Finite Group Databasebeta

← #25199463

Subgroups — #25199463

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137133C211yesmaximal, characteristic
2C4×#13063305C211yesmaximal, characteristic
3#19136020C211yesmaximal, characteristic
4#19135793C211yesmaximal, characteristic
5#19135789C211yesmaximal, characteristic
6#19135604C211yesmaximal, characteristic
7#19135227C211yesmaximal, characteristic, complemented
8#19135182C211yesmaximal, characteristic, complemented
9#19135180C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134934C211yesmaximal, characteristic, complemented
12#19134852C211yesmaximal, characteristic, complemented
13#19134851C211yesmaximal, characteristic, complemented
14#19134662C211yesmaximal, characteristic
15C43×#1927C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582786—21no—
34#14582784—21no—
35#14582773—21no—
36#14582773—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43—21no—
41#14582750—21no—
42C4×(C2×D43)⋊C4—21no—
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063305—22no—
69#13063305—22no—
70#13063301—22no—
71#13063301—22no—
72Q8×Dic43—41no—
73Q8×Dic43—41no—
74C4×Dic86—41no—
75C4×Dic86—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C42×D43—41no—
96C42×D43—41no—
97#13063259—41no—
98#13063256—22no—
99#13063250—22no—
100#13063250—41no—
101#13063249—41no—
102#13063248—22no—
103(C2×D43)⋊C8—41no—
104(C2×D43)⋊C8—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#103×C43—22no—
122#103×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—22no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43#4112yes—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—42no—
180#10621885—44no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192C4⋊Dic43—42no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C4×Dic43—41no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43C22×D411yescharacteristic
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43#13512yes—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—41no—
221Q8×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43#13712yes—
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43#13712yes—
267C4×D43—44no—
268C4×D43—44no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277C8×C43—41no—
278C8×C43—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#29416—431nomaximal, Sylow
282C22×C43#52511yescharacteristic
283C22×C43#52511yescharacteristic
284C22×C43#53411yescharacteristic
285C22×C43C2×#13511yescharacteristic
286C22×C43C2×#13711yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57511yescharacteristic
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C4×C43—22no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#55111yescharacteristic
303C4×C43#55311yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55911yescharacteristic
306Dic43—22no—
307Dic43—42no—
308Dic43—41no—
309Dic43—42no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313C4×C22⋊Q8—431no—
314C4×C22⋊Q8—431no—
315#2075—431no—
316#2035—431no—
317#2035—431no—
318#2001—431no—
319#1927—431no—
320#1927D4311yescharacteristic, complemented
321#1920—431no—
322#1920—431no—
323#1878—431no—
324#1878—431no—
325#1863—431no—
326#1863—431no—
327#1817—431no—
328C2×C43#260011yescharacteristic
329C2×C43#310811yescharacteristic
330C2×C43#310811yescharacteristic
331C2×C43#311611yescharacteristic
332C2×C43#311611yescharacteristic
333C2×C43#319111yescharacteristic
334C2×C43#319511yescharacteristic
335D43—42no—
336C22×Q16—431no—
337C2×C22⋊Q8—431no—
338C2×C22⋊Q8—431no—
339C2×C4×Q8—431no—
340C2×C4×Q8—431no—
341C22×C42—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106C2×D4311yescharacteristic
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#103C2×D4311yescharacteristic
350C2×#103C2×D4311yescharacteristic
351C2×C22⋊C8—431no—
352C2×C22⋊C8—431no—
353#391—431no—
354#391C2×D4311yescharacteristic
355#389—431no—
356#389—431no—
357#387—861no—
358#387—861no—
359#385—861no—
360#385—861no—
361#380—431no—
362#380—431no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4—861no—
365C4×C4⋊C4—861no—
366C4×C4⋊C4C2×D4311yescharacteristic
367C4×C22⋊C4—861no—
368C4×C22⋊C4—861no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340C2×D4311yescharacteristic
375#336—431no—
376#336—431no—
377#336—431no—
378#336C2×D4311yescharacteristic
379C43#2941611yescharacteristic, complemented, Sylow
380C22×Q8—431no—
381C22×Q8C22×D4311yescharacteristic
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—431no—
385C2×Q16—862no—
386C2×Q16—862no—
387C2×Q16—1721no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C4×Q8—1721no—
397C4×Q8—1721no—
398C4×Q8—1721no—
399C4×Q8—1721no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C42—21no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42—1721no—
424C2×C42—1721no—
425C2×C42C22×D4311yescharacteristic
426#107—1721no—
427#106—22no—
428#106—862no—
429#103—22no—
430#103—22no—
431#103—862no—
432#103—862no—
433#103—1721no—
434#103—1721no—
435C22⋊C8—1721no—
436C22⋊C8—1721no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24—431no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8#1062189812yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—1721no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486Q16—1724no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—432no—
505C4⋊C4—864no—
506C4⋊C4—864no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4#1062190012yes—
517C22⋊C4—864no—
518C22⋊C4—864no—
519C22⋊C4—1722no—
520C22⋊C4—1722no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—861no—
525C42—861no—
526C42—1721no—
527C42—1721no—
528C42—1722no—
529C42—1722no—
530C42—1722no—
531C23—432no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—861no—
536C23—861no—
537C23—861no—
538C23C2×D4×D4311yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—41no—
542Q8—41no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—432no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—862no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—1724no—
576C2×C4—1724no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4#1306335412yes—
592C2×C4#41×D4311yescharacteristic
593C2×C4#41×D4311yescharacteristic
594C2×C4C2×#1062190011yescharacteristic
595C2×C4C2×#1062189811yescharacteristic
596C2×C4#1306337111yescharacteristic
597C2×C4#1306337111yescharacteristic
598C8—41no—
599C8—41no—
600C8—1721no—
601C8—1721no—
602C22—862no—
603C22—862no—
604C22—862no—
605C22—1721no—
606C22—1721no—
607C22—1721no—
608C22—1721no—
609C22#1458340811yescharacteristic
610C22#1458340911yescharacteristic
611C22#1458346011yescharacteristic
612C22#135×D4311yescharacteristic
613C22#137×D4311yescharacteristic
614C22C2×#1306335411yescharacteristic
615C22#1458369811yescharacteristic
616C4—22no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—862no—
623C4—3441no—
624C4—3441no—
625C4—1722no—
626C4—1721no—
627C4—1722no—
628C4—1721no—
629C4#1458357311yescharacteristic
630C4#1458359511yescharacteristic
631C4#1458360011yescharacteristic
632C4#1458363111yescharacteristic
633C2—1722no—
634C2#1914018011yescharacteristic
635C2#1914467311yescharacteristic
636C2#1914467411yescharacteristic
637C2#1914475411yescharacteristic
638C2#1914475511yescharacteristic
639C2#1914539011yescharacteristic
640C2#1914541811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1927D43
hypocenterC43#29416
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
7. #19135227C2semidirect
8. #19135182C2semidirect
9. #19135180C2semidirect
10. #19134939C2semidirect
11. #19134934C2semidirect
12. #19134852C2semidirect
13. #19134851C2semidirect
15. C43×#1927C2semidirect
320. #1927D43semidirect
379. C43#29416semidirect

Maximal subgroups

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

subgroupindex
#191371332
C4×#130633052
#191360202
#191357932
#191357892
#191356042
#191352272
#191351822
#191351802
#191349392
#191349342
#191348522
#191348512
#191346622
C43×#19272
#2941643