Finite Group Databasebeta

← #25164573

Subgroups — #25164573

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138356C211yesmaximal, characteristic
2#19137693C211yesmaximal, characteristic, complemented
3#19136093C211yesmaximal, characteristic, complemented
4#19135826C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic, complemented
7#19135294C211yesmaximal, characteristic, complemented
8#19135224C211yesmaximal, characteristic, complemented
9#19135218C211yesmaximal, characteristic, complemented
10#19135218C211yesmaximal, characteristic, complemented
11#19135166C211yesmaximal, characteristic, complemented
12#19135156C211yesmaximal, characteristic, complemented
13#19134858C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C43×#1982C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063306—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26#14582813—21no—
27#14582813—21no—
28#14582802C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582796—21no—
35#14582783—21no—
36#14582782—21no—
37#14582779—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×Dic43⋊C4C2211yescharacteristic
41C4×C4⋊Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#127×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063316—22no—
63#13063316—22no—
64#13063306—44no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
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×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063258—22no—
90#13063257—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—41no—
95#13063235—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43—21no—
104C22×D4×C43—21no—
105C22×D4×C43C2311yescharacteristic
106C22×D4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#127×C43—22no—
110#127×C43—41no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C4⋊C8×C43—41no—
116#102×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#95×C43—21no—
121C24×C43—21no—
122C24×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—42no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—42no—
138C2×D4×C43—81no—
139C2×D4×C43—81no—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—81no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43#4112yes—
166C4⋊C4×C43#4112yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—42no—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C22⋊Dic43—42no—
173C22⋊Dic43—42no—
174C22⋊Dic43—81no—
175C22⋊Dic43—81no—
176C22⋊Dic43—81no—
177C4⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—41no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C22×D411yescharacteristic
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—84no—
228D4×C43—84no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43AGL(1,ℤ/8)12yes—
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
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—41no—
270C2×Dic43—41no—
271C2×Dic43—84no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#26716—431nomaximal, Sylow
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43#52511yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43#54811yescharacteristic
294C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57611yescharacteristic
297C22×C43#57711yescharacteristic
298C4×C43—22no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43#52911yescharacteristic
303C4×C43#54211yescharacteristic
304C4×C43#55211yescharacteristic
305C4×C43#55911yescharacteristic
306Dic43—41no—
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314#2445—431no—
315#2370—431no—
316#2088—431no—
317#2041—431no—
318#2025—431no—
319#2025—431no—
320#1982D4311yescharacteristic
321#1936—431no—
322#1926—431no—
323#1925—431no—
324#1925—431no—
325#1918—431no—
326#1917—431no—
327#1864—431no—
328#1762—431no—
329C2×C43—82no—
330C2×C43—161no—
331C2×C43#245811yescharacteristic
332C2×C43#311511yescharacteristic
333C2×C43#311911yescharacteristic
334C2×C43#331011yescharacteristic
335C2×C43#332211yescharacteristic
336C2×C43#336611yescharacteristic
337C2×C43#337111yescharacteristic
338C2×#127C2×D4311yescharacteristic
339C2×#125—431no—
340C2×#123—861no—
341C2×C4×D4—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×C4⋊C8C2×D4311yescharacteristic
345C2×#102—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102C2×D4311yescharacteristic
350C2×#102C2×D4311yescharacteristic
351C2×#102C2×D4311yescharacteristic
352C2×#102C2×D4311yescharacteristic
353C2×#97—431no—
354#394—861no—
355#394—861no—
356#390—431no—
357#390—431no—
358#390—431no—
359#389—431no—
360#389—431no—
361#389—431no—
362#389—861no—
363#387—861no—
364#387—861no—
365#386—861no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—861no—
370C4×C4⋊C4C2×D4311yescharacteristic
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#336—431no—
378#336—431no—
379#336—431no—
380#336—431no—
381C43#2671611yescharacteristic, complemented, Sylow
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C22×D4311yescharacteristic
385C22×D4C22×D4311yescharacteristic
386C23×C4—861no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#127—22no—
392#127—41no—
393#125—862no—
394#125—862no—
395#123—1724no—
396C4×D4—862no—
397C4×D4—1721no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—21no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#107—862no—
425#106—1721no—
426C4⋊C8—41no—
427#102—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431#102—862no—
432#102—862no—
433#102—862no—
434#102—1721no—
435#97—1721no—
436#95—21no—
437#95—431no—
438#95—431no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444C24—21no—
445C24—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4#1062189812yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—862no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—1721no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4#1062190012yes—
510C4⋊C4#1062190012yes—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—3441no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—3441no—
526C42—3441no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C2×D4×D4311yescharacteristic
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—84no—
551D4—84no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—3444no—
577C2×C4—1721no—
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—1721no—
587C2×C4—1721no—
588C2×C4#1306334912yes—
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062190011yescharacteristic
591C2×C4C2×#1062190011yescharacteristic
592C2×C4C2×#1062189811yescharacteristic
593C2×C4#1306337011yescharacteristic
594C2×C4#1306337211yescharacteristic
595C8—41no—
596C8—41no—
597C8—1721no—
598C8—1721no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1458340911yescharacteristic
614C22#1458353911yescharacteristic
615C22#1458355511yescharacteristic
616C22C2×#1306334911yescharacteristic
617C22#1458369511yescharacteristic
618C22#1458370311yescharacteristic
619C22#1458370511yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—42no—
624C4—3441no—
625C4—3441no—
626C4—3441no—
627C4—1721no—
628C4—1721no—
629C4—1721no—
630C4—1722no—
631C4—1721no—
632C4#1458342911yescharacteristic
633C4#1458351311yescharacteristic
634C4#1458358911yescharacteristic
635C4#1458363511yescharacteristic
636C2—82no—
637C2—161no—
638C2#1913852211yescharacteristic
639C2#1914474311yescharacteristic
640C2#1914479311yescharacteristic
641C2#1914661211yescharacteristic
642C2#1914679211yescharacteristic
643C2#1914730611yescharacteristic
644C2#1914735611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1982C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#1982D43
hypocenterC43#26716
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #19137693C2semidirect
3. #19136093C2semidirect
5. #19135739C2semidirect
6. #19135739C2semidirect
7. #19135294C2semidirect
8. #19135224C2semidirect
9. #19135218C2semidirect
10. #19135218C2semidirect
11. #19135166C2semidirect
12. #19135156C2semidirect
13. #19134858C2semidirect
14. #19134422C2semidirect
381. C43#26716semidirect

Maximal subgroups

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

subgroupindex
#191383562
#191376932
#191360932
#191358262
#191357392
#191352942
#191352242
#191352182
#191351662
#191351562
#191348582
#191344222
C43×#19822
#2671643