Finite Group Databasebeta

← D43×#2110 #25249252

Subgroups — D43×#2110 #25249252

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D43C212yesmaximal
2#405×D43C211yesmaximal, characteristic
3#19136200C211yesmaximal, characteristic, complemented
4#19136199C212yesmaximal, complemented
5#19136198C214yesmaximal, complemented
6#347×D43C214yesmaximal, complemented
7C43×#2110C211yesmaximal, characteristic, complemented
8C2×M16×D43C411yescharacteristic
9C22×C8×D43C2211yescharacteristic
10#117×D43C411yescharacteristic
11C2×#13063265C2212yes—
12C2×#13063264C414yescomplemented
13M32×D43C414yescomplemented
14M32×D43C414yescomplemented
15M32×D43C2214yes—
16M32×D43C2214yes—
17C2×C16×D43C414yescomplemented
18#14582857C411yescharacteristic
19#14582856C2212yes—
20#14582855C411yescharacteristic
21#14582854C2211yescharacteristic
22#14582853C412yes—
23#97×D43C2212yes—
24C4×C8×D43C412yes—
25#14582677C2214yescomplemented
26#14582676C2218yescomplemented
27C2×M32×C43C2212yes—
28C43×#405C2211yescharacteristic
29C43×#347C2214yescomplemented
30C22×C4×D43C2×C411yescharacteristic
31C2×#10621877C2×C411yescharacteristic
32C2×#10621872C2×C412yes—
33M16×D43—22no—
34M16×D43—22no—
35C22×C43⋊C8C2×C411yescharacteristic
36C2×C8×D43C2×C412yes—
37C2×C8×D43C2×C411yescharacteristic
38C2×C8×D43C2×C411yescharacteristic
39C2×C8×D43C2×C412yes—
40C2×C8×D43C2×C412yes—
41C2×C8×D43C2×C412yes—
42C2×C8×D43C2×C412yes—
43C2×C8×D43C2311yescharacteristic
44C2×C8×D43C2311yescharacteristic
45#13063284C2×C411yescharacteristic
46#13063283—21no—
47#13063282C2×C412yes—
48#13063281—21no—
49C4⋊C4×D43—21no—
50C22⋊C4×D43—21no—
51C42×D43C2×C412yes—
52#13063265C2×C414yescomplemented
53#13063265C2314yes—
54#13063264C2×C418yes—
55#13063264C2×C418yescomplemented
56C2×C43⋊C16C2×C414yescomplemented
57C16×D43C2×C418yes—
58C16×D43C2×C418yescomplemented
59#13063236C2×C412yes—
60#13063235C2×C412yes—
61#13063235C2312yes—
62C4×C43⋊C8C2×C412yes—
63C8×Dic43C2×C412yes—
64C8×Dic43C2×C412yes—
65C2×M16×C43C2×C411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67#117×C43C2×C411yescharacteristic
68M32×C43C2×C414yescomplemented
69M32×C43C2314yes—
70C2×C16×C43C2×C414yescomplemented
71#97×C43C2312yes—
72C4×C8×C43C2×C412yes—
73C23×D43M1611yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×Dic43M1611yescharacteristic
76C2×C4×D43—22no—
77C2×C4×D43C4212yes—
78C2×C4×D43C4212yes—
79C2×C4×D43M1612yes—
80C2×C4×D43M1612yes—
81C2×C4×D43M1611yescharacteristic
82C2×C4×D43M1611yescharacteristic
83C2×C4×D43C22×C411yescharacteristic
84C2×C4×D43C22×C411yescharacteristic
85M16×C43—22no—
86C2×C8×C43C22×C412yes—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C22×C412yes—
89C2×C8×C43C22×C412yes—
90C2×C8×C43C2411yescharacteristic
91C4⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C42×C43C22×C412yes—
94C22⋊Dic43—21no—
95(C2×D43)⋊C4—22no—
96C4⋊Dic43—21no—
97Dic43⋊C4—22no—
98C4×Dic43—22no—
99C4×Dic43C22×C412yes—
100#10621877—22no—
101C2×C43⋊C8C4212yes—
102C2×C43⋊C8C4212yes—
103C2×C43⋊C8C22×C412yes—
104C2×C43⋊C8C22×C411yescharacteristic
105C2×C43⋊C8C22×C411yescharacteristic
106#10621872—24no—
107C8×D43—22no—
108C8×D43—22no—
109C8×D43C4211yescharacteristic
110C8×D43C4211yescharacteristic
111C8×D43C4212yes—
112C8×D43C4211yescharacteristic
113C8×D43C4211yescharacteristic
114C8×D43C4212yes—
115C8×D43C22×C412yes—
116C8×D43C22×C412yes—
117C8×D43C22×C412yes—
118C8×D43C22×C412yes—
119C16×C43C22×C418yes—
120C43⋊C16C22×C418yes—
121C23×C43C2×M1611yescharacteristic
122C22×D43—42no—
123C22×D43#9712yes—
124C22×D43#9712yes—
125C22×D43C2×M1611yescharacteristic
126C22×D43C2×M1611yescharacteristic
127C2×C4×C43—22no—
128C2×C4×C43C2×C4212yes—
129C2×C4×C43C2×M1612yes—
130C2×C4×C43C2×M1611yescharacteristic
131C2×C4×C43C23×C411yescharacteristic
132C2×Dic43—22no—
133C2×Dic43#9712yes—
134C2×Dic43#9712yes—
135C2×Dic43C2×M1611yescharacteristic
136C2×Dic43C2×M1611yescharacteristic
137C4×D43—44no—
138C4×D43#9712yes—
139C4×D43#9712yes—
140C4×D43#9712yes—
141C4×D43#9712yes—
142C4×D43C2×C4212yes—
143C4×D43C2×C4211yescharacteristic
144C4×D43C2×C4211yescharacteristic
145C4×D43C2×M1611yescharacteristic
146C4×D43C2×M1611yescharacteristic
147C4×D43C2×M1612yes—
148C8×C43—22no—
149C8×C43C2×C4211yescharacteristic
150C8×C43C2×C4211yescharacteristic
151C8×C43C23×C412yes—
152C43⋊C8—22no—
153C43⋊C8C2×C4212yes—
154C43⋊C8C2×C4211yescharacteristic
155C43⋊C8C2×C4211yescharacteristic
156C2×#2110—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43C2×#9712yes—
159C22×C43C22×M1611yescharacteristic
160C2×D43—24no—
161C2×D43—22no—
162C2×D43—42no—
163C2×D43—41no—
164C2×D43C2×#9712yes—
165C2×D43C2×#9711yescharacteristic
166C2×D43C2×#9711yescharacteristic
167C4×C43—42no—
168C4×C43C2×#9712yes—
169C4×C43C22×C4211yescharacteristic
170C4×C43C22×M1611yescharacteristic
171Dic43—42no—
172Dic43C2×#9711yescharacteristic
173Dic43C2×#9711yescharacteristic
174Dic43C2×#9712yes—
175C22×M32—432no—
176C2×#405—431no—
177#2110—432no—
178#2110—431no—
179#2110—434no—
180#2110D4311yescharacteristic, direct product factor
181C2×#347—434no—
182C2×C43—21no—
183C2×C43—22no—
184C2×C43C22×#9711yescharacteristic
185D43—22no—
186D43—21no—
187D43#211012yesdirect product factor
188C22×M16—431no—
189C23×C8—431no—
190C2×#117—431no—
191C2×M32—432no—
192C2×M32—434no—
193C2×M32—434no—
194C2×M32—434no—
195C2×M32—434no—
196C2×M32—434no—
197C2×M32C2×D4312yes—
198C22×C16—434no—
199#405—431no—
200#405—431no—
201#405—431no—
202#405—432no—
203#405—432no—
204#405C2×D4311yescharacteristic
205C2×#97—432no—
206C2×C4×C8—432no—
207#347—438no—
208#347—434no—
209#347C2×D4314yescomplemented
210C43C2×#211011yescharacteristic, complemented, Sylow
211C23×C4—431no—
212C2×M16—431no—
213C2×M16—432no—
214C2×M16—862no—
215C2×M16—862no—
216C2×M16C4×D4311yescharacteristic
217C22×C8—431no—
218C22×C8—431no—
219C22×C8—431no—
220C22×C8—432no—
221C22×C8—432no—
222C22×C8—432no—
223C22×C8—432no—
224C22×C8—431no—
225C22×C8—431no—
226C22×C8—432no—
227C22×C8C22×D4311yescharacteristic
228#117—431no—
229#117—432no—
230#117—861no—
231#117—861no—
232#117C4×D4311yescharacteristic
233C2×C4⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C42—432no—
236M32—434no—
237M32—434no—
238M32—438no—
239M32—438no—
240M32C4×D4314yescomplemented
241M32C22×D4314yes—
242C2×C16—434no—
243C2×C16—438no—
244C2×C16—438no—
245C2×C16C4×D4314yescomplemented
246#97—432no—
247#97—432no—
248#97—432no—
249#97C22×D4312yes—
250C4×C8—432no—
251C4×C8—432no—
252C4×C8—432no—
253C4×C8C4×D4312yes—
254C24—431no—
255C22×C4—431no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—432no—
261C22×C4—432no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—862no—
265C22×C4C2×C4×D4311yescharacteristic
266M16—22no—
267M16—864no—
268M16—862no—
269C2×C8—432no—
270C2×C8—432no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8—432no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—432no—
279C2×C8—432no—
280C2×C8—432no—
281C2×C8—432no—
282C2×C8—432no—
283C2×C8—432no—
284C2×C8—862no—
285C2×C8—862no—
286C2×C8C2×C4×D4312yes—
287C2×C8C2×C4×D4311yescharacteristic
288C2×C8C2×C4×D4312yes—
289C2×C8C2×C4×D4312yes—
290C2×C8C23×D4311yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—862no—
293C4⋊C4—861no—
294C22⋊C4—21no—
295C22⋊C4—862no—
296C22⋊C4—861no—
297C42—432no—
298C42—862no—
299C42C2×C4×D4312yes—
300C16—438no—
301C16C2×C4×D4318yes—
302C23—432no—
303C23—431no—
304C23—432no—
305C23—431no—
306C23—1722no—
307C23M16×D4311yescharacteristic
308C2×C4—22no—
309C2×C4—432no—
310C2×C4—432no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—432no—
315C2×C4—431no—
316C2×C4—432no—
317C2×C4—432no—
318C2×C4—432no—
319C2×C4—432no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—432no—
323C2×C4—862no—
324C2×C4—1724no—
325C2×C4C42×D4312yes—
326C2×C4M16×D4311yescharacteristic
327C2×C4M16×D4312yes—
328C2×C4C22×C4×D4311yescharacteristic
329C8—22no—
330C8—431no—
331C8—431no—
332C8—432no—
333C8—862no—
334C8C42×D4311yescharacteristic
335C8C42×D4311yescharacteristic
336C8C22×C4×D4312yes—
337C22—41no—
338C22—431no—
339C22—431no—
340C22—432no—
341C22—862no—
342C22—864no—
343C22—1721no—
344C22—1722no—
345C22#97×D4312yes—
346C22C2×M16×D4311yescharacteristic
347C4—42no—
348C4—431no—
349C4—431no—
350C4—432no—
351C4—1722no—
352C4#97×D4312yes—
353C4C2×C42×D4311yescharacteristic
354C4C2×M16×D4311yescharacteristic
355C2—21no—
356C2—22no—
357C2—432no—
358C2—861no—
359C2—862no—
360C2C2×#97×D4311yescharacteristic
subgroupG/H
centerC8C42×D43
commutatorC4×C43C22×C42
FrattiniC2×C8C23×D43
FittingC43×#2110C2
socleC2×C43C22×#97
prime radicalC23×D43M16
cosocleC2×C8×C43C24
hypercenter#2110D43
hypocenterC43C2×#2110
LCSG ▷ C4×C43 ▷ C43
UCSC1 ◁ C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
3. #19136200C2semidirect
4. #19136199C2semidirect
5. #19136198C2semidirect
6. #347×D43C2semidirect
7. C43×#2110C2semidirect
12. C2×#13063264C4semidirect
13. M32×D43C4semidirect
14. M32×D43C4semidirect
17. C2×C16×D43C4semidirect
25. #14582677C22semidirect
26. #14582676C22semidirect
29. C43×#347C22semidirect
52. #13063265C2×C4semidirect
55. #13063264C2×C4semidirect
56. C2×C43⋊C16C2×C4semidirect
58. C16×D43C2×C4semidirect
68. M32×C43C2×C4semidirect
70. C2×C16×C43C2×C4semidirect
180. #2110D43direct (N × H)
187. D43#2110direct (N × H)
209. #347C2×D43semidirect
210. C43C2×#2110semidirect
240. M32C4×D43semidirect
245. C2×C16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
#405×D432
#191362002
#191361992
#191361982
#347×D432
C43×#21102
C2×#211043