Finite Group Databasebeta

← #25169879

Subgroups — #25169879

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139190C211yesmaximal, characteristic, complemented
2#19137670C211yesmaximal, characteristic, complemented
3#19136118C211yesmaximal, characteristic, complemented
4#19135903C211yesmaximal, characteristic
5#19135831C211yesmaximal, characteristic, complemented
6#19135451C211yesmaximal, characteristic, complemented
7#19135239C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19135174C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134945C211yesmaximal, characteristic
13#19134608C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2012C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582827—21no—
29#14582824—21no—
30#14582806C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582792—21no—
36#14582792—21no—
37#14582792—21no—
38#14582787—21no—
39#14582774—21no—
40#14582764C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×#124×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—22no—
63Q8×Dic43—41no—
64D4×Dic43—22no—
65D4×Dic43—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063258—41no—
87#13063257—22no—
88Dic43⋊C8—41no—
89#13063249—22no—
90#13063249—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246—41no—
94#13063246—41no—
95C8×Dic43—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43C2311yescharacteristic
106C22×D4×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C2×SD16×C43—22no—
109C2×SD16×C43—22no—
110C2×SD16×C43—41no—
111C2×D8×C43—22no—
112C2×D8×C43—41no—
113C2×D8×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#124×C43—22no—
117#124×C43—22no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#103×C43—41no—
125#102×C43—22no—
126C24×C43—21no—
127C24×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43#4112yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—81no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162SD16×C43—44no—
163D8×C43—44no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43#4112yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—81no—
176C42×C43—21no—
177C42×C43—21no—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—22no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43—42no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—81no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—42no—
202C4×Dic43—81no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22×D411yescharacteristic
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—84no—
279C2×Dic43#13512yes—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#27072—431nomaximal, Sylow
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43#52511yescharacteristic
300C22×C43#54611yescharacteristic
301C22×C43#55011yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57611yescharacteristic
305C22×C43#57711yescharacteristic
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—42no—
309C4×C43—81no—
310C4×C43#52911yescharacteristic
311C4×C43#53811yescharacteristic
312C4×C43#55111yescharacteristic
313C4×C43#55311yescharacteristic
314Dic43—22no—
315Dic43—41no—
316Dic43—42no—
317Dic43—41no—
318Dic43—41no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2513—431no—
323#2367—431no—
324#2092—431no—
325#2054—431no—
326#2042—431no—
327#2012D4311yescharacteristic
328#1968—431no—
329#1928—431no—
330#1925—431no—
331#1919—431no—
332#1916—431no—
333#1880—431no—
334#1879—431no—
335#1805—431no—
336C4×#102—431no—
337C2×C43—82no—
338C2×C43—161no—
339C2×C43#246711yescharacteristic
340C2×C43#310211yescharacteristic
341C2×C43#311911yescharacteristic
342C2×C43#329711yescharacteristic
343C2×C43#332111yescharacteristic
344C2×C43#339411yescharacteristic
345C2×C43#340311yescharacteristic
346C22×SD16C2×D4311yescharacteristic
347C22×D8C2×D4311yescharacteristic
348C2×#124C2×D4311yescharacteristic
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×#107—431no—
352C2×#106—431no—
353C2×C4⋊C8—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102C2×D4311yescharacteristic
362C2×C4×C8—431no—
363#397—861no—
364#397—861no—
365#391—431no—
366#390—431no—
367#390—431no—
368#390—431no—
369#390C2×D4311yescharacteristic
370#389—431no—
371#388—861no—
372#388—861no—
373#388—861no—
374#388—861no—
375#385—861no—
376#382—431no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C22⋊C4—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2707211yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4C22×D4311yescharacteristic
392C22×D4C22×D4311yescharacteristic
393C23×C4—861no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16—41no—
397C2×D8—22no—
398C2×D8—41no—
399C2×D8—41no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#124—22no—
405#124—22no—
406C4×Q8—862no—
407C4×Q8—1721no—
408C4×D4—862no—
409C4×D4—1721no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436#107—1721no—
437#106—862no—
438C4⋊C8—1721no—
439#103—41no—
440#103—862no—
441#103—1721no—
442#102—22no—
443#102—862no—
444#102—862no—
445#102—1721no—
446#102—1721no—
447C4×C8—1721no—
448#95—431no—
449#95—431no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C24—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8#1062190012yes—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4#1062190012yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—44no—
494D8—44no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8#1062190012yes—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—432no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—1721no—
520C4⋊C4—1722no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C42—21no—
533C42—21no—
534C42—861no—
535C42—861no—
536C42—861no—
537C42—861no—
538C42—3441no—
539C42—3441no—
540C42—1722no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—3444no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4C2×#1062190011yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—22no—
612C8—41no—
613C8—1721no—
614C8—1721no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22#1458340511yescharacteristic
630C22#1458354611yescharacteristic
631C22#1458356911yescharacteristic
632C22#135×D4311yescharacteristic
633C22#1458369511yescharacteristic
634C22#1458370311yescharacteristic
635C22#1458370611yescharacteristic
636C4—42no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—862no—
641C4—3441no—
642C4—3441no—
643C4—3441no—
644C4—1721no—
645C4—1721no—
646C4—1721no—
647C4—1722no—
648C4#1458343011yescharacteristic
649C4#1458348411yescharacteristic
650C4#1458358011yescharacteristic
651C4#1458359211yescharacteristic
652C2—82no—
653C2—161no—
654C2#1913864111yescharacteristic
655C2#1914460611yescharacteristic
656C2#1914479511yescharacteristic
657C2#1914645211yescharacteristic
658C2#1914678811yescharacteristic
659C2#1914758811yescharacteristic
660C2#1914768011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2012C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#2012D43
hypocenterC43#27072
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

Complements

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

NH ≅ G/Ntype
1. #19139190C2semidirect
2. #19137670C2semidirect
3. #19136118C2semidirect
5. #19135831C2semidirect
6. #19135451C2semidirect
7. #19135239C2semidirect
8. #19135212C2semidirect
9. #19135174C2semidirect
10. #19135151C2semidirect
11. #19134952C2semidirect
13. #19134608C2semidirect
14. #102×Dic43C2semidirect
389. C43#27072semidirect

Maximal subgroups

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

subgroupindex
#191391902
#191376702
#191361182
#191359032
#191358312
#191354512
#191352392
#191352122
#191351742
#191351512
#191349522
#191349452
#191346082
#102×Dic432
C43×#20122
#2707243