Finite Group Databasebeta

← #19145301

Subgroups — #19145301

Order 5504.

366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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#14583428C211yesmaximal, characteristic
3#14583308C211yesmaximal, characteristic, complemented
4#14583267C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583137C212yesmaximal, complemented
7#14583125C212yesmaximal
8#14583006C212yesmaximal, complemented
9#14583000C212yesmaximal, complemented
10#97×D43C211yesmaximal, characteristic, complemented
11C43×#497C211yesmaximal, characteristic, complemented
12C2×C8×D43C2212yes—
13#13063325C2211yescharacteristic
14#13063318—21no—
15#13063317C2211yescharacteristic
16#13063316—21no—
17#13063307—21no—
18#13063305—21no—
19#13063301C2212yes—
20#13063301C2211yescharacteristic
21#13063296C2211yescharacteristic
22Q8×Dic43C2211yescharacteristic
23Q8×Dic43C2212yes—
24#13063290—21no—
25D4×Dic43C2211yescharacteristic
26(C22⋊D43)⋊C4—21no—
27#13063283—21no—
28#13063281—21no—
29C42×D43C2211yescharacteristic
30#13063259C2212yes—
31#13063257C2212yes—
32#13063249C2212yes—
33#13063249C2212yes—
34#13063249C2212yes—
35#13063246C2212yes—
36#13063236C2211yescharacteristic
37#13063235C2212yes—
38C2×Q16×C43C2212yes—
39C2×SD16×C43C2212yes—
40C4⋊Q8×C43C2211yescharacteristic
41#124×C43C2211yescharacteristic
42#97×C43C2211yescharacteristic
43C2×Q8×C43C2311yescharacteristic
44C2×Q8×C43C2312yes—
45C2×D4×C43C2311yescharacteristic
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48C2×C4×D43D411yescharacteristic
49C2×C4×D43D411yescharacteristic
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52Q16×C43—24no—
53SD16×C43—24no—
54C2×C8×C43C2312yes—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—21no—
57C22⋊C4×C43—21no—
58C22⋊C4×C43—21no—
59C42×C43C2311yescharacteristic
60C22⋊Dic43—21no—
61C22⋊Dic43—21no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43—22no—
66C4⋊Dic43—21no—
67C4⋊Dic43C2312yes—
68C4⋊Dic43C2311yescharacteristic
69C4⋊Dic43C2311yescharacteristic
70Dic43⋊C4—21no—
71Dic43⋊C4—21no—
72Dic43⋊C4—21no—
73Dic43⋊C4—22no—
74C4×Dic43—21no—
75C4×Dic43—22no—
76C4×Dic43D411yescharacteristic
77C4×Dic43D411yescharacteristic
78C4×Dic43C2311yescharacteristic
79C2×C43⋊C8C2312yes—
80C8×D43—24no—
81C23×C43—21no—
82C22×D43C2×D411yescharacteristic
83Q8×C43—22no—
84Q8×C43—22no—
85Q8×C43—22no—
86D4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43C2×D411yescharacteristic
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2411yescharacteristic
92C22⋊D43—42no—
93C2×Dic43—21no—
94C2×Dic43—22no—
95C2×Dic43—21no—
96C2×Dic43—42no—
97C2×Dic43C2×D411yescharacteristic
98C2×Dic43C2×D411yescharacteristic
99C2×Dic43C2×D411yescharacteristic
100C4×D43—22no—
101C4×D43—22no—
102C4×D43—41no—
103Dic86—42no—
104C8×C43#4114yes—
105C43⋊C8—22no—
106C22×C43—41no—
107C22×C43—41no—
108C22×C43—41no—
109C22×C43C22×D411yescharacteristic
110C2×D43—21no—
111C2×D43—21no—
112C2×D43#13712yes—
113C4×C43—21no—
114C4×C43—21no—
115C4×C43—41no—
116C4×C43—42no—
117C4×C43C2×#4112yes—
118Dic43—21no—
119Dic43—21no—
120Dic43—21no—
121Dic43—41no—
122Dic43—42no—
123Dic43—41no—
124#3181—431nomaximal, Sylow
125C2×C43—81no—
126C2×C43#53211yescharacteristic
127C2×C43C2×#13711yescharacteristic
128C2×C43#57511yescharacteristic
129D43—22no—
130#533—431no—
131#529—431no—
132#501—431no—
133#497D4311yescharacteristic, complemented
134#491—431no—
135#489—431no—
136#467—432no—
137#465—432no—
138#441—432no—
139#440—432no—
140C2×#97—431no—
141C43#318111yescharacteristic, complemented, Sylow
142C2×Q16C2×D4312yes—
143C2×SD16C2×D4312yes—
144C22×C8—432no—
145C4⋊Q8—431no—
146C4⋊Q8C2×D4311yescharacteristic
147#126—861no—
148#125—431no—
149#125—861no—
150#124C2×D4311yescharacteristic
151#123—861no—
152C22⋊Q8—431no—
153C22⋊Q8—432no—
154C22⋊Q8—861no—
155#121—431no—
156C4×Q8—431no—
157C4×Q8—432no—
158C4×Q8—861no—
159C4×D4—431no—
160C4×D4—861no—
161#117—861no—
162#117—861no—
163C2×C42—431no—
164#107—432no—
165#106—432no—
166#103—432no—
167#103—432no—
168#103—432no—
169#102—432no—
170#97—432no—
171#97—431no—
172#97C2×D4311yescharacteristic
173C2×Q8—861no—
174C2×Q8C22×D4311yescharacteristic
175C2×Q8C22×D4312yes—
176C2×D4—861no—
177C2×D4C22×D4311yescharacteristic
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—861no—
182Q16—24no—
183SD16—24no—
184C2×C8—432no—
185C2×C8—864no—
186C2×C8C22×D4312yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—432no—
190C4⋊C4—431no—
191C4⋊C4—431no—
192C4⋊C4—861no—
193C4⋊C4—862no—
194C4⋊C4—861no—
195C4⋊C4—862no—
196C4⋊C4—861no—
197C4⋊C4—861no—
198C4⋊C4—861no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—862no—
202C22⋊C4—861no—
203C22⋊C4—861no—
204C22⋊C4—861no—
205C42—431no—
206C42—431no—
207C42—431no—
208C42—861no—
209C42—862no—
210C42C22×D4311yescharacteristic
211C23—21no—
212C23—431no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—1722no—
217D4—22no—
218D4—1722no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—431no—
222C2×C4—431no—
223C2×C4—431no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—861no—
227C2×C4—862no—
228C2×C4—861no—
229C2×C4—1721no—
230C2×C4—1722no—
231C2×C4D4×D4311yescharacteristic
232C2×C4D4×D4311yescharacteristic
233C2×C4C23×D4311yescharacteristic
234C8—862no—
235C8#1062190014yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—432no—
240C22—861no—
241C22—861no—
242C22C2×D4×D4311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—861no—
248C4—861no—
249C4—861no—
250C4—1721no—
251C4—1721no—
252C4—1722no—
253C4C2×#1062190012yes—
254C2—81no—
255C2—862no—
256C2#1458344711yescharacteristic
257C2#137×D4311yescharacteristic
258C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#497C2
socleC22×C43C22×D4
hypercenter#497D43
hypocenterC43#3181
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583308C2semidirect
4. #14583267C2semidirect
5. #14583258C2semidirect
6. #14583137C2semidirect
8. #14583006C2semidirect
9. #14583000C2semidirect
10. #97×D43C2semidirect
11. C43×#497C2semidirect
133. #497D43semidirect
141. C43#3181semidirect