Finite Group Databasebeta

← #25063321

Subgroups — #25063321

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#19147892C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3C2×#14582950C211yesmaximal, characteristic, complemented
4#19133050C211yesmaximal, characteristic, complemented
5#19133047C211yesmaximal, characteristic, complemented
6#19133045C211yesmaximal, characteristic, complemented
7#19133028C214yesmaximal, complemented
8#19133002C214yesmaximal, complemented
9C43×#1493C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic
11#14583454C411yescharacteristic
12#14583450C411yescharacteristic
13#14583450C411yescharacteristic
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436C2212yes—
17#14583435—21no—
18#14583435C412yes—
19#14583434—21no—
20#14583434—21no—
21#14583412—21no—
22#14583412C412yes—
23#14583411—21no—
24C4×#10621902—21no—
25C4×#10621902C2212yes—
26#14583367—21no—
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
42Q8⋊(C43⋊C8)C2214yescomplemented
43#14582628C2214yescomplemented
44#14582626C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902C2×C412yes—
51C2×#10621898—21no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57#13063325C2×C411yescharacteristic
58#13063322C2×C411yescharacteristic
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316C2×C412yes—
63#13063314—21no—
64#13063314C2×C412yes—
65#13063313—21no—
66#13063310—22no—
67#13063310—22no—
68#13063309—22no—
69#13063305—21no—
70#13063305—21no—
71#13063301—21no—
72#13063301C2×C412yes—
73#13063300—21no—
74#13063300—21no—
75#13063300—21no—
76#13063300C2×C412yes—
77#13063299—21no—
78#13063299C2×C412yes—
79#13063295—22no—
80Q8×Dic43—21no—
81Q8×Dic43C2×C412yes—
82#13063290—21no—
83#13063290—21no—
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—21no—
87C4×D172C2312yes—
88#13063287—22no—
89#13063287—22no—
90#13063287—21no—
91#13063287—21no—
92#13063287—21no—
93#13063287C2×C412yes—
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96#13063283—21no—
97#13063283—22no—
98#13063283—22no—
99#13063283C2×C412yes—
100#13063282—22no—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C42×D43—22no—
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×M16×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2×C412yes—
132C4×Q8×C43—21no—
133C4×Q8×C43C2312yes—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—22no—
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150#10621902—44no—
151#10621902—44no—
152#10621898—42no—
153#10621898—42no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172C22×C412yes—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×Dic86—21no—
179M16×C43—42no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—42no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43C22×C412yes—
189C22⋊C4×C43—22no—
190C42×C43—22no—
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2411yescharacteristic
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—22no—
208Dic43⋊C4—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×C43C2×C22⋊C411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234Q8×C43—24no—
235Q8×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43#13512yes—
244C2×C4×C43#13512yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—44no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259D172—24no—
260D172—44no—
261D172—44no—
262D172—42no—
263D172—42no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—21no—
267C4×D43—21no—
268C4×D43—21no—
269C4×D43—21no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—44no—
279C4×D43—44no—
280C4×D43—42no—
281C4×D43—42no—
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#41612yes—
291C22×C43C22×C22⋊C411yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—44no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43#41612yes—
307C4×C43#42112yes—
308C4×C43#56812yes—
309C4×C43C2×#13511yescharacteristic
310C4×C43C2×#13511yescharacteristic
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—42no—
318#3444—431no—
319#2920—431no—
320C2×#431—431no—
321#1493—431no—
322#1493D4311yescharacteristic, complemented
323#1492—431no—
324#1492—431no—
325#1488—434no—
326#1482—434no—
327C2×C43—22no—
328C2×C43#287911yescharacteristic
329C2×C43C2×#41611yescharacteristic
330C2×C43C2×#42111yescharacteristic
331D43—41no—
332D43—41no—
333D43—82no—
334#533—431no—
335#533—431no—
336#533C2×D4311yescharacteristic
337#532—431no—
338#532—431no—
339#532—431no—
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⋊C8C2×D4314yescomplemented
371D4⋊C8—434no—
372D4⋊C8—434no—
373C43#1748911yescharacteristic, complemented, Sylow
374C2×#41—432no—
375C2×#41—861no—
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⋊Q8C4×D4311yescharacteristic
386C4⋊Q8C4×D4311yescharacteristic
387#127—431no—
388#126—862no—
389#126—862no—
390#125—21no—
391#125—432no—
392#125—861no—
393#124—432no—
394#124—861no—
395#124—861no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8C4×D4312yes—
405#121—432no—
406#121—432no—
407#121—861no—
408#121—861no—
409#121—861no—
410#121—861no—
411#120—862no—
412C4×Q8—21no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8C22×D4312yes—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—861no—
430#117—21no—
431#117—432no—
432#117—862no—
433#117—862no—
434#117—862no—
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—1724no—
467#41—1724no—
468#41—1722no—
469#41—1722no—
470C2×Q8—21no—
471C2×Q8—861no—
472C2×Q8C2×C4×D4312yes—
473C2×D4—432no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—862no—
477C2×D4—861no—
478C2×D4—861no—
479C22×C4—431no—
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—862no—
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—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—432no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C42—22no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—862no—
547C42—862no—
548C42C2×C4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42C23×D4311yescharacteristic
552C23—431no—
553C23—431no—
554C23—862no—
555C23—862no—
556C23—1721no—
557C23—1721no—
558C23C22⋊C4×D4311yescharacteristic
559Q8—24no—
560Q8—42no—
561Q8—1722no—
562D4—864no—
563D4—1724no—
564D4—1724no—
565D4—1724no—
566D4—1722no—
567D4—1722no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—862no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1724no—
595C2×C4—1724no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4#1306334612yes—
604C2×C4#1306334812yes—
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—861no—
615C22—861no—
616C22—861no—
617C22—861no—
618C22—861no—
619C22—861no—
620C22—1724no—
621C22—1722no—
622C22—1722no—
623C22—1722no—
624C22#1458289412yes—
625C22C2×C22⋊C4×D4311yescharacteristic
626C4—21no—
627C4—21no—
628C4—42no—
629C4—42no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—861no—
636C4—1722no—
637C4#1458289412yes—
638C4#1458291412yes—
639C4#1458366412yes—
640C4C2×#1306334611yescharacteristic
641C4C2×#1306334811yescharacteristic
642C2—22no—
643C2—3442no—
644C2—1721no—
645C2—1721no—
646C2#1914303711yescharacteristic
647C2C2×#1458289411yescharacteristic
648C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1493C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1493D43
hypocenterC43#17489
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. C2×#14582950C2semidirect
4. #19133050C2semidirect
5. #19133047C2semidirect
6. #19133045C2semidirect
7. #19133028C2semidirect
8. #19133002C2semidirect
9. C43×#1493C2semidirect
42. Q8⋊(C43⋊C8)C22semidirect
43. #14582628C22semidirect
44. #14582626C22semidirect
48. C43×Q8⋊C8C22semidirect
322. #1493D43semidirect
370. Q8⋊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
#191478922
#191432272
C2×#145829502
#191330502
#191330472
#191330452
#191330282
#191330022
C43×#14932
#1748943