Finite Group Databasebeta

← #24995577

Subgroups — #24995577

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142938C211yesmaximal, characteristic
2C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582634C211yesmaximal, characteristic, complemented
4C2×#14582633C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic, complemented
6Dic43⋊#95C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic, complemented
8C2×#13063321C411yescharacteristic, complemented
9C2×#13063299C2211yescharacteristic
10C2×#13063297—21no—
11C2×#13063297—21no—
12C22×Dic43⋊C4—21no—
13C22×C4×Dic43C2211yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C8×Dic43—21no—
16#14582802C411yescharacteristic, complemented
17#14582800C411yescharacteristic, complemented
18#14582799—21no—
19#14582799—21no—
20#14582768C411yescharacteristic, complemented
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582634—22no—
25#14582633—22no—
26#14582632—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#327—22no—
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C23×Dic43—21no—
36C23×Dic43D411yescharacteristic
37C23×Dic43D411yescharacteristic
38C22×C43⋊C8—21no—
39#13063321—42no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44#13063297—42no—
45#13063297—42no—
46#13063297—42no—
47#13063297—42no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C2×C4×Dic43—42no—
60C2×C4×Dic43C2×C411yescharacteristic
61C2×C4×Dic43C2×C411yescharacteristic
62C2×C4×Dic43D411yescharacteristic
63C2×C4×Dic43D411yescharacteristic
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)D412yescomplemented
66C8×Dic43—42no—
67C43⋊#95—21no—
68C43⋊#95—21no—
69C43⋊#95—42no—
70C22×D4×C43—21no—
71C22×D4×C43C2×C411yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C22×C8×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77#121×C43—21no—
78#121×C43—21no—
79C2×C4⋊C4×C43C2×C411yescharacteristic
80C2×C22⋊C4×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43D412yescomplemented
83#95×C43—21no—
84#95×C43—21no—
85C24×C43—21no—
86C24×C43C2×D411yescharacteristic
87C23×D43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C22×C4×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—42no—
115C2×C22⋊D43—42no—
116C2×C22⋊D43—42no—
117C2×C22⋊D43—42no—
118C2×C22⋊D43—42no—
119C2×C22⋊D43—42no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43C22⋊C411yescharacteristic
139C22×Dic43C22⋊C411yescharacteristic
140C22×Dic43C22⋊C411yescharacteristic
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43D812yes—
143C22×Dic43D812yes—
144C22×Dic43SD1612yes—
145C22×Dic43SD1612yes—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—41no—
149C2×D172—41no—
150C2×C8×C43—22no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C22⋊Dic43—42no—
158C22⋊Dic43—42no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—42no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165Dic43⋊C4—48no—
166Dic43⋊C4—42no—
167Dic43⋊C4—42no—
168C4×Dic43—22no—
169C4×Dic43—22no—
170C4×Dic43—41no—
171C4×Dic43—41no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43C2×C22⋊C411yescharacteristic
187C23×C43#12411yescharacteristic
188C23×C43#12711yescharacteristic
189C23×C43C2×D811yescharacteristic
190C23×C43C2×D811yescharacteristic
191C23×C43C2×SD1611yescharacteristic
192C23×C43C2×SD1611yescharacteristic
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200D4×C43—81no—
201D4×C43—81no—
202D4×C43—81no—
203D4×C43—81no—
204D4×C43—81no—
205D4×C43—81no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—81no—
221C2×C4×C43—81no—
222C2×C4×C43—81no—
223C2×C4×C43—81no—
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C22⋊D43—84no—
229C22⋊D43—81no—
230C22⋊D43—81no—
231C22⋊D43—81no—
232C22⋊D43—81no—
233C22⋊D43—84no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—81no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254C2×Dic43#9912yes—
255C2×Dic43#10212yes—
256C2×Dic43#10212yes—
257C2×Dic43#10212yes—
258C2×Dic43#10212yes—
259C2×Dic43#10412yes—
260D172—81no—
261D172—81no—
262C8×C43—42no—
263C43⋊C8—42no—
264#9680—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43#39011yescharacteristic
285C22×C43C2×#9911yescharacteristic
286C22×C43#41011yescharacteristic
287C22×C43C2×#10211yescharacteristic
288C22×C43C2×#10211yescharacteristic
289C22×C43C2×#10411yescharacteristic
290C22×C43#42111yescharacteristic
291C22×C43#48611yescharacteristic
292C22×C43#48611yescharacteristic
293C22×C43#49211yescharacteristic
294C22×C43#49311yescharacteristic
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—82no—
307C4×C43—81no—
308Dic43—22no—
309Dic43—22no—
310Dic43—22no—
311Dic43—82no—
312Dic43—81no—
313Dic43#32714yescomplemented
314#2856—431no—
315C4×C22⋊C8—431no—
316C2×#327—431no—
317C2×#327—431no—
318C2×#327—431no—
319C2×#327D4311yescharacteristic, complemented
320C4⋊#95—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—161no—
326C2×C43C2×#32711yescharacteristic
327C2×C43#150211yescharacteristic
328C2×C43#151711yescharacteristic
329C2×C43#151911yescharacteristic
330C2×C43#195711yescharacteristic
331C2×C43#196411yescharacteristic
332C2×C43#198011yescharacteristic
333D43—161no—
334C2×#127—431no—
335C2×#121—431no—
336C2×#121—861no—
337C2×#121—861no—
338C2×#121C2×D4311yescharacteristic
339C22×C4⋊C4—861no—
340C22×C42—431no—
341C2×C22⋊C8—431no—
342C2×C22⋊C8C2×D4311yescharacteristic
343C2×C4×C8—861no—
344#390—431no—
345#390—431no—
346#390—861no—
347#390—861no—
348#384—431no—
349C2×#95—431no—
350C2×#95—861no—
351C2×#95C2×D4311yescharacteristic
352#336—861no—
353#327—22no—
354#327—862no—
355#327—862no—
356#327—862no—
357C43#968011yescharacteristic, complemented, Sylow
358C22×D4—21no—
359C22×D4—431no—
360C22×D4—861no—
361C22×D4—861no—
362C22×D4—861no—
363C22×D4C4×D4311yescharacteristic
364C23×C4—21no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—861no—
368C23×C4C22×D4311yescharacteristic
369C22×C8—21no—
370C22×C8—861no—
371#127—1722no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—861no—
377#121—861no—
378#121—861no—
379#121—861no—
380#121—1722no—
381#121—1722no—
382#121—1722no—
383#121—1722no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—1722no—
389C2×C4⋊C4—1722no—
390C2×C4⋊C4C4×D4311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—1722no—
402C22⋊C8—21no—
403C22⋊C8—432no—
404C22⋊C8—861no—
405C22⋊C8C22⋊D4312yescomplemented
406C4×C8—1722no—
407#95—21no—
408#95—21no—
409#95—861no—
410#95—861no—
411#95—1722no—
412C24—21no—
413C24—861no—
414C24D4×D4311yescharacteristic
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—1721no—
428C2×D4—1721no—
429C2×D4—1722no—
430C2×D4—1722no—
431C2×D4—1722no—
432C2×D4—1722no—
433C2×D4—1722no—
434C2×D4—1722no—
435C2×D4—1721no—
436C2×D4—1721no—
437C2×D4—1721no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4—1721no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4—1721no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4—1721no—
471C22×C4C2×C4×D4311yescharacteristic
472C22×C4#1062189811yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190011yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—862no—
481C2×C8—1721no—
482C2×C8—1721no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4—1728no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C22⋊C4—1722no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C42—862no—
499C42—862no—
500C42—1721no—
501C42—1721no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23C22⋊C4×D4311yescharacteristic
521C23#1306331111yescharacteristic
522C23#1306332111yescharacteristic
523C23D8×D4311yescharacteristic
524C23D8×D4311yescharacteristic
525C23SD16×D4311yescharacteristic
526C23SD16×D4311yescharacteristic
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532D4—81no—
533D4—3441no—
534D4—3441no—
535D4—3444no—
536D4—3444no—
537D4—3441no—
538D4—3441no—
539D4—3441no—
540D4—3441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—432no—
564C2×C4—432no—
565C2×C4—864no—
566C2×C4—864no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3441no—
574C2×C4—3441no—
575C2×C4—3441no—
576C2×C4—3441no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4(C22⋊D43)⋊C411yescharacteristic
586C2×C4C4×C22⋊D4311yescharacteristic
587C2×C4#1306329711yescharacteristic
588C2×C4#1306329811yescharacteristic
589C8—42no—
590C8—1722no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22#1458279911yescharacteristic
618C22#99×D4311yescharacteristic
619C22#1458287111yescharacteristic
620C22#102×D4311yescharacteristic
621C22#102×D4311yescharacteristic
622C22#104×D4311yescharacteristic
623C22#1458291411yescharacteristic
624C22#1458324411yescharacteristic
625C22#1458324411yescharacteristic
626C22#1458327011yescharacteristic
627C22#1458327411yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—82no—
633C4—81no—
634C4—434no—
635C4—862no—
636C4—862no—
637C4—862no—
638C4—3442no—
639C4—3441no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—161no—
645C2—6881no—
646C2#327×D4311yescharacteristic
647C2#1913308811yescharacteristic
648C2#1913315311yescharacteristic
649C2#1913316111yescharacteristic
650C2#1913539911yescharacteristic
651C2#1913542911yescharacteristic
652C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radical#19142938C2
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#9680
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×Dic43C2semidirect
3. C2×#14582634C2semidirect
4. C2×#14582633C2semidirect
5. C2×#14582632C2semidirect
6. Dic43⋊#95C2semidirect
7. C2×C43×#327C2semidirect
8. C2×#13063321C4semidirect
16. #14582802C4semidirect
17. #14582800C4semidirect
20. #14582768C4semidirect
65. C22⋊(C43⋊C8)D4semidirect
82. C22⋊C8×C43D4semidirect
313. Dic43#327semidirect
319. C2×#327D43semidirect
357. C43#9680semidirect
405. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191429382
C22⋊C8×Dic432
C2×#145826342
C2×#145826332
C2×#145826322
Dic43⋊#952
C2×C43×#3272
#968043