C2212yes—
28C42×D43C2211yescharacteristic
29#13063259C2212yes—
30#13063258C2212yes—
31#13063256C2212yes—
32C4⋊(C43⋊C8)C2211yescharacteristic
33#13063249C2212yes—
34#13063247C2212yes—
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063235C2212yes—
38C4⋊Q8×C43C2211yescharacteristic
39C4×Q8×C43C2211yescharacteristic
40#106×C43C2212yes—
41C4⋊C8×C43C2211yescharacteristic
42#103×C43C2212yes—
43C2×Q8×C43—21no—
44C2×Q8×C43C2311yescharacteristic
45Q8×D43—44no—
46C2×D172—21no—
47C2×D172C2311yescharacteristic
48C2×C4×D43—21no—
49C2×C4×D43—22no—
50C2×C4×D43D411yescharacteristic
51C2×C4×D43D411yescharacteristic
52C2×C4×D43C2311yescharacteristic
53C2×Dic86—21no—
54C2×Dic86—22no—
55C2×C8×C43C2312yes—
56C4⋊C4×C43—21no—
57C4⋊C4×C43—21no—
58C4⋊C4×C43C2312yes—
59C4⋊C4×C43C2311yescharacteristic
60C42×C43—21no—
61C42×C43C2311yescharacteristic
62(C2×D43)⋊C4—21no—
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—21no—
65(C2×D43)⋊C4—21no—
66(C2×D43)⋊C4—21no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43C2312yes—
70C4⋊Dic43C2311yescharacteristic
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—21no—
74Dic43⋊C4—21no—
75C4×Dic43D411yescharacteristic
76C4×Dic43D411yescharacteristic
77C4×Dic43C2311yescharacteristic
78C2×C43⋊C8C2312yes—
79C22×D43—21no—
80C22×D43C2×D411yescharacteristic
81Q8×C43—21no—
82Q8×C43—21no—
83Q8×C43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43C2411yescharacteristic
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43C2×D411yescharacteristic
93C2×Dic43C2×D411yescharacteristic
94C2×Dic43C2×D411yescharacteristic
95D172—21no—
96D172—21no—
97D172—42no—
98C4×D43—22no—
99C4×D43—22no—
100C4×D43—21no—
101C4×D43—21no—
102C4×D43—44no—
103C4×D43—42no—
104Dic86—44no—
105Dic86—42no—
106C8×C43—22no—
107C43⋊C8—22no—
108C22×C43C22×D411yescharacteristic
109C2×D43—21no—
110C2×D43—21no—
111C2×D43—41no—
112C2×D43—41no—
113C2×D43—41no—
114C2×D43#13712yes—
115C4×C43—21no—
116C4×C43—41no—
117C4×C43—42no—
118C4×C43—41no—
119C4×C43AGL(1,ℤ/8)12yes—
120C4×C432−1+411yescharacteristic
121C4×C432−1+411yescharacteristic
122Dic43—21no—
123Dic43—21no—
124Dic43—21no—
125Dic43—42no—
126Dic43—41no—
127#3239—431nomaximal, Sylow
128C2×C43#53611yescharacteristic
129C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C43C2×#13711yescharacteristic
131D43—22no—
132D43—81no—
133C2×C4⋊Q8—431no—
134#529—431no—
135#501—432no—
136#489—432no—
137#484—432no—
138#481—432no—
139#475—431no—
140#475D4311yescharacteristic, complemented
141#474—431no—
142#474—431no—
143#432—431no—
144C43#323911yescharacteristic, complemented, Sylow
145C22×Q8—861no—
146C4⋊Q8—432no—
147C4⋊Q8—431no—
148C4⋊Q8—861no—
149C4⋊Q8—861no—
150C4⋊Q8C2×D4311yescharacteristic
151#126—861no—
152#125—431no—
153#124—431no—
154#123—861no—
155C22⋊Q8—431no—
156#121—431no—
157C4×Q8C2×D4311yescharacteristic
158C4×D4—431no—
159C4×D4—861no—
160#117—861no—
161C2×C4⋊C4—432no—
162C2×C4⋊C4—861no—
163C2×C42—431no—
164#107—432no—
165#107—432no—
166#106—432no—
167#106C2×D4312yes—
168C4⋊C8—431no—
169C4⋊C8C2×D4311yescharacteristic
170#103—432no—
171#103C2×D4312yes—
172#102—432no—
173#102—432no—
174C22⋊C8—432no—
175#97—432no—
176C2×Q8—21no—
177C2×Q8—862no—
178C2×Q8—861no—
179C2×Q8—1724no—
180C2×Q8C22×D4311yescharacteristic
181C2×D4—431no—
182C2×D4—861no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4—862no—
187C22×C4—861no—
188C2×C8—432no—
189C2×C8C22×D4312yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—432no—
193C4⋊C4—431no—
194C4⋊C4—862no—
195C4⋊C4—862no—
196C4⋊C4—861no—
197C4⋊C4—861no—
198C4⋊C4—861no—
199C4⋊C4—861no—
200C4⋊C4C22×D4312yes—
201C4⋊C4C22×D4311yescharacteristic
202C22⋊C4—861no—
203C22⋊C4—861no—
204C22⋊C4—861no—
205C22⋊C4—861no—
206C22⋊C4—861no—
207C42—21no—
208C42—431no—
209C42—431no—
210C42—431no—
211C42C22×D4311yescharacteristic
212C23—431no—
213C23—861no—
214Q8—21no—
215Q8—21no—
216Q8—42no—
217Q8—1724no—
218Q8—1722no—
219D4—861no—
220D4—861no—
221D4—1722no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—431no—
226C2×C4—431no—
227C2×C4—431no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—862no—
234C2×C4—1724no—
235C2×C4—1722no—
236C2×C4D4×D4311yescharacteristic
237C2×C4D4×D4311yescharacteristic
238C2×C4C23×D4311yescharacteristic
239C8—22no—
240C8—862no—
241C22—432no—
242C22—861no—
243C22—861no—
244C22—1721no—
245C22—1721no—
246C22—1721no—
247C22C2×D4×D4311yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—861no—
253C4—861no—
254C4—861no—
255C4—1722no—
256C4—1721no—
257C4#1306335212yes—
258C4#1306337211yescharacteristic
259C4#1306337311yescharacteristic
260C2—862no—
261C2—3441no—
262C2#1458347211yescharacteristic
263C2C2×#1306335211yescharacteristic
264C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3239
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D43C2semidirect
3. #14583306C2semidirect
4. #14583260C2semidirect
5. #14583233C2semidirect
7. #14583184C2semidirect
8. #14583180C2semidirect
9. #14583176C2semidirect
10. #14582955C2semidirect
11. C43×#475C2semidirect
140. #475D43semidirect
144. C43#3239semidirect