Finite Group Databasebeta

← #25101086

Subgroups — #25101086

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2#19143012C211yesmaximal, characteristic
3#19137075C211yesmaximal, characteristic
4#19135540C211yesmaximal, characteristic, complemented
5#19135539C211yesmaximal, characteristic, complemented
6#19135538C211yesmaximal, characteristic, complemented
7#19135537C212yesmaximal, complemented
8#19135537C212yesmaximal, complemented
9#19134303C212yesmaximal
10#339×D43C212yesmaximal
11C43×#1986C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583529C412yescomplemented
14#14583529C412yescomplemented
15#14583528—21no—
16#14583528—21no—
17#14583526C412yescomplemented
18#14583526C412yescomplemented
19#14583524—21no—
20#14583524—21no—
21#14583456C2211yescharacteristic
22#14583453—22no—
23#14583453—22no—
24#14583452C2212yes—
25C2×#13063282C2211yescharacteristic
26C2×#13063282C2211yescharacteristic
27#117×D43C2212yes—
28C2×C42×D43C2211yescharacteristic
29#14582856—22no—
30#14582853—22no—
31C4×#10621877C2211yescharacteristic
32M16×Dic43C2212yes—
33#14582796—21no—
34#14582794—21no—
35#14582773—21no—
36#14582770—21no—
37C4×Dic43⋊C4C2211yescharacteristic
38C4×Dic43⋊C4C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40#14582660C2212yes—
41#14582660C2212yes—
42#14582659C2212yes—
43#14582659C2212yes—
44#14582658C2212yes—
45#14582658C2212yes—
46C43×#533C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C43×#339C2212yes—
50C43×#339C2212yes—
51C22×C4×D43—21no—
52C22×C4×D43C2311yescharacteristic
53C2×#10621877C2312yes—
54C2×#10621872—22no—
55M16×D43—24no—
56M16×D43Q818yescomplemented
57C2×C8×D43—22no—
58#13063325C2×C411yescharacteristic, complemented
59#13063325C2×C411yescharacteristic, complemented
60#13063324—22no—
61#13063324—22no—
62#13063324C2×C412yescomplemented
63#13063324C2×C412yescomplemented
64#13063323—22no—
65#13063323—22no—
66#13063317C2×C412yescomplemented
67#13063316C2×C412yescomplemented
68#13063316C2×C412yescomplemented
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063315—22no—
73#13063305—22no—
74#13063305—22no—
75#13063304—21no—
76#13063304—21no—
77#13063303—22no—
78#13063303—22no—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301—22no—
84#13063301—22no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89#13063284C2312yes—
90#13063283C2×C412yes—
91#13063283C2×C412yes—
92#13063282—22no—
93#13063282—24no—
94#13063282C2×C412yes—
95#13063282C2×C412yes—
96#13063282D412yes—
97#13063282D412yes—
98#13063281—22no—
99C2×C4⋊Dic43—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C2×Dic43⋊C4D411yescharacteristic
105C4⋊C4×D43C2×C412yes—
106C4⋊C4×D43C2×C412yes—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×(C2×D43)⋊C4D411yescharacteristic
110C22⋊C4×D43—22no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C42×D43—22no—
116C42×D43—24no—
117#13063236—21no—
118#13063235—22no—
119C4×C43⋊C8—21no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C2×M16×C43C2312yes—
125C4⋊Q8×C43C2×C411yescharacteristic, complemented
126C4⋊Q8×C43C2×C411yescharacteristic, complemented
127#125×C43C2×C412yescomplemented
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132#117×C43C2312yes—
133C2×C4⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#97×C43—21no—
138C4×C8×C43—21no—
139#95×C43—21no—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43C22×C412yes—
159C2×C4×D43C2×D412yes—
160C2×C4×D43C2×Q814yes—
161C2×C4×D43#4114yes—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—22no—
165C2×Dic86—22no—
166M16×C43—22no—
167M16×C43C2×Q814yes—
168C2×C8×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C22×C412yes—
175C4⋊C4×C43C22×C412yes—
176C22⋊C4×C43—22no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43C22×C411yescharacteristic
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C22⋊Dic43—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4C22⋊C412yes—
189(C2×D43)⋊C4C22⋊C412yes—
190(C2×D43)⋊C4C22⋊C412yes—
191(C2×D43)⋊C4C22⋊C412yes—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43—42no—
197C4⋊Dic43C22×C412yes—
198C4⋊Dic43C22×C412yes—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—42no—
220C4×Dic43C22×C412yes—
221C4×Dic43C2×D412yes—
222#10621877—22no—
223#10621877C2×Q814yes—
224C2×C43⋊C8—22no—
225#10621872—28no—
226C8×D43—28no—
227C23×C43C22×D411yescharacteristic
228C22×D43—41no—
229C22×D43—41no—
230C22×D43C2×C22⋊C412yes—
231C22×D43#12412yes—
232C22×D43C4⋊Q812yes—
233Q8×C43—81no—
234Q8×C43—81no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q812yes—
252C2×C4×C43C2×#4112yes—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43#12412yes—
267C2×Dic43C4⋊Q812yes—
268C4×D43—48no—
269C4×D43—82no—
270C4×D43—82no—
271C4×D43C4×Q818yes—
272C4×D43C22⋊Q814yes—
273C4×D43C22⋊Q814yes—
274Dic86—82no—
275Dic86—82no—
276Dic86—81no—
277Dic86—81no—
278C8×C43—24no—
279C43⋊C8—24no—
280#21307—431nomaximal, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43C22×C22⋊C411yescharacteristic
284C22×C43C2×#12411yescharacteristic
285C22×C43C2×C4⋊Q811yescharacteristic
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43#39114yes—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—81no—
299C4×C43C2×C4×Q812yes—
300C4×C43C2×C22⋊Q812yes—
301Dic43—22no—
302Dic43—22no—
303Dic43—42no—
304Dic43—42no—
305Dic43—42no—
306Dic43—81no—
307Dic43#39114yes—
308#3458—431no—
309#2873—431no—
310#2296—431no—
311#1986—431no—
312#1986—431no—
313#1986—432no—
314#1986—432no—
315#1986—431no—
316#1986D4311yescharacteristic, complemented
317#1733—432no—
318C2×#339—432no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43C2×#39111yescharacteristic
322C2×C43#290111yescharacteristic
323C2×C43#290111yescharacteristic
324D43—24no—
325C22×M16—432no—
326#544—432no—
327#544—432no—
328#544—432no—
329#544—432no—
330#544—861no—
331#544—861no—
332#543—861no—
333#543—861no—
334#533—432no—
335#533—431no—
336#533—862no—
337#533—862no—
338#533C2×D4311yescharacteristic
339C2×#117—431no—
340C2×#117—431no—
341C2×#117—432no—
342C22×C42—431no—
343#405—862no—
344#405—862no—
345C4×M16—432no—
346C4×M16—431no—
347C4×M16C2×D4311yescharacteristic
348#389—861no—
349#389—861no—
350#385—861no—
351#385—861no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4C2×D4311yescharacteristic
356#339—432no—
357#339—432no—
358#339—432no—
359#339—432no—
360#339—432no—
361#339—432no—
362#339C2×D4312yes—
363#339C2×D4312yes—
364C43#2130711yescharacteristic, complemented, Sylow
365C23×C4—431no—
366C23×C4—861no—
367C2×M16—432no—
368C2×M16—438no—
369C2×M16—862no—
370C2×M16—864no—
371C2×M16C22×D4312yes—
372C22×C8—862no—
373C4⋊Q8—432no—
374C4⋊Q8—432no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—862no—
378C4⋊Q8—862no—
379C4⋊Q8—862no—
380C4⋊Q8—862no—
381C4⋊Q8C4×D4311yescharacteristic, complemented
382C4⋊Q8C4×D4311yescharacteristic, complemented
383#125—432no—
384#125—432no—
385#125—432no—
386#125—862no—
387#125—862no—
388#125—862no—
389#125—862no—
390#125C4×D4312yescomplemented
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—861no—
410C4×Q8—861no—
411#117—432no—
412#117—432no—
413#117—432no—
414#117—432no—
415#117—432no—
416#117—432no—
417#117—432no—
418#117—862no—
419#117—864no—
420#117—862no—
421#117C22×D4312yes—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—862no—
434C2×C22⋊C4—861no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—862no—
439C2×C42—864no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444#97—21no—
445#97—862no—
446#97—861no—
447C4×C8—21no—
448C4×C8—862no—
449C4×C8—861no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—431no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—861no—
460C2×Q8—861no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480M16—22no—
481M16—434no—
482M16—868no—
483M16—862no—
484M16Q8×D4314yes—
485C2×C8—22no—
486C2×C8—868no—
487C2×C8—862no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—42no—
493C4⋊C4—432no—
494C4⋊C4—432no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—432no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4C2×C4×D4312yes—
516C4⋊C4C2×C4×D4312yes—
517C22⋊C4—22no—
518C22⋊C4—432no—
519C22⋊C4—432no—
520C22⋊C4—432no—
521C22⋊C4—432no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—1722no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—432no—
530C42—432no—
531C42—862no—
532C42—862no—
533C42—862no—
534C42—862no—
535C42—862no—
536C42—1722no—
537C42C2×C4×D4311yescharacteristic
538C42C2×C4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42D4×D4311yescharacteristic
541C23—432no—
542C23—432no—
543C23—432no—
544C23—1721no—
545C23—1721no—
546C23C2×D4×D4311yescharacteristic
547Q8—81no—
548Q8—81no—
549Q8—3441no—
550Q8—3441no—
551Q8—3442no—
552Q8—3442no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—432no—
564C2×C4—432no—
565C2×C4—432no—
566C2×C4—438no—
567C2×C4—434no—
568C2×C4—434no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—3442no—
575C2×C4—3442no—
576C2×C4—1728no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22⋊C4×D4311yescharacteristic
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×Q8×D4312yes—
591C2×C4#41×D4312yes—
592C8—24no—
593C8—864no—
594C22—21no—
595C22—21no—
596C22—434no—
597C22—862no—
598C22—862no—
599C22—1722no—
600C22—1722no—
601C22C2×C22⋊C4×D4311yescharacteristic
602C22#124×D4311yescharacteristic
603C22C4⋊Q8×D4311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—81no—
612C4—434no—
613C4—862no—
614C4—862no—
615C4—3441no—
616C4—1722no—
617C4—1722no—
618C4—1722no—
619C4C4×Q8×D4312yes—
620C4C22⋊Q8×D4312yes—
621C2—21no—
622C2—21no—
623C2—864no—
624C2#391×D4311yescharacteristic
625C2#1914313911yescharacteristic
626C2#1914314111yescharacteristic
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#21307
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
8. #19135537C2semidirect
11. C43×#1986C2semidirect
13. #14583529C4semidirect
14. #14583529C4semidirect
17. #14583526C4semidirect
18. #14583526C4semidirect
56. M16×D43Q8semidirect
58. #13063325C2×C4semidirect
59. #13063325C2×C4semidirect
62. #13063324C2×C4semidirect
63. #13063324C2×C4semidirect
66. #13063317C2×C4semidirect
67. #13063316C2×C4semidirect
68. #13063316C2×C4semidirect
125. C4⋊Q8×C43C2×C4semidirect
126. C4⋊Q8×C43C2×C4semidirect
127. #125×C43C2×C4semidirect
316. #1986D43semidirect
364. C43#21307semidirect
381. C4⋊Q8C4×D43semidirect
382. C4⋊Q8C4×D43semidirect
390. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191479982
#191430122
#191370752
#191355402
#191355392
#191355382
#191355372
#191343032
#339×D432
C43×#19862
#2130743