Finite Group Databasebeta

← D43×#1412 #25016940

Subgroups — D43×#1412 #25016940

Order 11008.

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

normal subgroups only

This group has 390 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#490×D43C211yesmaximal, characteristic
2#353×D43C212yesmaximal
3#19132766C211yesmaximal, characteristic, complemented
4#19132765C212yesmaximal, complemented
5C43×#1412C211yesmaximal, characteristic, complemented
6#127×D43C2211yescharacteristic
7#125×D43C411yescharacteristic, complemented
8#14583265C411yescharacteristic, complemented
9#14583264C411yescharacteristic, complemented
10#14583263C2211yescharacteristic
11#14583262—22no—
12#102×D43—22no—
13#99×D43—22no—
14#97×D43C411yescharacteristic, complemented
15#14582692C2212yes—
16#14582691—22no—
17C43×#490C2211yescharacteristic
18C43×#353C2212yes—
19C2×D4×D43—41no—
20C2×D4×D43D412yes—
21C2×C8×D43—21no—
22#13063322C2×C411yescharacteristic
23#13063321—41no—
24#13063321D412yes—
25#13063317C2×C411yescharacteristic, complemented
26#13063316—21no—
27#13063315—41no—
28C4⋊C4×D43—21no—
29C4⋊C4×D43—41no—
30C22⋊C4×D43—42no—
31C42×D43C2×C411yescharacteristic
32#13063247—22no—
33#13063246—22no—
34#13063245—22no—
35#13063240—22no—
36#13063239—42no—
37#13063236C2×C411yescharacteristic, complemented
38#13063235—21no—
39#127×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic, complemented
41#102×C43—22no—
42#99×C43—22no—
43#97×C43C2×C411yescharacteristic, complemented
44C23×D43—22no—
45C2×D4×C43—41no—
46C2×D4×C43C2×D412yes—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—42no—
49D4×D43—42no—
50D4×D43—42no—
51D4×D43—84no—
52C2×D172—41no—
53C2×D172C22⋊C412yes—
54C2×C4×D43—21no—
55C2×C4×D43—41no—
56C2×C4×D43—82no—
57C2×C4×D43C22⋊C411yescharacteristic
58C2×C8×C43—21no—
59C4⋊C4×C43—21no—
60C4⋊C4×C43—41no—
61C22⋊C4×C43—42no—
62C42×C43C22×C411yescharacteristic
63C22⋊Dic43—42no—
64(C2×D43)⋊C4—82no—
65C4⋊Dic43—21no—
66C4⋊Dic43—41no—
67Dic43⋊C4—41no—
68Dic43⋊C4—41no—
69Dic43⋊C4—41no—
70C4×Dic43—21no—
71C4×Dic43C22⋊C411yescharacteristic
72C2×C43⋊C8—21no—
73C8×D43—41no—
74C8×D43—41no—
75C23×C43—22no—
76C22×D43—22no—
77C22×D43—42no—
78C22×D43—42no—
79C22×D43—84no—
80C22×D43#9911yescharacteristic
81D4×C43—42no—
82D4×C43—82no—
83C2×C4×C43—21no—
84C2×C4×C43—41no—
85C2×C4×C43—82no—
86C2×C4×C43C2×C22⋊C411yescharacteristic
87C22⋊D43—82no—
88C22⋊D43—84no—
89C2×Dic43—21no—
90C2×Dic43—41no—
91C2×Dic43—82no—
92C2×Dic43#9911yescharacteristic
93D172—42no—
94D172—82no—
95C4×D43—21no—
96C4×D43—21no—
97C4×D43—42no—
98C4×D43—82no—
99C4×D43—164no—
100C8×C43—41no—
101C43⋊C8—41no—
102C2×#1412—431nomaximal, Sylow
103C22×C43—42no—
104C22×C43—82no—
105C22×C43C2×#9911yescharacteristic
106C2×D43—22no—
107C2×D43—42no—
108C2×D43—84no—
109C2×D43—82no—
110C2×D43—162no—
111C2×D43#35411yescharacteristic
112C2×D43#35411yescharacteristic
113C4×C43—21no—
114C4×C43—41no—
115C4×C43—81no—
116C4×C43—162no—
117Dic43—21no—
118Dic43—41no—
119Dic43—81no—
120Dic43—162no—
121C2×#490—431no—
122C2×#353—432no—
123#1412—431no—
124#1412—432no—
125#1412D4311yescharacteristic, direct product factor
126C2×C43—21no—
127C2×C43—82no—
128C2×C43C2×#35411yescharacteristic
129D43—21no—
130D43—82no—
131D43#141212yesdirect product factor
132C2×#127—431no—
133C2×#125—431no—
134#490—431no—
135#490—431no—
136#490—431no—
137#490—862no—
138#490C2×D4311yescharacteristic
139C2×#102—862no—
140C2×#99—862no—
141C2×#97—431no—
142#353—432no—
143#353—862no—
144#353C2×D4312yes—
145C43C2×#141211yescharacteristic, complemented, Sylow
146C22×D4—432no—
147C22×D4—1721no—
148C22×C8—861no—
149#127—432no—
150#127—431no—
151#127—1721no—
152#127C22×D4311yescharacteristic
153#125—431no—
154#125—861no—
155#125—1721no—
156#125C4×D4311yescharacteristic, complemented
157C2×C4⋊C4—861no—
158C2×C4⋊C4—1721no—
159C2×C22⋊C4—1722no—
160C2×C42—431no—
161#102—22no—
162#102—862no—
163#102—862no—
164#102—862no—
165#99—22no—
166#99—862no—
167#99—1722no—
168#97—431no—
169#97—861no—
170#97C4×D4311yescharacteristic, complemented
171C24—862no—
172C2×D4—41no—
173C2×D4—432no—
174C2×D4—862no—
175C2×D4—3444no—
176C2×D4—1721no—
177C2×D4—1722no—
178C2×D4—1722no—
179C2×D4—1722no—
180C2×D4D4×D4312yes—
181C22×C4—431no—
182C22×C4—861no—
183C22×C4—3442no—
184C22×C4—1721no—
185C2×C8—21no—
186C2×C8—861no—
187C2×C8—1721no—
188C2×C8—1721no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—861no—
192C4⋊C4—1721no—
193C4⋊C4—1721no—
194C4⋊C4—1721no—
195C4⋊C4—1721no—
196C22⋊C4—42no—
197C22⋊C4—3442no—
198C22⋊C4—1722no—
199C42—431no—
200C42—861no—
201C42C2×C4×D4311yescharacteristic
202C23—22no—
203C23—431no—
204C23—862no—
205C23—3444no—
206C23—1722no—
207C23—1722no—
208D4—42no—
209D4—82no—
210D4—3442no—
211D4—3442no—
212D4—3444no—
213D4—1722no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—82no—
217C2×C4—431no—
218C2×C4—861no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—3442no—
222C2×C4—3442no—
223C2×C4—1722no—
224C2×C4—1721no—
225C2×C4—6884no—
226C2×C4C22⋊C4×D4311yescharacteristic
227C8—41no—
228C8—1721no—
229C22—42no—
230C22—82no—
231C22—431no—
232C22—431no—
233C22—862no—
234C22—3442no—
235C22—3444no—
236C22—1722no—
237C22—6882no—
238C22#99×D4311yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—162no—
243C4—861no—
244C4—3441no—
245C4—1721no—
246C4—6882no—
247C2—21no—
248C2—82no—
249C2—432no—
250C2—861no—
251C2—3442no—
252C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1412C2
socleC2×C43C2×#354
prime radical#127×D43C22
cosocle#127×C43C23
hypercenter#1412D43
hypocenterC43C2×#1412
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #19132766C2semidirect
4. #19132765C2semidirect
5. C43×#1412C2semidirect
7. #125×D43C4semidirect
8. #14583265C4semidirect
9. #14583264C4semidirect
14. #97×D43C4semidirect
25. #13063317C2×C4semidirect
37. #13063236C2×C4semidirect
40. #125×C43C2×C4semidirect
43. #97×C43C2×C4semidirect
125. #1412D43direct (N × H)
131. D43#1412direct (N × H)
145. C43C2×#1412semidirect
156. #125C4×D43semidirect
170. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
#490×D432
#353×D432
#191327662
#191327652
C43×#14122
C2×#141243