Finite Group Databasebeta

← #25200717

Subgroups — #25200717

Order 11008.

788 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#19140561C211yesmaximal, characteristic, complemented
2#19137321C211yesmaximal, characteristic
3#19136078C211yesmaximal, characteristic, complemented
4#19136013C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic
6#19135478C211yesmaximal, characteristic, complemented
7#19135451C211yesmaximal, characteristic, complemented
8#19135289C211yesmaximal, characteristic, complemented
9#19135275C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic, complemented
12#19134858C211yesmaximal, characteristic, complemented
13#19134844C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#2014C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28C43⋊#401—21no—
29#14582841—21no—
30#14582840—21no—
31#14582839—21no—
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582779—21no—
40#14582779—21no—
41#14582779—21no—
42#14582779—21no—
43#14582765C2211yescharacteristic
44#14582745C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#127×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—41no—
64D4×Dic43—41no—
65D4×Dic43—41no—
66D4×Dic43—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
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×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063259—41no—
83#13063257—41no—
84#13063249—41no—
85#13063249—41no—
86#13063246—22no—
87#13063246—22no—
88#13063246—41no—
89#13063246—41no—
90#13063235—22no—
91C8×Dic43—22no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43C2311yescharacteristic
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C2×SD16×C43—22no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43—41no—
115C2×SD16×C43—41no—
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#127×C43—22no—
119#127×C43—22no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#102×C43—22no—
123#102×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
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—21no—
134C2×D4×C43—24no—
135C2×D4×C43—24no—
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—81no—
147C2×D4×C43—81no—
148C2×D4×C43—81no—
149C2×D4×C43—81no—
150C2×D4×C43#4112yes—
151C2×D4×C43#4112yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—81no—
164C22×Dic43—81no—
165C22×Dic43—81no—
166C22×Dic43—81no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171SD16×C43—44no—
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43#4112yes—
178C2×C8×C43#4112yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—81no—
186C22⋊Dic43—81no—
187C22⋊Dic43—81no—
188C22⋊Dic43—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—81no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
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—22no—
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—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—84no—
238D4×C43—84no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
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—41no—
281C2×Dic43—84no—
282C2×Dic43—84no—
283C8×C43—22no—
284C8×C43—22no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#29504—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
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#53211yescharacteristic
304C22×C43#53511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57711yescharacteristic
308C22×C43#57711yescharacteristic
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43#55111yescharacteristic
314C4×C43#55111yescharacteristic
315C4×C43#55311yescharacteristic
316C4×C43#55311yescharacteristic
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325#2645—431no—
326#2328—431no—
327#2085—431no—
328#2074—431no—
329#2041—431no—
330#2014D4311yescharacteristic
331#1973—431no—
332#1968—431no—
333#1936—431no—
334#1934—431no—
335#1877—431no—
336#1877—431no—
337#1864—431no—
338#1862—431no—
339#1746—431no—
340C2×C43—82no—
341C2×C43—82no—
342C2×C43#260311yescharacteristic
343C2×C43#311811yescharacteristic
344C2×C43#312311yescharacteristic
345C2×C43#317411yescharacteristic
346C2×C43#317911yescharacteristic
347C2×C43#322211yescharacteristic
348C2×C43#322411yescharacteristic
349C22×SD16C2×D4311yescharacteristic
350C22×SD16C2×D4311yescharacteristic
351C2×#127C2×D4311yescharacteristic
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102C2×D4311yescharacteristic
363C2×#102C2×D4311yescharacteristic
364C2×#97—431no—
365C2×C4×C8—431no—
366#401—861no—
367#400—861no—
368#400—861no—
369#400—861no—
370#391—431no—
371#391—431no—
372#391C2×D4311yescharacteristic
373#390—431no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—431no—
378#386—861no—
379#386—861no—
380#386—861no—
381#386—861no—
382#382—431no—
383#376—431no—
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#2950411yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×D4—21no—
395C22×D4—21no—
396C22×D4C22×D4311yescharacteristic
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C23×C4—861no—
400C2×SD16—22no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16—41no—
405C2×SD16—41no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#127—22no—
411#127—22no—
412C4×D4—1721no—
413C4×D4—1721no—
414C4×D4—1721no—
415C4×D4—1721no—
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⋊C4C22×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
433#107—1721no—
434#106—1721no—
435#103—1721no—
436#103—1721no—
437#102—22no—
438#102—22no—
439#102—862no—
440#102—862no—
441#102—1721no—
442#102—1721no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—431no—
448#95—431no—
449#95—431no—
450#95—431no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—21no—
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×D4—24no—
469C2×D4—24no—
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—81no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—81no—
484C2×D4#1062190012yes—
485C2×D4#1062190012yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—3441no—
497C22×C4—3441no—
498C22×C4—3441no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505SD16—44no—
506SD16—44no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8#1062190012yes—
518C2×C8#1062190012yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—3441no—
530C4⋊C4—3441no—
531C4⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—3441no—
534C22⋊C4—3441no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—861no—
544C23—22no—
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C2×D4×D4311yescharacteristic
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563D4—22no—
564D4—22no—
565D4—22no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—84no—
572D4—84no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
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—3444no—
598C2×C4—3444no—
599C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
612C2×C4C2×#1062190011yescharacteristic
613C2×C4C2×#1062190011yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337111yescharacteristic
617C8—22no—
618C8—22no—
619C8—1721no—
620C8—1721no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1458340511yescharacteristic
636C22#1458344711yescharacteristic
637C22#1458346511yescharacteristic
638C22#1458370311yescharacteristic
639C22#1458370511yescharacteristic
640C22#1458370511yescharacteristic
641C22#1458370911yescharacteristic
642C4—41no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—3441no—
647C4—3441no—
648C4—3441no—
649C4—3441no—
650C4—1721no—
651C4—1721no—
652C4—1721no—
653C4—1721no—
654C4#1458358011yescharacteristic
655C4#1458358011yescharacteristic
656C4#1458360111yescharacteristic
657C4#1458360111yescharacteristic
658C2—82no—
659C2—82no—
660C2#1914021511yescharacteristic
661C2#1914478011yescharacteristic
662C2#1914484111yescharacteristic
663C2#1914522011yescharacteristic
664C2#1914527511yescharacteristic
665C2#1914566611yescharacteristic
666C2#1914569411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2014C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#2014D43
hypocenterC43#29504
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2014

Complements

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

NH ≅ G/Ntype
1. #19140561C2semidirect
3. #19136078C2semidirect
4. #19136013C2semidirect
6. #19135478C2semidirect
7. #19135451C2semidirect
8. #19135289C2semidirect
9. #19135275C2semidirect
10. #19134931C2semidirect
11. #19134931C2semidirect
12. #19134858C2semidirect
13. #19134844C2semidirect
14. #19134345C2semidirect
392. C43#29504semidirect

Maximal subgroups

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

subgroupindex
#191405612
#191373212
#191360782
#191360132
#191358262
#191354782
#191354512
#191352892
#191352752
#191349312
#191348582
#191348442
#191343452
C43×#20142
#2950443