Finite Group Databasebeta

← #25033363

Subgroups — #25033363

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582828C212yesmaximal
2C2×#14582826C211yesmaximal, characteristic
3C2×#14582825C211yesmaximal, characteristic
4C2×#14582768C211yesmaximal, characteristic, complemented
5C2×#14582758C212yesmaximal
6C2×#14582746C211yesmaximal, characteristic
7#19132862C211yesmaximal, characteristic, complemented
8#19132861C212yesmaximal, complemented
9Dic43⋊#95C212yesmaximal, complemented
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11C43×#1445C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582828—28no—
24#14582826—24no—
25#14582825—24no—
26#14582768—24no—
27#14582758—28no—
28#14582746—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2212yes—
41C24×D43C2311yescharacteristic
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2311yescharacteristic
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43D414yes—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4D414yes—
75C2×(C2×D43)⋊C4D414yes—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43D414yes—
80C43⋊#95—22no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—22no—
87C23×C4×C43C2312yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95#95×C43—22no—
96#95×C43—24no—
97#95×C43—22no—
98#95×C43—24no—
99C24×C43C2411yescharacteristic
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43C2×D412yes—
109C23×D43C2×D412yes—
110C23×D43C2×D412yes—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43#4112yes—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162C22×Dic43C2×D412yes—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D412yes—
165C22×Dic43#4112yes—
166C22×Dic43#4112yes—
167C22×Dic43#4114yes—
168C22×Dic43#4114yes—
169C2×C4×D43—28no—
170C2×C4×D43—216no—
171C2×C4×D43—44no—
172C2×C4×D43—44no—
173C2×C4×D43—48no—
174C4⋊C4×C43—44no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—48no—
178(C2×D43)⋊C4—48no—
179C4⋊Dic43—44no—
180Dic43⋊C4—48no—
181Dic43⋊C4—48no—
182Dic43⋊C4—48no—
183C4×Dic43—28no—
184C4×Dic43—44no—
185C23×C43C22×D411yescharacteristic
186C23×C43C22×D411yescharacteristic
187C23×C43C22×D411yescharacteristic
188C23×C43C22×D411yescharacteristic
189C23×C43C2×#4111yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C43C2×#4112yes—
192C23×C43C2×#4112yes—
193C23×C43C2×#4111yescharacteristic
194C23×C432−1+412yes—
195C23×C432−1+412yes—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—24no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—42no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43#12714yes—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43#12114yes—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—22no—
253C2×Dic43—24no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43#12114yes—
272C2×Dic43#12114yes—
273C2×Dic43#12314yes—
274C2×Dic43#12318yes—
275C2×Dic43#12414yes—
276C2×Dic43#12618yes—
277C4×D43—416no—
278#15150—431nomaximal, Sylow
279C22×C43C2×#12111yescharacteristic
280C22×C43C2×#12111yescharacteristic
281C22×C43C2×#12111yescharacteristic
282C22×C43C2×#12311yescharacteristic
283C22×C43C2×#12312yes—
284C22×C43C2×#12411yescharacteristic
285C22×C43C2×#12612yes—
286C22×C43C2×#12711yescharacteristic
287C22×C43#53211yescharacteristic
288C22×C43#53211yescharacteristic
289C22×C43#53211yescharacteristic
290C22×C43#53611yescharacteristic
291C22×C43#53612yes—
292C22×C43#53611yescharacteristic
293C22×C43#54112yes—
294C22×C43#54712yes—
295C22×C43#54712yes—
296C22×C43#54712yes—
297C22×C43#54712yes—
298C22×C43#55212yes—
299C22×C43#55212yes—
300C22×C43#55612yes—
301C22×C43#55612yes—
302C2×D43—24no—
303C2×D43—28no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—42no—
312C2×D43—42no—
313C4×C43—24no—
314C4×C43—42no—
315C4×C43—42no—
316C4×C43—82no—
317C4×C43—82no—
318Dic43—24no—
319Dic43—42no—
320Dic43—82no—
321Dic43—82no—
322Dic43#39718yescomplemented
323C2×#397—431no—
324C2×#397—432no—
325C2×#397—431no—
326C2×#384—431no—
327C2×#380—432no—
328C2×C4×C22⋊C4—431no—
329#1445—432no—
330#1445—431no—
331#1445D4311yescharacteristic, complemented
332C4⋊#95—431no—
333C4⋊#95—432no—
334C2×C43C2×#39711yescharacteristic
335C2×C43#248611yescharacteristic
336C2×C43#248611yescharacteristic
337C2×C43#249612yes—
338C2×C43#249612yes—
339C2×C43#249912yes—
340C2×C43#250112yes—
341C2×C43#254711yescharacteristic
342C2×C43#254711yescharacteristic
343C2×C43#262111yescharacteristic
344C2×C43#285611yescharacteristic
345D43—44no—
346C24×C4—431no—
347C22×C4⋊C4—432no—
348C22×C4⋊C4—432no—
349C22×C4⋊C4—432no—
350C22×C4⋊C4—431no—
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C22⋊C4—431no—
353C22×C22⋊C4—431no—
354C22×C22⋊C4—432no—
355C22×C22⋊C4—432no—
356C22×C42—431no—
357C22×C42—431no—
358#397—864no—
359#397—868no—
360#397—864no—
361#384—864no—
362#380—868no—
363C4×C22⋊C4—864no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—431no—
369C2×#95—431no—
370C2×#95—432no—
371C2×#95C2×D4312yes—
372C2×#95C2×D4311yescharacteristic
373C2×#95C2×D4311yescharacteristic
374C2×#95C2×D4312yes—
375C43#1515011yescharacteristic, complemented, Sylow
376C25—431no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—434no—
381C23×C4—432no—
382C23×C4—432no—
383C23×C4—862no—
384C23×C4—864no—
385C23×C4—864no—
386C23×C4—862no—
387C23×C4C22×D4312yes—
388C23×C4C22×D4312yes—
389C23×C4C22×D4311yescharacteristic
390C23×C4C22×D4311yescharacteristic
391C23×C4C22×D4311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—864no—
402C2×C4⋊C4—864no—
403C2×C4⋊C4—864no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—862no—
407C2×C22⋊C4—434no—
408C2×C22⋊C4—434no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—864no—
415C2×C22⋊C4—864no—
416C2×C22⋊C4—864no—
417C2×C22⋊C4—864no—
418C2×C22⋊C4—864no—
419C2×C42—434no—
420C2×C42—864no—
421C2×C42—862no—
422C2×C42—864no—
423#95—22no—
424#95—24no—
425#95—22no—
426#95—24no—
427#95—862no—
428#95—864no—
429#95—864no—
430#95—864no—
431#95—864no—
432#95—862no—
433#95—864no—
434C24—432no—
435C24—432no—
436C24—432no—
437C24—861no—
438C24—861no—
439C24—861no—
440C24—862no—
441C24—862no—
442C24—861no—
443C24—862no—
444C24—862no—
445C24C23×D4311yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—434no—
473C22×C4—434no—
474C22×C4—432no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—868no—
480C22×C4—8616no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—861no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—1724no—
502C22×C4—1724no—
503C22×C4—1728no—
504C22×C4#1062189812yes—
505C22×C4D4×D4312yes—
506C22×C4D4×D4312yes—
507C22×C4D4×D4312yes—
508C22×C4D4×D4312yes—
509C4⋊C4—44no—
510C4⋊C4—1728no—
511C4⋊C4—1728no—
512C4⋊C4—1728no—
513C4⋊C4—1724no—
514C22⋊C4—868no—
515C22⋊C4—868no—
516C22⋊C4—1728no—
517C22⋊C4—1728no—
518C42—868no—
519C42—1724no—
520C23—434no—
521C23—862no—
522C23—862no—
523C23—862no—
524C23—864no—
525C23—862no—
526C23—862no—
527C23—862no—
528C23—864no—
529C23—864no—
530C23—864no—
531C23—864no—
532C23—864no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23—1721no—
538C23—1721no—
539C23—1722no—
540C23—1721no—
541C23—1721no—
542C23—1722no—
543C23C2×D4×D4311yescharacteristic
544C23C2×D4×D4311yescharacteristic
545C23C2×D4×D4311yescharacteristic
546C23C2×D4×D4311yescharacteristic
547C23#41×D4311yescharacteristic
548C23#41×D4312yes—
549C23#41×D4312yes—
550C23#41×D4311yescharacteristic
551C23C2×#1062189811yescharacteristic
552C23#1306337212yes—
553C23#1306337312yes—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—434no—
583C2×C4—434no—
584C2×C4—438no—
585C2×C4—434no—
586C2×C4—438no—
587C2×C4—434no—
588C2×C4—864no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—864no—
594C2×C4—17216no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4#1306329814yes—
613C22—864no—
614C22—868no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1724no—
622C22—1724no—
623C22—1724no—
624C22#121×D4311yescharacteristic
625C22#121×D4311yescharacteristic
626C22C2×#1306329811yescharacteristic
627C22#123×D4311yescharacteristic
628C22#123×D4312yes—
629C22#124×D4311yescharacteristic
630C22#126×D4312yes—
631C22#127×D4311yescharacteristic
632C22#1458344611yescharacteristic
633C22#1458344611yescharacteristic
634C22#1458344811yescharacteristic
635C22#1458347111yescharacteristic
636C22#1458347212yes—
637C22#1458347411yescharacteristic
638C22#1458350812yes—
639C22#1458354712yes—
640C22#1458354712yes—
641C22#1458355112yes—
642C22#1458355112yes—
643C22#1458358112yes—
644C22#1458358212yes—
645C22#1458361612yes—
646C22#1458362112yes—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—82no—
651C4—82no—
652C4—438no—
653C4—864no—
654C4—3442no—
655C4—3442no—
656C4—1722no—
657C2—1724no—
658C2#397×D4311yescharacteristic
659C2#1913889811yescharacteristic
660C2#1913890211yescharacteristic
661C2#1913901212yes—
662C2#1913901612yes—
663C2#1913904612yes—
664C2#1913906112yes—
665C2#1913958611yescharacteristic
666C2#1913959211yescharacteristic
667C2#1914036311yescharacteristic
668C2#1914293911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×#1445C2
prime radicalC24×D43C23
hypercenter#1445D43
hypocenterC43#15150
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. C2×#14582768C2semidirect
7. #19132862C2semidirect
8. #19132861C2semidirect
9. Dic43⋊#95C2semidirect
10. Dic43⋊#95C2semidirect
11. C43×#1445C2semidirect
322. Dic43#397semidirect
331. #1445D43semidirect
375. C43#15150semidirect

Maximal subgroups

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

subgroupindex
C2×#145828282
C2×#145828262
C2×#145828252
C2×#145827682
C2×#145827582
C2×#145827462
#191328622
#191328612
Dic43⋊#952
C43×#14452
#1515043