Finite Group Databasebeta

← D43×#2608 #25268024

Subgroups — D43×#2608 #25268024

Order 11008.

2270 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140265C211yesmaximal, characteristic, complemented
2#19140264C214yesmaximal, complemented
3#19140263C214yesmaximal, complemented
4#19140262C212yesmaximal, complemented
5#19140261C214yesmaximal, complemented
6#396×D43C214yesmaximal
7#389×D43C214yesmaximal, complemented
8#387×D43C214yesmaximal, complemented
9#381×D43C211yesmaximal, characteristic
10C4×C22⋊C4×D43C212yesmaximal
11C43×#2608C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×C4⋊C4×D43C2214yes—
14C2×C4⋊C4×D43C2214yes—
15C2×C4⋊C4×D43C2214yes—
16C2×C22⋊C4×D43C2214yes—
17C2×C22⋊C4×D43C2212yes—
18C2×C42×D43C2212yes—
19C2×C42×D43C2212yes—
20#14582823C2214yes—
21#14582822C2214yes—
22#14582822C2214yes—
23#14582822C2214yes—
24#14582821C2214yes—
25#14582821C2214yes—
26#14582821C2214yes—
27#14582798C2214yescomplemented
28#14582797C2214yescomplemented
29#14582796C2214yescomplemented
30#14582796C2214yescomplemented
31#14582795C2214yescomplemented
32#14582794C2214yescomplemented
33#14582794C2214yescomplemented
34#14582786C2214yescomplemented
35#14582785C2214yescomplemented
36#14582784C2214yescomplemented
37#14582783C2214yescomplemented
38#14582782C2214yescomplemented
39#14582781C2214yescomplemented
40#14582780C2214yescomplemented
41#14582762C2211yescharacteristic
42#14582761C2214yes—
43#14582760C2212yes—
44C22⋊C4×Dic43C2214yes—
45C4×(C2×D43)⋊C4C2212yes—
46C4×(C2×D43)⋊C4C2212yes—
47C4×C22⋊Dic43C2212yes—
48#14582746C2214yes—
49#95×D43C2214yes—
50#95×D43C2214yes—
51#95×D43C2214yes—
52C43×#396C2214yes—
53C43×#389C2214yescomplemented
54C43×#387C2214yescomplemented
55C43×#381C2211yescharacteristic
56C4×C22⋊C4×C43C2212yes—
57C24×D43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C22×C4×D43—44no—
60C22×C4×D43Q818yes—
61C22×C4×D43C2314yes—
62C22×C4×D43C2314yes—
63C22×C4×D43C2312yes—
64C22×C4×D43C2314yes—
65C22×C4×D43C2312yes—
66C2×C4⋊Dic43C2314yes—
67C2×C4⋊Dic43C2314yes—
68C2×C4⋊Dic43C2314yes—
69C2×Dic43⋊C4C2314yes—
70C2×Dic43⋊C4C2314yes—
71C2×Dic43⋊C4C2314yes—
72C2×Dic43⋊C4C2314yes—
73C2×Dic43⋊C4C2314yes—
74C2×Dic43⋊C4C2314yes—
75C4⋊C4×D43—216no—
76C4⋊C4×D43—216no—
77C4⋊C4×D43—48no—
78C2×C22⋊Dic43C2314yes—
79C2×C22⋊Dic43C2312yes—
80C2×(C2×D43)⋊C4C2314yes—
81C2×(C2×D43)⋊C4C2314yes—
82C2×(C2×D43)⋊C4C2314yes—
83C22⋊C4×D43—216no—
84C22⋊C4×D43—44no—
85C2×C4×Dic43C2314yes—
86C2×C4×Dic43C2312yes—
87C2×C4×Dic43C2314yes—
88C2×C4×Dic43C2312yes—
89C42×D43—44no—
90C42×D43—44no—
91C43⋊#95C2314yes—
92C43⋊#95C2314yes—
93C43⋊#95C2314yes—
94C43⋊#95C2314yes—
95C43⋊#95C2314yes—
96C43⋊#95C2314yes—
97C43⋊#95C2314yes—
98C43⋊#95C2314yes—
99C43⋊#95C2314yes—
100C23×C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2314yes—
102C2×C4⋊C4×C43C2314yes—
103C2×C4⋊C4×C43C2314yes—
104C2×C22⋊C4×C43C2314yes—
105C2×C22⋊C4×C43C2312yes—
106C2×C42×C43C2312yes—
107C2×C42×C43C2312yes—
108#95×C43C2314yes—
109#95×C43C2314yes—
110#95×C43C2314yes—
111C24×C43C2411yescharacteristic
112C23×D43—28no—
113C23×D43—24no—
114C23×D43C2×Q814yes—
115C23×D43C2411yescharacteristic
116C23×D43C2411yescharacteristic
117C22×C4×C43—42no—
118C22×C4×C43C2×Q814yes—
119C22×C4×C43C2414yes—
120C22×C4×C43C2414yes—
121C22×C4×C43C2412yes—
122C22×C4×C43C2414yes—
123C22×Dic43—42no—
124C22×Dic43C2×Q814yes—
125C22×Dic43C2414yes—
126C22×Dic43C2414yes—
127C22×Dic43C2412yes—
128C22×Dic43C2414yes—
129C2×C4×D43—28no—
130C2×C4×D43—28no—
131C2×C4×D43—28no—
132C2×C4×D43—28no—
133C2×C4×D43—28no—
134C2×C4×D43—28no—
135C2×C4×D43—24no—
136C2×C4×D43—24no—
137C2×C4×D43—28no—
138C2×C4×D43—28no—
139C2×C4×D43—416no—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×C4×D43C2×Q818yes—
143C2×C4×D43C2×Q818yes—
144C2×C4×D43#41116yes—
145C4⋊C4×C43—28no—
146C4⋊C4×C43—28no—
147C4⋊C4×C43—44no—
148C22⋊C4×C43—28no—
149C22⋊C4×C43—42no—
150C42×C43—42no—
151C42×C43—42no—
152C22⋊Dic43—28no—
153C22⋊Dic43—42no—
154(C2×D43)⋊C4—28no—
155(C2×D43)⋊C4—28no—
156(C2×D43)⋊C4—44no—
157C4⋊Dic43—28no—
158C4⋊Dic43—28no—
159C4⋊Dic43—44no—
160Dic43⋊C4—28no—
161Dic43⋊C4—28no—
162Dic43⋊C4—28no—
163Dic43⋊C4—28no—
164Dic43⋊C4—44no—
165Dic43⋊C4—44no—
166C4×Dic43—42no—
167C4×Dic43—44no—
168C4×Dic43—44no—
169C4×Dic43—42no—
170C23×C43—24no—
171C23×C43—22no—
172C23×C43C22×Q812yes—
173C23×C43C2511yescharacteristic
174C22×D43—24no—
175C22×D43—22no—
176C22×D43—216no—
177C22×D43—28no—
178C22×D43—416no—
179C22×D43C22×Q812yes—
180C22×D43C22×Q812yes—
181C22×D43C2×#4118yes—
182C22×D43H(5,𝔽2)14yes—
183C2×C4×C43—24no—
184C2×C4×C43—24no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—24no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—24no—
192C2×C4×C43—24no—
193C2×C4×C43—44no—
194C2×C4×C43C22×Q814yes—
195C2×C4×C43C2×#4118yes—
196C2×Dic43—24no—
197C2×Dic43—24no—
198C2×Dic43—22no—
199C2×Dic43—22no—
200C2×Dic43—24no—
201C2×Dic43—24no—
202C2×Dic43—24no—
203C2×Dic43—24no—
204C2×Dic43—24no—
205C2×Dic43—24no—
206C2×Dic43—44no—
207C2×Dic43C22×Q814yes—
208C2×Dic43C2×#4118yes—
209C4×D43—216no—
210C4×D43—232no—
211C4×D43—48no—
212C4×D43—416no—
213C4×D43—416no—
214C2×#2608—431nomaximal, Sylow
215C22×C43—24no—
216C22×C43—22no—
217C22×C43—44no—
218C22×C43C23×Q811yescharacteristic
219C22×C43C22×#4114yes—
220C22×C43C2×H(5,𝔽2)12yes—
221C2×D43—24no—
222C2×D43—22no—
223C2×D43—44no—
224C2×D43—416no—
225C2×D43#53318yes—
226C2×D43#54314yes—
227C2×D43#553116yes—
228C4×C43—24no—
229C4×C43—28no—
230C4×C43—44no—
231C4×C43—44no—
232Dic43—24no—
233Dic43—28no—
234Dic43—44no—
235Dic43—44no—
236#2608—434no—
237#2608—434no—
238#2608—434no—
239#2608—431no—
240#2608—432no—
241#2608D4311yescharacteristic, direct product factor
242C2×#396—434no—
243C2×#389—434no—
244C2×#387—434no—
245C2×#381—431no—
246C2×C4×C22⋊C4—432no—
247C2×C43—42no—
248C2×C43C2×#53312yes—
249C2×C43C2×#54311yescharacteristic
250C2×C43C2×#55314yes—
251D43—42no—
252D43#260818yesdirect product factor
253C24×C4—431no—
254C22×C4⋊C4—434no—
255C22×C4⋊C4—434no—
256C22×C4⋊C4—434no—
257C22×C22⋊C4—434no—
258C22×C22⋊C4—432no—
259C22×C42—432no—
260C22×C42—432no—
261#396—434no—
262#396—434no—
263#396—434no—
264#396—434no—
265#396—434no—
266#396—434no—
267#396—434no—
268#396C2×D4314yes—
269#389—434no—
270#389—434no—
271#389—434no—
272#389—434no—
273#389—434no—
274#389—434no—
275#389—434no—
276#389C2×D4314yescomplemented
277#387—434no—
278#387—434no—
279#387—434no—
280#387—434no—
281#387—434no—
282#387—434no—
283#387—434no—
284#387C2×D4314yescomplemented
285#381—431no—
286#381—432no—
287#381—434no—
288#381C2×D4311yescharacteristic
289C4×C22⋊C4—432no—
290C4×C22⋊C4—434no—
291C4×C22⋊C4—432no—
292C4×C22⋊C4—432no—
293C4×C22⋊C4—434no—
294C4×C22⋊C4C2×D4312yes—
295C2×#95—434no—
296C2×#95—434no—
297C2×#95—434no—
298C43C2×#260811yescharacteristic, complemented, Sylow
299C25—431no—
300C23×C4—431no—
301C23×C4—434no—
302C23×C4—432no—
303C23×C4—438no—
304C23×C4—432no—
305C23×C4—434no—
306C23×C4—434no—
307C23×C4—1724no—
308C23×C4C22×D4311yescharacteristic
309C2×C4⋊C4—434no—
310C2×C4⋊C4—434no—
311C2×C4⋊C4—434no—
312C2×C4⋊C4—434no—
313C2×C4⋊C4—434no—
314C2×C4⋊C4—434no—
315C2×C4⋊C4—434no—
316C2×C4⋊C4—434no—
317C2×C4⋊C4—434no—
318C2×C4⋊C4—8616no—
319C2×C4⋊C4—8616no—
320C2×C4⋊C4—1728no—
321C2×C4⋊C4C22×D4314yes—
322C2×C4⋊C4C22×D4314yes—
323C2×C4⋊C4C22×D4314yes—
324C2×C22⋊C4—434no—
325C2×C22⋊C4—434no—
326C2×C22⋊C4—434no—
327C2×C22⋊C4—432no—
328C2×C22⋊C4—434no—
329C2×C22⋊C4—8616no—
330C2×C22⋊C4—1724no—
331C2×C22⋊C4C22×D4314yes—
332C2×C22⋊C4C22×D4312yes—
333C2×C42—434no—
334C2×C42—432no—
335C2×C42—434no—
336C2×C42—432no—
337C2×C42—1724no—
338C2×C42—1724no—
339C2×C42C22×D4312yes—
340C2×C42C22×D4312yes—
341#95—434no—
342#95—434no—
343#95—434no—
344#95—434no—
345#95—434no—
346#95—434no—
347#95—434no—
348#95—434no—
349#95—434no—
350#95C22×D4314yes—
351#95C22×D4314yes—
352#95C22×D4314yes—
353C24—431no—
354C24—434no—
355C24—431no—
356C24—868no—
357C24—864no—
358C24C23×D4311yescharacteristic
359C22×C4—42no—
360C22×C4—432no—
361C22×C4—434no—
362C22×C4—434no—
363C22×C4—438no—
364C22×C4—4316no—
365C22×C4—438no—
366C22×C4—434no—
367C22×C4—434no—
368C22×C4—868no—
369C22×C4—864no—
370C22×C4—864no—
371C22×C4—868no—
372C22×C4—868no—
373C22×C4—868no—
374C22×C4—868no—
375C22×C4—868no—
376C22×C4—868no—
377C22×C4—868no—
378C22×C4—1722no—
379C22×C4—1722no—
380C22×C4—17216no—
381C22×C4—1722no—
382C22×C4Q8×D4314yes—
383C22×C4C23×D4314yes—
384C22×C4C23×D4314yes—
385C22×C4C23×D4312yes—
386C22×C4C23×D4314yes—
387C4⋊C4—28no—
388C4⋊C4—28no—
389C4⋊C4—44no—
390C4⋊C4—868no—
391C4⋊C4—868no—
392C4⋊C4—868no—
393C4⋊C4—868no—
394C4⋊C4—868no—
395C4⋊C4—868no—
396C4⋊C4—1724no—
397C4⋊C4—1724no—
398C4⋊C4—1724no—
399C22⋊C4—28no—
400C22⋊C4—42no—
401C22⋊C4—868no—
402C22⋊C4—868no—
403C22⋊C4—868no—
404C22⋊C4—1724no—
405C22⋊C4—1722no—
406C42—42no—
407C42—42no—
408C42—1724no—
409C42—1722no—
410C42—1722no—
411C42—1724no—
412C23—24no—
413C23—22no—
414C23—432no—
415C23—438no—
416C23—434no—
417C23—432no—
418C23—868no—
419C23—8616no—
420C23—864no—
421C23—862no—
422C23—17216no—
423C23C2×Q8×D4312yes—
424C23C24×D4311yescharacteristic
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—434no—
437C2×C4—438no—
438C2×C4—8616no—
439C2×C4—8632no—
440C2×C4—864no—
441C2×C4—864no—
442C2×C4—862no—
443C2×C4—862no—
444C2×C4—864no—
445C2×C4—864no—
446C2×C4—864no—
447C2×C4—864no—
448C2×C4—864no—
449C2×C4—864no—
450C2×C4—1728no—
451C2×C4—17216no—
452C2×C4—17216no—
453C2×C4—1724no—
454C2×C4C2×Q8×D4314yes—
455C2×C4#41×D4318yes—
456C22—24no—
457C22—22no—
458C22—44no—
459C22—4316no—
460C22—438no—
461C22—434no—
462C22—864no—
463C22—862no—
464C22—17216no—
465C22—1724no—
466C22C22×Q8×D4311yescharacteristic
467C22C2×#41×D4314yes—
468C22H(5,𝔽2)×D4312yes—
469C4—28no—
470C4—24no—
471C4—44no—
472C4—44no—
473C4—868no—
474C4—864no—
475C4—1724no—
476C4—1724no—
477C2—42no—
478C2—438no—
479C2—1722no—
480C2#533×D4312yes—
481C2#543×D4311yescharacteristic
482C2#553×D4314yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2608C2
prime radicalC24×D43C23
hypercenter#2608D43
hypocenterC43C2×#2608
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2608

Complements

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

NH ≅ G/Ntype
1. #19140265C2semidirect
2. #19140264C2semidirect
3. #19140263C2semidirect
4. #19140262C2semidirect
5. #19140261C2semidirect
7. #389×D43C2semidirect
8. #387×D43C2semidirect
11. C43×#2608C2semidirect
27. #14582798C22semidirect
28. #14582797C22semidirect
29. #14582796C22semidirect
30. #14582796C22semidirect
31. #14582795C22semidirect
32. #14582794C22semidirect
33. #14582794C22semidirect
34. #14582786C22semidirect
35. #14582785C22semidirect
36. #14582784C22semidirect
37. #14582783C22semidirect
38. #14582782C22semidirect
39. #14582781C22semidirect
40. #14582780C22semidirect
53. C43×#389C22semidirect
54. C43×#387C22semidirect
241. #2608D43direct (N × H)
252. D43#2608direct (N × H)
276. #389C2×D43semidirect
284. #387C2×D43semidirect
298. C43C2×#2608semidirect

Maximal subgroups

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

subgroupindex
#191402652
#191402642
#191402632
#191402622
#191402612
#396×D432
#389×D432
#387×D432
#381×D432
C4×C22⋊C4×D432
C43×#26082
C2×#260843