Finite Group Databasebeta

← D43×#1409 #25016903

Subgroups — D43×#1409 #25016903

Order 11008.

474 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 61 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#492×D43C211yesmaximal, characteristic
2#353×D43C212yesmaximal
3#19132760C211yesmaximal, characteristic, complemented
4#19132759C212yesmaximal, complemented
5C43×#1409C211yesmaximal, characteristic, complemented
6C2×SD16×D43—22no—
7C4⋊Q8×D43C411yescharacteristic, complemented
8#127×D43C2211yescharacteristic
9#14583273C411yescharacteristic, complemented
10#14583272C411yescharacteristic, complemented
11#14583271C2211yescharacteristic
12#14583270—22no—
13#99×D43—22no—
14C4×C8×D43C411yescharacteristic, complemented
15#14582692C2212yes—
16#14582691—22no—
17C43×#492C2211yescharacteristic
18C43×#353C2212yes—
19C2×Q8×D43—21no—
20C2×D4×D43—41no—
21C2×D4×D43D412yes—
22C2×#10621873—22no—
23C2×#10621883—22no—
24C2×#10621884—22no—
25SD16×D43—44no—
26SD16×D43—44no—
27C2×C8×D43—21no—
28#13063325C2×C411yescharacteristic, complemented
29#13063324—41no—
30#13063323—21no—
31#13063322C2×C411yescharacteristic
32#13063321—41no—
33#13063321D412yes—
34C4⋊C4×D43—41no—
35C22⋊C4×D43—42no—
36C42×D43C2×C411yescharacteristic
37#13063240—22no—
38#13063239—42no—
39C4×C43⋊C8C2×C411yescharacteristic, complemented
40C8×Dic43—21no—
41C2×SD16×C43—22no—
42C4⋊Q8×C43C2×C411yescharacteristic, complemented
43#127×C43C2311yescharacteristic
44#99×C43—22no—
45C4×C8×C43C2×C411yescharacteristic, complemented
46C23×D43—22no—
47C2×Q8×C43—21no—
48C2×D4×C43—41no—
49C2×D4×C43C2×D412yes—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—42no—
52Q8×D43—42no—
53Q8×D43—42no—
54D4×D43—42no—
55D4×D43—42no—
56D4×D43—84no—
57C2×D172—41no—
58C2×D172C22⋊C412yes—
59C2×C4×D43—21no—
60C2×C4×D43—41no—
61C2×C4×D43—82no—
62C2×C4×D43C22⋊C411yescharacteristic
63C2×Dic86—21no—
64C2×Dic86—41no—
65SD16×C43—44no—
66C2×C8×C43—21no—
67C4⋊C4×C43—41no—
68C22⋊C4×C43—42no—
69C42×C43C22×C411yescharacteristic
70C22⋊Dic43—42no—
71#10621884—44no—
72#10621883—44no—
73(C2×D43)⋊C4—82no—
74C4⋊Dic43—41no—
75Dic43⋊C4—42no—
76C4×Dic43—21no—
77C4×Dic43C22⋊C411yescharacteristic
78C2×C43⋊C8—21no—
79#10621873—44no—
80C8×D43—22no—
81C8×D43—22no—
82C23×C43—22no—
83C22×D43—22no—
84C22×D43—42no—
85C22×D43—42no—
86C22×D43—84no—
87C22×D43#9911yescharacteristic
88Q8×C43—42no—
89D4×C43—42no—
90D4×C43—82no—
91C2×C4×C43—21no—
92C2×C4×C43—41no—
93C2×C4×C43—82no—
94C2×C4×C43C2×C22⋊C411yescharacteristic
95C22⋊D43—82no—
96C22⋊D43—84no—
97C2×Dic43—21no—
98C2×Dic43—41no—
99C2×Dic43—82no—
100C2×Dic43#9911yescharacteristic
101D172—42no—
102D172—82no—
103C4×D43—24no—
104C4×D43—21no—
105C4×D43—21no—
106C4×D43—81no—
107C4×D43—81no—
108C4×D43—164no—
109Dic86—42no—
110Dic86—82no—
111C8×C43—22no—
112C43⋊C8—22no—
113C2×#1409—431nomaximal, Sylow
114C22×C43—42no—
115C22×C43—82no—
116C22×C43C2×#9911yescharacteristic
117C2×D43—22no—
118C2×D43—42no—
119C2×D43—84no—
120C2×D43—82no—
121C2×D43—162no—
122C2×D43#35311yescharacteristic
123C2×D43#35311yescharacteristic
124C4×C43—22no—
125C4×C43—21no—
126C4×C43—81no—
127C4×C43—162no—
128Dic43—22no—
129Dic43—21no—
130Dic43—81no—
131Dic43—162no—
132C2×#492—431no—
133C2×#353—432no—
134#1409—431no—
135#1409—432no—
136#1409D4311yescharacteristic, direct product factor
137C2×C43—21no—
138C2×C43—82no—
139C2×C43C2×#35311yescharacteristic
140D43—21no—
141D43—82no—
142D43#140912yesdirect product factor
143C22×SD16—862no—
144C2×C4⋊Q8—431no—
145C2×#127—431no—
146#492—431no—
147#492—431no—
148#492—431no—
149#492—862no—
150#492C2×D4311yescharacteristic
151C2×#99—862no—
152C2×C4×C8—431no—
153#353—432no—
154#353—862no—
155#353C2×D4312yes—
156C43C2×#140911yescharacteristic, complemented, Sylow
157C22×Q8—861no—
158C22×D4—432no—
159C22×D4—1721no—
160C2×SD16—22no—
161C2×SD16—862no—
162C2×SD16—862no—
163C2×SD16—862no—
164C2×SD16—1724no—
165C2×SD16—1724no—
166C22×C8—861no—
167C4⋊Q8—431no—
168C4⋊Q8—861no—
169C4⋊Q8—1721no—
170C4⋊Q8C4×D4311yescharacteristic, complemented
171#127—432no—
172#127—431no—
173#127—1721no—
174#127C22×D4311yescharacteristic
175C2×C4⋊C4—1721no—
176C2×C22⋊C4—1722no—
177C2×C42—431no—
178#99—22no—
179#99—862no—
180#99—1722no—
181C4×C8—431no—
182C4×C8—861no—
183C4×C8C4×D4311yescharacteristic, complemented
184C24—862no—
185C2×Q8—21no—
186C2×Q8—861no—
187C2×Q8—1721no—
188C2×Q8—1722no—
189C2×Q8—1722no—
190C2×D4—41no—
191C2×D4—432no—
192C2×D4—862no—
193C2×D4—3444no—
194C2×D4—1721no—
195C2×D4—1722no—
196C2×D4—1722no—
197C2×D4—1722no—
198C2×D4D4×D4312yes—
199C22×C4—431no—
200C22×C4—861no—
201C22×C4—3442no—
202C22×C4—1721no—
203SD16—44no—
204SD16—1724no—
205SD16—1724no—
206SD16—1724no—
207C2×C8—21no—
208C2×C8—862no—
209C2×C8—862no—
210C2×C8—861no—
211C4⋊C4—41no—
212C4⋊C4—1721no—
213C4⋊C4—1722no—
214C22⋊C4—42no—
215C22⋊C4—3442no—
216C22⋊C4—1722no—
217C42—431no—
218C42—861no—
219C42C2×C4×D4311yescharacteristic
220C23—22no—
221C23—431no—
222C23—862no—
223C23—3444no—
224C23—1722no—
225C23—1722no—
226Q8—42no—
227Q8—3442no—
228Q8—1722no—
229D4—42no—
230D4—82no—
231D4—3442no—
232D4—3442no—
233D4—3444no—
234D4—1722no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—431no—
239C2×C4—861no—
240C2×C4—861no—
241C2×C4—864no—
242C2×C4—861no—
243C2×C4—3441no—
244C2×C4—3441no—
245C2×C4—3442no—
246C2×C4—1721no—
247C2×C4—6884no—
248C2×C4C22⋊C4×D4311yescharacteristic
249C8—22no—
250C8—862no—
251C22—42no—
252C22—82no—
253C22—431no—
254C22—431no—
255C22—862no—
256C22—3442no—
257C22—3444no—
258C22—1722no—
259C22—6882no—
260C22#99×D4311yescharacteristic
261C4—22no—
262C4—21no—
263C4—81no—
264C4—162no—
265C4—862no—
266C4—861no—
267C4—3441no—
268C4—6882no—
269C2—21no—
270C2—82no—
271C2—432no—
272C2—861no—
273C2—3442no—
274C2#353×D4311yescharacteristic
subgroupG/H
centerC2#353×D43
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1409C2
socleC2×C43C2×#353
prime radical#127×D43C22
cosocle#127×C43C23
hypercenter#1409D43
hypocenterC43C2×#1409
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1409

Complements

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

NH ≅ G/Ntype
3. #19132760C2semidirect
4. #19132759C2semidirect
5. C43×#1409C2semidirect
7. C4⋊Q8×D43C4semidirect
9. #14583273C4semidirect
10. #14583272C4semidirect
14. C4×C8×D43C4semidirect
28. #13063325C2×C4semidirect
39. C4×C43⋊C8C2×C4semidirect
42. C4⋊Q8×C43C2×C4semidirect
45. C4×C8×C43C2×C4semidirect
136. #1409D43direct (N × H)
142. D43#1409direct (N × H)
156. C43C2×#1409semidirect
170. C4⋊Q8C4×D43semidirect
183. C4×C8C4×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#492×D432
#353×D432
#191327602
#191327592
C43×#14092
C2×#140943