Finite Group Databasebeta

← #25156674

Subgroups — #25156674

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583120C211yesmaximal, characteristic
2C2×#14582990C211yesmaximal, characteristic
3#19138380C211yesmaximal, characteristic
4#19137512C211yesmaximal, characteristic, complemented
5#19136146C211yesmaximal, characteristic, complemented
6#19136099C211yesmaximal, characteristic, complemented
7#19135834C211yesmaximal, characteristic
8#19135269C211yesmaximal, characteristic, complemented
9#19135151C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134937C211yesmaximal, characteristic, complemented
12#19134935C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134840C211yesmaximal, characteristic
15C43×#2073C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583120—24no—
24#14582990—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582824—21no—
36#14582824—21no—
37#14582805C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582796—21no—
41#14582796—21no—
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582774—21no—
45#14582763—21no—
46#14582760—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582750—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063312—22no—
73#13063312—41no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79#13063290—41no—
80D4×Dic43—22no—
81D4×Dic43—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063258—41no—
101#13063256—22no—
102Dic43⋊C8—22no—
103#13063250—22no—
104#13063250—22no—
105#13063248—22no—
106#13063248—22no—
107#13063248—41no—
108#13063246—22no—
109C8×Dic43—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#102×C43—22no—
129#102×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C2×D412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—81no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×D412yes—
166C2×Dic86#4112yes—
167C2×Dic86#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—81no—
182C42×C43—21no—
183C42×C43—21no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187#10621883—28no—
188C4⋊Dic43—21no—
189C4⋊Dic43—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—81no—
194C4⋊Dic43#4112yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200C4×Dic43—24no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C2×D412yes—
213Dic172—44no—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
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—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C22×D411yescharacteristic
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—22no—
248C2×Dic43—21no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
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—84no—
271C2×Dic43#13512yes—
272Dic86—22no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86#12314yes—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#26165—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#52511yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43C2×#12311yescharacteristic
305C4×C43#53911yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#55311yescharacteristic
308Dic43—24no—
309Dic43—22no—
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316C2×#464—431no—
317C2×C4×SD16—431no—
318#2447—431no—
319#2351—431no—
320#2097—431no—
321#2088—431no—
322#2073D4311yescharacteristic
323#2042—431no—
324#1933—431no—
325#1916—431no—
326#1880—431no—
327#1878—431no—
328#1878—431no—
329#1863—431no—
330#1862—431no—
331C2×C43—82no—
332C2×C43#244311yescharacteristic
333C2×C43#310211yescharacteristic
334C2×C43#312111yescharacteristic
335C2×C43#326911yescharacteristic
336C2×C43#328211yescharacteristic
337C2×C43#336411yescharacteristic
338C2×C43#337111yescharacteristic
339C22×Q16—431no—
340C22×SD16—431no—
341C2×#124—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—431no—
345C2×C4×D4—431no—
346#464—864no—
347C4×SD16—864no—
348C2×#107—431no—
349C2×#106—431no—
350C2×C4⋊C8—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×C4×C8—431no—
360#397—861no—
361#397—861no—
362#391—431no—
363#391—431no—
364#390C2×D4311yescharacteristic
365#389—431no—
366#389—431no—
367#389—431no—
368#389—861no—
369#389—861no—
370#385—861no—
371#382—861no—
372#382C2×D4311yescharacteristic
373#381—861no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—861no—
376#340—431no—
377#340—431no—
378#340C2×D4311yescharacteristic
379#340C2×D4311yescharacteristic
380#336—431no—
381#336—431no—
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2616511yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—431no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—861no—
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—862no—
392C2×SD16—434no—
393C2×SD16—862no—
394C2×SD16—862no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#124—862no—
400#124—1721no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C4×D4—862no—
408C4×D4—1721no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—1721no—
434#106—862no—
435C4⋊C8—862no—
436#103—862no—
437#103—862no—
438#103—862no—
439#103—862no—
440#103—1721no—
441#102—22no—
442#102—22no—
443#102—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—431no—
448#95—431no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C2×Q8—432no—
458C2×Q8—432no—
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4D4×D4312yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—1724no—
493SD16—868no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—432no—
513C4⋊C4—862no—
514C4⋊C4—864no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—1721no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—864no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1722no—
537C42—1722no—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C2×D4×D4311yescharacteristic
546Q8—434no—
547Q8—862no—
548Q8—862no—
549Q8—862no—
550Q8—1721no—
551Q8—1721no—
552Q8—1721no—
553Q8—1721no—
554D4—22no—
555D4—22no—
556D4—41no—
557D4—41no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—432no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—861no—
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—3444no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#1306337111yescharacteristic
603C2×C4#1306337211yescharacteristic
604C8—41no—
605C8—41no—
606C8—862no—
607C8—1721no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1458340711yescharacteristic
616C22#1458353311yescharacteristic
617C22#1458355711yescharacteristic
618C22#135×D4311yescharacteristic
619C22#1458369511yescharacteristic
620C22#1458370911yescharacteristic
621C22#1458371311yescharacteristic
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—864no—
628C4—862no—
629C4—3441no—
630C4—3441no—
631C4—1721no—
632C4—1722no—
633C4—1721no—
634C4—1721no—
635C4#123×D4311yescharacteristic
636C4#1458349011yescharacteristic
637C4#1458354711yescharacteristic
638C4#1458360011yescharacteristic
639C2—82no—
640C2#1913832511yescharacteristic
641C2#1914460811yescharacteristic
642C2#1914481911yescharacteristic
643C2#1914615611yescharacteristic
644C2#1914630811yescharacteristic
645C2#1914727711yescharacteristic
646C2#1914735811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2073C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2073D43
hypocenterC43#26165
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
4. #19137512C2semidirect
5. #19136146C2semidirect
6. #19136099C2semidirect
8. #19135269C2semidirect
9. #19135151C2semidirect
11. #19134937C2semidirect
12. #19134935C2semidirect
13. #19134850C2semidirect
384. C43#26165semidirect

Maximal subgroups

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

subgroupindex
C2×#145831202
C2×#145829902
#191383802
#191375122
#191361462
#191360992
#191358342
#191352692
#191351512
#191349532
#191349372
#191349352
#191348502
#191348402
C43×#20732
#2616543