Finite Group Databasebeta

← #25130486

Subgroups — #25130486

Order 11008.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic, complemented
2C2×#14583179C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19135777C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135555C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134913C212yesmaximal, complemented
9#19134782C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#2537C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C22×#10621882C2211yescharacteristic
14#14583553—24no—
15#14583553—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063309—22no—
18C2×#13063305—21no—
19C2×#13063299C2212yes—
20C2×C4×D172C2211yescharacteristic
21C22×C4⋊Dic43C2212yes—
22#14583179—24no—
23C4×#10621882—24no—
24C2×#13063258C2212yes—
25C2×#13063258C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2212yes—
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37C2×#121×C43—21no—
38C2×#121×C43C2212yes—
39C2×C4×D4×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C43×#394—22no—
42C43×#384C2211yescharacteristic
43C43×#380—21no—
44C43×#380C2212yes—
45C2×#10621900—28no—
46C2×#10621900—44no—
47C2×#10621900—44no—
48C22×Dic86—21no—
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—22no—
51C23×Dic43—22no—
52C22×C4×D43—21no—
53C2×#10621882—22no—
54C2×#10621882—22no—
55C2×#10621882—22no—
56C22×C43⋊C8C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2311yescharacteristic
59#13063325—22no—
60#13063325D414yescomplemented
61#13063309—216no—
62#13063305—28no—
63#13063299—24no—
64#13063299—24no—
65C4×D172—22no—
66C4×D172D414yescomplemented
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—22no—
75#13063258—24no—
76#13063258—22no—
77C4⋊(C43⋊C8)—22no—
78#13063246—24no—
79#13063246—22no—
80#13063245—22no—
81#13063245—42no—
82C22⋊(C43⋊C8)—24no—
83C22⋊(C43⋊C8)—42no—
84C4×C43⋊C8—22no—
85C22×D4×C43—22no—
86C22×D4×C43D411yescharacteristic
87C22×D4×C43C2311yescharacteristic
88C23×C4×C43—21no—
89C23×C4×C43C2312yes—
90#121×C43—24no—
91#121×C43—42no—
92#121×C43—44no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2312yes—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43D412yes—
106C2×C42×C43C2311yescharacteristic
107#95×C43—22no—
108C24×C43—21no—
109C24×C43C2×D412yes—
110C23×D43—21no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—44no—
119C2×D4×C43—44no—
120C2×D4×C43—82no—
121C2×D4×C43D814yescomplemented
122C2×D4×C43#4112yescomplemented
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—28no—
139C2×C22⋊D43—44no—
140C2×C22⋊D43—44no—
141C22×Dic43—28no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—44no—
145C22×Dic43—44no—
146#10621900—432no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C2×D412yes—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×Dic86—24no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—81no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—44no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—44no—
170C42×C43C2×D412yes—
171C42×C43C2×D412yes—
172#10621882—28no—
173(C2×D43)⋊C4—28no—
174(C2×D43)⋊C4—24no—
175C4⋊Dic43—28no—
176C4⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43—22no—
179C4⋊Dic43C2×D412yes—
180C4⋊Dic43C2×D414yes—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8#4112yescomplemented
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43C2×D814yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—28no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—88no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—84no—
234C2×C4×C43#12012yes—
235C2×C4×C43#12012yes—
236C2×C4×C43C2×D812yes—
237C2×C4×C43AGL(1,ℤ/8)12yes—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C22⋊D43—416no—
245C2×Dic43—24no—
246C2×Dic43—22no—
247C2×Dic43—416no—
248C2×Dic43—42no—
249C2×Dic43—41no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252D172—22no—
253D172—22no—
254D172—41no—
255D172—41no—
256C4×D43—48no—
257Dic86—48no—
258C43⋊C8—22no—
259C43⋊C8—41no—
260C43⋊C8—42no—
261#24116—431nomaximal, Sylow
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—24no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12011yescharacteristic
277C22×C43#54611yescharacteristic
278C22×C43#54711yescharacteristic
279C22×C43C22×D811yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—82no—
294C4×C43#44714yes—
295C4×C43#52511yescharacteristic
296C4×C43#53711yescharacteristic
297C4×C43#54811yescharacteristic
298C4×C43#55011yescharacteristic
299Dic43—44no—
300Dic43—42no—
301C2×#547—431no—
302C2×#474—431no—
303C2×C4×D8—431no—
304#2537D4311yescharacteristic, complemented
305#2033—432no—
306#1999—432no—
307#1990—431no—
308#1954—431no—
309#1874—432no—
310#1852—432no—
311#1802—431no—
312C2×C43—44no—
313C2×C43—82no—
314C2×C43#240711yescharacteristic
315C2×C43C2×#44711yescharacteristic
316C2×C43#301311yescharacteristic
317C2×C43#329411yescharacteristic
318C2×C43#333011yescharacteristic
319C2×C43#333411yescharacteristic
320C2×C43#335411yescharacteristic
321D43—82no—
322C22×#41—861no—
323C22×D8—431no—
324#547—864no—
325#547—864no—
326C2×C4⋊Q8—431no—
327C2×#123—862no—
328C2×C22⋊Q8—861no—
329C2×#121—21no—
330C2×#121—432no—
331C2×#121C2×D4312yes—
332C2×C4×D4—431no—
333C2×C4×D4C2×D4311yescharacteristic
334C2×C4×D4C2×D4311yescharacteristic
335C22×C4⋊C4—432no—
336#474—864no—
337C4×D8—864no—
338C2×#107—431no—
339C2×#107—432no—
340C2×C4⋊C8—431no—
341C2×#102—431no—
342C2×#102—432no—
343C2×#102—431no—
344C2×#102—432no—
345C2×C22⋊C8—432no—
346C2×C22⋊C8—432no—
347C2×C4×C8—431no—
348#394—22no—
349#384C2×D4311yescharacteristic
350#380—21no—
351#380C2×D4312yes—
352#340—432no—
353#340—432no—
354#340—432no—
355C43#2411611yescharacteristic, complemented, Sylow
356C2×#41—868no—
357C2×#41—1724no—
358C2×#41—1724no—
359C22×Q8—861no—
360C22×D4—22no—
361C22×D4—431no—
362C22×D4—862no—
363C22×D4C22⋊D4311yescharacteristic
364C22×D4C22×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—862no—
367C23×C4—861no—
368C23×C4C22×D4312yes—
369C2×D8—862no—
370C2×D8—862no—
371C2×D8—862no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—432no—
375C4⋊Q8—434no—
376C4⋊Q8—862no—
377#123—8616no—
378C22⋊Q8—868no—
379#121—24no—
380#121—42no—
381#121—44no—
382#121—864no—
383#121—864no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—434no—
389C4×D4—862no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—432no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22⋊D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4312yes—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4C22⋊D4312yes—
407C2×C42C22×D4311yescharacteristic
408#107—862no—
409#107—864no—
410C4⋊C8—862no—
411#102—862no—
412#102—862no—
413#102—864no—
414#102—1722no—
415C22⋊C8—864no—
416C22⋊C8—1722no—
417C4×C8—862no—
418#95—22no—
419C24—21no—
420C24—861no—
421C24C2×C22⋊D4312yes—
422#41—17232no—
423C2×Q8—864no—
424C2×Q8—1722no—
425C2×Q8—1722no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—82no—
436C2×D4—432no—
437C2×D4—868no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1724no—
444C2×D4—1724no—
445C2×D4#1062188214yescomplemented
446C2×D4#1062190012yescomplemented
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—868no—
459C22×C4—861no—
460C22×C4—862no—
461C22×C4—864no—
462C22×C4—1724no—
463C22×C4—1724no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4C2×C22⋊D4312yes—
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470D8—868no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—861no—
478C2×C8—862no—
479C2×C8—861no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4—432no—
488C4⋊C4—434no—
489C4⋊C4—868no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—862no—
493C22⋊C4—24no—
494C22⋊C4—44no—
495C22⋊C4—44no—
496C22⋊C4—42no—
497C22⋊C4—868no—
498C22⋊C4—864no—
499C42D4×D4312yes—
500C42D4×D4312yes—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—862no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23C2×#1062188214yes—
522C23C22×C22⋊D4311yescharacteristic
523Q8—1728no—
524D4—22no—
525D4—22no—
526D4—28no—
527D4—41no—
528D4—41no—
529D4—88no—
530D4—862no—
531D4—862no—
532D4—17216no—
533D4—1721no—
534D4—1721no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4—862no—
552C2×C4—864no—
553C2×C4—17216no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4—1722no—
558C2×C4—1728no—
559C2×C4#1306329312yes—
560C2×C4#1306329312yes—
561C2×C4C2×#1062188212yes—
562C2×C4#1306335012yes—
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4C2×#1062190011yescharacteristic
567C2×C4#1306337011yescharacteristic
568C2×C4#1306337211yescharacteristic
569C8—862no—
570C8—1722no—
571C8—1721no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—3441no—
590C22—1722no—
591C22—1722no—
592C22—1722no—
593C22C2×#1306329311yescharacteristic
594C22#1458354311yescharacteristic
595C22#1458354811yescharacteristic
596C22C22×#1062188211yescharacteristic
597C22C2×#1306335011yescharacteristic
598C22#1458371011yescharacteristic
599C22#1458371411yescharacteristic
600C4—22no—
601C4—42no—
602C4—81no—
603C4—82no—
604C4—1722no—
605C4—1724no—
606C4#1458303214yes—
607C4#1458340911yescharacteristic
608C4#1458347811yescharacteristic
609C4#1458355511yescharacteristic
610C4#1458356711yescharacteristic
611C2—44no—
612C2—82no—
613C2—3442no—
614C2#1913793611yescharacteristic
615C2C2×#1458303211yescharacteristic
616C2#1914390711yescharacteristic
617C2#1914640811yescharacteristic
618C2#1914690011yescharacteristic
619C2#1914693811yescharacteristic
620C2#1914718411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2537C2
socleC23×C43C22×D4
hypercenter#2537D43
hypocenterC43#24116
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#14583553C2semidirect
2. C2×#14583179C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19135777C2semidirect
5. #19135591C2semidirect
6. #19135555C2semidirect
7. #19135390C2semidirect
8. #19134913C2semidirect
9. #19134782C2semidirect
10. #19134592C2semidirect
11. C43×#2537C2semidirect
60. #13063325D4semidirect
66. C4×D172D4semidirect
121. C2×D4×C43D8semidirect
122. C2×D4×C43#41semidirect
189. C2×C43⋊C8#41semidirect
304. #2537D43semidirect
355. C43#24116semidirect
445. C2×D4#10621882semidirect
446. C2×D4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
C2×#145831792
C2×C4×#106218822
#191357772
#191355912
#191355552
#191353902
#191349132
#191347822
#191345922
C43×#25372
#2411643