Finite Group Databasebeta

← #25107804

Subgroups — #25107804

Order 11008.

1296 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583035C211yesmaximal, characteristic
2C4×#13063299C211yesmaximal, characteristic, complemented
3C2×#14582801C211yesmaximal, characteristic, complemented
4#19135471C212yesmaximal, complemented
5#19135292C212yesmaximal, complemented
6#19135223C212yesmaximal, complemented
7#19134942C212yesmaximal, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134790C211yesmaximal, characteristic, complemented
10#19134527C211yesmaximal, characteristic, complemented
11C43×#1749C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C22×D344C2212yes—
14C2×#13063299C2211yescharacteristic
15C2×C4×D172C2211yescharacteristic, complemented
16C2×C4×C22⋊D43—21no—
17C22×C4⋊Dic43C2211yescharacteristic
18C22×(C2×D43)⋊C4—21no—
19C22×(C2×D43)⋊C4—21no—
20#14583035C418yescomplemented
21C2×#13063257C2212yescomplemented
22C2×#13063247C2212yes—
23C2×#13063247C2212yes—
24C2×#13063247C2212yes—
25C2×#13063247C2212yescomplemented
26#14582801—21no—
27#14582801—21no—
28#14582801C2212yes—
29#14582801C2212yes—
30#14582801C2211yescharacteristic, complemented
31#14582797C2211yescharacteristic, complemented
32#14582790—21no—
33#14582778—21no—
34#14582759C2211yescharacteristic
35C4×C4⋊Dic43C2211yescharacteristic, complemented
36C4×(C2×D43)⋊C4—21no—
37#14582662C2212yescomplemented
38#14582662C2212yescomplemented
39C22×C42×C43C2211yescharacteristic
40C2×C22⋊C8×C43C2211yescharacteristic
41C2×C22⋊C8×C43C2211yescharacteristic
42C2×#97×C43C2212yescomplemented
43C43×#336C2212yescomplemented
44C24×D43—21no—
45C22×D172—21no—
46C22×D172—22no—
47C22×D172—42no—
48C22×D172—42no—
49C22×D172C2×C414yescomplemented
50C22×D172C2312yes—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C23×Dic43—21no—
54C22×C4×D43—21no—
55C2×D344—42no—
56C2×D344—42no—
57C2×D344C2×C418yescomplemented
58#13063299—22no—
59#13063299C2×C414yes—
60C4×D172—42no—
61C4×C22⋊D43—44no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—42no—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2312yes—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—44no—
79C2×(C2×D43)⋊C4—44no—
80C2×C4×Dic43—21no—
81#13063257—42no—
82#13063247—42no—
83#13063247—42no—
84#13063247—42no—
85#13063247C2×C418yescomplemented
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43C2312yes—
93C22×C8×C43C2312yes—
94C2×C42×C43—42no—
95C2×C42×C43D411yescharacteristic
96C2×C42×C43D411yescharacteristic
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2311yescharacteristic
99C22⋊C8×C43—22no—
100C22⋊C8×C43C2×C414yescomplemented
101#97×C43—42no—
102C24×C43C2×D411yescharacteristic
103C23×D43—24no—
104C23×D43—21no—
105C23×D43—22no—
106C23×D43—42no—
107C23×D43—42no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43—42no—
111C23×D43—42no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43C22×C412yes—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4112yes—
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—24no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—42no—
136C22×Dic43—42no—
137C22×Dic43—42no—
138C2×D172—24no—
139C2×D172—21no—
140C2×D172—22no—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—48no—
148C2×D172—48no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172C22×C414yes—
152C2×D172C22×C412yes—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43C22×C414yes—
162C42×C43—22no—
163C42×C43—22no—
164C42×C43—41no—
165C42×C43—41no—
166C22⋊Dic43—42no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—44no—
170(C2×D43)⋊C4—44no—
171(C2×D43)⋊C4—44no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—44no—
175C4⋊Dic43—21no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—42no—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—42no—
183C4×Dic43—42no—
184D344—48no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43C4×D412yes—
190C23×C43AGL(1,ℤ/8)12yes—
191C23×C43AGL(1,ℤ/8)12yes—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—24no—
195C22×D43—48no—
196C22×D43—48no—
197C22×D43—41no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—41no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—42no—
207C22×D43—41no—
208C22×D43—42no—
209C22×D43—48no—
210C22×D43—84no—
211C22×D43—84no—
212C22×D43—84no—
213C22×D43—84no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—44no—
230C2×C4×C43—44no—
231C2×C4×C43C4×D412yes—
232C2×C4×C43AGL(1,ℤ/8)12yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)12yes—
236C2×C4×C43H(5,𝔽2)12yes—
237C22⋊D43—48no—
238C2×Dic43—22no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—42no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—84no—
251D172—24no—
252D172—24no—
253D172—24no—
254D172—48no—
255D172—42no—
256D172—42no—
257D172—42no—
258C4×D43—84no—
259C8×C43—24no—
260C8×C43—42no—
261#22046—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43#44214yes—
269C22×C43C2×C4×D411yescharacteristic
270C22×C43#53411yescharacteristic
271C22×C43#53511yescharacteristic
272C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43#57511yescharacteristic
276C2×D43—44no—
277C2×D43—42no—
278C2×D43—44no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—44no—
282C2×D43—816no—
283C2×D43—82no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—82no—
287C2×D43—81no—
288C2×D43—82no—
289C2×D43—81no—
290C2×D43—82no—
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43#51812yes—
297C4×C43#53812yes—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301Dic43—82no—
302C2×#447—431no—
303C4×#121—431no—
304C2×#390—431no—
305#1972—432no—
306#1936—432no—
307#1926—432no—
308#1879—432no—
309#1874—431no—
310#1853—431no—
311#1786—431no—
312#1749D4311yescharacteristic, complemented
313C2×C43—24no—
314C2×C43#232111yescharacteristic
315C2×C43C2×#44211yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#319211yescharacteristic
318C2×C43#319411yescharacteristic
319C2×C43#321311yescharacteristic
320C2×C43#321711yescharacteristic
321D43—82no—
322D43—84no—
323C23×D4—431no—
324C22×D8—432no—
325C2×#121—431no—
326C2×C4×D4—431no—
327C2×C4×D4—861no—
328C22×C4⋊C4—431no—
329C22×C22⋊C4—861no—
330C22×C22⋊C4—861no—
331C22×C42C2×D4311yescharacteristic
332#447—438no—
333C2×#106—432no—
334C2×#102—432no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102—432no—
338C2×C22⋊C8C2×D4311yescharacteristic
339C2×C22⋊C8C2×D4311yescharacteristic
340C2×#97C2×D4312yescomplemented
341#390—432no—
342#390—432no—
343#390—431no—
344#390—861no—
345#390—861no—
346#389—431no—
347#388—861no—
348#386—861no—
349#380—431no—
350C4×C4⋊C4—431no—
351C4×C22⋊C4—861no—
352#340—432no—
353#340—432no—
354#336C2×D4312yescomplemented
355C43#2204611yescharacteristic, complemented, Sylow
356C25—861no—
357C22×D4—434no—
358C22×D4—431no—
359C22×D4—432no—
360C22×D4—861no—
361C22×D4—861no—
362C22×D4—862no—
363C22×D4—1722no—
364C22×D4—1722no—
365C23×C4—861no—
366C23×C4—861no—
367C23×C4D17211yescharacteristic
368C23×C4D17211yescharacteristic
369C23×C4C22×D4311yescharacteristic
370C2×D8—438no—
371C2×D8—1722no—
372C2×D8—1722no—
373C22×C8C22×D4312yes—
374C22×C8C22×D4312yes—
375#121—434no—
376#121—862no—
377C4×D4—1722no—
378C4×D4—1724no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—432no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—1722no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—1724no—
396C2×C22⋊C4—1724no—
397C2×C42—42no—
398C2×C42—861no—
399C2×C42D17211yescharacteristic
400C2×C42D17211yescharacteristic
401C2×C42C22×D4311yescharacteristic
402C2×C42C22×D4311yescharacteristic
403#106—1722no—
404#102—438no—
405#102—1722no—
406#102—1722no—
407#102—1722no—
408C22⋊C8—22no—
409C22⋊C8C4×D4314yescomplemented
410#97—42no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—864no—
415C24—861no—
416C24—862no—
417C24—1722no—
418C24—1722no—
419C24—1722no—
420C24—1722no—
421C24—1722no—
422C24—1722no—
423C24C2×D17211yescharacteristic
424C2×D4—434no—
425C2×D4—432no—
426C2×D4—864no—
427C2×D4—864no—
428C2×D4—861no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—862no—
432C2×D4—862no—
433C2×D4—862no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4—1728no—
437C2×D4—1722no—
438C2×D4—1722no—
439C2×D4—1728no—
440C2×D4—1722no—
441C2×D4—1722no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4—1722no—
460C22×C4C2×C4×D4312yes—
461C22×C4C2×D17211yescharacteristic
462C22×C4C2×D17211yescharacteristic
463C22×C4C2×D17211yescharacteristic
464C22×C4C2×D17211yescharacteristic
465C22×C4C2×D17211yescharacteristic
466C22×C4#1062189812yes—
467C22×C4C23×D4311yescharacteristic
468D8—1728no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8C2×C4×D4314yes—
475C4⋊C4—432no—
476C4⋊C4—861no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C22⋊C4—864no—
484C22⋊C4—1724no—
485C22⋊C4—1724no—
486C22⋊C4—1724no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C22⋊C4—1724no—
492C42—22no—
493C42—22no—
494C42—41no—
495C42—41no—
496C42—1722no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—862no—
502C23—864no—
503C23—3444no—
504C23—3444no—
505C23—3444no—
506C23—3444no—
507C23—1728no—
508C23—1728no—
509C23—1722no—
510C23—1722no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1722no—
515C23—1721no—
516C23—1722no—
517C23—1721no—
518C23—1722no—
519C23—1722no—
520C23—1721no—
521C23—1728no—
522C23C4×D17212yes—
523C23#1306335312yes—
524C23#1306335312yes—
525C23C22×D17211yescharacteristic
526D4—864no—
527D4—864no—
528D4—864no—
529D4—1728no—
530D4—1728no—
531D4—1722no—
532D4—1722no—
533D4—1722no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—862no—
552C2×C4—3444no—
553C2×C4—3444no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1722no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4C4×D17212yes—
566C2×C4#1306335312yes—
567C2×C4C22×C4×D4311yescharacteristic
568C2×C4C2×#1062189811yescharacteristic
569C2×C4#1306337012yes—
570C2×C4#1306337112yes—
571C8—24no—
572C8—42no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—34416no—
580C22—3442no—
581C22—3441no—
582C22—3442no—
583C22—3441no—
584C22—3441no—
585C22—3442no—
586C22—3442no—
587C22—3441no—
588C22—1722no—
589C22—1724no—
590C22—1724no—
591C22—1722no—
592C22—1724no—
593C22—1722no—
594C22#1458301214yes—
595C22C2×C4×D17211yescharacteristic
596C22#1458346111yescharacteristic
597C22#1458346811yescharacteristic
598C22C2×#1306335311yescharacteristic
599C22C2×#1306335311yescharacteristic
600C22C2×#1306335311yescharacteristic
601C22#1458369911yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—3441no—
608C4—3442no—
609C4—3441no—
610C4—1722no—
611C4#1458337112yes—
612C4#1458348212yes—
613C2—24no—
614C2—3444no—
615C2—3442no—
616C2#1913725511yescharacteristic
617C2C2×#1458301211yescharacteristic
618C2C4×#1306335311yescharacteristic
619C2#1914539511yescharacteristic
620C2#1914541111yescharacteristic
621C2#1914558411yescharacteristic
622C2#1914561511yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1749C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1749D43
hypocenterC43#22046
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C4×#13063299C2semidirect
3. C2×#14582801C2semidirect
4. #19135471C2semidirect
5. #19135292C2semidirect
6. #19135223C2semidirect
7. #19134942C2semidirect
8. #19134910C2semidirect
9. #19134790C2semidirect
10. #19134527C2semidirect
11. C43×#1749C2semidirect
15. C2×C4×D172C22semidirect
20. #14583035C4semidirect
21. C2×#13063257C22semidirect
25. C2×#13063247C22semidirect
30. #14582801C22semidirect
31. #14582797C22semidirect
35. C4×C4⋊Dic43C22semidirect
37. #14582662C22semidirect
38. #14582662C22semidirect
42. C2×#97×C43C22semidirect
43. C43×#336C22semidirect
49. C22×D172C2×C4semidirect
57. C2×D344C2×C4semidirect
85. #13063247C2×C4semidirect
100. C22⋊C8×C43C2×C4semidirect
312. #1749D43semidirect
340. C2×#97C2×D43semidirect
354. #336C2×D43semidirect
355. C43#22046semidirect
409. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830352
C4×#130632992
C2×#145828012
#191354712
#191352922
#191352232
#191349422
#191349102
#191347902
#191345272
C43×#17492
#2204643