Finite Group Databasebeta

← #25062930

Subgroups — #25062930

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583632C211yesmaximal, characteristic
2#19143631C212yesmaximal, complemented
3#19132945C212yesmaximal, complemented
4#19132944C212yesmaximal, complemented
5#19132940C212yesmaximal, complemented
6#19132937C211yesmaximal, characteristic, complemented
7#19132932C211yesmaximal, characteristic, complemented
8#19132917C211yesmaximal, characteristic, complemented
9#19132913C211yesmaximal, characteristic, complemented
10#19132912C211yesmaximal, characteristic, complemented
11C43×#1465C211yesmaximal, characteristic, complemented
12#14583632—22no—
13#14583632—22no—
14#14583632—22no—
15#14583632—22no—
16C2×#13063321C411yescharacteristic
17C2×#13063313C411yescharacteristic
18C2×#13063312C411yescharacteristic
19C2×#13063311C411yescharacteristic
20C2×#13063311C2211yescharacteristic
21C2×#13063308C411yescharacteristic
22C2×#13063308C2211yescharacteristic
23C2×#13063307C411yescharacteristic
24C2×#13063307C2211yescharacteristic
25C2×C4×Dic86C411yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×C4×C22⋊D43C411yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30#14582975—22no—
31#14582968—22no—
32#14582967—22no—
33(C22⋊D43)⋊C8—22no—
34#14582953C2212yes—
35#14582949C2212yes—
36#14582861C2212yes—
37C2×C22⋊(C43⋊C8)C2212yes—
38C22⋊C8×D43C2212yes—
39#14582625C2211yescharacteristic
40#14582625C2211yescharacteristic
41#14582624C2212yes—
42#14582624C2212yes—
43#14582623C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C43×#407C2212yes—
48C43×#324C2211yescharacteristic
49C43×#324C2211yescharacteristic
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621872—22no—
61C22×C43⋊C8—22no—
62C2×C8×D43—22no—
63#13063321—22no—
64#13063321—22no—
65#13063313—22no—
66#13063313—22no—
67#13063312—22no—
68#13063312—22no—
69#13063311—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063308—22no—
74#13063308—22no—
75#13063308—22no—
76#13063308—22no—
77#13063307—22no—
78#13063307—22no—
79#13063307—22no—
80#13063307—22no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85#13063290—22no—
86#13063290—22no—
87#13063287—22no—
88#13063287—22no—
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93C4×C22⋊D43D412yes—
94C4×C22⋊D43D412yes—
95C4×C22⋊D43D412yes—
96C4×C22⋊D43D412yes—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2311yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×C22⋊Dic43C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2311yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2×C411yescharacteristic
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—22no—
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—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2311yescharacteristic
134C2×C42×C43C2×C411yescharacteristic
135C22⋊C8×C43—22no—
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2312yes—
138C24×C43C22×C411yescharacteristic
139C24×C43C22×C411yescharacteristic
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43—41no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—21no—
157C2×C22⋊D43—21no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—81no—
163C2×C22⋊D43—81no—
164C2×C22⋊D43C22⋊C412yes—
165C2×C22⋊D43C22⋊C412yes—
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—41no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×Dic86—22no—
182C2×Dic86—22no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—41no—
186C2×Dic86—42no—
187M16×C43—82no—
188C2×C8×C43—22no—
189C2×C8×C43—22no—
190C4⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C42×C43—21no—
194C42×C43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43C22⋊C412yes—
200C22⋊Dic43C22⋊C412yes—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4C22⋊C412yes—
208(C2×D43)⋊C4C22⋊C412yes—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4C22⋊C411yescharacteristic
216Dic43⋊C4C22⋊C411yescharacteristic
217Dic43⋊C4C22⋊C411yescharacteristic
218Dic43⋊C4C22⋊C411yescharacteristic
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43C2×D412yes—
226C4×Dic43C2×D412yes—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—82no—
230#10621872—82no—
231C8×D43—82no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43C2×C22⋊C412yes—
242C23×C43C23×C411yescharacteristic
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43C2×C22⋊C412yes—
253D4×C43—44no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—81no—
265C2×C4×C43—81no—
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C2×C4×C43C2×C22⋊C411yescharacteristic
268C2×C4×C43#13112yes—
269C2×C4×C43C22×D412yes—
270C22⋊D43—24no—
271C22⋊D43—42no—
272C22⋊D43—42no—
273C22⋊D43—42no—
274C22⋊D43—82no—
275C22⋊D43—82no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—22no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C412yes—
291C2×Dic43C2×C22⋊C411yescharacteristic
292D172—44no—
293C4×D43—42no—
294C4×D43—42no—
295C4×D43—81no—
296C4×D43—81no—
297Dic86—44no—
298Dic86—42no—
299Dic86—42no—
300C8×C43—42no—
301C8×C43—42no—
302C43⋊C8—42no—
303C43⋊C8—42no—
304#17429—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43C22×C22⋊C411yescharacteristic
318C22×C43C2×#13111yescharacteristic
319C22×C43#56811yescharacteristic
320C2×D43—22no—
321C2×D43—22no—
322C2×D43—22no—
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C2×D43—81no—
327C2×D43—81no—
328C2×D43—81no—
329C2×D43—81no—
330C4×C43—22no—
331C4×C43—22no—
332C4×C43—21no—
333C4×C43—21no—
334C4×C43—41no—
335C4×C43—41no—
336Dic43—22no—
337Dic43—21no—
338Dic43—21no—
339Dic43—21no—
340Dic43—41no—
341Dic43—41no—
342Dic43—41no—
343Dic43#41312yes—
344C2×#559—431no—
345#2974—432no—
346#1469—432no—
347#1468—432no—
348#1468—432no—
349#1467—431no—
350#1465—431no—
351#1465D4311yescharacteristic, complemented
352#1461—431no—
353#1459—431no—
354#1459—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—42no—
358C2×C43—81no—
359C2×C43#288011yescharacteristic
360C2×C43#288311yescharacteristic
361C2×C43C2×#41311yescharacteristic
362D43—42no—
363D43—81no—
364#559—862no—
365#559—862no—
366#559—862no—
367#559—862no—
368C2×#127—431no—
369C2×#124—431no—
370C2×#124—431no—
371C2×#124—431no—
372C2×#124—431no—
373C2×#123—431no—
374C2×#123—431no—
375C2×#123—431no—
376C2×#123—431no—
377C2×C4×Q8—431no—
378C2×C4×Q8—431no—
379C2×C4×D4—431no—
380C2×C4×D4—431no—
381C2×C4×D4—431no—
382C2×C4×D4C2×D4311yescharacteristic
383#436—862no—
384#435—862no—
385#435—862no—
386C8×D4—862no—
387#432—432no—
388#431—432no—
389#407—432no—
390#407C2×D4312yes—
391C2×C22⋊C8—432no—
392C2×C22⋊C8—432no—
393#324—431no—
394#324—431no—
395#324—432no—
396#324—432no—
397#324C2×D4311yescharacteristic
398#324C2×D4311yescharacteristic
399#323—432no—
400#323—432no—
401#323—432no—
402#323C2×D4312yes—
403C43#1742911yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8—431no—
406C22×D4—431no—
407C22×D4—431no—
408C22×D4—431no—
409C22×D4—431no—
410C22×D4—431no—
411C22×D4C4×D4311yescharacteristic
412C23×C4—431no—
413C23×C4—431no—
414C23×C4C4×D4311yescharacteristic
415C23×C4C22×D4311yescharacteristic
416C2×M16—22no—
417C2×M16—862no—
418C22×C8—862no—
419C22×C8—862no—
420#127—862no—
421#127—862no—
422#124—862no—
423#124—862no—
424#124—862no—
425#124—862no—
426#124—862no—
427#124—862no—
428#124—862no—
429#124—862no—
430#123—862no—
431#123—862no—
432#123—862no—
433#123—862no—
434#123—862no—
435#123—862no—
436#123—862no—
437#123—862no—
438C4×Q8—861no—
439C4×Q8—861no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—862no—
443C4×Q8—862no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—432no—
447C4×D4—432no—
448C4×D4—432no—
449C4×D4—432no—
450C4×D4—862no—
451C4×D4—862no—
452C4×D4—861no—
453C4×D4—861no—
454C4×D4—861no—
455C4×D4—861no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C22⋊C4—431no—
463C2×C22⋊C4—431no—
464C2×C22⋊C4—431no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4—431no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4—431no—
469C2×C22⋊C4—431no—
470C2×C22⋊C4—431no—
471C2×C22⋊C4—431no—
472C2×C22⋊C4C4×D4311yescharacteristic
473C2×C22⋊C4C22×D4311yescharacteristic
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—431no—
477C2×C42—431no—
478C2×C42C4×D4311yescharacteristic
479C4⋊C8—862no—
480C4⋊C8—862no—
481C22⋊C8—22no—
482C22⋊C8—432no—
483C22⋊C8—432no—
484C22⋊C8—862no—
485C22⋊C8—862no—
486C22⋊C8—862no—
487C22⋊C8C22×D4312yes—
488C22⋊C8C22×D4312yes—
489#97—862no—
490C4×C8—862no—
491C24—431no—
492C24—431no—
493C24C2×C4×D4311yescharacteristic
494C24C2×C4×D4311yescharacteristic
495C2×Q8—862no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—862no—
499C2×Q8—1721no—
500C2×Q8—1722no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—432no—
505C2×D4—432no—
506C2×D4—862no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—862no—
510C2×D4—862no—
511C2×D4—862no—
512C2×D4—3441no—
513C2×D4—3441no—
514C2×D4—1721no—
515C2×D4—1722no—
516C2×D4—1722no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—432no—
525C22×C4—432no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—3441no—
532C22×C4—3441no—
533C22×C4C2×C4×D4311yescharacteristic
534C22×C4C2×C4×D4311yescharacteristic
535C22×C4C2×C4×D4311yescharacteristic
536C22×C4C2×C4×D4311yescharacteristic
537C22×C4D4×D4312yes—
538C22×C4D4×D4312yes—
539C22×C4C23×D4311yescharacteristic
540M16—82no—
541M16—3442no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—862no—
545C2×C8—862no—
546C2×C8—3442no—
547C2×C8—3442no—
548C4⋊C4—22no—
549C4⋊C4—431no—
550C4⋊C4—431no—
551C4⋊C4—431no—
552C4⋊C4—431no—
553C4⋊C4—862no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—862no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—432no—
562C22⋊C4—432no—
563C22⋊C4—432no—
564C22⋊C4—432no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—862no—
571C22⋊C4—862no—
572C22⋊C4—861no—
573C22⋊C4—861no—
574C22⋊C4—862no—
575C42—21no—
576C42—21no—
577C42—432no—
578C42—432no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—861no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—432no—
595C23—861no—
596C23—861no—
597C23—861no—
598C23—861no—
599C23—861no—
600C23—1721no—
601C23—1721no—
602C23—1721no—
603C23—1721no—
604C23C22⋊C4×D4312yes—
605C23C22×C4×D4311yescharacteristic
606Q8—1724no—
607Q8—1722no—
608Q8—1722no—
609D4—44no—
610D4—864no—
611D4—3442no—
612D4—3442no—
613D4—1724no—
614D4—1722no—
615D4—1722no—
616D4—1722no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—431no—
630C2×C4—431no—
631C2×C4—432no—
632C2×C4—431no—
633C2×C4—431no—
634C2×C4—862no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—861no—
639C2×C4—861no—
640C2×C4—861no—
641C2×C4—861no—
642C2×C4—3441no—
643C2×C4—3441no—
644C2×C4—1722no—
645C2×C4—1722no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4#1306333312yes—
652C2×C4C2×D4×D4312yes—
653C8—42no—
654C8—42no—
655C8—1722no—
656C8—1722no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—862no—
670C22—862no—
671C22—862no—
672C22—3441no—
673C22—3441no—
674C22—3441no—
675C22—3441no—
676C22—1721no—
677C22—1721no—
678C22—1721no—
679C22C2×C22⋊C4×D4311yescharacteristic
680C22C2×#1306333311yescharacteristic
681C22#1458366511yescharacteristic
682C4—22no—
683C4—22no—
684C4—21no—
685C4—21no—
686C4—41no—
687C4—41no—
688C4—432no—
689C4—862no—
690C4—861no—
691C4—861no—
692C4—861no—
693C4—1721no—
694C4—1721no—
695C4—1721no—
696C2—21no—
697C2—21no—
698C2—42no—
699C2—81no—
700C2—3441no—
701C2—1722no—
702C2#1914304511yescharacteristic
703C2#1914305311yescharacteristic
704C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1465C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenter#1465D43
hypocenterC43#17429
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. #19143631C2semidirect
3. #19132945C2semidirect
4. #19132944C2semidirect
5. #19132940C2semidirect
6. #19132937C2semidirect
7. #19132932C2semidirect
8. #19132917C2semidirect
9. #19132913C2semidirect
10. #19132912C2semidirect
11. C43×#1465C2semidirect
351. #1465D43semidirect
403. C43#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#145836322
#191436312
#191329452
#191329442
#191329402
#191329372
#191329322
#191329172
#191329132
#191329122
C43×#14652
#1742943