Finite Group Databasebeta

← D43×#2298 #25254989

Subgroups — D43×#2298 #25254989

Order 11008.

2902 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#19137093C211yesmaximal, characteristic, complemented
3#19137092C211yesmaximal, characteristic, complemented
4#19137091C212yesmaximal, complemented
5#19137090C211yesmaximal, characteristic, complemented
6#19137089C214yesmaximal, complemented
7#19137088C212yesmaximal, complemented
8#19137087C214yesmaximal, complemented
9#388×D43C214yesmaximal
10#387×D43C214yesmaximal, complemented
11C4×C4⋊C4×D43C212yesmaximal, complemented
12C4×C22⋊C4×D43C212yesmaximal
13#376×D43C211yesmaximal, characteristic, complemented
14C43×D43C211yesmaximal, characteristic, complemented
15C43×#2298C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063283C2212yes—
19C2×#13063282C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063281C2212yes—
22#117×D43C4116yescomplemented
23C2×C4⋊C4×D43C2214yes—
24C2×C4⋊C4×D43C2212yes—
25C2×C22⋊C4×D43C2214yes—
26C2×C22⋊C4×D43C2212yes—
27C2×C42×D43C2212yes—
28C2×C42×D43C2214yes—
29C2×C42×D43C2212yes—
30C2×C42×D43C2211yescharacteristic
31C2×C42×D43C2211yescharacteristic
32#14582793C2214yes—
33#14582792C2214yes—
34#14582791C2214yes—
35#14582790C2214yes—
36#14582789C2214yes—
37#14582788C2214yes—
38#14582787C2214yes—
39#14582786C2214yescomplemented
40#14582785C2214yescomplemented
41#14582784C2214yescomplemented
42#14582783C2214yescomplemented
43#14582782C2214yescomplemented
44#14582781C2214yescomplemented
45#14582780C2214yescomplemented
46C4⋊C4×Dic43C2214yescomplemented
47C4×Dic43⋊C4C2212yescomplemented
48C4×Dic43⋊C4C2212yescomplemented
49C4×C4⋊Dic43C2212yescomplemented
50#14582750C2214yescomplemented
51C22⋊C4×Dic43C2214yes—
52C4×(C2×D43)⋊C4C2212yes—
53C4×(C2×D43)⋊C4C2212yes—
54C4×C22⋊Dic43C2212yes—
55#14582746C2214yes—
56#14582745C2212yescomplemented
57#14582745C2211yescharacteristic, complemented
58#14582744C2214yescomplemented
59#95×D43C2214yes—
60#95×D43C2214yes—
61#95×D43C2214yes—
62C42×Dic43C2214yescomplemented
63C42×Dic43C2212yescomplemented
64C42×Dic43C2211yescharacteristic, complemented
65C2×#117×C43C2211yescharacteristic
66C43×#388C2214yes—
67C43×#387C2214yescomplemented
68C4×C4⋊C4×C43C2212yescomplemented
69C4×C22⋊C4×C43C2212yes—
70C43×#376C2211yescharacteristic, complemented
71C43×C43C2211yescharacteristic, complemented
72C24×D43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C22×C4×D43—28no—
75C22×C4×D43C2×C418yes—
76C22×C4×D43C2314yes—
77C22×C4×D43C2312yes—
78C22×C4×D43C2312yes—
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2311yescharacteristic
82C22×C4×D43C2314yes—
83C22×C4×D43C2311yescharacteristic
84#13063284C2×C418yescomplemented
85#13063283C2×C4116yescomplemented
86#13063282C2×C418yescomplemented
87#13063282C2×C418yescomplemented
88#13063281C2×C4116yescomplemented
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2312yes—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2312yes—
94C2×Dic43⋊C4C2312yes—
95C4⋊C4×D43—216no—
96C4⋊C4×D43C2×C4116yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2312yes—
99C2×(C2×D43)⋊C4C2314yes—
100C2×(C2×D43)⋊C4C2314yes—
101C2×(C2×D43)⋊C4C2312yes—
102C2×(C2×D43)⋊C4C2312yes—
103C22⋊C4×D43—216no—
104C22⋊C4×D43C2×C4116yes—
105C2×C4×Dic43C2314yes—
106C2×C4×Dic43C2314yes—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C2×C4×Dic43C2312yes—
110C2×C4×Dic43C2314yes—
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2312yes—
114C2×C4×Dic43C2311yescharacteristic
115C2×C4×Dic43C2311yescharacteristic
116C42×D43—216no—
117C42×D43—28no—
118C42×D43—28no—
119C42×D43C2×C418yes—
120C42×D43C2×C418yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C23×C4×C43C2311yescharacteristic
131#117×C43C2×C418yescomplemented
132C2×C4⋊C4×C43C2314yes—
133C2×C4⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2314yes—
135C2×C22⋊C4×C43C2312yes—
136C2×C42×C43C2314yes—
137C2×C42×C43C2312yes—
138C2×C42×C43C2312yes—
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43C2411yescharacteristic
145C23×D43—28no—
146C23×D43—24no—
147C23×D43C22×C414yes—
148C23×D43C2411yescharacteristic
149C23×D43C2411yescharacteristic
150C22×C4×C43—24no—
151C22×C4×C43C22×C414yes—
152C22×C4×C43C2414yes—
153C22×C4×C43C2411yescharacteristic
154C22×C4×C43C2412yes—
155C22×C4×C43C2412yes—
156C22×C4×C43C2414yes—
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—24no—
159C22×Dic43C22×C414yes—
160C22×Dic43C2414yes—
161C22×Dic43C2411yescharacteristic
162C22×Dic43C2412yes—
163C22×Dic43C2412yes—
164C22×Dic43C2414yes—
165C22×Dic43C2411yescharacteristic
166C2×C4×D43—24no—
167C2×C4×D43—24no—
168C2×C4×D43—232no—
169C2×C4×D43—28no—
170C2×C4×D43—28no—
171C2×C4×D43—28no—
172C2×C4×D43—28no—
173C2×C4×D43—24no—
174C2×C4×D43—28no—
175C2×C4×D43—28no—
176C2×C4×D43—28no—
177C2×C4×D43C22×C418yes—
178C2×C4×D43C22×C418yes—
179C2×C4×D43C22×C414yes—
180C2×C4×D43C22×C414yes—
181C2×C4×D43C22×C414yes—
182C2×C4×D43C22×C414yes—
183C2×C4×D43#41116yes—
184C2×C4×D43#4118yes—
185C4⋊C4×C43—28no—
186C4⋊C4×C43C22×C418yes—
187C22⋊C4×C43—28no—
188C22⋊C4×C43C22×C418yes—
189C42×C43—28no—
190C42×C43—24no—
191C42×C43—24no—
192C42×C43C22×C414yes—
193C42×C43C22×C414yes—
194C22⋊Dic43—28no—
195C22⋊Dic43C22×C418yes—
196(C2×D43)⋊C4—28no—
197(C2×D43)⋊C4—28no—
198(C2×D43)⋊C4C22×C418yes—
199(C2×D43)⋊C4C22×C418yes—
200C4⋊Dic43—28no—
201C4⋊Dic43C22×C418yes—
202Dic43⋊C4—28no—
203Dic43⋊C4—28no—
204Dic43⋊C4C22×C418yes—
205Dic43⋊C4C22×C418yes—
206C4×Dic43—28no—
207C4×Dic43—24no—
208C4×Dic43—24no—
209C4×Dic43—28no—
210C4×Dic43—28no—
211C4×Dic43—28no—
212C4×Dic43—28no—
213C4×Dic43C22×C418yes—
214C4×Dic43C22×C418yes—
215C4×Dic43C22×C414yes—
216C4×Dic43C22×C414yes—
217C23×C43—24no—
218C23×C43—22no—
219C23×C43C23×C412yes—
220C23×C43C2511yescharacteristic
221C22×D43—24no—
222C22×D43—22no—
223C22×D43—28no—
224C22×D43—216no—
225C22×D43—416no—
226C22×D43C23×C412yes—
227C22×D43C23×C412yes—
228C22×D43C2×#4114yes—
229C22×D43C2×#4118yes—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—22no—
235C2×C4×C43—28no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—24no—
239C2×C4×C43C23×C414yes—
240C2×C4×C43C23×C414yes—
241C2×C4×C43C23×C412yes—
242C2×C4×C43C23×C412yes—
243C2×C4×C43C2×#4118yes—
244C2×C4×C43C2×#4114yes—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—22no—
250C2×Dic43—28no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43C23×C414yes—
255C2×Dic43C23×C414yes—
256C2×Dic43C23×C412yes—
257C2×Dic43C23×C412yes—
258C2×Dic43C2×#4118yes—
259C2×Dic43C2×#4114yes—
260C4×D43—28no—
261C4×D43—216no—
262C4×D43—216no—
263C4×D43—232no—
264C4×D43—28no—
265C4×D43—28no—
266C4×D43—416no—
267C4×D43#117116yes—
268C2×#2298—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—24no—
271C22×C43—44no—
272C22×C43C24×C411yescharacteristic
273C22×C43C22×#4112yes—
274C22×C43C22×#4114yes—
275C2×D43—22no—
276C2×D43—24no—
277C2×D43—44no—
278C2×D43—416no—
279C2×D43C2×#11714yes—
280C2×D43C4×#4118yes—
281C2×D43#529116yes—
282C4×C43—22no—
283C4×C43—24no—
284C4×C43—24no—
285C4×C43—28no—
286C4×C43—44no—
287C4×C43C2×#11714yes—
288Dic43—22no—
289Dic43—24no—
290Dic43—24no—
291Dic43—28no—
292Dic43—44no—
293Dic43C2×#11714yes—
294C22×#117—431no—
295#2298—434no—
296#2298—434no—
297#2298—432no—
298#2298—432no—
299#2298—431no—
300#2298—431no—
301#2298—431no—
302#2298D4311yescharacteristic, direct product factor
303C2×#388—434no—
304C2×#387—434no—
305C2×C4×C4⋊C4—432no—
306C2×C4×C22⋊C4—432no—
307C2×#376—431no—
308C2×C43—431no—
309C2×C43—42no—
310C2×C43C22×#11711yescharacteristic
311C2×C43C2×C4×#4112yes—
312C2×C43C2×#52914yes—
313D43—42no—
314D43#229818yesdirect product factor
315C24×C4—431no—
316C2×#117—431no—
317C2×#117—4316no—
318C2×#117—432no—
319C2×#117—432no—
320C2×#117—431no—
321C2×#117—431no—
322C2×#117C2×D4311yescharacteristic
323C22×C4⋊C4—432no—
324C22×C4⋊C4—434no—
325C22×C22⋊C4—432no—
326C22×C22⋊C4—434no—
327C22×C42—431no—
328C22×C42—431no—
329C22×C42—432no—
330C22×C42—434no—
331C22×C42—432no—
332#388—434no—
333#388—434no—
334#388—434no—
335#388—434no—
336#388—434no—
337#388—434no—
338#388—434no—
339#388C2×D4314yes—
340#387—434no—
341#387—434no—
342#387—434no—
343#387—434no—
344#387—434no—
345#387—434no—
346#387—434no—
347#387C2×D4314yescomplemented
348C4×C4⋊C4—434no—
349C4×C4⋊C4—432no—
350C4×C4⋊C4—432no—
351C4×C4⋊C4—432no—
352C4×C4⋊C4—434no—
353C4×C4⋊C4C2×D4312yescomplemented
354C4×C22⋊C4—432no—
355C4×C22⋊C4—434no—
356C4×C22⋊C4—432no—
357C4×C22⋊C4—432no—
358C4×C22⋊C4—434no—
359C4×C22⋊C4C2×D4312yes—
360#376—432no—
361#376—431no—
362#376—434no—
363#376C2×D4311yescharacteristic, complemented
364C2×#95—434no—
365C2×#95—434no—
366C2×#95—434no—
367C43—434no—
368C43—432no—
369C43—431no—
370C43C2×D4311yescharacteristic, complemented
371C43C2×#229811yescharacteristic, complemented, Sylow
372C25—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—438no—
376C23×C4—432no—
377C23×C4—432no—
378C23×C4—434no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—434no—
383C23×C4—868no—
384C23×C4C22×D4311yescharacteristic
385#117—438no—
386#117—4316no—
387#117—4316no—
388#117—438no—
389#117—438no—
390#117C4×D4318yescomplemented
391C2×C4⋊C4—432no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—432no—
394C2×C4⋊C4—4316no—
395C2×C4⋊C4—434no—
396C2×C4⋊C4—434no—
397C2×C4⋊C4—434no—
398C2×C4⋊C4—8616no—
399C2×C4⋊C4C22×D4314yes—
400C2×C4⋊C4C22×D4312yes—
401C2×C22⋊C4—432no—
402C2×C22⋊C4—432no—
403C2×C22⋊C4—432no—
404C2×C22⋊C4—4316no—
405C2×C22⋊C4—434no—
406C2×C22⋊C4—434no—
407C2×C22⋊C4—434no—
408C2×C22⋊C4—8616no—
409C2×C22⋊C4C22×D4314yes—
410C2×C22⋊C4C22×D4312yes—
411C2×C42—432no—
412C2×C42—432no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—438no—
416C2×C42—438no—
417C2×C42—434no—
418C2×C42—434no—
419C2×C42—434no—
420C2×C42—434no—
421C2×C42—434no—
422C2×C42—432no—
423C2×C42—432no—
424C2×C42—868no—
425C2×C42—868no—
426C2×C42—8616no—
427C2×C42C22×D4314yes—
428C2×C42C22×D4312yes—
429C2×C42C22×D4312yes—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432#95—434no—
433#95—434no—
434#95—434no—
435#95—434no—
436#95—434no—
437#95—434no—
438#95—434no—
439#95—434no—
440#95—434no—
441#95C22×D4314yes—
442#95C22×D4314yes—
443#95C22×D4314yes—
444C24—431no—
445C24—434no—
446C24—431no—
447C24—868no—
448C24—864no—
449C24C23×D4311yescharacteristic
450C22×C4—24no—
451C22×C4—431no—
452C22×C4—434no—
453C22×C4—438no—
454C22×C4—434no—
455C22×C4—431no—
456C22×C4—432no—
457C22×C4—434no—
458C22×C4—432no—
459C22×C4—438no—
460C22×C4—438no—
461C22×C4—434no—
462C22×C4—434no—
463C22×C4—434no—
464C22×C4—4316no—
465C22×C4—434no—
466C22×C4—864no—
467C22×C4—8632no—
468C22×C4—868no—
469C22×C4—868no—
470C22×C4—868no—
471C22×C4—868no—
472C22×C4—864no—
473C22×C4—868no—
474C22×C4—868no—
475C22×C4—868no—
476C22×C4—864no—
477C22×C4—864no—
478C22×C4C2×C4×D4314yes—
479C22×C4C23×D4314yes—
480C22×C4C23×D4311yescharacteristic
481C22×C4C23×D4312yes—
482C22×C4C23×D4312yes—
483C22×C4C23×D4314yes—
484C22×C4C23×D4311yescharacteristic
485C4⋊C4—28no—
486C4⋊C4—438no—
487C4⋊C4—438no—
488C4⋊C4—438no—
489C4⋊C4—868no—
490C4⋊C4—868no—
491C4⋊C4—868no—
492C4⋊C4C2×C4×D4318yes—
493C22⋊C4—28no—
494C22⋊C4—438no—
495C22⋊C4—438no—
496C22⋊C4—438no—
497C22⋊C4—868no—
498C22⋊C4—868no—
499C22⋊C4—868no—
500C22⋊C4C2×C4×D4318yes—
501C42—28no—
502C42—24no—
503C42—24no—
504C42—438no—
505C42—438no—
506C42—434no—
507C42—434no—
508C42—868no—
509C42—868no—
510C42—868no—
511C42—868no—
512C42—868no—
513C42—864no—
514C42—864no—
515C42C2×C4×D4314yes—
516C42C2×C4×D4314yes—
517C23—24no—
518C23—22no—
519C23—432no—
520C23—434no—
521C23—438no—
522C23—432no—
523C23—868no—
524C23—8616no—
525C23—864no—
526C23—862no—
527C23—17216no—
528C23C22×C4×D4312yes—
529C23C24×D4311yescharacteristic
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—432no—
540C2×C4—434no—
541C2×C4—4316no—
542C2×C4—434no—
543C2×C4—434no—
544C2×C4—432no—
545C2×C4—438no—
546C2×C4—868no—
547C2×C4—868no—
548C2×C4—8632no—
549C2×C4—8616no—
550C2×C4—8616no—
551C2×C4—868no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—862no—
557C2×C4—868no—
558C2×C4—864no—
559C2×C4—864no—
560C2×C4—864no—
561C2×C4—17216no—
562C2×C4C22×C4×D4314yes—
563C2×C4C22×C4×D4314yes—
564C2×C4C22×C4×D4312yes—
565C2×C4C22×C4×D4312yes—
566C2×C4#41×D4318yes—
567C2×C4#41×D4314yes—
568C22—22no—
569C22—24no—
570C22—44no—
571C22—4316no—
572C22—434no—
573C22—438no—
574C22—862no—
575C22—864no—
576C22—17216no—
577C22—1724no—
578C22C23×C4×D4311yescharacteristic
579C22C2×#41×D4312yes—
580C22C2×#41×D4314yes—
581C4—28no—
582C4—22no—
583C4—24no—
584C4—24no—
585C4—44no—
586C4—434no—
587C4—868no—
588C4—862no—
589C4—864no—
590C4—864no—
591C4—1724no—
592C4#117×D4314yes—
593C2—42no—
594C2—438no—
595C2—1722no—
596C2C2×#117×D4311yescharacteristic
597C2C4×#41×D4312yes—
598C2#529×D4314yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC43×#2298C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenter#2298D43
hypocenterC43C2×#2298
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #19137093C2semidirect
3. #19137092C2semidirect
4. #19137091C2semidirect
5. #19137090C2semidirect
6. #19137089C2semidirect
7. #19137088C2semidirect
8. #19137087C2semidirect
10. #387×D43C2semidirect
11. C4×C4⋊C4×D43C2semidirect
13. #376×D43C2semidirect
14. C43×D43C2semidirect
15. C43×#2298C2semidirect
22. #117×D43C4semidirect
39. #14582786C22semidirect
40. #14582785C22semidirect
41. #14582784C22semidirect
42. #14582783C22semidirect
43. #14582782C22semidirect
44. #14582781C22semidirect
45. #14582780C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. C4×Dic43⋊C4C22semidirect
48. C4×Dic43⋊C4C22semidirect
49. C4×C4⋊Dic43C22semidirect
50. #14582750C22semidirect
56. #14582745C22semidirect
57. #14582745C22semidirect
58. #14582744C22semidirect
62. C42×Dic43C22semidirect
63. C42×Dic43C22semidirect
64. C42×Dic43C22semidirect
67. C43×#387C22semidirect
68. C4×C4⋊C4×C43C22semidirect
70. C43×#376C22semidirect
71. C43×C43C22semidirect
84. #13063284C2×C4semidirect
85. #13063283C2×C4semidirect
86. #13063282C2×C4semidirect
87. #13063282C2×C4semidirect
88. #13063281C2×C4semidirect
131. #117×C43C2×C4semidirect
302. #2298D43direct (N × H)
314. D43#2298direct (N × H)
347. #387C2×D43semidirect
353. C4×C4⋊C4C2×D43semidirect
363. #376C2×D43semidirect
370. C43C2×D43semidirect
371. C43C2×#2298semidirect
390. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
#191370932
#191370922
#191370912
#191370902
#191370892
#191370882
#191370872
#388×D432
#387×D432
C4×C4⋊C4×D432
C4×C22⋊C4×D432
#376×D432
C43×D432
C43×#22982
C2×#229843