Finite Group Databasebeta

← D43×#2219 #25251045

Subgroups — D43×#2219 #25251045

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q32×D43C211yesmaximal, characteristic, complemented
2C2×M32×D43C211yesmaximal, characteristic
3#467×D43C212yesmaximal
4#19136704C211yesmaximal, characteristic, complemented
5#19136703C211yesmaximal, characteristic, complemented
6#19136702C212yesmaximal, complemented
7#19136701C212yesmaximal, complemented
8#19136700C211yesmaximal, characteristic, complemented
9#367×D43C211yesmaximal, characteristic, complemented
10#358×D43C212yesmaximal, complemented
11C43×#2219C211yesmaximal, characteristic, complemented
12C2×Q16×D43C2212yes—
13C22×C8×D43C2211yescharacteristic
14C22⋊Q8×D43—22no—
15C2×Dic344C2211yescharacteristic, complemented
16C2×#13063271C2212yescomplemented
17Q32×D43—24no—
18C2×#13063265C2211yescharacteristic
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21M32×D43—24no—
22C2×C16×D43C2211yescharacteristic
23C2×C16×D43C2211yescharacteristic
24#14583141C2212yes—
25#14583140C2212yes—
26#14583139—22no—
27#14583138—22no—
28#14583137C2212yes—
29#107×D43C2212yes—
30#103×D43—22no—
31#14582727C2211yescharacteristic, complemented
32#14582726C2212yescomplemented
33#14582704C2212yescomplemented
34#14582703C2212yescomplemented
35#14582702C2212yescomplemented
36C2×Q32×C43C2211yescharacteristic, complemented
37C2×M32×C43C2211yescharacteristic
38C43×#467C2212yes—
39C43×#367C2211yescharacteristic, complemented
40C43×#358C2212yescomplemented
41C2×Q8×D43—22no—
42C22×C4×D43D411yescharacteristic
43C2×Dic172C2312yes—
44C2×#10621885—22no—
45Q16×D43—24no—
46Q16×D43—24no—
47C22×C43⋊C8D411yescharacteristic
48C2×C8×D43—22no—
49C2×C8×D43—22no—
50C2×C8×D43D411yescharacteristic
51C2×C8×D43D411yescharacteristic
52C2×C8×D43C2311yescharacteristic
53C2×C8×D43C2311yescharacteristic
54#13063305—22no—
55#13063304—22no—
56#13063303—42no—
57#13063302—42no—
58#13063301—22no—
59C4⋊C4×D43—22no—
60C4⋊C4×D43—42no—
61C22⋊C4×D43—42no—
62Dic344—22no—
63#13063271—24no—
64#13063265—22no—
65#13063264—22no—
66#13063264—22no—
67C2×C43⋊C16C2311yescharacteristic
68C2×C43⋊C16C2311yescharacteristic
69C16×D43—22no—
70C16×D43D414yes—
71#13063259C2312yes—
72#13063258—22no—
73#13063250—22no—
74#13063249—22no—
75#13063248—22no—
76C2×Q16×C43C2312yes—
77C22×C8×C43C2311yescharacteristic
78C22⋊Q8×C43—22no—
79Q32×C43—22no—
80M32×C43—22no—
81C2×C16×C43C2311yescharacteristic
82C2×C16×C43C2311yescharacteristic
83#107×C43C2312yes—
84#103×C43—22no—
85C23×D43D811yescharacteristic
86C2×Q8×C43—22no—
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43D811yescharacteristic
89Q8×D43—44no—
90Q8×D43—44no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×C4×D43D811yescharacteristic
96C2×C4×D43D811yescharacteristic
97C2×C4×D43C2×D411yescharacteristic
98C2×C4×D43C2×D411yescharacteristic
99C2×Dic86—22no—
100C2×Dic86—42no—
101Q16×C43—22no—
102Q16×C43—22no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2411yescharacteristic
107C4⋊C4×C43—22no—
108C4⋊C4×C43—42no—
109C22⋊C4×C43—42no—
110C22⋊Dic43—42no—
111#10621885—44no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114C4⋊Dic43—22no—
115C4⋊Dic43—42no—
116Dic43⋊C4—42no—
117Dic43⋊C4—42no—
118Dic43⋊C4—42no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8C2×D411yescharacteristic
121C2×C43⋊C8C2×D411yescharacteristic
122Dic172—22no—
123Dic172—22no—
124C8×D43—22no—
125C8×D43—21no—
126C8×D43—21no—
127C8×D43—22no—
128C8×D43C2×D412yes—
129C8×D43#4112yes—
130C16×C43—21no—
131C16×C43C2×D412yes—
132C43⋊C16—21no—
133C43⋊C16C2×D412yes—
134C23×C43C2×D811yescharacteristic
135C22×D43—22no—
136C22×D43—24no—
137C22×D43C2×D811yescharacteristic
138C22×D43C2×D811yescharacteristic
139Q8×C43—42no—
140Q8×C43—42no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43C2×D811yescharacteristic
146C2×C4×C43C22×D411yescharacteristic
147C2×Dic43—22no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43C2×D811yescharacteristic
151C2×Dic43C2×D811yescharacteristic
152C4×D43—22no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—22no—
156C4×D43—84no—
157C4×D43—84no—
158C4×D43#12112yes—
159C4×D43#13512yes—
160Dic86—42no—
161Dic86—42no—
162Dic86—84no—
163C8×C43—21no—
164C8×C43C22×D411yescharacteristic
165C8×C43C2×#4111yescharacteristic
166C43⋊C8—21no—
167C43⋊C8#12112yes—
168C2×#2219—431nomaximal, Sylow
169C22×C43—22no—
170C22×C43—21no—
171C22×C43C22×D811yescharacteristic
172C2×D43—22no—
173C2×D43—21no—
174C2×D43—44no—
175C2×D43#46612yes—
176C2×D43#51014yes—
177C4×C43—21no—
178C4×C43—82no—
179C4×C43—82no—
180C4×C43C2×#12111yescharacteristic
181C4×C43C2×#13511yescharacteristic
182Dic43—21no—
183Dic43—82no—
184Dic43—82no—
185Dic43#46612yes—
186C22×Q32—431no—
187C22×M32—431no—
188C2×#467—432no—
189#2219—431no—
190#2219—431no—
191#2219—432no—
192#2219—431no—
193#2219—432no—
194#2219D4311yescharacteristic, direct product factor
195C2×#367—431no—
196C2×#358—432no—
197C2×C43—41no—
198C2×C43C2×#46611yescharacteristic
199C2×C43C2×#51012yes—
200D43—41no—
201D43#221914yesdirect product factor
202C22×Q16—432no—
203C23×C8—431no—
204C2×C22⋊Q8—862no—
205C2×Q32—432no—
206C2×Q32—431no—
207C2×Q32—864no—
208C2×Q32C2×D4311yescharacteristic, complemented
209C2×M32—431no—
210C2×M32—431no—
211C2×M32—431no—
212C2×M32—864no—
213C2×M32C2×D4311yescharacteristic
214C22×C16—431no—
215C22×C16—431no—
216#467—432no—
217#467—432no—
218#467—432no—
219#467—862no—
220#467—862no—
221#467C2×D4312yes—
222C2×#107—432no—
223C2×#103—862no—
224#367—431no—
225#367—432no—
226#367C2×D4311yescharacteristic, complemented
227#358—432no—
228#358—432no—
229#358—432no—
230#358C2×D4312yescomplemented
231C43C2×#221911yescharacteristic, complemented, Sylow
232C22×Q8—862no—
233C23×C4—431no—
234C2×Q16—432no—
235C2×Q16—864no—
236C2×Q16—864no—
237C2×Q16—862no—
238C2×Q16C22×D4312yes—
239C22×C8—431no—
240C22×C8—431no—
241C22×C8—431no—
242C22×C8—431no—
243C22×C8—431no—
244C22×C8—862no—
245C22×C8—862no—
246C22×C8C22×D4311yescharacteristic
247C22⋊Q8—22no—
248C22⋊Q8—862no—
249C22⋊Q8—862no—
250C22⋊Q8—862no—
251C22⋊Q8—1722no—
252C22⋊Q8—1722no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4—1722no—
255C2×C22⋊C4—1722no—
256Q32—22no—
257Q32—864no—
258Q32—862no—
259M32—22no—
260M32—862no—
261M32—862no—
262M32—862no—
263C2×C16—431no—
264C2×C16—434no—
265C2×C16—431no—
266C2×C16—862no—
267C2×C16C22×D4311yescharacteristic
268C2×C16C22×D4311yescharacteristic
269#107—432no—
270#107—862no—
271#107C22×D4312yes—
272#103—22no—
273#103—862no—
274#103—862no—
275#103—862no—
276C24—431no—
277C2×Q8—22no—
278C2×Q8—862no—
279C2×Q8—1722no—
280C2×Q8—1724no—
281C2×Q8—1724no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—431no—
287C22×C4—862no—
288C22×C4—862no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4D4×D4311yescharacteristic
292Q16—22no—
293Q16—22no—
294Q16—862no—
295Q16—862no—
296Q16—1724no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—431no—
300C2×C8—432no—
301C2×C8—432no—
302C2×C8—431no—
303C2×C8—862no—
304C2×C8—862no—
305C2×C8—862no—
306C2×C8—861no—
307C2×C8—861no—
308C2×C8D4×D4311yescharacteristic
309C2×C8C23×D4311yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—42no—
312C4⋊C4—862no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C4⋊C4—1722no—
316C4⋊C4—1722no—
317C22⋊C4—42no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C16—21no—
322C16—432no—
323C16—861no—
324C16D4×D4312yes—
325C23—431no—
326C23—431no—
327C23—862no—
328C23—864no—
329C23D8×D4311yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—3444no—
333Q8—1722no—
334Q8—1722no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—431no—
340C2×C4—432no—
341C2×C4—432no—
342C2×C4—431no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—3444no—
349C2×C4—3444no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4D8×D4311yescharacteristic
353C2×C4C2×D4×D4311yescharacteristic
354C8—21no—
355C8—432no—
356C8—861no—
357C8C2×D4×D4311yescharacteristic
358C8#41×D4311yescharacteristic
359C22—22no—
360C22—21no—
361C22—434no—
362C22—432no—
363C22—862no—
364C22—861no—
365C22—1724no—
366C22C2×D8×D4311yescharacteristic
367C4—21no—
368C4—82no—
369C4—82no—
370C4—432no—
371C4—861no—
372C4—3442no—
373C4—3442no—
374C4#121×D4311yescharacteristic
375C4#135×D4311yescharacteristic
376C2—41no—
377C2—434no—
378C2—1721no—
379C2#466×D4311yescharacteristic
380C2#510×D4312yes—
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2219C2
socleC22×C43C22×D8
prime radicalC23×D43D8
hypercenter#2219D43
hypocenterC43C2×#2219
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D43C2semidirect
4. #19136704C2semidirect
5. #19136703C2semidirect
6. #19136702C2semidirect
7. #19136701C2semidirect
8. #19136700C2semidirect
9. #367×D43C2semidirect
10. #358×D43C2semidirect
11. C43×#2219C2semidirect
15. C2×Dic344C22semidirect
16. C2×#13063271C22semidirect
31. #14582727C22semidirect
32. #14582726C22semidirect
33. #14582704C22semidirect
34. #14582703C22semidirect
35. #14582702C22semidirect
36. C2×Q32×C43C22semidirect
39. C43×#367C22semidirect
40. C43×#358C22semidirect
194. #2219D43direct (N × H)
201. D43#2219direct (N × H)
208. C2×Q32C2×D43semidirect
226. #367C2×D43semidirect
230. #358C2×D43semidirect
231. C43C2×#2219semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×D432
C2×M32×D432
#467×D432
#191367042
#191367032
#191367022
#191367012
#191367002
#367×D432
#358×D432
C43×#22192
C2×#221943