Finite Group Databasebeta

← #25099829

Subgroups — #25099829

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143396C211yesmaximal, characteristic
2#19143235C211yesmaximal, characteristic, complemented
3#131×Dic43C211yesmaximal, characteristic, complemented
4#19135246C211yesmaximal, characteristic, complemented
5#19135240C211yesmaximal, characteristic, complemented
6#19135195C211yesmaximal, characteristic, complemented
7#19135193C211yesmaximal, characteristic, complemented
8#19134924C211yesmaximal, characteristic
9#19134870C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic, complemented
11#19134500C211yesmaximal, characteristic, complemented
12#19134407C211yesmaximal, characteristic, complemented
13#19134407C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1876C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#41×Dic43C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19#14583011C411yescharacteristic, complemented
20#14583011C411yescharacteristic, complemented
21#14583006C411yescharacteristic, complemented
22#14583006C411yescharacteristic, complemented
23#14583000C411yescharacteristic, complemented
24#14583000C411yescharacteristic, complemented
25#14583000C411yescharacteristic, complemented
26#14583000C411yescharacteristic, complemented
27#14582957—21no—
28#14582957—21no—
29#14582949—21no—
30#14582949—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582937C2211yescharacteristic
34#14582927C2211yescharacteristic
35#14582925C2211yescharacteristic
36C2×#13063252C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38#14582895C2211yescharacteristic
39#14582895C2211yescharacteristic
40#14582866C2211yescharacteristic
41#14582857—21no—
42#14582857C2211yescharacteristic
43#14582854—21no—
44#14582854C2211yescharacteristic
45M16×Dic43—21no—
46M16×Dic43C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48C2×#13063235C2211yescharacteristic
49C2×C8×Dic43—21no—
50C2×C8×Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#135×C43C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#336C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75Q8×Dic43C2×C411yescharacteristic
76Q8×Dic43C2×C411yescharacteristic
77Q8×Dic43C2×C411yescharacteristic
78Q8×Dic43C2×C411yescharacteristic
79D4×Dic43—21no—
80D4×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43C2×C411yescharacteristic
84D4×Dic43C2×C411yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86D4×Dic43C2×C411yescharacteristic
87#13063284—21no—
88#13063284—21no—
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063260—22no—
96#13063260—22no—
97#13063259C2×C411yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063257C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063252—22no—
106#13063252—22no—
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117#13063235—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235C2×C411yescharacteristic
122#13063235C2×C411yescharacteristic
123#13063235C2×C411yescharacteristic
124#13063235C2×C411yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C8×Dic43D411yescharacteristic
133C43⋊#95—21no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136C2×#41×C43C2311yescharacteristic
137#135×C43—22no—
138#135×C43—22no—
139C2×Q16×C43C2×C411yescharacteristic
140C2×SD16×C43C2×C411yescharacteristic
141C2×SD16×C43C2×C411yescharacteristic
142C2×D8×C43C2×C411yescharacteristic
143#131×C43—22no—
144#131×C43—22no—
145C2×M16×C43—21no—
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C22×C8×C43—21no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
152#104×C43—22no—
153#104×C43—22no—
154C22⋊C8×C43—21no—
155C22⋊C8×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43—21no—
161#41×C43—21no—
162#41×C43#4112yes—
163#41×C43#4112yes—
164C2×Q8×C43C22×C411yescharacteristic
165C2×Q8×C43C22×C411yescharacteristic
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C22×C411yescharacteristic
169C2×D4×C43C22×C411yescharacteristic
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43#4111yescharacteristic
180C22×Dic43#4111yescharacteristic
181Q16×C43—22no—
182SD16×C43—22no—
183SD16×C43—22no—
184D8×C43—22no—
185M16×C43—24no—
186M16×C43—21no—
187M16×C43—21no—
188M16×C43—21no—
189M16×C43#4112yes—
190C2×C8×C43—24no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C22×C411yescharacteristic
198C2×C8×C43C22×C411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C2×C8×C43C2×D411yescharacteristic
201C42×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C22⋊Dic43—21no—
206C22⋊Dic43—21no—
207C22⋊Dic43—21no—
208C22⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216C4⋊Dic43C22×C411yescharacteristic
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—24no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877#4112yes—
234C2×C43⋊C8—24no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C22×C411yescharacteristic
242C2×C43⋊C8C22×C411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C23×C43—21no—
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248Q8×C43—21no—
249Q8×C43—21no—
250Q8×C43—21no—
251Q8×C43#11712yes—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43—21no—
255D4×C43—21no—
256D4×C43—21no—
257D4×C43—41no—
258D4×C43—41no—
259D4×C43#11712yes—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43C23×C411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43C4×D411yescharacteristic
289C2×Dic43C4×D411yescharacteristic
290C2×Dic43C4×D411yescharacteristic
291C2×Dic43C4×D411yescharacteristic
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—22no—
296C8×C43—21no—
297C8×C43—41no—
298C43⋊C8—21no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—22no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304#21138—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—22no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43C2×C4×D411yescharacteristic
314C22×C43#52911yescharacteristic
315C22×C43#52911yescharacteristic
316C4×C43—22no—
317C4×C43—41no—
318C4×C43—81no—
319C4×C43C2×#11711yescharacteristic
320C4×C43C4×#4111yescharacteristic
321C4×C43#52511yescharacteristic
322C4×C43#52511yescharacteristic
323Dic43—21no—
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—81no—
332#2943—431no—
333#2922—431no—
334C4×#131—431no—
335#1929—431no—
336#1929—431no—
337#1922—431no—
338#1922—431no—
339#1876—431no—
340#1876D4311yescharacteristic
341#1866—431no—
342#1866—431no—
343#1778—431no—
344#1759—431no—
345#1759—431no—
346#1746—431no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—42no—
350C2×C43—81no—
351C2×C43#229011yescharacteristic
352C2×C43#295511yescharacteristic
353C2×C43#295511yescharacteristic
354C2×#135C2×D4311yescharacteristic
355C2×#131—431no—
356C2×#131C2×D4311yescharacteristic
357C4×#41—431no—
358C4×#41—431no—
359#442—431no—
360#442—431no—
361#441—431no—
362#441—431no—
363#440—431no—
364#440—431no—
365#440—431no—
366#440—431no—
367#433—861no—
368#433—861no—
369#431—861no—
370#431—861no—
371C2×#108—431no—
372C2×#108—431no—
373#427—431no—
374#424—431no—
375#424—431no—
376C2×#104—431no—
377C2×#104—431no—
378C2×#104C2×D4311yescharacteristic
379C2×#104C2×D4311yescharacteristic
380#416—431no—
381#416—431no—
382#408—431no—
383#408C2×D4311yescharacteristic
384#405—431no—
385#405—431no—
386#405—861no—
387#405—861no—
388C4×M16—431no—
389C4×M16—431no—
390C4×M16—861no—
391C2×#97—431no—
392C2×C4×C8—431no—
393C2×C4×C8—861no—
394#376—431no—
395#341—431no—
396#341C2×D4311yescharacteristic
397#339—431no—
398#339—431no—
399#339—431no—
400#339—431no—
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2113811yescharacteristic, complemented, Sylow
406C2×#41C22×D4311yescharacteristic
407C2×#41C22×D4311yescharacteristic
408#135—22no—
409#135—22no—
410C2×Q16C4×D4311yescharacteristic
411C2×SD16C4×D4311yescharacteristic
412C2×SD16C4×D4311yescharacteristic
413C2×D8C4×D4311yescharacteristic
414#131—22no—
415#131—22no—
416#131—862no—
417#131—862no—
418C2×M16—21no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—861no—
422C2×M16C22×D4311yescharacteristic
423C2×M16C22×D4311yescharacteristic
424C22×C8—21no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8—861no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4×Q8—431no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×D4—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442#117—431no—
443#117—431no—
444#117—861no—
445#117—861no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451#108—862no—
452#108—862no—
453#107—431no—
454#107—431no—
455#106—431no—
456#106—431no—
457C4⋊C8—861no—
458C4⋊C8—861no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461#104—22no—
462#104—22no—
463#104—862no—
464#104—862no—
465#103—431no—
466#103—431no—
467#103—431no—
468#103—431no—
469#102—431no—
470#102—431no—
471#102—431no—
472#102—431no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477#97—431no—
478#97—431no—
479#97—431no—
480#97—431no—
481#97—861no—
482#97—861no—
483#97—861no—
484#97—861no—
485C4×C8—431no—
486C4×C8—431no—
487C4×C8—431no—
488C4×C8—431no—
489C4×C8—861no—
490C4×C8—861no—
491C4×C8—861no—
492C4×C8—861no—
493#95—861no—
494#95—861no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41#1062190012yes—
502#41#1062190012yes—
503C2×Q8C2×C4×D4311yescharacteristic
504C2×Q8C2×C4×D4311yescharacteristic
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C2×C4×D4311yescharacteristic
508C2×D4C2×C4×D4311yescharacteristic
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4C23×D4311yescharacteristic
520Q16—22no—
521SD16—22no—
522SD16—22no—
523D8—22no—
524M16—24no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—432no—
529M16—864no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16#1062190012yes—
534C2×C8—24no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—431no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—864no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8C2×C4×D4311yescharacteristic
553C2×C8C2×C4×D4311yescharacteristic
554C2×C8D4×D4311yescharacteristic
555C2×C8D4×D4311yescharacteristic
556C4⋊C4—431no—
557C4⋊C4—431no—
558C4⋊C4—431no—
559C4⋊C4—431no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C22⋊C4—861no—
565C22⋊C4—861no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C42—21no—
571C42—21no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—861no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C23—21no—
585C23—21no—
586C23#41×D4311yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—21no—
590Q8#1306328112yes—
591D4—22no—
592D4—22no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—41no—
597D4—41no—
598D4#1306328112yes—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—431no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4C22×C4×D4311yescharacteristic
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C2×C4C2×#1062190011yescharacteristic
630C2×C4C2×#1062190011yescharacteristic
631C8—21no—
632C8—21no—
633C8—21no—
634C8—22no—
635C8—21no—
636C8—41no—
637C8—861no—
638C8—861no—
639C8—861no—
640C8—861no—
641C8—862no—
642C8—1721no—
643C22—21no—
644C22—21no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C4×D4×D4311yescharacteristic
652C22#1458342611yescharacteristic
653C22#1458343011yescharacteristic
654C4—22no—
655C4—41no—
656C4—81no—
657C4—861no—
658C4—861no—
659C4—861no—
660C4—861no—
661C4—3441no—
662C4—1721no—
663C4—1721no—
664C4—1721no—
665C4—1721no—
666C4C2×#1306328111yescharacteristic
667C4C4×#1062190011yescharacteristic
668C4#1458340511yescharacteristic
669C4#1458340911yescharacteristic
670C2—21no—
671C2—21no—
672C2—42no—
673C2—81no—
674C2#1913703511yescharacteristic
675C2#1914349311yescharacteristic
676C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1876C2
socleC22×C43C2×C4×D4
prime radicalC2×#135×C43C22
cosocleC22×C4×C43C24
hypercenter#1876D43
hypocenterC43#21138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #19143235C2semidirect
3. #131×Dic43C2semidirect
4. #19135246C2semidirect
5. #19135240C2semidirect
6. #19135195C2semidirect
7. #19135193C2semidirect
9. #19134870C2semidirect
10. #19134868C2semidirect
11. #19134500C2semidirect
12. #19134407C2semidirect
13. #19134407C2semidirect
14. #19134345C2semidirect
19. #14583011C4semidirect
20. #14583011C4semidirect
21. #14583006C4semidirect
22. #14583006C4semidirect
23. #14583000C4semidirect
24. #14583000C4semidirect
25. #14583000C4semidirect
26. #14583000C4semidirect
405. C43#21138semidirect

Maximal subgroups

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

subgroupindex
#191433962
#191432352
#131×Dic432
#191352462
#191352402
#191351952
#191351932
#191349242
#191348702
#191348682
#191345002
#191344072
#191343452
C43×#18762
#2113843