Finite Group Databasebeta

← #25101081

Subgroups — #25101081

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2C4×M16×D43C211yesmaximal, characteristic
3#19136999C211yesmaximal, characteristic
4#19135540C211yesmaximal, characteristic, complemented
5#19135539C211yesmaximal, characteristic, complemented
6#19135538C211yesmaximal, characteristic, complemented
7#19135537C214yesmaximal, complemented
8#19134303C214yesmaximal
9C43×#1986C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583456C2211yescharacteristic
12#14583455C412yescomplemented
13#14583454C411yescharacteristic, complemented
14#14583454C411yescharacteristic, complemented
15#14583453—21no—
16#14583453—21no—
17#14583452C2212yes—
18#14583451—21no—
19#14583451—21no—
20C4⋊Q8×D43C411yescharacteristic, complemented
21C4⋊Q8×D43C411yescharacteristic, complemented
22#125×D43C412yescomplemented
23C22⋊Q8×D43—21no—
24C22⋊Q8×D43—21no—
25C4×Q8×D43—21no—
26C4×Q8×D43—21no—
27C2×#13063282C2212yes—
28#117×D43C2212yes—
29C2×C42×D43C2211yescharacteristic
30C4×#10621877C2211yescharacteristic
31#14582851—21no—
32M16×Dic43C2212yes—
33C4×#10621872—21no—
34#97×D43—21no—
35C4×C8×D43—21no—
36#14582768—21no—
37#14582763—21no—
38#14582758—21no—
39#14582756—21no—
40C4×Dic43⋊C4C2212yes—
41C4×C4⋊Dic43C2211yescharacteristic
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55C2×#10621872—22no—
56M16×D43—24no—
57M16×D43Q818yescomplemented
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#13063317C2×C412yes—
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#13063284C2312yes—
93#13063283C2×C412yes—
94#13063283C2×C412yes—
95#13063282—22no—
96#13063282—28no—
97#13063281—22no—
98C2×C4⋊Dic43—21no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—22no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43C2×C412yes—
106C4⋊C4×D43C2×C412yes—
107C2×(C2×D43)⋊C4—22no—
108C22⋊C4×D43—22no—
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2311yescharacteristic
113C42×D43—22no—
114C42×D43C2×C411yescharacteristic
115C42×D43C2×C411yescharacteristic
116C42×D43C2×C411yescharacteristic
117C42×D43C2×C411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C42×D43D411yescharacteristic
122#13063236—21no—
123#13063235—22no—
124C4×C43⋊C8—21no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—22no—
128C2×M16×C43C2312yes—
129C4⋊Q8×C43C2×C411yescharacteristic
130C4⋊Q8×C43C2×C411yescharacteristic
131#125×C43C2×C412yes—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136#117×C43C2312yes—
137C2×C4⋊C4×C43—21no—
138C2×C42×C43C2312yes—
139C2×C42×C43C2311yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142#95×C43—21no—
143C23×D43C2×D411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—22no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154Q8×D43—44no—
155Q8×D43—44no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×Q814yes—
173C2×C4×D43#4114yes—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178M16×C43—22no—
179M16×C43C2×Q814yescomplemented
180C2×C8×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C22×C412yes—
187C4⋊C4×C43C22×C412yes—
188C22⋊C4×C43—22no—
189C42×C43—22no—
190C42×C43—24no—
191C42×C43C22×C411yescharacteristic
192C42×C43C22×C411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C22⋊Dic43—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—44no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43—42no—
204C4⋊Dic43C22×C412yes—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—44no—
215Dic43⋊C4—44no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—24no—
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22×C411yescharacteristic
229C4×Dic43C22×C411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232#10621877—22no—
233#10621877C2×Q814yescomplemented
234C2×C43⋊C8—22no—
235#10621872—28no—
236C8×D43—28no—
237C23×C43C22×D411yescharacteristic
238C22×D43—41no—
239C22×D43—41no—
240C22×D43C2×C22⋊C411yescharacteristic
241C22×D43C2×C22⋊C411yescharacteristic
242C22×D43#12412yes—
243C22×D43C4⋊Q812yes—
244Q8×C43—42no—
245Q8×C43—42no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q812yes—
260C2×C4×C43C2×#4112yes—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43#12412yes—
275C2×Dic43C4⋊Q812yes—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—44no—
285C4×D43—44no—
286C4×D43C4×Q814yes—
287C4×D43C4×Q814yes—
288C4×D43C22⋊Q814yes—
289C4×D43C22⋊Q814yes—
290Dic86—44no—
291Dic86—42no—
292Dic86—42no—
293Dic86—44no—
294C8×C43—24no—
295C43⋊C8—24no—
296#21306—431nomaximal, Sylow
297C22×C43—21no—
298C22×C43—21no—
299C22×C43C22×C22⋊C411yescharacteristic
300C22×C43C2×#12411yescharacteristic
301C22×C43C2×C4⋊Q811yescharacteristic
302C2×D43—21no—
303C2×D43—21no—
304C2×D43—21no—
305C2×D43—21no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43#39112yes—
309C2×D43#39112yes—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—82no—
316C4×C43#42112yes—
317C4×C43C2×C4×Q812yes—
318C4×C43C2×C22⋊Q812yes—
319Dic43—21no—
320Dic43—21no—
321Dic43—21no—
322Dic43—42no—
323Dic43—42no—
324Dic43—82no—
325Dic43#39112yes—
326Dic43#39112yes—
327Dic43#42112yes—
328C2×#533—431no—
329C2×C4×M16—431no—
330#2285—431no—
331#1986—431no—
332#1986—431no—
333#1986—434no—
334#1986—431no—
335#1986D4311yescharacteristic, complemented
336#1733—434no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43C2×#39111yescharacteristic
340C2×C43C2×#42111yescharacteristic
341C2×C43C2×#42111yescharacteristic
342D43—22no—
343D43—22no—
344C22×M16—432no—
345#533—431no—
346#533—431no—
347#533—432no—
348#533—432no—
349#533—431no—
350#533—861no—
351#533—861no—
352#533—861no—
353#533—861no—
354#533C2×D4311yescharacteristic
355C2×C4⋊Q8—431no—
356C2×C4⋊Q8—431no—
357C2×#125—432no—
358C2×C22⋊Q8—861no—
359C2×C22⋊Q8—861no—
360C2×C4×Q8—861no—
361C2×C4×Q8—861no—
362C2×#117—432no—
363C2×#117—432no—
364C22×C42—431no—
365C4×M16—432no—
366C4×M16—431no—
367C4×M16—861no—
368C4×M16—861no—
369C4×M16C2×D4311yescharacteristic
370C2×#97—861no—
371C2×C4×C8—861no—
372#384—861no—
373#382—861no—
374#380—861no—
375#380—861no—
376C4×C4⋊C4—432no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4C2×D4311yescharacteristic
379#339—434no—
380#339—434no—
381#339—434no—
382#339C2×D4314yes—
383C43#2130611yescharacteristic, complemented, Sylow
384C22×Q8—861no—
385C22×Q8—861no—
386C23×C4—431no—
387C23×C4—431no—
388C23×C4—431no—
389C2×M16—432no—
390C2×M16—438no—
391C2×M16—862no—
392C2×M16—864no—
393C2×M16C22×D4312yes—
394C22×C8—862no—
395C4⋊Q8—432no—
396C4⋊Q8—432no—
397C4⋊Q8—431no—
398C4⋊Q8—431no—
399C4⋊Q8—861no—
400C4⋊Q8—861no—
401C4⋊Q8—861no—
402C4⋊Q8—861no—
403C4⋊Q8C4×D4311yescharacteristic
404C4⋊Q8C4×D4311yescharacteristic
405#125—432no—
406#125—432no—
407#125—432no—
408#125—862no—
409#125—862no—
410#125C4×D4312yes—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—862no—
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—862no—
417C22⋊Q8—861no—
418C22⋊Q8—861no—
419C22⋊Q8—861no—
420C22⋊Q8—861no—
421C22⋊Q8—861no—
422C22⋊Q8—861no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—861no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8—861no—
433C4×Q8—861no—
434C4×Q8—861no—
435#117—432no—
436#117—432no—
437#117—432no—
438#117—862no—
439#117—868no—
440#117—862no—
441#117C22×D4312yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—432no—
444C2×C4⋊C4—432no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—862no—
450C2×C4⋊C4—862no—
451C2×C4⋊C4—861no—
452C2×C22⋊C4—862no—
453C2×C22⋊C4—862no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—432no—
466C2×C42—862no—
467C2×C42C22×D4312yes—
468C2×C42C22×D4311yescharacteristic
469#97—21no—
470#97—862no—
471#97—861no—
472C4×C8—21no—
473C4×C8—862no—
474C4×C8—861no—
475#95—21no—
476#95—862no—
477#95—861no—
478C24—431no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—862no—
482C2×Q8—862no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—1724no—
486C2×Q8—1724no—
487C22×C4—22no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—434no—
494C22×C4—434no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513M16—22no—
514M16—434no—
515M16—868no—
516M16—862no—
517M16Q8×D4314yescomplemented
518C2×C8—22no—
519C2×C8—868no—
520C2×C8—862no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1722no—
541C4⋊C4—1724no—
542C4⋊C4—1724no—
543C4⋊C4C2×C4×D4312yes—
544C4⋊C4C2×C4×D4312yes—
545C22⋊C4—22no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—1724no—
550C42—22no—
551C42—24no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—862no—
565C42—862no—
566C42—862no—
567C42—864no—
568C42C2×C4×D4311yescharacteristic
569C42C2×C4×D4311yescharacteristic
570C42D4×D4311yescharacteristic
571C42D4×D4311yescharacteristic
572C23—431no—
573C23—431no—
574C23—432no—
575C23—432no—
576C23—1721no—
577C23—1721no—
578C23C2×D4×D4311yescharacteristic
579Q8—42no—
580Q8—42no—
581Q8—1722no—
582Q8—1724no—
583Q8—1724no—
584Q8—1722no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—431no—
593C2×C4—431no—
594C2×C4—431no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—434no—
598C2×C4—434no—
599C2×C4—434no—
600C2×C4—434no—
601C2×C4—431no—
602C2×C4—431no—
603C2×C4—431no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1724no—
616C2×C4—1724no—
617C2×C4—1721no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4C22⋊C4×D4311yescharacteristic
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4C22⋊C4×D4311yescharacteristic
625C2×C4C22×C4×D4311yescharacteristic
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4C2×Q8×D4312yes—
628C2×C4#41×D4312yes—
629C8—24no—
630C8—864no—
631C22—21no—
632C22—21no—
633C22—432no—
634C22—432no—
635C22—861no—
636C22—861no—
637C22—861no—
638C22—861no—
639C22—1722no—
640C22—1722no—
641C22C2×C22⋊C4×D4311yescharacteristic
642C22#124×D4311yescharacteristic
643C22C4⋊Q8×D4311yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—42no—
648C4—42no—
649C4—82no—
650C4—432no—
651C4—432no—
652C4—432no—
653C4—861no—
654C4—861no—
655C4—861no—
656C4—3442no—
657C4—1722no—
658C4—1722no—
659C4#1458291412yes—
660C4C4×Q8×D4312yes—
661C4C22⋊Q8×D4312yes—
662C2—21no—
663C2—21no—
664C2—862no—
665C2—862no—
666C2#391×D4311yescharacteristic
667C2#421×D4311yescharacteristic
668C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #19135540C2semidirect
5. #19135539C2semidirect
6. #19135538C2semidirect
7. #19135537C2semidirect
9. C43×#1986C2semidirect
12. #14583455C4semidirect
13. #14583454C4semidirect
14. #14583454C4semidirect
20. C4⋊Q8×D43C4semidirect
21. C4⋊Q8×D43C4semidirect
22. #125×D43C4semidirect
57. M16×D43Q8semidirect
179. M16×C43C2×Q8semidirect
233. #10621877C2×Q8semidirect
335. #1986D43semidirect
383. C43#21306semidirect
517. M16Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#533×D432
C4×M16×D432
#191369992
#191355402
#191355392
#191355382
#191355372
#191343032
C43×#19862
#2130643