Finite Group Databasebeta

← #25063319

Subgroups — #25063319

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3C2×#14582950C211yesmaximal, characteristic, complemented
4#19133051C211yesmaximal, characteristic, complemented
5#19133049C211yesmaximal, characteristic, complemented
6#19133046C211yesmaximal, characteristic, complemented
7#19133026C214yesmaximal, complemented
8#19133000C214yesmaximal, complemented
9C43×#1492C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic
12#14583454C411yescharacteristic
13#14583447C411yescharacteristic
14#14583447C411yescharacteristic
15#14583431—21no—
16#14583431C2212yes—
17#14583430—21no—
18#14583430C412yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C412yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C2212yes—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582955C2212yes—
30#14582951—21no—
31#14582951C2212yes—
32#14582950—21no—
33#14582950—21no—
34#14582950C2212yes—
35#14582950C2212yes—
36#14582923C2211yescharacteristic
37C2×Dic43⋊C8—21no—
38#14582862—21no—
39C2×(C2×D43)⋊C8—21no—
40M16×Dic43—21no—
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C43×#532C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C22×C43⋊C8—21no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063318—22no—
59#13063318—22no—
60#13063317—21no—
61#13063316—21no—
62#13063316C2×C412yes—
63#13063312—21no—
64#13063312C2×C412yes—
65#13063307—22no—
66#13063307—22no—
67#13063306—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2×C412yes—
72#13063301—21no—
73#13063301—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296—21no—
77#13063296C2×C412yes—
78#13063293—22no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2312yes—
83#13063290—21no—
84#13063290C2×C412yes—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43C2×C412yes—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063284—21no—
96#13063284—22no—
97#13063283—21no—
98#13063283C2×C412yes—
99#13063281—22no—
100#13063281—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)C2312yes—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C2×#41×C43—21no—
126C2×M16×C43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129#127×C43C2×C411yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43C2×C412yes—
133C4×D4×C43—21no—
134C4×D4×C43C2312yes—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141#41×C43—42no—
142#41×C43—42no—
143C2×Q8×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43C22⋊C411yescharacteristic
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C411yescharacteristic
159#10621900—44no—
160#10621900—44no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179M16×C43—42no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—42no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C22×C411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223#10621877—42no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226C2×C43⋊C8—42no—
227C23×C43—22no—
228C23×C43C2×C22⋊C411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234Q8×C43—42no—
235D4×C43—24no—
236D4×C43—44no—
237D4×C43—42no—
238D4×C43—42no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43#13512yes—
248C2×C4×C43#13512yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C22⋊D43—44no—
253C22⋊D43—44no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—44no—
260C2×Dic43—44no—
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—21no—
270C4×D43—21no—
271C4×D43—21no—
272C4×D43—21no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281Dic86—24no—
282Dic86—42no—
283C8×C43—42no—
284C8×C43—42no—
285C43⋊C8—42no—
286C43⋊C8—42no—
287#17489—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43#41612yes—
294C22×C43C22×C22⋊C411yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—44no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43#41612yes—
306C4×C43#42112yes—
307C4×C43#56812yes—
308C4×C43C2×#13511yescharacteristic
309C4×C43C2×#13511yescharacteristic
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—42no—
317Dic43—42no—
318#3444—431no—
319#2920—431no—
320C2×#431—431no—
321#1493—431no—
322#1493—431no—
323#1492—431no—
324#1492D4311yescharacteristic, complemented
325#1488—434no—
326#1482—434no—
327C2×C43—22no—
328C2×C43—82no—
329C2×C43#287911yescharacteristic
330C2×C43C2×#41611yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—41no—
333D43—41no—
334#533—431no—
335#533—431no—
336#533—431no—
337#532—431no—
338#532—431no—
339#532C2×D4311yescharacteristic
340#529—432no—
341#529—432no—
342#529—861no—
343#529—861no—
344#529—861no—
345#529—861no—
346#525—432no—
347#525—861no—
348#525—861no—
349C4×#41—432no—
350C4×#41—861no—
351C4×#41—861no—
352C22×C42—431no—
353#432—432no—
354#432—861no—
355#431—432no—
356#431—432no—
357#431—432no—
358#431—861no—
359#431—861no—
360#431—861no—
361#423—431no—
362#423C2×D4311yescharacteristic
363C2×C4⋊C8—861no—
364#407—861no—
365C2×C22⋊C8—861no—
366C4×M16—861no—
367C2×C4×C8—431no—
368C2×C4×C8C2×D4311yescharacteristic
369Q8⋊C8—434no—
370Q8⋊C8—434no—
371D4⋊C8—434no—
372D4⋊C8C2×D4314yescomplemented
373C43#1748911yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C2×#41—432no—
376C2×#41—861no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C2×M16—21no—
381C2×M16—861no—
382C22×C8—21no—
383C22×C8—861no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386C4⋊Q8C4×D4311yescharacteristic
387#127C4×D4311yescharacteristic
388#126—862no—
389#126—862no—
390#125—432no—
391#125—861no—
392#125—861no—
393#124—21no—
394#124—432no—
395#124—861no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—432no—
400C22⋊Q8—432no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405#121—21no—
406#121—432no—
407#121—861no—
408#121—861no—
409#121—861no—
410#121C4×D4312yes—
411#120—862no—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×D4—21no—
419C4×D4—432no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4C22×D4312yes—
430#117—432no—
431#117—862no—
432#117—862no—
433#117—862no—
434#117—861no—
435#117—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—862no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—432no—
451C4⋊C8—862no—
452C4⋊C8—862no—
453C4⋊C8—861no—
454C4⋊C8C22×D4312yes—
455C22⋊C8—862no—
456C22⋊C8—862no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459#97—862no—
460C4×C8—21no—
461C4×C8—432no—
462C4×C8—862no—
463C4×C8—861no—
464C4×C8C22×D4312yes—
465C24—431no—
466#41—42no—
467#41—42no—
468#41—1724no—
469#41—1724no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—861no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—862no—
477C2×D4—862no—
478C2×D4C2×C4×D4312yes—
479C22×C4—22no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4C2×C4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504M16—42no—
505M16—1722no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—1722no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—862no—
546C42—862no—
547C42—862no—
548C42C2×C4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42C23×D4311yescharacteristic
552C23—22no—
553C23—431no—
554C23—431no—
555C23—862no—
556C23—1721no—
557C23—1721no—
558C23C22⋊C4×D4311yescharacteristic
559Q8—42no—
560Q8—864no—
561Q8—1722no—
562D4—24no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—1724no—
567D4—1724no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1724no—
599C2×C4—1724no—
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4#1306334412yes—
604C2×C4#1306334612yes—
605C2×C4C22×C4×D4311yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C8—42no—
609C8—42no—
610C8—1722no—
611C8—1722no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—861no—
618C22—861no—
619C22—861no—
620C22—861no—
621C22—861no—
622C22—861no—
623C22—1724no—
624C22#1458289212yes—
625C22C2×C22⋊C4×D4311yescharacteristic
626C4—21no—
627C4—21no—
628C4—42no—
629C4—861no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—1722no—
636C4—1722no—
637C4#1458289212yes—
638C4#1458291412yes—
639C4#1458366412yes—
640C4C2×#1306334411yescharacteristic
641C4C2×#1306334611yescharacteristic
642C2—22no—
643C2—82no—
644C2—1721no—
645C2—1721no—
646C2#1914303711yescharacteristic
647C2C2×#1458289211yescharacteristic
648C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1492C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC42×C43C24
hypercenter#1492D43
hypocenterC43#17489
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. C2×#14582950C2semidirect
4. #19133051C2semidirect
5. #19133049C2semidirect
6. #19133046C2semidirect
7. #19133026C2semidirect
8. #19133000C2semidirect
9. C43×#1492C2semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
324. #1492D43semidirect
372. D4⋊C8C2×D43semidirect
373. C43#17489semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432272
C2×#145829502
#191330512
#191330492
#191330462
#191330262
#191330002
C43×#14922
#1748943