Finite Group Databasebeta

← D43×#1340 #25006740

Subgroups — D43×#1340 #25006740

Order 11008.

444 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 81 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#470×D43C211yesmaximal, characteristic
2#349×D43C211yesmaximal, characteristic
3H(3,ℤ/4)×D43C211yesmaximal, characteristic
4#19132584C211yesmaximal, characteristic, complemented
5#19132583C211yesmaximal, characteristic, complemented
6#19132582C211yesmaximal, characteristic, complemented
7C43×#1340C211yesmaximal, characteristic, complemented
8C2×Q16×D43C411yescharacteristic, complemented
9C2×M16×D43C2211yescharacteristic
10C22⋊Q8×D43—21no—
11#117×D43—21no—
12M32×D43—21no—
13#14583158C411yescharacteristic, complemented
14#14583157C2211yescharacteristic
15#14583156—21no—
16#14583155—21no—
17#14583154C411yescharacteristic, complemented
18#106×D43C411yescharacteristic, complemented
19#103×D43—21no—
20#14582681C2211yescharacteristic
21#14582680—21no—
22#14582656C2211yescharacteristic
23#14582655—21no—
24C43×#470C2211yescharacteristic
25C43×#349C2211yescharacteristic
26C43×H(3,ℤ/4)C2211yescharacteristic
27C2×Q8×D43—21no—
28C22×C4×D43D411yescharacteristic
29C2×Dic172C2×C411yescharacteristic, complemented
30C2×#10621885—21no—
31Q16×D43—41no—
32Q16×D43—41no—
33C2×#10621877D411yescharacteristic
34C2×#10621872C2×C411yescharacteristic
35C2×#10621872D411yescharacteristic
36M16×D43—41no—
37M16×D43—41no—
38C2×C8×D43C2×C411yescharacteristic
39C2×C8×D43D411yescharacteristic
40#13063305—21no—
41#13063304—21no—
42#13063303—41no—
43#13063302—41no—
44#13063301—21no—
45#13063284—21no—
46#13063283—41no—
47#13063282—22no—
48#13063281—41no—
49C4⋊C4×D43—21no—
50C4⋊C4×D43—41no—
51C4⋊C4×D43—41no—
52C22⋊C4×D43—41no—
53C22⋊C4×D43—41no—
54C42×D43—22no—
55#13063265—21no—
56#13063264—41no—
57C16×D43—41no—
58#13063257C2×C411yescharacteristic, complemented
59#13063256—21no—
60#13063250—21no—
61#13063249—21no—
62#13063248—21no—
63C2×Q16×C43C2×C411yescharacteristic, complemented
64C2×M16×C43C2311yescharacteristic
65C22⋊Q8×C43—21no—
66#117×C43—21no—
67M32×C43—21no—
68#106×C43C2×C411yescharacteristic, complemented
69#103×C43—21no—
70C23×D43D811yescharacteristic
71C2×Q8×C43—21no—
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43D811yescharacteristic
74Q8×D43—41no—
75Q8×D43—41no—
76Q8×D43—41no—
77Q8×D43—41no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—42no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43C22⋊C411yescharacteristic
86C2×C4×D43C22⋊C411yescharacteristic
87C2×C4×D43SD1611yescharacteristic
88C2×C4×D43SD1611yescharacteristic
89C2×Dic86—21no—
90C2×Dic86—41no—
91Q16×C43—41no—
92M16×C43—41no—
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—22no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103#10621885—42no—
104(C2×D43)⋊C4—42no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107C4⋊Dic43—21no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110Dic43⋊C4—42no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—22no—
115C4×Dic43—42no—
116#10621877—41no—
117C2×C43⋊C8C22⋊C411yescharacteristic
118C2×C43⋊C8C22⋊C411yescharacteristic
119Dic172—41no—
120#10621872—41no—
121#10621872—41no—
122C8×D43—21no—
123C8×D43—21no—
124C8×D43—21no—
125C8×D43—21no—
126C16×C43—41no—
127C43⋊C16—41no—
128C23×C43C2×D811yescharacteristic
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—42no—
132C22×D43#10211yescharacteristic
133C22×D43#10211yescharacteristic
134Q8×C43—41no—
135Q8×C43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C2×SD1611yescharacteristic
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43#10211yescharacteristic
149C2×Dic43#10211yescharacteristic
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—82no—
157C4×D43—84no—
158C4×D43—81no—
159C4×D43—81no—
160C4×D43#9911yescharacteristic
161C4×D43#9911yescharacteristic
162C4×D43#10411yescharacteristic
163C4×D43#10411yescharacteristic
164Dic86—41no—
165Dic86—41no—
166Dic86—81no—
167Dic86—81no—
168C8×C43—21no—
169C8×C43—21no—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C2×#1340—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—41no—
175C22×C43C2×#10211yescharacteristic
176C2×D43—22no—
177C2×D43—21no—
178C2×D43—42no—
179C2×D43—41no—
180C2×D43—81no—
181C2×D43#32711yescharacteristic
182C2×D43#32711yescharacteristic
183C4×C43—21no—
184C4×C43—81no—
185C4×C43—82no—
186C4×C43—81no—
187C4×C43C2×#9911yescharacteristic
188C4×C43C2×#10411yescharacteristic
189Dic43—21no—
190Dic43—81no—
191Dic43—82no—
192Dic43—81no—
193Dic43#32711yescharacteristic
194Dic43#32711yescharacteristic
195C2×#470—431no—
196C2×#349—431no—
197C2×H(3,ℤ/4)—431no—
198#1340—431no—
199#1340—431no—
200#1340—431no—
201#1340D4311yescharacteristic, direct product factor
202C2×C43—21no—
203C2×C43—41no—
204C2×C43C2×#32711yescharacteristic
205D43—21no—
206D43—41no—
207D43#134012yesdirect product factor
208C22×Q16—431no—
209C22×M16—431no—
210C2×C22⋊Q8—861no—
211C2×#117—861no—
212C2×M32—861no—
213#470—431no—
214#470—431no—
215#470—431no—
216#470—861no—
217#470—861no—
218#470C2×D4311yescharacteristic
219C2×#106—431no—
220C2×#103—861no—
221#349—431no—
222#349—861no—
223#349C2×D4311yescharacteristic
224H(3,ℤ/4)—431no—
225H(3,ℤ/4)—861no—
226H(3,ℤ/4)C2×D4311yescharacteristic
227C43C2×#134011yescharacteristic, complemented, Sylow
228C22×Q8—861no—
229C23×C4—431no—
230C2×Q16—431no—
231C2×Q16—861no—
232C2×Q16—1721no—
233C2×Q16—1721no—
234C2×Q16C4×D4311yescharacteristic, complemented
235C2×M16—431no—
236C2×M16—431no—
237C2×M16—431no—
238C2×M16—1721no—
239C2×M16—1721no—
240C2×M16C22×D4311yescharacteristic
241C22×C8—431no—
242C22×C8—431no—
243C22⋊Q8—21no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C22⋊Q8—861no—
247C22⋊Q8—1721no—
248C22⋊Q8—1721no—
249#117—21no—
250#117—862no—
251#117—861no—
252#117—1721no—
253#117—1721no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—1721no—
256C2×C4⋊C4—1721no—
257C2×C22⋊C4—1721no—
258C2×C22⋊C4—1721no—
259C2×C42—862no—
260M32—21no—
261M32—861no—
262M32—1721no—
263C2×C16—1721no—
264#106—431no—
265#106—861no—
266#106C4×D4311yescharacteristic, complemented
267#103—21no—
268#103—861no—
269#103—861no—
270#103—861no—
271C24—431no—
272C2×Q8—21no—
273C2×Q8—861no—
274C2×Q8—1721no—
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—1721no—
289C22×C4—1721no—
290C22×C4—1722no—
291C22×C4D4×D4311yescharacteristic
292Q16—41no—
293Q16—1721no—
294Q16—1722no—
295M16—41no—
296M16—1721no—
297M16—1721no—
298M16—1721no—
299C2×C8—431no—
300C2×C8—431no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8C2×C4×D4311yescharacteristic
306C2×C8D4×D4311yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—861no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1722no—
316C4⋊C4—1721no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1722no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C42—22no—
325C42—862no—
326C42—1722no—
327C16—41no—
328C16—1721no—
329C23—431no—
330C23—431no—
331C23—861no—
332C23—861no—
333C23—1722no—
334C23D8×D4311yescharacteristic
335Q8—41no—
336Q8—41no—
337Q8—3441no—
338Q8—3441no—
339Q8—1721no—
340Q8—1721no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—431no—
347C2×C4—431no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—431no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—3441no—
361C2×C4—3441no—
362C2×C4—3442no—
363C2×C4—3444no—
364C2×C4—1722no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4C22⋊C4×D4311yescharacteristic
368C2×C4SD16×D4311yescharacteristic
369C8—21no—
370C8—21no—
371C8—861no—
372C8—861no—
373C22—21no—
374C22—41no—
375C22—431no—
376C22—431no—
377C22—862no—
378C22—861no—
379C22—3441no—
380C22—1721no—
381C22—1722no—
382C22#102×D4311yescharacteristic
383C4—21no—
384C4—81no—
385C4—82no—
386C4—81no—
387C4—431no—
388C4—431no—
389C4—861no—
390C4—3441no—
391C4—3442no—
392C4—3441no—
393C4#99×D4311yescharacteristic
394C4#104×D4311yescharacteristic
395C2—21no—
396C2—41no—
397C2—432no—
398C2—861no—
399C2—1721no—
400C2#327×D4311yescharacteristic
subgroupG/H
centerC2#327×D43
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1340C2
socleC2×C43C2×#327
prime radicalC23×D43D8
cosocleC2×M16×C43C23
hypercenter#1340D43
hypocenterC43C2×#1340
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1340

Complements

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

NH ≅ G/Ntype
4. #19132584C2semidirect
5. #19132583C2semidirect
6. #19132582C2semidirect
7. C43×#1340C2semidirect
8. C2×Q16×D43C4semidirect
13. #14583158C4semidirect
17. #14583154C4semidirect
18. #106×D43C4semidirect
29. C2×Dic172C2×C4semidirect
58. #13063257C2×C4semidirect
63. C2×Q16×C43C2×C4semidirect
68. #106×C43C2×C4semidirect
201. #1340D43direct (N × H)
207. D43#1340direct (N × H)
227. C43C2×#1340semidirect
234. C2×Q16C4×D43semidirect
266. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
#470×D432
#349×D432
H(3,ℤ/4)×D432
#191325842
#191325832
#191325822
C43×#13402
C2×#134043