Finite Group Databasebeta

← #25200254

Subgroups — #25200254

Order 11008.

700 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140393C211yesmaximal, characteristic
2#19137279C211yesmaximal, characteristic
3#19136023C211yesmaximal, characteristic
4#19135788C211yesmaximal, characteristic
5#19135788C211yesmaximal, characteristic
6#19135457C211yesmaximal, characteristic, complemented
7#19135322C211yesmaximal, characteristic, complemented
8#19135287C211yesmaximal, characteristic, complemented
9#19135282C211yesmaximal, characteristic, complemented
10#19135232C211yesmaximal, characteristic, complemented
11#19135186C211yesmaximal, characteristic, complemented
12#19134938C211yesmaximal, characteristic, complemented
13#19134861C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic
15C43×#2001C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582838—21no—
29#14582829—21no—
30#14582827—21no—
31#14582827—21no—
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582798—21no—
36#14582798C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582792—21no—
40#14582792—21no—
41#14582785—21no—
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61Q8×Dic43—41no—
62Q8×Dic43—41no—
63#13063284—41no—
64#13063284—41no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43D411yescharacteristic
78C2×C22⋊Dic43D411yescharacteristic
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43C2311yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83#13063259—22no—
84#13063256—22no—
85#13063256—41no—
86#13063249—22no—
87#13063249—22no—
88#13063249—22no—
89#13063249—41no—
90C22⋊(C43⋊C8)—22no—
91#13063235—41no—
92C8×Dic43—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43C2311yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C2×Q16×C43—22no—
109C2×Q16×C43—22no—
110C2×Q16×C43—41no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—41no—
116C22⋊Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123#103×C43—22no—
124#103×C43—41no—
125C22⋊C8×C43—22no—
126C24×C43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159Q16×C43—44no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—42no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43—81no—
177C22⋊Dic43—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C4⋊Dic43—42no—
189C4⋊Dic43—81no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8#4112yes—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43C22×D411yescharacteristic
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
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×C43—41no—
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—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
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—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C8×C43—22no—
270C8×C43—41no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273#29471—431nomaximal, Sylow
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43#52511yescharacteristic
282C22×C43#53211yescharacteristic
283C22×C43#53411yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57811yescharacteristic
287C22×C43#57811yescharacteristic
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#55111yescharacteristic
294C4×C43#55311yescharacteristic
295C4×C43#55311yescharacteristic
296C4×C43#55911yescharacteristic
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305#2625—431no—
306#2323—431no—
307#2076—431no—
308#2035—431no—
309#2035—431no—
310#2001D4311yescharacteristic
311#1969—431no—
312#1941—431no—
313#1935—431no—
314#1935—431no—
315#1927—431no—
316#1921—431no—
317#1878—431no—
318#1865—431no—
319#1750—431no—
320C2×C43—81no—
321C2×C43#260211yescharacteristic
322C2×C43#312011yescharacteristic
323C2×C43#312111yescharacteristic
324C2×C43#317311yescharacteristic
325C2×C43#317711yescharacteristic
326C2×C43#320111yescharacteristic
327C2×C43#320111yescharacteristic
328C22×Q16C2×D4311yescharacteristic
329C2×C22⋊Q8C2×D4311yescharacteristic
330C2×C22⋊Q8C2×D4311yescharacteristic
331C2×C4×Q8—431no—
332C2×#117—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#103C2×D4311yescharacteristic
342C2×C22⋊C8—431no—
343C2×C22⋊C8C2×D4311yescharacteristic
344C2×#97—431no—
345C2×C4×C8—431no—
346#400—861no—
347#398—861no—
348#397—861no—
349#397—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#389—431no—
354#389—431no—
355#389—431no—
356#389—861no—
357#388—861no—
358#388—861no—
359#387—861no—
360#380—431no—
361#380—431no—
362C4×C4⋊C4—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371C43#2947111yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C22×Q8C22×D4311yescharacteristic
374C23×C4C22×D4311yescharacteristic
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—41no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—41no—
385C22⋊Q8—41no—
386C4×Q8—1721no—
387C4×Q8—1721no—
388#117—1721no—
389#117—1721no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—431no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414#107—862no—
415#106—862no—
416#106—1721no—
417#103—22no—
418#103—41no—
419#103—862no—
420#103—862no—
421#103—862no—
422#103—1721no—
423C22⋊C8—22no—
424C22⋊C8—862no—
425#97—1721no—
426C4×C8—1721no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24D4×D4311yescharacteristic
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#1062190012yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472Q16—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—432no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8#1062190012yes—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—3441no—
499C4⋊C4—3441no—
500C4⋊C4—3441no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1722no—
504C4⋊C4#1062190012yes—
505C22⋊C4—24no—
506C22⋊C4—42no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C42—861no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42—3441no—
516C42—1722no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C2×D4×D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4#41×D4311yescharacteristic
577C2×C4C2×#1062190011yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337011yescharacteristic
582C8—22no—
583C8—41no—
584C8—862no—
585C8—1721no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1458340511yescharacteristic
594C22#1458344411yescharacteristic
595C22#1458345911yescharacteristic
596C22#1458370811yescharacteristic
597C22#1458370811yescharacteristic
598C22#1458371211yescharacteristic
599C22#1458371311yescharacteristic
600C4—41no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—3441no—
609C4—1721no—
610C4—1721no—
611C4—1721no—
612C4—1721no—
613C4#1458358011yescharacteristic
614C4#1458359211yescharacteristic
615C4#1458359611yescharacteristic
616C4#1458363511yescharacteristic
617C2—81no—
618C2#1914020011yescharacteristic
619C2#1914481011yescharacteristic
620C2#1914482511yescharacteristic
621C2#1914521311yescharacteristic
622C2#1914524711yescharacteristic
623C2#1914547611yescharacteristic
624C2#1914548111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2001C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2001D43
hypocenterC43#29471
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
6. #19135457C2semidirect
7. #19135322C2semidirect
8. #19135287C2semidirect
9. #19135282C2semidirect
10. #19135232C2semidirect
11. #19135186C2semidirect
12. #19134938C2semidirect
13. #19134861C2semidirect
371. C43#29471semidirect

Maximal subgroups

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

subgroupindex
#191403932
#191372792
#191360232
#191357882
#191354572
#191353222
#191352872
#191352822
#191352322
#191351862
#191349382
#191348612
#191343632
C43×#20012
#2947143