Finite Group Databasebeta

← D43×#1324 #25005746

Subgroups — D43×#1324 #25005746

Order 11008.

510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 101 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#382×D43C211yesmaximal, characteristic
2#324×D43C212yesmaximal
3#19132539C211yesmaximal, characteristic, complemented
4#19132538C212yesmaximal, complemented
5C43×#1324C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D43C411yescharacteristic
7C2×C4⋊C4×D43C2211yescharacteristic
8C2×C42×D43C411yescharacteristic
9C22⋊C8×D43—22no—
10#14582765C411yescharacteristic
11#14582764C411yescharacteristic
12#14582764C2211yescharacteristic
13#14582763—22no—
14#95×D43—22no—
15#14582625C2212yes—
16#14582624—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×C4×D43—21no—
20C22×C4×D43—21no—
21C22×C4×D43C2×C411yescharacteristic
22C22×C4×D43D412yes—
23C2×C8×D43—42no—
24C2×C4⋊Dic43C2×C411yescharacteristic
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—21no—
27C2×Dic43⋊C4D412yes—
28C4⋊C4×D43—41no—
29C4⋊C4×D43—41no—
30C4⋊C4×D43—41no—
31C4⋊C4×D43—41no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C42×D43—22no—
35C42×D43C814yescomplemented
36C22⋊(C43⋊C8)—22no—
37(C2×D43)⋊C8—42no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C22⋊C8×C43—22no—
45#95×C43—22no—
46C23×D43C22⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C412yes—
55C2×C4×D43—24no—
56C2×C4×D43—21no—
57C2×C4×D43—21no—
58C2×C4×D43—22no—
59C2×C4×D43—22no—
60C2×C4×D43—22no—
61C2×C4×D43—42no—
62C2×C4×D43—42no—
63C2×C4×D43—44no—
64C2×C4×D43—44no—
65C2×C4×D43—41no—
66C2×C4×D43—41no—
67C2×C4×D43C2×C812yes—
68C2×C4×D43M1612yes—
69C2×C8×C43—42no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C42×C43—21no—
73C42×C43C2×C812yescomplemented
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78C4×Dic43—21no—
79C4×Dic43—24no—
80C4×Dic43C2×C812yescomplemented
81C2×C43⋊C8—42no—
82C8×D43—84no—
83C23×C43C2×C22⋊C411yescharacteristic
84C22×D43—22no—
85C22×D43—22no—
86C22×D43C22⋊C812yes—
87C22×D43#9911yescharacteristic
88C22×D43#9911yescharacteristic
89C22×D43#10112yes—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43C22×C811yescharacteristic
100C2×C4×C43C2×M1611yescharacteristic
101C2×Dic43—21no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—41no—
110C2×Dic43C22⋊C812yes—
111C4×D43—22no—
112C4×D43—22no—
113C4×D43—22no—
114C4×D43—22no—
115C4×D43—48no—
116C4×D43—44no—
117C4×D43—82no—
118C4×D43—82no—
119C4×D43—82no—
120C8×C43—82no—
121C43⋊C8—82no—
122C2×#1324—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—21no—
125C22×C43C2×C22⋊C811yescharacteristic
126C22×C43C2×#9911yescharacteristic
127C22×C43C2×#10111yescharacteristic
128C2×D43—21no—
129C2×D43—21no—
130C2×D43—24no—
131C2×D43—24no—
132C2×D43#32412yes—
133C2×D43#32412yes—
134C2×D43#35412yes—
135C2×D43#35512yes—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43—81no—
141Dic43—22no—
142Dic43—42no—
143Dic43—42no—
144Dic43—81no—
145C2×#382—431no—
146C2×#324—432no—
147#1324—431no—
148#1324—432no—
149#1324D4311yescharacteristic, direct product factor
150C2×C43—21no—
151C2×C43—21no—
152C2×C43C2×#32411yescharacteristic
153C2×C43C2×#35411yescharacteristic
154C2×C43C2×#35511yescharacteristic
155D43—22no—
156D43#132414yesdirect product factor
157C22×C4⋊C4—431no—
158C22×C4⋊C4—431no—
159C22×C42—431no—
160C2×C22⋊C8—862no—
161#382—431no—
162#382—431no—
163#382—431no—
164#382—862no—
165#382C2×D4311yescharacteristic
166C2×#95—862no—
167#324—432no—
168#324—862no—
169#324C2×D4312yes—
170C43C2×#132411yescharacteristic, complemented, Sylow
171C23×C4—431no—
172C23×C4—432no—
173C23×C4—861no—
174C23×C4—861no—
175C22×C8—1722no—
176C2×C4⋊C4—431no—
177C2×C4⋊C4—432no—
178C2×C4⋊C4—431no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4—1721no—
181C2×C4⋊C4—1721no—
182C2×C4⋊C4—1721no—
183C2×C4⋊C4—1721no—
184C2×C4⋊C4C4×D4311yescharacteristic
185C2×C4⋊C4C22×D4311yescharacteristic
186C2×C42—431no—
187C2×C42—434no—
188C2×C42—862no—
189C2×C42—861no—
190C2×C42C4×D4311yescharacteristic
191C22⋊C8—22no—
192C22⋊C8—862no—
193C22⋊C8—1722no—
194#95—22no—
195#95—862no—
196#95—862no—
197#95—862no—
198C24—431no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—431no—
202C22×C4—432no—
203C22×C4—432no—
204C22×C4—432no—
205C22×C4—861no—
206C22×C4—861no—
207C22×C4—862no—
208C22×C4—862no—
209C22×C4—864no—
210C22×C4—862no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4—1721no—
214C22×C4—1721no—
215C22×C4—1724no—
216C22×C4—1724no—
217C22×C4—1722no—
218C22×C4—1722no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4D4×D4312yes—
221C2×C8—42no—
222C2×C8—3444no—
223C2×C8—1722no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—1722no—
227C4⋊C4—1721no—
228C4⋊C4—1721no—
229C4⋊C4—1722no—
230C42—21no—
231C42—432no—
232C42—864no—
233C42—861no—
234C42C8×D4312yescomplemented
235C23—431no—
236C23—432no—
237C23—431no—
238C23—432no—
239C23—862no—
240C23—862no—
241C23C22⋊C4×D4311yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—432no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—861no—
257C2×C4—861no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—3442no—
261C2×C4—3442no—
262C2×C4—3442no—
263C2×C4—1724no—
264C2×C4—1728no—
265C2×C4—1722no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1722no—
270C2×C4C2×C8×D4311yescharacteristic
271C2×C4M16×D4311yescharacteristic
272C8—82no—
273C8—3442no—
274C22—21no—
275C22—21no—
276C22—432no—
277C22—432no—
278C22—432no—
279C22—432no—
280C22—864no—
281C22—864no—
282C22—861no—
283C22—861no—
284C22C22⋊C8×D4311yescharacteristic
285C22#99×D4311yescharacteristic
286C22#101×D4311yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—862no—
293C4—3441no—
294C4—1722no—
295C4—1722no—
296C2—21no—
297C2—21no—
298C2—434no—
299C2—862no—
300C2#324×D4311yescharacteristic
301C2#354×D4311yescharacteristic
302C2#355×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43C2×#1324
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #19132539C2semidirect
4. #19132538C2semidirect
5. C43×#1324C2semidirect
35. C42×D43C8semidirect
73. C42×C43C2×C8semidirect
80. C4×Dic43C2×C8semidirect
149. #1324D43direct (N × H)
156. D43#1324direct (N × H)
170. C43C2×#1324semidirect
234. C42C8×D43semidirect

Maximal subgroups

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

subgroupindex
#382×D432
#324×D432
#191325392
#191325382
C43×#13242
C2×#132443