Finite Group Databasebeta

← #19147296

Subgroups — #19147296

Order 5504.

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

normal subgroups only

This group has 348 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#14583635C211yesmaximal, characteristic
2#14583624C211yesmaximal, characteristic, complemented
3#14583252C212yesmaximal, complemented
4#14583197C212yesmaximal, complemented
5#14583181C211yesmaximal, characteristic, complemented
6#14583120C212yesmaximal, complemented
7#14583096C211yesmaximal, characteristic
8C8×Dic86C211yesmaximal, characteristic, complemented
9C4×Dic172C211yesmaximal, characteristic, complemented
10#14582990C212yesmaximal, complemented
11C43×#486C211yesmaximal, characteristic
12C2×Dic172C2211yescharacteristic
13C2×#10621883C2212yes—
14#13063323—21no—
15#13063316C2212yes—
16#13063315—22no—
17#13063312—21no—
18#13063312C2212yes—
19#13063306—22no—
20Q8×Dic43—21no—
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×Dic86C2211yescharacteristic
24#13063290C2212yes—
25D4×Dic43—21no—
26D4×Dic43C2212yes—
27#13063259C2211yescharacteristic
28#13063256C2212yes—
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063250C2211yescharacteristic
33#13063248C2212yes—
34#13063246C2212yes—
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37#127×C43C2211yescharacteristic
38#102×C43C2212yes—
39#102×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43C2312yes—
45C22×Dic43—22no—
46C2×Dic86D411yescharacteristic
47C2×Dic86C2311yescharacteristic
48C2×Dic86C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C2×C8×C43C2311yescharacteristic
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2312yes—
53C42×C43C2311yescharacteristic
54C22⋊Dic43—22no—
55C22⋊Dic43—22no—
56C22⋊Dic43—22no—
57#10621883—24no—
58C4⋊Dic43—22no—
59C4⋊Dic43D411yescharacteristic
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62Dic43⋊C4—21no—
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2312yes—
72Dic172—22no—
73C23×C43—22no—
74Q8×C43—42no—
75D4×C43—22no—
76D4×C43—22no—
77D4×C43—42no—
78D4×C43—81no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—82no—
88C2×Dic43C2×D412yes—
89C2×Dic43C2×D412yes—
90Dic86—22no—
91Dic86—21no—
92Dic86—21no—
93Dic86—21no—
94Dic86#4112yes—
95C8×C43—21no—
96C8×C43—21no—
97C43⋊C8—22no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43C22×D411yescharacteristic
102C4×C43—21no—
103C4×C43—42no—
104C4×C43#13512yes—
105C4×C43C2×#4111yescharacteristic
106C4×C432−1+411yescharacteristic
107Dic43—22no—
108Dic43—22no—
109Dic43—22no—
110Dic43—41no—
111Dic43—41no—
112Dic43—41no—
113#3365—431nomaximal, Sylow
114C2×C43—82no—
115C2×C43#54811yescharacteristic
116C2×C43C2×#13511yescharacteristic
117C2×C43#57711yescharacteristic
118#559—431no—
119#557—431no—
120#488—432no—
121#486D4311yescharacteristic
122#478—432no—
123#475—431no—
124#464—432no—
125#460—431no—
126C8×Q8—431no—
127C4×Q16—431no—
128C4×SD16—432no—
129C43#336511yescharacteristic, complemented, Sylow
130C2×Q16—431no—
131C2×SD16—432no—
132C4⋊Q8—861no—
133C4⋊Q8C2×D4311yescharacteristic
134#127C2×D4311yescharacteristic
135#125—432no—
136#125—862no—
137#124—432no—
138#124—861no—
139#123—862no—
140C4×Q8—431no—
141C4×Q8—432no—
142C4×Q8—431no—
143C4×Q8—431no—
144C4×Q8—861no—
145C4×D4—432no—
146C4×D4—861no—
147#107—431no—
148#106—432no—
149C4⋊C8—432no—
150C4⋊C8—431no—
151#103—431no—
152#103—431no—
153#103—432no—
154#102—432no—
155#102C2×D4312yes—
156#102C2×D4312yes—
157C4×C8—432no—
158C4×C8C2×D4311yescharacteristic
159C2×Q8—21no—
160C2×Q8—431no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D4312yes—
166C22×C4—862no—
167Q16—862no—
168SD16—864no—
169C2×C8—432no—
170C2×C8C22×D4311yescharacteristic
171C2×C8C22×D4311yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—431no—
174C4⋊C4—432no—
175C4⋊C4—431no—
176C4⋊C4—431no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—861no—
181C4⋊C4—861no—
182C4⋊C4C22×D4312yes—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C42—432no—
187C42—862no—
188C42—861no—
189C42—861no—
190C42C22×D4311yescharacteristic
191C23—22no—
192Q8—42no—
193Q8—432no—
194Q8—862no—
195Q8—861no—
196Q8—861no—
197Q8—861no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—81no—
202C2×C4—22no—
203C2×C4—432no—
204C2×C4—432no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—3442no—
210C2×C4D4×D4311yescharacteristic
211C2×C4D4×D4311yescharacteristic
212C2×C4C23×D4311yescharacteristic
213C8—21no—
214C8—21no—
215C8—862no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22C2×D4×D4311yescharacteristic
220C4—21no—
221C4—42no—
222C4—862no—
223C4—862no—
224C4—862no—
225C4—1721no—
226C4—1721no—
227C4—1721no—
228C4#1306334412yes—
229C4#41×D4311yescharacteristic
230C4#1306337211yescharacteristic
231C2—82no—
232C2#1458355711yescharacteristic
233C2C2×#1306334411yescharacteristic
234C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3365
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #14583624C2semidirect
3. #14583252C2semidirect
4. #14583197C2semidirect
5. #14583181C2semidirect
6. #14583120C2semidirect
8. C8×Dic86C2semidirect
9. C4×Dic172C2semidirect
10. #14582990C2semidirect
129. C43#3365semidirect