Finite Group Databasebeta

← #25062749

Subgroups — #25062749

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583491C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19143622C211yesmaximal, characteristic, complemented
4#19132961C212yesmaximal, complemented
5#19132957C212yesmaximal, complemented
6#19132949C212yesmaximal, complemented
7#19132940C212yesmaximal, complemented
8#19132933C211yesmaximal, characteristic, complemented
9#19132924C211yesmaximal, characteristic, complemented
10#19132924C211yesmaximal, characteristic, complemented
11C43×#1465C211yesmaximal, characteristic, complemented
12#14583491—22no—
13#14583491—22no—
14#14583491—22no—
15#14583491—22no—
16C2×#13063319C411yescharacteristic
17C2×#13063318C2211yescharacteristic
18C2×#13063317C411yescharacteristic
19C2×#13063315C2211yescharacteristic
20C2×#13063309C411yescharacteristic
21C2×#13063308C411yescharacteristic
22C2×#13063307C2211yescharacteristic
23C2×#13063306C411yescharacteristic
24C2×#13063304C411yescharacteristic
25C2×#13063303C2211yescharacteristic
26C2×#13063302C411yescharacteristic
27C2×#13063297C411yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30#14582975—22no—
31#14582974—22no—
32#14582973—22no—
33#14582968—22no—
34#14582953C2212yes—
35#14582949C2212yes—
36#14582863C2211yescharacteristic
37#14582863C2211yescharacteristic
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40#14582625C2212yes—
41#14582624C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582624C2212yes—
45#14582623C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C43×#407C2211yescharacteristic
49C43×#324C2212yes—
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C23×Dic43C2×C411yescharacteristic
55C23×Dic43C2×C411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063319—22no—
62#13063319—22no—
63#13063318—22no—
64#13063318—22no—
65#13063317—22no—
66#13063317—22no—
67#13063315—22no—
68#13063315—22no—
69#13063309—22no—
70#13063309—22no—
71#13063308—22no—
72#13063308—22no—
73#13063307—22no—
74#13063307—22no—
75#13063306—22no—
76#13063306—22no—
77#13063304—22no—
78#13063304—22no—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063297—22no—
84#13063297—22no—
85C4×C22⋊D43D412yes—
86C4×C22⋊D43D412yes—
87C4×C22⋊D43D412yes—
88C4×C22⋊D43D412yes—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C2×Dic43⋊C4C2311yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×C22⋊Dic43C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2×C411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43C2312yes—
141C22⋊C8×C43C2312yes—
142C24×C43C22×C411yescharacteristic
143C24×C43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—42no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—81no—
151C22×C4×C43—81no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—81no—
164C2×C22⋊D43C22⋊C412yes—
165C2×C22⋊D43C22⋊C412yes—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—42no—
171C22×Dic43—81no—
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C2×C4×D43—81no—
180C2×C4×D43C2×D412yes—
181C2×C4×D43C2×D412yes—
182C2×Dic86—22no—
183C2×Dic86—81no—
184M16×C43—81no—
185M16×C43—81no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43C22⋊C412yes—
200C22⋊Dic43C22⋊C412yes—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4C22⋊C412yes—
205(C2×D43)⋊C4C22⋊C412yes—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216Dic43⋊C4—21no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4C22⋊C412yes—
223Dic43⋊C4C22⋊C412yes—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226#10621877—81no—
227#10621877—81no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—22no—
230#10621872—82no—
231C8×D43—82no—
232C23×C43—22no—
233C23×C43—21no—
234C23×C43—22no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C2×C22⋊C411yescharacteristic
240C23×C43C2×C22⋊C411yescharacteristic
241C23×C43C23×C411yescharacteristic
242C22×D43—22no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43C2×C22⋊C412yes—
246D4×C43—42no—
247D4×C43—42no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—81no—
261C2×C4×C43—81no—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C22⋊D43—42no—
267C22⋊D43—42no—
268C22⋊D43—82no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—81no—
283C2×Dic43—81no—
284C2×Dic43C2×C22⋊C412yes—
285C2×Dic43C2×C22⋊C412yes—
286C2×Dic43C2×C22⋊C412yes—
287C4×D43—42no—
288C4×D43—42no—
289Dic86—82no—
290C8×C43—42no—
291C8×C43—42no—
292C43⋊C8—42no—
293C43⋊C8—42no—
294#17406—431nomaximal, Sylow
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—44no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—82no—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43#56812yes—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—82no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—41no—
321Dic43—22no—
322Dic43—22no—
323Dic43—22no—
324Dic43—41no—
325Dic43—41no—
326Dic43—41no—
327Dic43—41no—
328C2×#539—431no—
329#2975—431no—
330#2973—431no—
331#1473—432no—
332#1472—432no—
333#1470—432no—
334#1468—432no—
335#1465—431no—
336#1465D4311yescharacteristic, complemented
337#1463—431no—
338#1463—431no—
339C2×C43—22no—
340C2×C43—41no—
341C2×C43—41no—
342C2×C43—81no—
343C2×C43#287911yescharacteristic
344C2×C43#288311yescharacteristic
345C2×C43#288911yescharacteristic
346D43—42no—
347#539—862no—
348#539—862no—
349#539—862no—
350#539—862no—
351C2×#126—431no—
352C2×#126—431no—
353C2×#125—431no—
354C2×#125—431no—
355C2×#123—431no—
356C2×#123—431no—
357C2×#123—431no—
358C2×#123—431no—
359C2×C22⋊Q8—431no—
360C2×C22⋊Q8—431no—
361C2×C22⋊Q8—431no—
362C2×#121—431no—
363C2×C4×D4—431no—
364C2×C4×D4C2×D4311yescharacteristic
365C22×C4⋊C4—431no—
366#436—862no—
367#436—862no—
368#435—862no—
369#435—862no—
370#432—432no—
371#431—432no—
372#407—431no—
373#407—431no—
374#407—432no—
375#407C2×D4311yescharacteristic
376#407C2×D4311yescharacteristic
377C2×C22⋊C8—432no—
378#324—432no—
379#324—432no—
380#324—432no—
381#324—432no—
382#324—432no—
383#324C2×D4312yes—
384#323—432no—
385#323C2×D4312yes—
386C43#1740611yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×D4—431no—
389C22×D4—431no—
390C22×D4C4×D4311yescharacteristic
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4C4×D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—862no—
399C2×M16—861no—
400C2×M16—861no—
401C22×C8—862no—
402#126—862no—
403#126—862no—
404#126—862no—
405#126—862no—
406#125—862no—
407#125—862no—
408#125—862no—
409#125—862no—
410#123—862no—
411#123—862no—
412#123—862no—
413#123—862no—
414#123—862no—
415#123—862no—
416#123—862no—
417#123—862no—
418C22⋊Q8—862no—
419C22⋊Q8—862no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C22⋊Q8—862no—
423C22⋊Q8—862no—
424#121—862no—
425#121—862no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—432no—
431C4×D4—432no—
432C4×D4—432no—
433C4×D4—432no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—431no—
455C2×C22⋊C4—431no—
456C2×C22⋊C4—431no—
457C2×C22⋊C4—431no—
458C2×C22⋊C4—431no—
459C2×C22⋊C4—431no—
460C2×C22⋊C4C4×D4311yescharacteristic
461C2×C22⋊C4C22×D4311yescharacteristic
462C2×C42—431no—
463C2×C42C4×D4311yescharacteristic
464C4⋊C8—862no—
465C4⋊C8—862no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—432no—
469C22⋊C8—432no—
470C22⋊C8—862no—
471C22⋊C8—862no—
472C22⋊C8—861no—
473C22⋊C8—861no—
474C22⋊C8C22×D4312yes—
475C22⋊C8C22×D4312yes—
476#97—862no—
477C4×C8—862no—
478C24—431no—
479C24C2×C4×D4311yescharacteristic
480C24C2×C4×D4311yescharacteristic
481C2×Q8—862no—
482C2×Q8—3441no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—432no—
487C2×D4—432no—
488C2×D4—862no—
489C2×D4—3441no—
490C2×D4—1722no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—3441no—
509C22×C4—3441no—
510C22×C4—1722no—
511C22×C4C2×C4×D4311yescharacteristic
512C22×C4C2×C4×D4311yescharacteristic
513C22×C4C2×C4×D4311yescharacteristic
514C22×C4C2×C4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520M16—81no—
521M16—81no—
522M16—3442no—
523M16—3441no—
524M16—3441no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—862no—
528C2×C8—862no—
529C2×C8—3442no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—432no—
555C22⋊C4—432no—
556C22⋊C4—432no—
557C22⋊C4—432no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C42—21no—
565C42—21no—
566C42—432no—
567C42—432no—
568C23—22no—
569C23—21no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—432no—
576C23—862no—
577C23—1721no—
578C23—1721no—
579C23C22⋊C4×D4311yescharacteristic
580C23C22⋊C4×D4311yescharacteristic
581C23C22×C4×D4311yescharacteristic
582Q8—3442no—
583D4—42no—
584D4—42no—
585D4—3442no—
586D4—1722no—
587D4—1722no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—3441no—
613C2×C4—3441no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C2×D4×D4311yescharacteristic
626C8—42no—
627C8—42no—
628C8—1722no—
629C8—1722no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—44no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—82no—
643C22—862no—
644C22—862no—
645C22—862no—
646C22—3442no—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22#1458366512yes—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—862no—
657C4—862no—
658C4—862no—
659C4—1721no—
660C4—1721no—
661C4—1721no—
662C4—1721no—
663C2—22no—
664C2—41no—
665C2—41no—
666C2—81no—
667C2—1722no—
668C2#1914303811yescharacteristic
669C2#1914305311yescharacteristic
670C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1465C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1465D43
hypocenterC43#17406
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19143622C2semidirect
4. #19132961C2semidirect
5. #19132957C2semidirect
6. #19132949C2semidirect
7. #19132940C2semidirect
8. #19132933C2semidirect
9. #19132924C2semidirect
10. #19132924C2semidirect
11. C43×#1465C2semidirect
336. #1465D43semidirect
386. C43#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#145834912
#191436342
#191436222
#191329612
#191329572
#191329492
#191329402
#191329332
#191329242
C43×#14652
#1740643