Finite Group Databasebeta

← #24988002

Subgroups — #24988002

Order 11008.

954 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063372C211yesmaximal, characteristic
2#19135531C211yesmaximal, characteristic, complemented
3#19132983C211yesmaximal, characteristic, complemented
4#19132982C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic, complemented
6#19132918C211yesmaximal, characteristic, complemented
7C43×#1476C211yesmaximal, characteristic, complemented
8C2×#13063372C411yescharacteristic
9#14583382C411yescharacteristic
10#14583379—21no—
11#14583379C411yescharacteristic
12#14583378—22no—
13#14583378—21no—
14#14583376—21no—
15#14583376C411yescharacteristic
16#14583375—21no—
17C4×#10621898—21no—
18C4×#10621898C2211yescharacteristic
19C4×#10621900—22no—
20C4×#10621900—21no—
21C2×C4×Dic86—21no—
22C2×C4×Dic86C2211yescharacteristic
23C4×Q8×D43—21no—
24#14582952C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26#14582653—22no—
27#14582631—21no—
28#14582631—21no—
29Q8⋊(C43⋊C8)—21no—
30#14582628—21no—
31#14582628—21no—
32D4⋊(C43⋊C8)—21no—
33#14582624—22no—
34C4×#41×C43C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C2×C4×C8×C43C2211yescharacteristic
37C43×Q8⋊C8—21no—
38C43×D4⋊C8—21no—
39#13063372—22no—
40#13063372—22no—
41#13063372—22no—
42#13063372C814yescomplemented
43C2×#10621898—21no—
44C2×#10621898C2×C411yescharacteristic
45C2×#10621900—21no—
46C2×#10621900—22no—
47C22×Dic86—21no—
48C22×Dic86C2×C411yescharacteristic
49C2×Q8×D43—21no—
50C22×C43⋊C8—21no—
51Q8×Dic43—21no—
52C4×Dic86—22no—
53C4×Dic86—22no—
54C4×Dic86—21no—
55C4×Dic86—21no—
56C4×Dic86—21no—
57C4×Dic86—21no—
58C4×Dic86—21no—
59C4×Dic86—21no—
60C4×Dic86—21no—
61C4×Dic86D411yescharacteristic
62C4×Dic86D411yescharacteristic
63#13063290—22no—
64#13063290—22no—
65#13063290—21no—
66#13063290—21no—
67C4×D172—21no—
68C4×D172D411yescharacteristic
69C4×D172D411yescharacteristic
70D4×Dic43—21no—
71D4×Dic43—22no—
72C4×C22⋊D43—22no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—21no—
75C4×C22⋊D43—21no—
76(C22⋊D43)⋊C4—22no—
77(C22⋊D43)⋊C4—22no—
78(C22⋊D43)⋊C4—22no—
79#13063284—21no—
80#13063284C2×C411yescharacteristic
81#13063283—22no—
82#13063283—21no—
83#13063282—22no—
84#13063282—21no—
85#13063281—22no—
86#13063281—22no—
87#13063281—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4D412yes—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—21no—
94C2×C4×Dic43—22no—
95C2×C4×Dic43D412yes—
96C42×D43—22no—
97C42×D43—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C22⋊(C43⋊C8)—21no—
102C4×C43⋊C8—21no—
103C2×#41×C43C2×C411yescharacteristic
104C22×C8×C43—21no—
105C4×Q8×C43D411yescharacteristic
106C4×Q8×C43D411yescharacteristic
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43D411yescharacteristic
110C4×D4×C43D411yescharacteristic
111#117×C43—21no—
112#117×C43C2×C411yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C4⋊C8×C43—21no—
116C22⋊C8×C43—21no—
117C4×C8×C43—21no—
118C4×C8×C43—21no—
119C4×C8×C43—21no—
120#41×C43—21no—
121#41×C43—21no—
122#41×C43C2×C812yes—
123#41×C43M1612yes—
124C2×Q8×C43C22⋊C411yescharacteristic
125C2×D4×C43—21no—
126C2×D4×C43C22⋊C411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C22×C411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C2×C22⋊D43—22no—
134C2×C22⋊D43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43C22⋊C412yes—
138C22×Dic43C22⋊C412yes—
139Q8×D43—24no—
140Q8×D43—24no—
141#10621900—28no—
142#10621900—24no—
143#10621900—24no—
144#10621900—28no—
145#10621898—24no—
146#10621898—21no—
147#10621898—21no—
148#10621898—24no—
149#10621898C2×C812yes—
150#10621898M1612yes—
151C2×D172C22⋊C411yescharacteristic
152C2×C4×D43—22no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—22no—
156C2×C4×D43—21no—
157C2×Dic86—22no—
158C2×Dic86—24no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—24no—
164C2×Dic86C22⋊C411yescharacteristic
165C2×Dic86C2×C812yes—
166C2×Dic86M1612yes—
167C2×C8×C43—22no—
168C2×C8×C43—41no—
169C2×C8×C43—41no—
170C2×C8×C43—41no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22⋊C411yescharacteristic
174C4⋊C4×C43C22⋊C411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C22⋊Dic43—22no—
186C22⋊Dic43—21no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C22⋊C411yescharacteristic
194C4⋊Dic43C22⋊C411yescharacteristic
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—21no—
200Dic43⋊C4—22no—
201Dic43⋊C4—21no—
202C4×Dic43—22no—
203C4×Dic43—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—22no—
209C4×Dic43—21no—
210C4×Dic43—22no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8—41no—
213C2×C43⋊C8—41no—
214C23×C43—21no—
215C23×C43C2×C22⋊C411yescharacteristic
216C22×D43—21no—
217Q8×C43—21no—
218Q8×C43C22⋊C812yes—
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—21no—
222D4×C43C22⋊C812yes—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—81no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43C22×C811yescharacteristic
241C2×C4×C43C2×M1611yescharacteristic
242C2×C4×C43C2×M1611yescharacteristic
243C2×C4×C43C2×M1611yescharacteristic
244C22⋊D43—28no—
245C22⋊D43—22no—
246C22⋊D43—22no—
247C2×Dic43—28no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—42no—
255C2×Dic43—82no—
256C2×Dic43C22⋊C814yes—
257D172—21no—
258D172C22⋊C812yes—
259C4×D43—28no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—81no—
265C4×D43—82no—
266Dic86—28no—
267Dic86—22no—
268Dic86—22no—
269Dic86—21no—
270Dic86—22no—
271Dic86—22no—
272Dic86C22⋊C812yes—
273C8×C43—42no—
274C8×C43—81no—
275C43⋊C8—81no—
276C43⋊C8—81no—
277#8319—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—22no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43#37911yescharacteristic
284C22×C43C2×C22⋊C811yescharacteristic
285C22×C43#40711yescharacteristic
286C2×D43—22no—
287C2×D43—41no—
288C2×D43—41no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—22no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43C2×C22⋊C811yescharacteristic
296C4×C43C2×C22⋊C811yescharacteristic
297C4×C43#40711yescharacteristic
298C4×C43#40711yescharacteristic
299C4×C43#45411yescharacteristic
300C4×C43#45611yescharacteristic
301Dic43—24no—
302Dic43—22no—
303Dic43—41no—
304Dic43—42no—
305Dic43—41no—
306C4×2−1+4—431no—
307#1984—431no—
308#1477—431no—
309#1477—431no—
310#1476—431no—
311#1476D4311yescharacteristic, complemented
312#1461—431no—
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—42no—
316C2×C43#177911yescharacteristic
317C2×C43#179311yescharacteristic
318C2×C43#179411yescharacteristic
319D43—42no—
320C2×2−1+4—431no—
321#520—431no—
322#520—431no—
323#520—862no—
324#520—861no—
325#520—861no—
326#519—431no—
327#519—861no—
328#519—861no—
329C4×#41—431no—
330C4×#41—861no—
331C4×#41—862no—
332C4×#41—861no—
333C4×#41C2×D4311yescharacteristic
334C2×C4×Q8—431no—
335C2×C4×Q8—861no—
336C2×C4×Q8—861no—
337#431—431no—
338#431C2×D4311yescharacteristic
339C2×C4⋊C8—431no—
340C2×C4×C8C2×D4311yescharacteristic
341#336—862no—
342Q8⋊C8—21no—
343Q8⋊C8—861no—
344Q8⋊C8—861no—
345Q8⋊C8—861no—
346D4⋊C8—21no—
347D4⋊C8—861no—
348D4⋊C8—861no—
349D4⋊C8—861no—
350#324—862no—
351C43#831911yescharacteristic, complemented, Sylow
3522−1+4—434no—
3532−1+4—862no—
3542−1+4—862no—
3552−1+4—862no—
356C2×#41—431no—
357C2×#41—861no—
358C2×#41—862no—
359C2×#41—861no—
360C2×#41C4×D4311yescharacteristic
361C22×Q8—431no—
362C22×Q8—861no—
363C22×Q8—861no—
364C22×C8—21no—
365C22×C8—861no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—862no—
372C4×Q8—862no—
373C4×Q8—862no—
374C4×Q8—862no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×Q8D17211yescharacteristic
383C4×Q8C22⋊D4311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—431no—
387C4×D4—431no—
388C4×D4—861no—
389C4×D4—862no—
390C4×D4—862no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4D17211yescharacteristic
399C4×D4C22⋊D4311yescharacteristic
400#117—21no—
401#117—431no—
402#117—862no—
403#117—862no—
404#117—862no—
405#117—862no—
406#117—862no—
407#117—861no—
408#117—861no—
409#117—861no—
410#117C4×D4311yescharacteristic
411C2×C4⋊C4—431no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—861no—
417C2×C42—21no—
418C2×C42—432no—
419C2×C42—862no—
420C2×C42—862no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C22⋊C8—21no—
428C22⋊C8—861no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8—861no—
433#41—21no—
434#41—21no—
435#41—432no—
436#41—432no—
437#41—864no—
438#41—864no—
439#41—868no—
440#41—868no—
441#41—864no—
442#41—864no—
443#41—861no—
444#41—861no—
445#41C8×D4312yes—
446#41#1062187212yes—
447C2×Q8—432no—
448C2×Q8—432no—
449C2×Q8—431no—
450C2×Q8—864no—
451C2×Q8—862no—
452C2×Q8—864no—
453C2×Q8—864no—
454C2×Q8—864no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8(C2×D43)⋊C411yescharacteristic
460C2×D4—21no—
461C2×D4—431no—
462C2×D4—862no—
463C2×D4—861no—
464C2×D4(C2×D43)⋊C411yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4C2×C4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—1722no—
485C2×C8—1721no—
486C2×C8—1721no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—431no—
490C4⋊C4—431no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—862no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—862no—
501C4⋊C4(C2×D43)⋊C411yescharacteristic
502C4⋊C4(C2×D43)⋊C411yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—862no—
515C42—862no—
516C42—862no—
517C42—862no—
518C42—861no—
519C42—862no—
520C42—861no—
521C42—862no—
522C42—861no—
523C42C2×D17211yescharacteristic
524C42D4×D4311yescharacteristic
525C42D4×D4311yescharacteristic
526C42C2×C22⋊D4311yescharacteristic
527C23—21no—
528C23—861no—
529C23C22⋊C4×D4311yescharacteristic
530Q8—21no—
531Q8—432no—
532Q8—868no—
533Q8—862no—
534Q8—862no—
535Q8—862no—
536Q8—861no—
537Q8—862no—
538Q8(C2×D43)⋊C812yes—
539D4—22no—
540D4—22no—
541D4—21no—
542D4—432no—
543D4—868no—
544D4—862no—
545D4—862no—
546D4—861no—
547D4(C2×D43)⋊C812yes—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—434no—
560C2×C4—868no—
561C2×C4—868no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—862no—
570C2×C4—3441no—
571C2×C4—3442no—
572C2×C4—3442no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1722no—
576C2×C4C22⋊C4×D4311yescharacteristic
577C2×C4C2×(C2×D43)⋊C411yescharacteristic
578C2×C4#1306329311yescharacteristic
579C2×C4#1306329311yescharacteristic
580C2×C4#1306329511yescharacteristic
581C2×C4#1306329511yescharacteristic
582C2×C4C2×C8×D4311yescharacteristic
583C2×C4M16×D4311yescharacteristic
584C2×C4M16×D4311yescharacteristic
585C2×C4C2×#1062187211yescharacteristic
586C8—42no—
587C8—81no—
588C8—3441no—
589C8—3441no—
590C22—21no—
591C22—21no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—862no—
596C22—1721no—
597C22—1721no—
598C22#1458275411yescharacteristic
599C22C22⋊C8×D4311yescharacteristic
600C22#1458286111yescharacteristic
601C4—22no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—864no—
608C4—862no—
609C4—1721no—
610C4—1721no—
611C4—1722no—
612C4C22⋊C8×D4311yescharacteristic
613C4C2×(C2×D43)⋊C811yescharacteristic
614C4#1458286111yescharacteristic
615C4#1458286211yescharacteristic
616C4#1458307311yescharacteristic
617C4#1458308311yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—1722no—
622C2#1913450411yescharacteristic
623C2#1913455511yescharacteristic
624C2#1913456011yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1476C2
socleC22×C43#379
prime radicalC2×#13063372C4
cosocleC2×C42×C43C23
hypercenter#1476D43
hypocenterC43#8319
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #19135531C2semidirect
3. #19132983C2semidirect
4. #19132982C2semidirect
5. #19132978C2semidirect
6. #19132918C2semidirect
7. C43×#1476C2semidirect
42. #13063372C8semidirect
311. #1476D43semidirect
351. C43#8319semidirect

Maximal subgroups

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

subgroupindex
C4×#130633722
#191355312
#191329832
#191329822
#191329782
#191329182
C43×#14762
#831943