Finite Group Databasebeta

← D43×#1386 #25011510

Subgroups — D43×#1386 #25011510

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D43C211yesmaximal, characteristic
2#427×D43C211yesmaximal, characteristic
3C2×#106×D43C211yesmaximal, characteristic
4#19132702C211yesmaximal, characteristic, complemented
5#19132701C211yesmaximal, characteristic, complemented
6#19132700C211yesmaximal, characteristic, complemented
7C43×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9#117×D43—21no—
10C2×C4⋊C4×D43—21no—
11C2×#13063265C2211yescharacteristic
12C2×#13063264—21no—
13M32×D43—22no—
14M32×D43C414yescomplemented
15C2×C16×D43—21no—
16#14582937C2211yescharacteristic
17#14582936C412yescomplemented
18#14582935—21no—
19#14582934—21no—
20#107×D43C412yescomplemented
21C2×#13063257C2211yescharacteristic
22C2×#13063256—21no—
23#106×D43—21no—
24#106×D43—22no—
25#106×D43C414yescomplemented
26C2×M32×C43C2211yescharacteristic
27C43×#427C2211yescharacteristic
28C2×#106×C43C2211yescharacteristic
29C22×C4×D43—41no—
30C22×C4×D43D411yescharacteristic
31C22×C43⋊C8D411yescharacteristic
32C2×C8×D43C2×C412yes—
33C2×C8×D43C2×C412yes—
34C2×C8×D43C2×C411yescharacteristic
35C2×C8×D43C2×C411yescharacteristic
36C2×C8×D43D411yescharacteristic
37C2×C8×D43D412yes—
38C2×C8×D43D411yescharacteristic
39C2×C8×D43Q812yes—
40#13063284—21no—
41#13063283—22no—
42#13063282—41no—
43#13063281—41no—
44C2×C4⋊Dic43—21no—
45C2×Dic43⋊C4—41no—
46C4⋊C4×D43—24no—
47C4⋊C4×D43—22no—
48C4⋊C4×D43—42no—
49C22⋊C4×D43—41no—
50C42×D43—41no—
51#13063265—21no—
52#13063265C2×C412yescomplemented
53#13063264—24no—
54C2×C43⋊C16—21no—
55C16×D43—24no—
56#13063259C2×C412yescomplemented
57#13063258—22no—
58#13063257—21no—
59#13063257—21no—
60#13063257C2×C412yescomplemented
61#13063256—24no—
62#13063256—22no—
63C22×C8×C43C2311yescharacteristic
64#117×C43—21no—
65C2×C4⋊C4×C43—21no—
66M32×C43—21no—
67M32×C43C2×C412yescomplemented
68C2×C16×C43—21no—
69#107×C43C2×C412yescomplemented
70#106×C43—21no—
71#106×C43—21no—
72#106×C43C2×C412yescomplemented
73C23×D43D811yescharacteristic
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—41no—
77C22×Dic43D811yescharacteristic
78C2×C4×D43—42no—
79C2×C4×D43—44no—
80C2×C4×D43—84no—
81C2×C4×D43C22⋊C412yes—
82C2×C4×D43C22⋊C411yescharacteristic
83C2×C4×D43C22⋊C411yescharacteristic
84C2×C4×D43C4⋊C412yes—
85C2×C4×D43SD1611yescharacteristic
86C2×C4×D43SD1612yes—
87C2×C4×D43SD1611yescharacteristic
88C2×C4×D43Q1612yes—
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×Q811yescharacteristic
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43—41no—
100C22⋊Dic43—41no—
101(C2×D43)⋊C4—42no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—41no—
105Dic43⋊C4—44no—
106Dic43⋊C4—42no—
107C4×Dic43—41no—
108C4×Dic43—42no—
109C2×C43⋊C8C22⋊C412yes—
110C2×C43⋊C8C22⋊C411yescharacteristic
111C2×C43⋊C8C22⋊C411yescharacteristic
112C2×C43⋊C8C4⋊C412yes—
113C8×D43C4212yes—
114C8×D43C4212yes—
115C8×D43C22⋊C412yes—
116C8×D43C22⋊C412yes—
117C8×D43C4⋊C412yes—
118C8×D43C4⋊C412yes—
119C8×D43C4⋊C412yes—
120C8×D43C4⋊C412yes—
121C16×C43—22no—
122C43⋊C16—22no—
123C23×C43C2×D811yescharacteristic
124C22×D43—24no—
125C22×D43#10211yescharacteristic
126C22×D43#10212yes—
127C22×D43#10211yescharacteristic
128C22×D43#10712yes—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C2×C4⋊C411yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43C2×Q1611yescharacteristic
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—82no—
141C2×Dic43#10211yescharacteristic
142C2×Dic43#10212yes—
143C2×Dic43#10211yescharacteristic
144C2×Dic43#10712yes—
145C4×D43—88no—
146C4×D43—84no—
147C4×D43#9512yes—
148C4×D43#9512yes—
149C4×D43#10312yes—
150C4×D43#10312yes—
151C4×D43#10312yes—
152C4×D43#10312yes—
153C4×D43#10612yes—
154C4×D43#10612yes—
155C8×C43C2×C4211yescharacteristic
156C8×C43C2×C22⋊C411yescharacteristic
157C8×C43C2×C4⋊C411yescharacteristic
158C8×C43C2×C4⋊C411yescharacteristic
159C43⋊C8#9512yes—
160C43⋊C8#9512yes—
161C2×#1386—431nomaximal, Sylow
162C22×C43—22no—
163C22×C43C2×#10211yescharacteristic
164C22×C43C2×#10211yescharacteristic
165C22×C43C2×#10711yescharacteristic
166C2×D43—22no—
167C2×D43—24no—
168C2×D43—24no—
169C2×D43#34012yes—
170C2×D43#34012yes—
171C2×D43#36014yes—
172C4×C43—82no—
173C4×C43—82no—
174C4×C43C2×#9511yescharacteristic
175C4×C43C2×#10311yescharacteristic
176C4×C43C2×#10311yescharacteristic
177C4×C43C2×#10611yescharacteristic
178Dic43—82no—
179Dic43—82no—
180Dic43#34012yes—
181Dic43#34012yes—
182C22×M32—431no—
183C2×#427—431no—
184C22×#106—431no—
185#1386—431no—
186#1386—431no—
187#1386—431no—
188#1386D4311yescharacteristic, direct product factor
189C2×C43—21no—
190C2×C43—21no—
191C2×C43C2×#34011yescharacteristic
192C2×C43C2×#36012yes—
193D43—22no—
194D43#138614yesdirect product factor
195C23×C8—431no—
196C2×#117—861no—
197C22×C4⋊C4—861no—
198C2×M32—431no—
199C2×M32—434no—
200C2×M32—861no—
201C2×M32—862no—
202C2×M32C2×D4311yescharacteristic
203C22×C16—861no—
204#427—431no—
205#427—432no—
206#427—861no—
207#427—861no—
208#427C2×D4311yescharacteristic
209C2×#107—432no—
210C2×#106—431no—
211C2×#106—434no—
212C2×#106—862no—
213C2×#106—861no—
214C2×#106—861no—
215C2×#106C2×D4311yescharacteristic
216C43C2×#138611yescharacteristic, complemented, Sylow
217C23×C4—431no—
218C23×C4—1721no—
219C22×C8—431no—
220C22×C8—432no—
221C22×C8—431no—
222C22×C8—431no—
223C22×C8—432no—
224C22×C8—431no—
225C22×C8—432no—
226C22×C8—431no—
227C22×C8—432no—
228C22×C8C22×D4311yescharacteristic
229#117—21no—
230#117—862no—
231#117—861no—
232#117—1721no—
233#117—1721no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—864no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—1722no—
239C2×C4⋊C4—1721no—
240C2×C22⋊C4—1721no—
241C2×C42—1721no—
242M32—21no—
243M32—432no—
244M32—864no—
245M32—861no—
246M32C4×D4312yescomplemented
247C2×C16—21no—
248C2×C16—864no—
249C2×C16—861no—
250#107—432no—
251#107—862no—
252#107C4×D4312yescomplemented
253#106—21no—
254#106—21no—
255#106—432no—
256#106—864no—
257#106—862no—
258#106—861no—
259#106—861no—
260#106C4×D4312yescomplemented
261C24—431no—
262C22×C4—41no—
263C22×C4—431no—
264C22×C4—432no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—432no—
268C22×C4—431no—
269C22×C4—432no—
270C22×C4—431no—
271C22×C4—432no—
272C22×C4—3444no—
273C22×C4—1722no—
274C22×C4—1724no—
275C22×C4—1721no—
276C22×C4D4×D4311yescharacteristic
277C2×C8—432no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8—432no—
281C2×C8—432no—
282C2×C8—432no—
283C2×C8—432no—
284C2×C8—432no—
285C2×C8—432no—
286C2×C8—432no—
287C2×C8—432no—
288C2×C8—432no—
289C2×C8C2×C4×D4311yescharacteristic
290C2×C8C2×C4×D4311yescharacteristic
291C2×C8C2×C4×D4311yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8D4×D4311yescharacteristic
294C2×C8Q8×D4311yescharacteristic
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—862no—
299C4⋊C4—862no—
300C4⋊C4—1724no—
301C4⋊C4—1722no—
302C4⋊C4—1721no—
303C22⋊C4—41no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C42—41no—
307C42—1722no—
308C42—1721no—
309C16—22no—
310C16—862no—
311C23—431no—
312C23—432no—
313C23—431no—
314C23—432no—
315C23—864no—
316C23D8×D4311yescharacteristic
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—432no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—432no—
324C2×C4—432no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—432no—
328C2×C4—432no—
329C2×C4—432no—
330C2×C4—432no—
331C2×C4—432no—
332C2×C4—3444no—
333C2×C4—3448no—
334C2×C4—3442no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4C22⋊C4×D4311yescharacteristic
338C2×C4C22⋊C4×D4311yescharacteristic
339C2×C4C4⋊C4×D4311yescharacteristic
340C2×C4SD16×D4311yescharacteristic
341C2×C4SD16×D4311yescharacteristic
342C2×C4Q16×D4311yescharacteristic
343C8—432no—
344C8—432no—
345C8C42×D4311yescharacteristic
346C8C22⋊C4×D4311yescharacteristic
347C8C4⋊C4×D4311yescharacteristic
348C8C4⋊C4×D4311yescharacteristic
349C22—22no—
350C22—434no—
351C22—432no—
352C22—432no—
353C22—864no—
354C22—864no—
355C22—862no—
356C22#102×D4311yescharacteristic
357C22#102×D4311yescharacteristic
358C22#107×D4311yescharacteristic
359C4—82no—
360C4—82no—
361C4—432no—
362C4—432no—
363C4—3442no—
364C4—3442no—
365C4#95×D4311yescharacteristic
366C4#103×D4311yescharacteristic
367C4#103×D4311yescharacteristic
368C4#106×D4311yescharacteristic
369C2—21no—
370C2—21no—
371C2—434no—
372C2—862no—
373C2#340×D4311yescharacteristic
374C2#360×D4312yes—
subgroupG/H
centerC22#102×D43
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC43×#1386C2
socleC22×C43C2×#102
prime radicalC23×D43D8
cosocleC22×C8×C43C23
hypercenter#1386D43
hypocenterC43C2×#1386
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #19132702C2semidirect
5. #19132701C2semidirect
6. #19132700C2semidirect
7. C43×#1386C2semidirect
14. M32×D43C4semidirect
17. #14582936C4semidirect
20. #107×D43C4semidirect
25. #106×D43C4semidirect
52. #13063265C2×C4semidirect
56. #13063259C2×C4semidirect
60. #13063257C2×C4semidirect
67. M32×C43C2×C4semidirect
69. #107×C43C2×C4semidirect
72. #106×C43C2×C4semidirect
188. #1386D43direct (N × H)
194. D43#1386direct (N × H)
216. C43C2×#1386semidirect
246. M32C4×D43semidirect
252. #107C4×D43semidirect
260. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
#427×D432
C2×#106×D432
#191327022
#191327012
#191327002
C43×#13862
C2×#138643