Finite Group Databasebeta

← #25125465

Subgroups — #25125465

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582941C211yesmaximal, characteristic, complemented
2#19136978C211yesmaximal, characteristic
3C2×#14582759C211yesmaximal, characteristic
4#19136028C212yesmaximal, complemented
5#19136028C212yesmaximal, complemented
6#19136023C212yesmaximal, complemented
7#19136018C212yesmaximal, complemented
8#19134315C211yesmaximal, characteristic, complemented
9#19134315C211yesmaximal, characteristic, complemented
10#19134315C211yesmaximal, characteristic, complemented
11C2×C43×#407C211yesmaximal, characteristic
12C2×#13063284C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43—21no—
17#14582941—24no—
18C2×#13063259C2212yescomplemented
19C2×#13063257C2212yescomplemented
20#14582762—21no—
21#14582759—21no—
22#14582759—21no—
23#14582759C2211yescharacteristic
24#14582759C2212yes—
25#14582759C2211yescharacteristic
26#14582759C2212yes—
27#14582759C2211yescharacteristic
28#14582759C2211yescharacteristic
29#14582755—21no—
30C4×C22⋊Dic43—21no—
31C4×C22⋊Dic43—21no—
32C2×C43⋊#95—21no—
33#14582662C2212yescomplemented
34#14582662C2212yescomplemented
35#14582662C2212yescomplemented
36#14582662C2212yescomplemented
37#14582662C2212yescomplemented
38#14582662C2212yescomplemented
39C24×C4×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C43×#407—24no—
43C2×C22⋊C8×C43C2212yes—
44C2×C22⋊C8×C43C2212yes—
45C23×Dic43—21no—
46C23×Dic43—21no—
47#13063284—22no—
48#13063284—22no—
49#13063284—22no—
50#13063284—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43C2312yes—
58C2×C4⋊Dic43C2312yes—
59C2×C4⋊Dic43C2311yescharacteristic
60C2×C4⋊Dic43C2311yescharacteristic
61C2×C4⋊Dic43C2311yescharacteristic
62C2×C4⋊Dic43C2311yescharacteristic
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—44no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74#13063259—24no—
75#13063257—24no—
76C43⋊#95—22no—
77C43⋊#95—22no—
78C43⋊#95—21no—
79C43⋊#95—21no—
80C43⋊#95—21no—
81C43⋊#95—21no—
82C25×C43D411yescharacteristic
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D411yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×M16×C43—22no—
96C2×M16×C43—22no—
97C2×M16×C43—22no—
98C2×M16×C43—22no—
99C2×M16×C43—22no—
100C2×M16×C43D414yes—
101C22×C8×C43C2312yes—
102C22×C8×C43C2312yes—
103C22⋊C8×C43—24no—
104C22⋊C8×C43—24no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—41no—
111C24×C43—41no—
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
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—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—44no—
137C22×C4×C43—44no—
138C22×C4×C43—44no—
139C22×C4×C43—44no—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43#4112yes—
145C22×C4×C43#4112yes—
146C22×C4×C43#4112yes—
147C22×C4×C43#4112yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162M16×C43—28no—
163M16×C43—44no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C2×C8×C43C2×D414yes—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C22⋊Dic43—44no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C22⋊Dic43—44no—
177C22⋊Dic43—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—42no—
191C4⋊Dic43—42no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—28no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—44no—
212C23×C43—44no—
213C23×C43—44no—
214C23×C43—44no—
215C23×C43—44no—
216C23×C43—44no—
217C23×C43#12112yes—
218C23×C43#12312yes—
219C23×C43#12312yes—
220C23×C43AGL(1,ℤ/8)12yes—
221C23×C43#13712yes—
222C23×C43C22×D411yescharacteristic
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—44no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—44no—
239C2×C4×C43—44no—
240C2×C4×C43#12112yes—
241C2×C4×C43#12314yes—
242C2×C4×C43#12312yes—
243C2×C4×C43#12312yes—
244C2×C4×C43#12414yes—
245C2×C4×C43#12614yes—
246C2×C4×C43#12614yes—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—84no—
272C2×Dic43—84no—
273C8×C43—24no—
274C8×C43—42no—
275#23642—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—416no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43#39714yes—
298C22×C43C2×#12111yescharacteristic
299C22×C43C2×#12311yescharacteristic
300C22×C43C2×#12311yescharacteristic
301C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57511yescharacteristic
305C4×C43—41no—
306C4×C43—41no—
307C4×C43#39714yes—
308C4×C43C2×#12311yescharacteristic
309C4×C43C2×#12411yescharacteristic
310C4×C43C2×#12611yescharacteristic
311C4×C43C2×#12611yescharacteristic
312Dic43—81no—
313Dic43—81no—
314Dic43—82no—
315Dic43—81no—
316Dic43—82no—
317Dic43—81no—
318C2×#428—431no—
319C2×#407D4311yescharacteristic
320#2280—431no—
321C2×#380—431no—
322#2077—432no—
323#2077—432no—
324#2076—432no—
325#2075—432no—
326#1736—431no—
327#1736—431no—
328#1736—431no—
329C2×C43—24no—
330C2×C43—42no—
331C2×C43—42no—
332C2×C43C2×#39711yescharacteristic
333C2×C43#305511yescharacteristic
334C2×C43#305611yescharacteristic
335C2×C43#309211yescharacteristic
336C2×C43#309311yescharacteristic
337C2×C43#309411yescharacteristic
338C2×C43#309511yescharacteristic
339C24×C4C2×D4311yescharacteristic
340C22×M16C2×D4311yescharacteristic
341C22×M16C2×D4311yescharacteristic
342C2×#117—431no—
343C2×#117—431no—
344C22×C4⋊C4—431no—
345C22×C4⋊C4—431no—
346C22×C22⋊C4—861no—
347#428—864no—
348C2×#107—432no—
349C2×#106—432no—
350#407—24no—
351C2×C22⋊C8C2×D4312yes—
352C2×C22⋊C8C2×D4312yes—
353#381—861no—
354#380—431no—
355#380—432no—
356#380—431no—
357#380—432no—
358#380—431no—
359#380—431no—
360#380—861no—
361#380—861no—
362#379—861no—
363C4×C22⋊C4—861no—
364C4×C22⋊C4—861no—
365C2×#95—861no—
366#340—432no—
367#340—432no—
368#340—432no—
369#340—432no—
370#340—432no—
371#340—432no—
372C43#2364211yescharacteristic, complemented, Sylow
373C25D17211yescharacteristic
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—861no—
381C23×C4—861no—
382C23×C4D17211yescharacteristic
383C23×C4D17211yescharacteristic
384C23×C4D17211yescharacteristic
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4311yescharacteristic
387C23×C4C22×D4311yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16C22⋊D4314yes—
394C22×C8C22×D4312yes—
395C22×C8C22×D4312yes—
396#117—862no—
397#117—862no—
398#117—862no—
399#117—862no—
400C2×C4⋊C4—432no—
401C2×C4⋊C4—432no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—1724no—
421C2×C42—861no—
422C2×C42—861no—
423#107—864no—
424#106—864no—
425C22⋊C8—24no—
426C22⋊C8—24no—
427#95—862no—
428#95—862no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—41no—
439C24—41no—
440C24C2×D17211yescharacteristic
441C24C2×D17211yescharacteristic
442C24C2×D17211yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4#1062189812yes—
484C22×C4#1062190012yes—
485C22×C4#1062190012yes—
486C22×C4#1062190012yes—
487C22×C4#1062190012yes—
488C22×C4C2×C22⋊D4312yes—
489C22×C4C23×D4311yescharacteristic
490M16—28no—
491M16—44no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8C2×C22⋊D4314yes—
498C4⋊C4—861no—
499C4⋊C4—862no—
500C4⋊C4—861no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—862no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C22⋊C4—1724no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1724no—
518C22⋊C4—1722no—
519C22⋊C4—1722no—
520C42—1722no—
521C42—1722no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23#1306329912yes—
546C23#1306330912yes—
547C23#1306330912yes—
548C23#1306335312yes—
549C23#1306335812yes—
550C23C22×D17211yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—3444no—
569C2×C4—3444no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1722no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4#1306329912yes—
589C2×C4#1306330614yes—
590C2×C4#1306330912yes—
591C2×C4#1306330912yes—
592C2×C4#1306331214yes—
593C2×C4#1306331814yes—
594C2×C4#1306331814yes—
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4C2×#1062190011yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C8—24no—
602C8—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22#1458282414yes—
625C22C2×#1306329911yescharacteristic
626C22C2×#1306330911yescharacteristic
627C22C2×#1306330911yescharacteristic
628C22C2×#1306335311yescharacteristic
629C22C2×#1306335811yescharacteristic
630C22#1458369911yescharacteristic
631C22#1458369911yescharacteristic
632C4—41no—
633C4—41no—
634C4—3442no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3442no—
640C4#1458282414yes—
641C4C2×#1306330611yescharacteristic
642C4C2×#1306331211yescharacteristic
643C4C2×#1306331811yescharacteristic
644C4C2×#1306331811yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×#1458282411yescharacteristic
649C2#1914421411yescharacteristic
650C2#1914422511yescharacteristic
651C2#1914452011yescharacteristic
652C2#1914452811yescharacteristic
653C2#1914453611yescharacteristic
654C2#1914454411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC23×C43C22×D4
prime radicalC25×C43D4
hypercenterC2×#407D43
hypocenterC43#23642
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#14582941C2semidirect
4. #19136028C2semidirect
5. #19136028C2semidirect
6. #19136023C2semidirect
7. #19136018C2semidirect
8. #19134315C2semidirect
9. #19134315C2semidirect
10. #19134315C2semidirect
18. C2×#13063259C22semidirect
19. C2×#13063257C22semidirect
33. #14582662C22semidirect
34. #14582662C22semidirect
35. #14582662C22semidirect
36. #14582662C22semidirect
37. #14582662C22semidirect
38. #14582662C22semidirect
372. C43#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#145829412
#191369782
C2×#145827592
#191360282
#191360232
#191360182
#191343152
C2×C43×#4072
#2364243