Finite Group Databasebeta

← #25107807

Subgroups — #25107807

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×#14583032C211yesmaximal, characteristic
2#121×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582800C211yesmaximal, characteristic, complemented
4#19135468C212yesmaximal, complemented
5#19135293C212yesmaximal, complemented
6#19135220C212yesmaximal, complemented
7#19134941C212yesmaximal, complemented
8#19134788C211yesmaximal, characteristic, complemented
9#19134527C211yesmaximal, characteristic, complemented
10#19134359C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C22×#10621882C2212yes—
14C2×D4×Dic43—21no—
15C2×D4×Dic43C2211yescharacteristic, complemented
16C22×(C2×D43)⋊C4—21no—
17C22×(C2×D43)⋊C4—21no—
18C22×C4×Dic43C2211yescharacteristic
19#14583032C418yescomplemented
20C2×#13063256C2212yescomplemented
21C2×#13063247C2212yes—
22C2×#13063247C2212yes—
23C2×#13063245C2212yes—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2212yescomplemented
26#14582802C2211yescharacteristic, complemented
27#14582800—21no—
28#14582800—21no—
29#14582800C2212yes—
30#14582800C2212yes—
31#14582798C2211yescharacteristic, complemented
32#14582792—21no—
33#14582779—21no—
34#14582759C2211yescharacteristic
35C4⋊C4×Dic43C2211yescharacteristic, complemented
36C22⋊C4×Dic43—21no—
37#14582661C2212yescomplemented
38#14582653C2212yescomplemented
39C2×#121×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C2×#102×C43C2212yescomplemented
42C2×C22⋊C8×C43C2211yescharacteristic
43C43×#340C2212yescomplemented
44C24×D43—21no—
45C22×D172—21no—
46C22×D172—22no—
47C22×D172—42no—
48C22×D172—42no—
49C22×D172C2×C414yescomplemented
50C22×D172C2312yes—
51C23×Dic43—21no—
52C23×Dic43D411yescharacteristic
53C23×Dic43D411yescharacteristic
54C2×#10621882—42no—
55C2×#10621882—42no—
56C2×#10621882C2×C418yescomplemented
57C22×C43⋊C8C2312yes—
58D4×Dic43—42no—
59D4×Dic43—44no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2311yescharacteristic
62C2×C4⋊Dic43C2311yescharacteristic
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—44no—
72C2×(C2×D43)⋊C4—44no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—42no—
75C2×C4×Dic43D411yescharacteristic
76C2×C4×Dic43D411yescharacteristic
77C2×C4×Dic43C2311yescharacteristic
78C2×C4×Dic43C2311yescharacteristic
79#13063256—42no—
80#13063247—42no—
81#13063247—42no—
82#13063245C2×C418yescomplemented
83C22⋊(C43⋊C8)C2×C414yescomplemented
84#13063235—42no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C22×D4×C43—21no—
89C22×D4×C43C2311yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43C2312yes—
93#121×C43—22no—
94#121×C43C2×C414yes—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—42no—
97C2×C4⋊C4×C43C2312yes—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
100#102×C43—42no—
101C22⋊C8×C43—22no—
102C24×C43—21no—
103C24×C43C2×D411yescharacteristic
104C23×D43—24no—
105C23×D43—22no—
106C23×D43—42no—
107C23×D43—42no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43—42no—
111C23×D43—42no—
112C2×D4×C43—21no—
113C2×D4×C43—24no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—42no—
117C2×D4×C43—42no—
118C2×D4×C43C22×C412yes—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4112yes—
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C22×Dic43—42no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×D172—24no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—22no—
150C2×D172—22no—
151C2×D172—48no—
152C2×D172—48no—
153C2×D172—42no—
154C2×D172—42no—
155C2×D172C22×C414yes—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43C22×C412yes—
164C22⋊C4×C43—24no—
165C22⋊Dic43—42no—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169#10621882—48no—
170(C2×D43)⋊C4—44no—
171(C2×D43)⋊C4—44no—
172(C2×D43)⋊C4—44no—
173(C2×D43)⋊C4—44no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—42no—
177C4×Dic43—22no—
178C4×Dic43—22no—
179C4×Dic43—41no—
180C4×Dic43—41no—
181C4×Dic43—42no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8C22×C414yes—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—22no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43C4×D412yes—
197C23×C43AGL(1,ℤ/8)12yes—
198C23×C43AGL(1,ℤ/8)12yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—24no—
201C22×D43—48no—
202C22×D43—48no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—48no—
210C22×D43—84no—
211C22×D43—84no—
212C22×D43—84no—
213C22×D43—84no—
214D4×C43—24no—
215D4×C43—48no—
216D4×C43—42no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—84no—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)12yes—
232C2×C4×C43H(5,𝔽2)12yes—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—84no—
253C2×Dic43AGL(1,ℤ/8)12yes—
254D172—24no—
255D172—24no—
256D172—48no—
257D172—42no—
258D172—42no—
259C8×C43—42no—
260C43⋊C8—24no—
261#22046—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43#44214yes—
276C22×C43C2×C4×D411yescharacteristic
277C22×C43#53411yescharacteristic
278C22×C43#53511yescharacteristic
279C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43#57511yescharacteristic
283C2×D43—44no—
284C2×D43—44no—
285C2×D43—44no—
286C2×D43—816no—
287C2×D43—82no—
288C2×D43—82no—
289C2×D43—82no—
290C2×D43—82no—
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—82no—
294C4×C43#51812yes—
295C4×C43#53812yes—
296Dic43—22no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302C2×#447—431no—
303C4×#121—431no—
304C2×#390—431no—
305#1972—432no—
306#1936—432no—
307#1926—432no—
308#1879—432no—
309#1874D4311yescharacteristic, complemented
310#1853—431no—
311#1786—431no—
312#1749—431no—
313C2×C43—24no—
314C2×C43—82no—
315C2×C43#232111yescharacteristic
316C2×C43C2×#44211yescharacteristic
317C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C43#319211yescharacteristic
319C2×C43#319411yescharacteristic
320C2×C43#321311yescharacteristic
321C2×C43#321711yescharacteristic
322D43—84no—
323C23×D4—431no—
324C22×D8—432no—
325C2×#121C2×D4311yescharacteristic
326C2×C4×D4—431no—
327C2×C4×D4—861no—
328C22×C4⋊C4C2×D4311yescharacteristic
329C22×C22⋊C4—861no—
330C22×C22⋊C4—861no—
331C22×C42—431no—
332#447—438no—
333C2×#106—432no—
334C2×#102—432no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102C2×D4312yescomplemented
338C2×C22⋊C8—431no—
339C2×C22⋊C8C2×D4311yescharacteristic
340C2×#97—432no—
341#390—431no—
342#390—432no—
343#390—432no—
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#340C2×D4312yescomplemented
354#336—432no—
355C43#2204611yescharacteristic, complemented, Sylow
356C25—861no—
357C22×D4—21no—
358C22×D4—434no—
359C22×D4—432no—
360C22×D4—861no—
361C22×D4—862no—
362C22×D4—1722no—
363C22×D4—1722no—
364C22×D4C22×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—861no—
369C23×C4C22×D4311yescharacteristic
370C2×D8—438no—
371C2×D8—1722no—
372C2×D8—1722no—
373C22×C8—432no—
374C22×C8C22×D4312yes—
375#121—22no—
376#121C4×D4314yes—
377C4×D4—1722no—
378C4×D4—1724no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4312yes—
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—1724no—
396C2×C22⋊C4—1724no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—861no—
402C2×C42—1722no—
403#106—1722no—
404#102—42no—
405#102—438no—
406#102—1722no—
407#102—1722no—
408C22⋊C8—22no—
409C22⋊C8—434no—
410#97—1722no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—21no—
415C24—864no—
416C24—862no—
417C24—1722no—
418C24—1722no—
419C24—1722no—
420C24—1722no—
421C24—1722no—
422C24—1722no—
423C24D4×D4311yescharacteristic
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—434no—
431C2×D4—864no—
432C2×D4—862no—
433C2×D4—862no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4—862no—
437C2×D4—1728no—
438C2×D4—1722no—
439C2×D4—1722no—
440C2×D4—1728no—
441C2×D4C2×C4×D4312yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1722no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4C2×C4×D4312yes—
465C22×C4D4×D4311yescharacteristic
466C22×C4#1062190012yes—
467C22×C4C23×D4311yescharacteristic
468D8—1728no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—434no—
473C2×C8—862no—
474C2×C8—862no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—1722no—
482C4⋊C4C2×C4×D4312yes—
483C22⋊C4—24no—
484C22⋊C4—1724no—
485C22⋊C4—1724no—
486C22⋊C4—1724no—
487C22⋊C4—1724no—
488C22⋊C4—1722no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C42—862no—
493C42—862no—
494C42—1721no—
495C42—1721no—
496C42—1722no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—864no—
509C23—3444no—
510C23—3444no—
511C23—3444no—
512C23—3444no—
513C23—1728no—
514C23—1728no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1728no—
522C23(C22⋊D43)⋊C412yes—
523C23#1306334912yes—
524C23#1306335212yes—
525C23C2×D4×D4311yescharacteristic
526D4—24no—
527D4—48no—
528D4—42no—
529D4—864no—
530D4—864no—
531D4—1728no—
532D4—1722no—
533D4—1722no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3444no—
558C2×C4—1724no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1724no—
566C2×C4(C22⋊D43)⋊C412yes—
567C2×C4C22×C4×D4311yescharacteristic
568C2×C4C2×#1062190011yescharacteristic
569C2×C4#1306337012yes—
570C2×C4#1306337112yes—
571C8—42no—
572C8—864no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—34416no—
587C22—3442no—
588C22—3442no—
589C22—3442no—
590C22—3442no—
591C22—1724no—
592C22—1724no—
593C22—1724no—
594C22#1458300814yes—
595C22C2×(C22⋊D43)⋊C411yescharacteristic
596C22#1458346011yescharacteristic
597C22#1458346411yescharacteristic
598C22AGL(1,ℤ/8)×D4311yescharacteristic
599C22C2×#1306334911yescharacteristic
600C22C2×#1306335211yescharacteristic
601C22#1458369811yescharacteristic
602C4—22no—
603C4—42no—
604C4—82no—
605C4—862no—
606C4—3441no—
607C4—3441no—
608C4—1721no—
609C4—1721no—
610C4—1721no—
611C4#1458337112yes—
612C4#1458348612yes—
613C2—24no—
614C2—82no—
615C2—3444no—
616C2#1913725811yescharacteristic
617C2C2×#1458300811yescharacteristic
618C2#1914340811yescharacteristic
619C2#1914539411yescharacteristic
620C2#1914540811yescharacteristic
621C2#1914558111yescharacteristic
622C2#1914561111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#22046
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. #121×Dic43C2semidirect
3. C2×#14582800C2semidirect
4. #19135468C2semidirect
5. #19135293C2semidirect
6. #19135220C2semidirect
7. #19134941C2semidirect
8. #19134788C2semidirect
9. #19134527C2semidirect
10. #19134359C2semidirect
11. C43×#1874C2semidirect
15. C2×D4×Dic43C22semidirect
19. #14583032C4semidirect
20. C2×#13063256C22semidirect
25. C2×#13063235C22semidirect
26. #14582802C22semidirect
31. #14582798C22semidirect
35. C4⋊C4×Dic43C22semidirect
37. #14582661C22semidirect
38. #14582653C22semidirect
41. C2×#102×C43C22semidirect
43. C43×#340C22semidirect
49. C22×D172C2×C4semidirect
56. C2×#10621882C2×C4semidirect
82. #13063245C2×C4semidirect
83. C22⋊(C43⋊C8)C2×C4semidirect
309. #1874D43semidirect
337. C2×#102C2×D43semidirect
353. #340C2×D43semidirect
355. C43#22046semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
#121×Dic432
C2×#145828002
#191354682
#191352932
#191352202
#191349412
#191347882
#191345272
#191343592
C43×#18742
#2204643