Finite Group Databasebeta

← #25169801

Subgroups — #25169801

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139177C211yesmaximal, characteristic
2#19137649C211yesmaximal, characteristic, complemented
3#19136139C211yesmaximal, characteristic, complemented
4#19135913C211yesmaximal, characteristic
5#19135840C211yesmaximal, characteristic, complemented
6#19135679C211yesmaximal, characteristic
7#19135446C211yesmaximal, characteristic
8#19135232C211yesmaximal, characteristic, complemented
9#19135220C211yesmaximal, characteristic
10#19135176C211yesmaximal, characteristic, complemented
11#19135149C211yesmaximal, characteristic, complemented
12#19134951C211yesmaximal, characteristic
13#19134950C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1803C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063290C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582825—21no—
31#14582821—21no—
32#14582806C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582794—21no—
39#14582789—21no—
40#14582783—21no—
41#14582780—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C4×Dic43⋊C4C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#384C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C2×#10621873—22no—
62C2×#10621873—41no—
63C2×#10621873—41no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063323—22no—
70#13063323—22no—
71#13063320—44no—
72#13063290—22no—
73#13063290—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063256—22no—
94#13063256—41no—
95#13063250—22no—
96#13063249—22no—
97#13063248—22no—
98#13063248—41no—
99#13063247—41no—
100#13063245—22no—
101C8×Dic43—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×Q8×C43—22no—
115C4×Q8×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C4⋊C8×C43—41no—
125#103×C43—41no—
126#103×C43—41no—
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43#4112yes—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—42no—
178#10621884—44no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—42no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192Dic43⋊C4—41no—
193Dic43⋊C4—42no—
194Dic43⋊C4SD1614yescomplemented
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—42no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208#10621873—44no—
209C23×C43C22×D411yescharacteristic
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43—41no—
220Q8×C43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
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×C43C2×SD1612yes—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
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×Dic43C2×SD1612yes—
265C2×Dic43C2×SD1612yes—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—41no—
270Dic86—22no—
271Dic86—22no—
272Dic86—41no—
273Dic86—41no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278#27066—431nomaximal, Sylow
279C22×C43#52511yescharacteristic
280C22×C43#54611yescharacteristic
281C22×C43#55011yescharacteristic
282C22×C43C22×SD1611yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57811yescharacteristic
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#52911yescharacteristic
300C4×C43#53811yescharacteristic
301C4×C43#55111yescharacteristic
302C4×C43#55311yescharacteristic
303Dic43—22no—
304Dic43—22no—
305Dic43—41no—
306Dic43—42no—
307Dic43—41no—
308Dic43—81no—
309Dic43—81no—
310#2512—431no—
311#2365—431no—
312#2096—431no—
313#2055—431no—
314#2043—431no—
315#2013—431no—
316#1968—431no—
317#1927—431no—
318#1926—431no—
319#1919—431no—
320#1916—431no—
321#1880—431no—
322#1880—431no—
323#1803D4311yescharacteristic, complemented
324C4×#103—431no—
325C2×C43#246711yescharacteristic
326C2×C43#310311yescharacteristic
327C2×C43#312111yescharacteristic
328C2×C43#329811yescharacteristic
329C2×C43#330711yescharacteristic
330C2×C43#339211yescharacteristic
331C2×C43#340211yescharacteristic
332D43—161no—
333C22×SD16—431no—
334C22×SD16—431no—
335C2×C4⋊Q8—431no—
336C2×#126—861no—
337C2×C4×Q8—431no—
338C2×C4×Q8C2×D4311yescharacteristic
339C2×#106—431no—
340C2×#106—431no—
341C2×C4⋊C8C2×D4311yescharacteristic
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×#102—431no—
349C2×#102—431no—
350C2×C4×C8—431no—
351#397—861no—
352#396—861no—
353#391—431no—
354#391—431no—
355#390—431no—
356#390—431no—
357#390—431no—
358#389—431no—
359#389—861no—
360#388—861no—
361#387—861no—
362#387—861no—
363#384C2×D4311yescharacteristic
364C4×C4⋊C4—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—861no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#340C2×D4311yescharacteristic
372#336—431no—
373#336—431no—
374#336—431no—
375#336—431no—
376C43#2706611yescharacteristic, complemented, Sylow
377C22×Q8—431no—
378C22×Q8C22×D4311yescharacteristic
379C22×D4—431no—
380C2×SD16—862no—
381C2×SD16—862no—
382C2×SD16—862no—
383C2×SD16—1721no—
384C2×SD16—1721no—
385C2×SD16—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—862no—
391C4⋊Q8—862no—
392#126—1724no—
393C4×Q8—22no—
394C4×Q8—41no—
395C4×Q8—862no—
396C4×Q8—1721no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#106—862no—
425#106—1721no—
426C4⋊C8—41no—
427#103—41no—
428#103—41no—
429#103—862no—
430#103—862no—
431#103—862no—
432#103—1721no—
433#102—862no—
434#102—1721no—
435C4×C8—1721no—
436#95—431no—
437#95—431no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—861no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—432no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8#1062190212yes—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—1724no—
479SD16—1724no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—434no—
501C4⋊C4—864no—
502C4⋊C4—864no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4#1062189812yes—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—1722no—
525C42—1722no—
526C42—1722no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23C2×D4×D4311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—862no—
540Q8—862no—
541Q8—1721no—
542Q8—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
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—432no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
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×C4SD16×D4312yes—
586C2×C4#41×D4311yescharacteristic
587C2×C4#41×D4311yescharacteristic
588C2×C4C2×#1062189811yescharacteristic
589C2×C4C2×#1062190211yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337011yescharacteristic
592C8—41no—
593C8—41no—
594C8—862no—
595C8—1721no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22#1458341211yescharacteristic
604C22#1458353911yescharacteristic
605C22#1458356711yescharacteristic
606C22C2×SD16×D4311yescharacteristic
607C22#1458369811yescharacteristic
608C22#1458370911yescharacteristic
609C22#1458371211yescharacteristic
610C4—22no—
611C4—41no—
612C4—42no—
613C4—42no—
614C4—81no—
615C4—81no—
616C4—862no—
617C4—862no—
618C4—3441no—
619C4—3441no—
620C4—1721no—
621C4—1722no—
622C4—1721no—
623C4#1458342711yescharacteristic
624C4#1458348111yescharacteristic
625C4#1458357611yescharacteristic
626C4#1458359711yescharacteristic
627C2—6881no—
628C2#1913865311yescharacteristic
629C2#1914462811yescharacteristic
630C2#1914482911yescharacteristic
631C2#1914645611yescharacteristic
632C2#1914657211yescharacteristic
633C2#1914757511yescharacteristic
634C2#1914766911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1803D43
hypocenterC43#27066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #19137649C2semidirect
3. #19136139C2semidirect
5. #19135840C2semidirect
8. #19135232C2semidirect
10. #19135176C2semidirect
11. #19135149C2semidirect
14. #19134414C2semidirect
15. C43×#1803C2semidirect
194. Dic43⋊C4SD16semidirect
323. #1803D43semidirect
376. C43#27066semidirect

Maximal subgroups

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

subgroupindex
#191391772
#191376492
#191361392
#191359132
#191358402
#191356792
#191354462
#191352322
#191352202
#191351762
#191351492
#191349512
#191349502
#191344142
C43×#18032
#2706643