Finite Group Databasebeta

← #25169864

Subgroups — #25169864

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139179C211yesmaximal, characteristic, complemented
2#19137670C211yesmaximal, characteristic, complemented
3#19136126C211yesmaximal, characteristic, complemented
4#19135903C211yesmaximal, characteristic
5#19135831C211yesmaximal, characteristic, complemented
6#19135451C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19135181C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134945C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2012C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582827—21no—
30#14582822—21no—
31#14582806C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582793—21no—
37#14582792—21no—
38#14582792—21no—
39#14582774—21no—
40#14582768C2211yescharacteristic
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
62#13063318—44no—
63Q8×Dic43—22no—
64Q8×Dic43—41no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063257—22no—
90#13063256—41no—
91Dic43⋊C8—41no—
92#13063249—22no—
93#13063249—41no—
94#13063246—22no—
95#13063246—22no—
96#13063246—41no—
97#13063246—41no—
98C8×Dic43—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C2×SD16×C43—22no—
110C2×SD16×C43—22no—
111C2×SD16×C43—41no—
112C2×D8×C43—22no—
113C2×D8×C43—41no—
114C2×D8×C43—41no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117#124×C43—22no—
118#124×C43—22no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—41no—
126#102×C43—22no—
127C24×C43—21no—
128C24×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43#4112yes—
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—21no—
146C2×D4×C43#4112yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163SD16×C43—44no—
164D8×C43—44no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43#4112yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181C22⋊Dic43—42no—
182C22⋊Dic43—42no—
183C22⋊Dic43—42no—
184C22⋊Dic43—81no—
185C22⋊Dic43—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43#4112yes—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—81no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C23×C43—22no—
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×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
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—41no—
279C2×Dic43—41no—
280C2×Dic43—84no—
281C2×Dic43#13512yes—
282C2×Dic43AGL(1,ℤ/8)12yes—
283C8×C43—22no—
284C8×C43—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#27071—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
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—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43#52511yescharacteristic
303C22×C43#54611yescharacteristic
304C22×C43#55011yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43#57711yescharacteristic
308C22×C43#57711yescharacteristic
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43#52911yescharacteristic
314C4×C43#53811yescharacteristic
315C4×C43#55111yescharacteristic
316C4×C43#55311yescharacteristic
317Dic43—22no—
318Dic43—22no—
319Dic43—41no—
320Dic43—41no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325#2512—431no—
326#2367—431no—
327#2094—431no—
328#2054—431no—
329#2042—431no—
330#2012D4311yescharacteristic
331#1968—431no—
332#1927—431no—
333#1926—431no—
334#1920—431no—
335#1916—431no—
336#1880—431no—
337#1879—431no—
338#1803—431no—
339C4×#102—431no—
340C2×C43—82no—
341C2×C43—161no—
342C2×C43#246711yescharacteristic
343C2×C43#310611yescharacteristic
344C2×C43#312511yescharacteristic
345C2×C43#330111yescharacteristic
346C2×C43#330611yescharacteristic
347C2×C43#339411yescharacteristic
348C2×C43#339711yescharacteristic
349C22×SD16C2×D4311yescharacteristic
350C22×D8C2×D4311yescharacteristic
351C2×#126—861no—
352C2×#124C2×D4311yescharacteristic
353C2×C4×Q8—431no—
354C2×C4×D4—431no—
355C2×#106—431no—
356C2×#106—431no—
357C2×C4⋊C8—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103C2×D4311yescharacteristic
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102C2×D4311yescharacteristic
366C2×C4×C8—431no—
367#397—861no—
368#396—861no—
369#391—431no—
370#390—431no—
371#390—431no—
372#390—431no—
373#390C2×D4311yescharacteristic
374#389—431no—
375#388—861no—
376#388—861no—
377#388—861no—
378#385—861no—
379#384—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—431no—
383C4×C22⋊C4—861no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#336—431no—
389#336—431no—
390#336—431no—
391#336C2×D4311yescharacteristic
392C43#2707111yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×D4C22×D4311yescharacteristic
395C22×D4C22×D4311yescharacteristic
396C23×C4—861no—
397C2×SD16—22no—
398C2×SD16—22no—
399C2×SD16—41no—
400C2×D8—22no—
401C2×D8—41no—
402C2×D8—41no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#126—1724no—
408#124—22no—
409#124—22no—
410C4×Q8—862no—
411C4×Q8—1721no—
412C4×D4—862no—
413C4×D4—1721no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442#106—862no—
443#106—1721no—
444C4⋊C8—1721no—
445#103—41no—
446#103—862no—
447#103—1721no—
448#102—22no—
449#102—862no—
450#102—862no—
451#102—1721no—
452#102—1721no—
453C4×C8—1721no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C24—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8#1062190012yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4#1062190012yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3441no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—44no—
498D8—44no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8#1062190012yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—3441no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—3441no—
545C42—1722no—
546C42—1722no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—3444no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#41×D4311yescharacteristic
612C2×C4C2×#1062190011yescharacteristic
613C2×C4C2×#1062190011yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337011yescharacteristic
617C8—22no—
618C8—41no—
619C8—1721no—
620C8—1721no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1458340511yescharacteristic
636C22#1458354611yescharacteristic
637C22#1458356911yescharacteristic
638C22#135×D4311yescharacteristic
639C22AGL(1,ℤ/8)×D4311yescharacteristic
640C22#1458370611yescharacteristic
641C22#1458370911yescharacteristic
642C4—42no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—3441no—
650C4—3441no—
651C4—1721no—
652C4—1721no—
653C4—1722no—
654C4#1458343011yescharacteristic
655C4#1458348411yescharacteristic
656C4#1458358011yescharacteristic
657C4#1458359211yescharacteristic
658C2—82no—
659C2—161no—
660C2#1913864111yescharacteristic
661C2#1914464811yescharacteristic
662C2#1914487311yescharacteristic
663C2#1914650411yescharacteristic
664C2#1914656311yescharacteristic
665C2#1914758811yescharacteristic
666C2#1914761211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2012C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#2012D43
hypocenterC43#27071
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. #19139179C2semidirect
2. #19137670C2semidirect
3. #19136126C2semidirect
5. #19135831C2semidirect
6. #19135451C2semidirect
7. #19135232C2semidirect
8. #19135219C2semidirect
9. #19135181C2semidirect
10. #19135151C2semidirect
11. #19134952C2semidirect
13. #19134598C2semidirect
14. #102×Dic43C2semidirect
392. C43#27071semidirect

Maximal subgroups

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

subgroupindex
#191391792
#191376702
#191361262
#191359032
#191358312
#191354512
#191352322
#191352192
#191351812
#191351512
#191349522
#191349452
#191345982
#102×Dic432
C43×#20122
#2707143