Finite Group Databasebeta

← #25064549

Subgroups — #25064549

Order 11008.

1036 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
1#533×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3C4×M16×D43C211yesmaximal, characteristic
4#19133208C214yesmaximal, complemented
5#19133195C214yesmaximal, complemented
6#19133190C211yesmaximal, characteristic, complemented
7#19133189C211yesmaximal, characteristic, complemented
8#19133189C211yesmaximal, characteristic, complemented
9C43×#1526C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583456C2211yescharacteristic
12#14583455C2212yes—
13#14583454C411yescharacteristic
14#14583454C411yescharacteristic
15#14583453—21no—
16#14583453—21no—
17#14583452C412yes—
18#14583451—21no—
19#14583451—21no—
20C4⋊Q8×D43C411yescharacteristic
21C4⋊Q8×D43C411yescharacteristic
22#125×D43C2212yes—
23C22⋊Q8×D43—21no—
24C22⋊Q8×D43—21no—
25C4×Q8×D43—21no—
26C4×Q8×D43—21no—
27#117×D43C412yes—
28C2×C42×D43C2211yescharacteristic
29#14582954C2212yes—
30#14582954C2212yes—
31#14582950—21no—
32#14582950—21no—
33#14582922—21no—
34#14582862—21no—
35C4×#10621877C2211yescharacteristic
36C4×#10621877C2211yescharacteristic
37#14582851C2212yes—
38M16×Dic43—21no—
39C4×#10621872—21no—
40#97×D43C2212yes—
41C4×C8×D43—21no—
42#14582641C2214yescomplemented
43#14582640C2214yescomplemented
44#14582640C2214yescomplemented
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#330C2214yescomplemented
49C2×Q8×D43—21no—
50C2×Q8×D43—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621872—22no—
57M16×D43—28no—
58C2×C8×D43—22no—
59#13063325C2×C411yescharacteristic
60#13063325C2×C411yescharacteristic
61#13063324—21no—
62#13063324—21no—
63#13063324C2×C412yes—
64#13063324C2×C412yes—
65#13063323—21no—
66#13063323—21no—
67#13063317C2312yes—
68#13063316C2×C412yes—
69#13063316C2×C412yes—
70#13063315—22no—
71#13063315—22no—
72#13063305—21no—
73#13063305—21no—
74#13063304—21no—
75#13063304—21no—
76#13063303—22no—
77#13063303—22no—
78#13063302—22no—
79#13063302—22no—
80#13063301—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063290—21no—
89#13063290—21no—
90#13063290—22no—
91#13063290—22no—
92#13063284C2×C412yes—
93#13063283C2×C412yes—
94#13063283C2×C412yes—
95#13063282—22no—
96#13063281—22no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43C2×C412yes—
102C4⋊C4×D43C2×C412yes—
103C22⋊C4×D43—22no—
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C42×D43—22no—
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063236C2312yes—
121#13063236C2312yes—
122#13063235—22no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C8×Dic43—22no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129C4⋊Q8×C43C2×C411yescharacteristic
130#125×C43C2312yes—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43C2×C412yes—
136C2×C42×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2312yes—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150Q8×D43—44no—
151Q8×D43—44no—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—42no—
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173M16×C43—24no—
174M16×C43—42no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43C22×C412yes—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43C22×C412yes—
197C4⋊Dic43C22×C412yes—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221#10621877—24no—
222#10621877—42no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225#10621872—28no—
226C8×D43—28no—
227C23×C43C2×C22⋊C411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—42no—
234Q8×C43—42no—
235C2×C4×C43—22no—
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×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43C2×C22⋊C411yescharacteristic
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—44no—
268C4×D43—44no—
269C4×D43#10114yes—
270C4×D43#10414yes—
271Dic86—44no—
272Dic86—42no—
273Dic86—42no—
274Dic86—44no—
275C8×C43—24no—
276C8×C43—42no—
277C43⋊C8—24no—
278C43⋊C8—42no—
279#17648—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43C22×C22⋊C411yescharacteristic
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—44no—
289C2×D43C2×#10112yes—
290C2×D43C2×#10412yes—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43C2×#10112yes—
297C4×C43C2×#10412yes—
298C4×C43#42112yes—
299Dic43—21no—
300Dic43—21no—
301Dic43—21no—
302Dic43—21no—
303Dic43—42no—
304Dic43—42no—
305Dic43C2×#10112yes—
306Dic43C2×#10412yes—
307C2×#533—431no—
308#2920—431no—
309C2×C4×M16—431no—
310#1531—434no—
311#1528—434no—
312#1526—431no—
313#1526—431no—
314#1526—431no—
315#1526D4311yescharacteristic, complemented
316C2×C43—41no—
317C2×C43C22×#10111yescharacteristic
318C2×C43C22×#10411yescharacteristic
319C2×C43C2×#42111yescharacteristic
320D43—22no—
321D43—22no—
322C22×M16—861no—
323#533—431no—
324#533—431no—
325#533—432no—
326#533—432no—
327#533—431no—
328#533—861no—
329#533—861no—
330#533—861no—
331#533—861no—
332#533C2×D4311yescharacteristic
333C2×C4⋊Q8—431no—
334C2×C4⋊Q8—431no—
335C2×#125—432no—
336C2×C22⋊Q8—861no—
337C2×C22⋊Q8—861no—
338C2×C4×Q8—861no—
339C2×C4×Q8—861no—
340C2×#117—432no—
341C22×C42—431no—
342#432—432no—
343#432—432no—
344#431—861no—
345#431—861no—
346#423—861no—
347#407—861no—
348C4×M16—431no—
349C4×M16—431no—
350C4×M16—432no—
351C4×M16—861no—
352C4×M16—861no—
353C4×M16C2×D4311yescharacteristic
354C4×M16C2×D4311yescharacteristic
355C2×#97—432no—
356C2×C4×C8—861no—
357#330—434no—
358#330—434no—
359#330—434no—
360#330C2×D4314yescomplemented
361C43#1764811yescharacteristic, complemented, Sylow
362C22×Q8—861no—
363C22×Q8—861no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—431no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—862no—
370C2×M16—868no—
371C2×M16—861no—
372C2×M16—861no—
373C22×C8—862no—
374C4⋊Q8—432no—
375C4⋊Q8—432no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8C4×D4311yescharacteristic
383C4⋊Q8C4×D4311yescharacteristic
384#125—432no—
385#125—432no—
386#125—432no—
387#125—862no—
388#125—862no—
389#125C22×D4312yes—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—861no—
414#117—432no—
415#117—432no—
416#117—432no—
417#117—862no—
418#117—862no—
419#117C4×D4312yes—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C22⋊C4—862no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—862no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—862no—
441C4⋊C8—862no—
442C22⋊C8—862no—
443C22⋊C8—862no—
444#97—432no—
445#97—432no—
446#97—862no—
447#97C22×D4312yes—
448#97C22×D4312yes—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8—862no—
452C4×C8—861no—
453C4×C8—861no—
454C24—431no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—1724no—
462C2×Q8—1724no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—1722no—
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486M16—24no—
487M16—42no—
488M16—868no—
489M16—864no—
490M16—1722no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—868no—
494C2×C8—862no—
495C2×C8—862no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4C2×C4×D4312yes—
515C4⋊C4C2×C4×D4312yes—
516C22⋊C4—22no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C42—22no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—862no—
534C42—862no—
535C42—862no—
536C42C2×C4×D4311yescharacteristic
537C42D4×D4311yescharacteristic
538C42D4×D4311yescharacteristic
539C42C23×D4311yescharacteristic
540C23—431no—
541C23—431no—
542C23—862no—
543C23—862no—
544C23—1721no—
545C23C22⋊C4×D4311yescharacteristic
546Q8—42no—
547Q8—42no—
548Q8—1724no—
549Q8—1724no—
550Q8—1722no—
551Q8—1722no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1724no—
580C2×C4—1724no—
581C2×C4—1721no—
582C2×C4C22⋊C4×D4311yescharacteristic
583C2×C4C22⋊C4×D4311yescharacteristic
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22×C4×D4311yescharacteristic
586C2×C4C2×D4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C8—24no—
589C8—42no—
590C8—864no—
591C8—1722no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—432no—
596C22—432no—
597C22—861no—
598C22—861no—
599C22—861no—
600C22—861no—
601C22—1724no—
602C22C2×C22⋊C4×D4311yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—432no—
609C4—432no—
610C4—861no—
611C4—861no—
612C4—861no—
613C4—861no—
614C4—1722no—
615C4—1722no—
616C4#101×D4312yes—
617C4#104×D4312yes—
618C4#1458291412yes—
619C2—41no—
620C2—862no—
621C2—862no—
622C2C2×#101×D4311yescharacteristic
623C2C2×#104×D4311yescharacteristic
624C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1526C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1526D43
hypocenterC43#17648
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
4. #19133208C2semidirect
5. #19133195C2semidirect
6. #19133190C2semidirect
7. #19133189C2semidirect
8. #19133189C2semidirect
9. C43×#1526C2semidirect
42. #14582641C22semidirect
43. #14582640C22semidirect
44. #14582640C22semidirect
48. C43×#330C22semidirect
315. #1526D43semidirect
360. #330C2×D43semidirect
361. C43#17648semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432262
C4×M16×D432
#191332082
#191331952
#191331902
#191331892
C43×#15262
#1764843