Finite Group Databasebeta

← D43×#3195 #25967203

Subgroups — D43×#3195 #25967203

Order 11008.

2322 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C212yesmaximal
2#19145419C211yesmaximal, characteristic, complemented
3#19145418C214yesmaximal, complemented
4#19145417C214yesmaximal, complemented
5#19145416C212yesmaximal, complemented
6#19145415C214yesmaximal, complemented
7#483×D43C214yesmaximal, complemented
8#470×D43C214yesmaximal, complemented
9#451×D43C214yesmaximal, complemented
10#407×D43C211yesmaximal, characteristic
11C43×#3195C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2212yes—
13C23×C4×D43C2211yescharacteristic
14C2×Q16×D43C2214yescomplemented
15C2×M16×D43C2212yes—
16C2×#13063305C2212yes—
17C2×#13063304C2212yes—
18C2×#13063303—22no—
19C2×#13063302—22no—
20C2×#13063301C2212yes—
21C22⋊Q8×D43—22no—
22C22⋊Q8×D43—22no—
23C22⋊Q8×D43—22no—
24C22⋊Q8×D43—22no—
25C22⋊Q8×D43C2214yes—
26C22⋊Q8×D43C2214yes—
27C22⋊Q8×D43C2214yes—
28C22⋊Q8×D43C2214yes—
29C2×C4⋊C4×D43—22no—
30C2×C4⋊C4×D43C2212yes—
31C2×C22⋊C4×D43—22no—
32#14583231C2218yescomplemented
33#14583230C2214yescomplemented
34#14583229C2214yescomplemented
35#14583228C2218yescomplemented
36#14583227C2214yescomplemented
37#14583158C2214yescomplemented
38#14583157C2214yescomplemented
39#14583156C2218yescomplemented
40#14583155C2218yescomplemented
41#14583154C2214yescomplemented
42#14583057C2214yescomplemented
43#14583056C2218yescomplemented
44#14583055C2214yescomplemented
45#14583054C2214yescomplemented
46#14583053C2218yescomplemented
47#106×D43C2214yescomplemented
48#103×D43C2218yescomplemented
49#14582863C2211yescharacteristic
50#14582862C2212yes—
51#14582861C2214yes—
52C22⋊C8×D43C2214yes—
53C2×C22⋊Q8×C43C2212yes—
54C43×#483C2214yescomplemented
55C43×#470C2214yescomplemented
56C43×#451C2214yescomplemented
57C43×#407C2211yescharacteristic
58C24×D43D411yescharacteristic
59C22×Dic86—22no—
60C22×Dic86C2312yes—
61C2×Q8×D43—22no—
62C2×Q8×D43—22no—
63C2×Q8×D43—48no—
64C2×Q8×D43C2314yes—
65C2×Q8×D43C2314yes—
66C23×Dic43D411yescharacteristic
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—44no—
70C22×C4×D43D412yes—
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D411yescharacteristic
73C22×C4×D43D412yes—
74C22×C4×D43C2312yes—
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2312yes—
77C22×C4×D43C2311yescharacteristic
78C2×Dic172C2314yescomplemented
79C2×#10621885C2318yescomplemented
80Q16×D43—48no—
81C2×#10621877C2312yes—
82C2×#10621872C2314yes—
83M16×D43—44no—
84C2×C8×D43C2314yes—
85#13063305—22no—
86#13063305—22no—
87#13063305C2314yes—
88#13063305C2314yes—
89#13063304—22no—
90#13063304—22no—
91#13063304C2314yes—
92#13063304C2314yes—
93#13063303—24no—
94#13063303—24no—
95#13063303—24no—
96#13063303—24no—
97#13063302—24no—
98#13063302—24no—
99#13063302—24no—
100#13063302—24no—
101#13063301—22no—
102#13063301—22no—
103#13063301C2314yes—
104#13063301C2314yes—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43C2312yes—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C4⋊C4×D43—24no—
111C4⋊C4×D43—24no—
112C4⋊C4×D43—24no—
113C4⋊C4×D43—24no—
114C4⋊C4×D43—22no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43C2314yes—
117C4⋊C4×D43C2314yes—
118C2×C22⋊Dic43—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C22⋊C4×D43—24no—
122C22⋊C4×D43—24no—
123C22⋊C4×D43—24no—
124C22⋊C4×D43—24no—
125#13063257C2314yescomplemented
126#13063256C2318yescomplemented
127#13063250C2318yescomplemented
128#13063249C2318yescomplemented
129#13063248C2318yescomplemented
130C22⋊(C43⋊C8)C2314yes—
131(C2×D43)⋊C8C2318yes—
132C22×Q8×C43C2312yes—
133C23×C4×C43C2311yescharacteristic
134C2×Q16×C43C2314yescomplemented
135C2×M16×C43C2312yes—
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43C2314yes—
139C22⋊Q8×C43C2314yes—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43C2312yes—
142C2×C22⋊C4×C43—22no—
143#106×C43C2314yescomplemented
144#103×C43C2318yescomplemented
145C22⋊C8×C43C2314yes—
146C24×C43C2×D411yescharacteristic
147C23×D43—28no—
148C23×D43—42no—
149C23×D43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C23×D43C2×D412yes—
152C23×D43C2×D412yes—
153C2×Q8×C43—22no—
154C2×Q8×C43—44no—
155C2×Q8×C43C2414yes—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—42no—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2412yes—
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—42no—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D411yescharacteristic
170Q8×D43—216no—
171Q8×D43—48no—
172Q8×D43—48no—
173Q8×D43—48no—
174C2×C4×D43—24no—
175C2×C4×D43—28no—
176C2×C4×D43—24no—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—44no—
181C2×C4×D43—42no—
182C2×C4×D43—48no—
183C2×C4×D43—44no—
184C2×C4×D43—42no—
185C2×C4×D43—44no—
186C2×C4×D43—42no—
187C2×C4×D43—48no—
188C2×C4×D43C2×D411yescharacteristic
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191C2×C4×D43C2×D411yescharacteristic
192C2×C4×D43C2×D412yes—
193C2×C4×D43C2×D412yes—
194C2×C4×D43C2×D412yes—
195C2×C4×D43C2412yes—
196C2×C4×D43C2411yescharacteristic
197C2×C4×D43C2411yescharacteristic
198C2×Dic86—22no—
199C2×Dic86—24no—
200C2×Dic86—24no—
201C2×Dic86—44no—
202C2×Dic86—48no—
203C2×Dic86C2414yes—
204Q16×C43—44no—
205M16×C43—42no—
206C2×C8×C43C2414yes—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43C2414yes—
211C22⋊C4×C43—24no—
212C22⋊C4×C43—24no—
213C22⋊Dic43—24no—
214C22⋊Dic43—24no—
215#10621885—48no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219(C2×D43)⋊C4—24no—
220C4⋊Dic43—22no—
221C4⋊Dic43—24no—
222C4⋊Dic43—24no—
223C4⋊Dic43C2414yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230#10621877—42no—
231C2×C43⋊C8C2414yes—
232Dic172—44no—
233#10621872—44no—
234C8×D43—28no—
235C23×C43—24no—
236C23×C43—41no—
237C23×C43C22×D411yescharacteristic
238C23×C43C22×D412yes—
239C22×D43—24no—
240C22×D43—24no—
241C22×D43—24no—
242C22×D43—22no—
243C22×D43—24no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—41no—
247C22×D43—42no—
248C22×D43—416no—
249C22×D43#13718yes—
250C22×D43C22×D411yescharacteristic
251C22×D43C22×D412yes—
252C22×D43C22×D411yescharacteristic
253Q8×C43—28no—
254Q8×C43—44no—
255C2×C4×C43—22no—
256C2×C4×C43—24no—
257C2×C4×C43—24no—
258C2×C4×C43—24no—
259C2×C4×C43—41no—
260C2×C4×C43—42no—
261C2×C4×C43—44no—
262C2×C4×C43—44no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D412yes—
265C2×C4×C43C2511yescharacteristic
266C2×Dic43—24no—
267C2×Dic43—22no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—44no—
273C2×Dic43—44no—
274C2×Dic43C22×D411yescharacteristic
275C2×Dic43C22×D412yes—
276C2×Dic43C22×D411yescharacteristic
277C4×D43—22no—
278C4×D43—24no—
279C4×D43—22no—
280C4×D43—24no—
281C4×D43—22no—
282C4×D43—24no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—48no—
287C4×D43—48no—
288C4×D43—48no—
289C4×D43—48no—
290C4×D43H(5,𝔽2)14yes—
291Dic86—28no—
292Dic86—48no—
293Dic86—44no—
294Dic86—48no—
295C8×C43—24no—
296C43⋊C8—24no—
297C2×#3195—431nomaximal, Sylow
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—21no—
301C22×C43—22no—
302C22×C43—44no—
303C22×C43C2×#13714yes—
304C22×C43C23×D411yescharacteristic
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—216no—
308C2×D43—21no—
309C2×D43—22no—
310C2×D43—44no—
311C2×D43—48no—
312C2×D43—44no—
313C2×D43#53412yes—
314C2×D43C2×#13714yes—
315C2×D43C2×#13714yes—
316C4×C43—22no—
317C4×C43—21no—
318C4×C43—44no—
319C4×C43—44no—
320C4×C43C2×H(5,𝔽2)12yes—
321Dic43—22no—
322Dic43—21no—
323Dic43—44no—
324Dic43—44no—
325Dic43#53412yes—
326C22×C22⋊Q8—432no—
327#3195—434no—
328#3195—434no—
329#3195—434no—
330#3195—431no—
331#3195—432no—
332#3195D4311yescharacteristic, direct product factor
333C2×#483—434no—
334C2×#470—434no—
335C2×#451—434no—
336C2×#407—431no—
337C2×C43—24no—
338C2×C43—41no—
339C2×C43C2×#53411yescharacteristic
340C2×C43C22×#13712yes—
341D43—24no—
342D43—41no—
343D43#319514yesdirect product factor
344C23×Q8—432no—
345C24×C4—431no—
346C22×Q16—434no—
347C22×M16—432no—
348C2×C22⋊Q8—432no—
349C2×C22⋊Q8—432no—
350C2×C22⋊Q8—434no—
351C2×C22⋊Q8—434no—
352C2×C22⋊Q8—434no—
353C2×C22⋊Q8—434no—
354C2×C22⋊Q8—432no—
355C2×C22⋊Q8—862no—
356C2×C22⋊Q8—862no—
357C2×C22⋊Q8—862no—
358C2×C22⋊Q8—862no—
359C2×C22⋊Q8—862no—
360C2×C22⋊Q8—862no—
361C2×C22⋊Q8C2×D4312yes—
362C22×C4⋊C4—432no—
363C22×C4⋊C4—862no—
364C22×C22⋊C4—862no—
365#483—434no—
366#483—434no—
367#483—438no—
368#483—438no—
369#483—434no—
370#483C2×D4314yescomplemented
371#470—434no—
372#470—434no—
373#470—438no—
374#470—434no—
375#470—438no—
376#470C2×D4314yescomplemented
377#451—434no—
378#451—438no—
379#451—434no—
380#451—438no—
381#451—434no—
382#451C2×D4314yescomplemented
383C2×#106—434no—
384C2×#103—438no—
385#407—431no—
386#407—432no—
387#407—434no—
388#407C2×D4311yescharacteristic
389C2×C22⋊C8—434no—
390C43C2×#319511yescharacteristic, complemented, Sylow
391C25—431no—
392C22×Q8—434no—
393C22×Q8—434no—
394C22×Q8—432no—
395C22×Q8—862no—
396C22×Q8—862no—
397C22×Q8—862no—
398C22×Q8—1728no—
399C22×Q8C22×D4312yes—
400C23×C4—431no—
401C23×C4—432no—
402C23×C4—431no—
403C23×C4—432no—
404C23×C4—432no—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—432no—
408C23×C4—431no—
409C23×C4—862no—
410C23×C4—862no—
411C23×C4—1724no—
412C23×C4C22×D4311yescharacteristic
413C2×Q16—438no—
414C2×Q16—434no—
415C2×Q16—1728no—
416C2×Q16C22×D4314yescomplemented
417C2×M16—432no—
418C2×M16—434no—
419C2×M16—1724no—
420C2×M16C22×D4312yes—
421C22×C8—434no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—434no—
425C22⋊Q8—434no—
426C22⋊Q8—434no—
427C22⋊Q8—434no—
428C22⋊Q8—434no—
429C22⋊Q8—434no—
430C22⋊Q8—864no—
431C22⋊Q8—864no—
432C22⋊Q8—864no—
433C22⋊Q8—864no—
434C22⋊Q8—864no—
435C22⋊Q8—864no—
436C22⋊Q8—864no—
437C22⋊Q8—864no—
438C22⋊Q8—862no—
439C22⋊Q8—862no—
440C22⋊Q8—862no—
441C22⋊Q8—862no—
442C22⋊Q8—862no—
443C22⋊Q8—862no—
444C22⋊Q8C22×D4314yes—
445C22⋊Q8C22×D4314yes—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—432no—
448C2×C4⋊C4—434no—
449C2×C4⋊C4—434no—
450C2×C4⋊C4—862no—
451C2×C4⋊C4—862no—
452C2×C4⋊C4—864no—
453C2×C4⋊C4—864no—
454C2×C4⋊C4—864no—
455C2×C4⋊C4—864no—
456C2×C4⋊C4—862no—
457C2×C4⋊C4—862no—
458C2×C4⋊C4—862no—
459C2×C4⋊C4—862no—
460C2×C4⋊C4C22×D4312yes—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—864no—
463C2×C22⋊C4—864no—
464C2×C22⋊C4—864no—
465C2×C22⋊C4—864no—
466C2×C22⋊C4—862no—
467C2×C22⋊C4—862no—
468C2×C22⋊C4—862no—
469#106—434no—
470#106—438no—
471#106C22×D4314yescomplemented
472#103—438no—
473#103—438no—
474#103—438no—
475#103C22×D4318yescomplemented
476C22⋊C8—434no—
477C22⋊C8—438no—
478C22⋊C8C22×D4314yes—
479C24—432no—
480C24—431no—
481C24—431no—
482C24—432no—
483C24—868no—
484C24—1722no—
485C24D4×D4311yescharacteristic
486C2×Q8—22no—
487C2×Q8—44no—
488C2×Q8—434no—
489C2×Q8—864no—
490C2×Q8—864no—
491C2×Q8—8616no—
492C2×Q8—862no—
493C2×Q8—1724no—
494C2×Q8—1728no—
495C2×Q8—1728no—
496C2×Q8—1728no—
497C2×Q8—1728no—
498C2×Q8C23×D4314yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—42no—
502C22×C4—431no—
503C22×C4—432no—
504C22×C4—431no—
505C22×C4—432no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—431no—
511C22×C4—432no—
512C22×C4—431no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—864no—
517C22×C4—868no—
518C22×C4—864no—
519C22×C4—864no—
520C22×C4—864no—
521C22×C4—864no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—1722no—
525C22×C4—1724no—
526C22×C4—1722no—
527C22×C4—1724no—
528C22×C4—1722no—
529C22×C4—1724no—
530C22×C4—1728no—
531C22×C4—1728no—
532C22×C4—1722no—
533C22×C4D4×D4312yes—
534C22×C4D4×D4311yescharacteristic
535C22×C4C23×D4312yes—
536C22×C4C23×D4311yescharacteristic
537Q16—44no—
538Q16—1724no—
539Q16—1728no—
540M16—42no—
541M16—1724no—
542M16—1722no—
543C2×C8—434no—
544C2×C8—868no—
545C2×C8C23×D4314yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—434no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—864no—
554C4⋊C4—864no—
555C4⋊C4—864no—
556C4⋊C4—862no—
557C4⋊C4—864no—
558C4⋊C4—864no—
559C4⋊C4C23×D4314yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—864no—
563C22⋊C4—864no—
564C22⋊C4—864no—
565C22⋊C4—864no—
566C22⋊C4—864no—
567C22⋊C4—864no—
568C23—24no—
569C23—41no—
570C23—431no—
571C23—438no—
572C23—432no—
573C23—431no—
574C23—864no—
575C23—864no—
576C23—862no—
577C23—864no—
578C23—864no—
579C23—864no—
580C23—864no—
581C23—1722no—
582C23—1721no—
583C23—17216no—
584C23C2×D4×D4311yescharacteristic
585C23C2×D4×D4312yes—
586Q8—28no—
587Q8—44no—
588Q8—868no—
589Q8—1724no—
590Q8—1728no—
591Q8—1728no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—431no—
601C2×C4—434no—
602C2×C4—431no—
603C2×C4—432no—
604C2×C4—864no—
605C2×C4—862no—
606C2×C4—864no—
607C2×C4—862no—
608C2×C4—864no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1728no—
618C2×C4—1728no—
619C2×C4—1728no—
620C2×C4—1728no—
621C2×C4—1721no—
622C2×C4—1722no—
623C2×C4—1724no—
624C2×C4—1724no—
625C2×C4C2×D4×D4311yescharacteristic
626C2×C4C2×D4×D4312yes—
627C2×C4C24×D4311yescharacteristic
628C8—24no—
629C8—864no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—21no—
634C22—44no—
635C22—434no—
636C22—432no—
637C22—434no—
638C22—8616no—
639C22—862no—
640C22—862no—
641C22—862no—
642C22—861no—
643C22—1728no—
644C22—1724no—
645C22—1724no—
646C22#137×D4314yes—
647C22C22×D4×D4311yescharacteristic
648C4—22no—
649C4—21no—
650C4—44no—
651C4—44no—
652C4—432no—
653C4—862no—
654C4—861no—
655C4—1724no—
656C4—1724no—
657C4H(5,𝔽2)×D4312yes—
658C2—24no—
659C2—41no—
660C2—434no—
661C2—864no—
662C2—1721no—
663C2#534×D4311yescharacteristic
664C2C2×#137×D4312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3195C2
socleC22×C43C23×D4
prime radicalC24×D43D4
hypercenter#3195D43
hypocenterC43C2×#3195
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
2. #19145419C2semidirect
3. #19145418C2semidirect
4. #19145417C2semidirect
5. #19145416C2semidirect
6. #19145415C2semidirect
7. #483×D43C2semidirect
8. #470×D43C2semidirect
9. #451×D43C2semidirect
11. C43×#3195C2semidirect
14. C2×Q16×D43C22semidirect
32. #14583231C22semidirect
33. #14583230C22semidirect
34. #14583229C22semidirect
35. #14583228C22semidirect
36. #14583227C22semidirect
37. #14583158C22semidirect
38. #14583157C22semidirect
39. #14583156C22semidirect
40. #14583155C22semidirect
41. #14583154C22semidirect
42. #14583057C22semidirect
43. #14583056C22semidirect
44. #14583055C22semidirect
45. #14583054C22semidirect
46. #14583053C22semidirect
47. #106×D43C22semidirect
48. #103×D43C22semidirect
54. C43×#483C22semidirect
55. C43×#470C22semidirect
56. C43×#451C22semidirect
78. C2×Dic172C23semidirect
79. C2×#10621885C23semidirect
125. #13063257C23semidirect
126. #13063256C23semidirect
127. #13063250C23semidirect
128. #13063249C23semidirect
129. #13063248C23semidirect
134. C2×Q16×C43C23semidirect
143. #106×C43C23semidirect
144. #103×C43C23semidirect
332. #3195D43direct (N × H)
343. D43#3195direct (N × H)
370. #483C2×D43semidirect
376. #470C2×D43semidirect
382. #451C2×D43semidirect
390. C43C2×#3195semidirect
416. C2×Q16C22×D43semidirect
471. #106C22×D43semidirect
475. #103C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
#191454192
#191454182
#191454172
#191454162
#191454152
#483×D432
#470×D432
#451×D432
#407×D432
C43×#31952
C2×#319543