Finite Group Databasebeta

← #25157043

Subgroups — #25157043

Order 11008.

812 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
1C2×#14583121C211yesmaximal, characteristic
2C2×#14583003C211yesmaximal, characteristic, complemented
3#19138395C211yesmaximal, characteristic
4#19137513C211yesmaximal, characteristic, complemented
5#19136113C211yesmaximal, characteristic
6#19136096C211yesmaximal, characteristic, complemented
7#19136017C211yesmaximal, characteristic, complemented
8#19135837C211yesmaximal, characteristic
9#19135290C211yesmaximal, characteristic
10#19135162C211yesmaximal, characteristic, complemented
11#19134948C211yesmaximal, characteristic
12#19134948C211yesmaximal, characteristic
13#19134934C211yesmaximal, characteristic, complemented
14#19134846C211yesmaximal, characteristic, complemented
15C43×#1863C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22#14583121—24no—
23#14583003—24no—
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33#14582834—21no—
34#14582828—21no—
35#14582804C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582797—21no—
39#14582797C2211yescharacteristic
40#14582795—21no—
41#14582795C2211yescharacteristic
42#14582789—21no—
43#14582788—21no—
44#14582764—21no—
45#14582764C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885D414yes—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063313—22no—
72#13063313—41no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75Q8×Dic43—22no—
76Q8×Dic43—41no—
77#13063290—22no—
78#13063290—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063256—22no—
100C4⋊(C43⋊C8)—22no—
101#13063250—22no—
102#13063250—22no—
103#13063248—22no—
104#13063247—22no—
105#13063247—41no—
106#13063245—22no—
107#13063235—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C4×Q8×C43—22no—
120C4×Q8×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43—41no—
129#103×C43—22no—
130#103×C43—22no—
131#95×C43—21no—
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×D412yes—
137C2×Q8×C43#4112yes—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
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×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D412yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—42no—
182#10621885—28no—
183#10621884—44no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—24no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201C4×Dic43—24no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D412yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—22no—
225Q8×C43#12314yes—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
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×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275Dic86—22no—
276Dic86—22no—
277Dic86—41no—
278Dic86—41no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283#26189—431nomaximal, Sylow
284C22×C43#52511yescharacteristic
285C22×C43D4211yescharacteristic
286C22×C43#54811yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—24no—
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—41no—
309Dic43—42no—
310Dic43—41no—
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315C2×#464—431no—
316C2×#441—431no—
317#2448—431no—
318#2351—431no—
319#2092—431no—
320#2088—431no—
321#2074—431no—
322#2042—431no—
323#1936—431no—
324#1917—431no—
325#1880—431no—
326#1880—431no—
327#1878—431no—
328#1863—431no—
329#1863D4311yescharacteristic, complemented
330C2×C43#244311yescharacteristic
331C2×C43#311111yescharacteristic
332C2×C43#312111yescharacteristic
333C2×C43#327111yescharacteristic
334C2×C43#327711yescharacteristic
335C2×C43#337111yescharacteristic
336C2×C43#337711yescharacteristic
337D43—161no—
338C22×Q16—431no—
339C22×SD16—431no—
340C2×#124—431no—
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8C2×D4311yescharacteristic
345#464—864no—
346#441—864no—
347C2×#107C2×D4311yescharacteristic
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103C2×D4311yescharacteristic
354C2×#103C2×D4311yescharacteristic
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#97—431no—
359#399—861no—
360#397—861no—
361#391—431no—
362#390—431no—
363#390—431no—
364#389—431no—
365#389—431no—
366#389—861no—
367#389—861no—
368#389C2×D4311yescharacteristic
369#388—861no—
370#388—861no—
371#382—431no—
372#382—861no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—861no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340C2×D4311yescharacteristic
379#336—431no—
380#336—431no—
381#336—431no—
382#336C2×D4311yescharacteristic
383C43#2618911yescharacteristic, complemented, Sylow
384C22×Q8—431no—
385C22×Q8C22×D4311yescharacteristic
386C22×D4—431no—
387C2×Q16—434no—
388C2×Q16—862no—
389C2×Q16—862no—
390C2×SD16—862no—
391C2×SD16—862no—
392C2×SD16—862no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#124—862no—
398#124—1721no—
399C4×Q8—22no—
400C4×Q8—41no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—21no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#107—41no—
435#106—862no—
436C4⋊C8—862no—
437#103—22no—
438#103—22no—
439#103—862no—
440#103—862no—
441#103—862no—
442#102—862no—
443#102—862no—
444#102—1721no—
445#97—862no—
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—
455C24—861no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8#1062189812yes—
466C2×Q8D4×D4312yes—
467C2×Q8#1062190212yes—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C22×C4—21no—
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×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4C23×D4311yescharacteristic
488Q16—868no—
489SD16—1724no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—432no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—432no—
511C4⋊C4—864no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C22⋊C4—3441no—
522C22⋊C4—3441no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—864no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C42—1722no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23C2×D4×D4311yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—862no—
549Q8—862no—
550Q8—1721no—
551Q8—1721no—
552Q8#1306331014yes—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—861no—
576C2×C4—862no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
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—862no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4C2×#1062190211yescharacteristic
600C2×C4#1306337011yescharacteristic
601C2×C4#1306337211yescharacteristic
602C8—41no—
603C8—41no—
604C8—862no—
605C8—1721no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22#1458341211yescharacteristic
614C22#1458353111yescharacteristic
615C22#1458355811yescharacteristic
616C22#1458369611yescharacteristic
617C22#1458369811yescharacteristic
618C22#1458370911yescharacteristic
619C22#1458371211yescharacteristic
620C4—24no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—3441no—
627C4—1721no—
628C4—1722no—
629C4—1721no—
630C4—1722no—
631C4—1721no—
632C4—1721no—
633C4C2×#1306331011yescharacteristic
634C4#1458349811yescharacteristic
635C4#1458354711yescharacteristic
636C4#1458359811yescharacteristic
637C2—6881no—
638C2#1913833411yescharacteristic
639C2#1914471111yescharacteristic
640C2#1914482911yescharacteristic
641C2#1914617311yescharacteristic
642C2#1914625211yescharacteristic
643C2#1914736811yescharacteristic
644C2#1914743311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1863C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1863D43
hypocenterC43#26189
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
2. C2×#14583003C2semidirect
4. #19137513C2semidirect
6. #19136096C2semidirect
7. #19136017C2semidirect
10. #19135162C2semidirect
13. #19134934C2semidirect
14. #19134846C2semidirect
15. C43×#1863C2semidirect
329. #1863D43semidirect
383. C43#26189semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×#145830032
#191383952
#191375132
#191361132
#191360962
#191360172
#191358372
#191352902
#191351622
#191349482
#191349342
#191348462
C43×#18632
#2618943