Finite Group Databasebeta

← #25199584

Subgroups — #25199584

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137279C211yesmaximal, characteristic
2#19137273C211yesmaximal, characteristic
3#19136031C211yesmaximal, characteristic
4#19135792C211yesmaximal, characteristic
5#19135603C211yesmaximal, characteristic
6#19135235C211yesmaximal, characteristic, complemented
7#19135231C211yesmaximal, characteristic, complemented
8#19135189C211yesmaximal, characteristic, complemented
9#19135179C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134933C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134861C211yesmaximal, characteristic, complemented
14#19134664C211yesmaximal, characteristic
15C43×#2036C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28#14582806C2211yescharacteristic
29#14582804C2211yescharacteristic
30#14582798—21no—
31#14582798C2211yescharacteristic
32#14582796—21no—
33#14582795C2211yescharacteristic
34#14582793—21no—
35#14582792—21no—
36#14582792—21no—
37#14582787—21no—
38#14582786—21no—
39#14582785—21no—
40#14582759C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621885—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063304—22no—
66#13063304—22no—
67Q8×Dic43—41no—
68Q8×Dic43—41no—
69#13063290—41no—
70#13063290—41no—
71#13063284—41no—
72#13063284—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×C22⋊Dic43D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063257—22no—
94#13063256—41no—
95#13063250—22no—
96#13063250—41no—
97#13063249—22no—
98#13063248—22no—
99C22⋊(C43⋊C8)—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#107×C43—22no—
122#103×C43—22no—
123#103×C43—41no—
124C22⋊C8×C43—41no—
125#95×C43—21no—
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#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—81no—
174C22⋊Dic43—24no—
175C22⋊Dic43—41no—
176C22⋊Dic43—41no—
177C22⋊Dic43—81no—
178#10621885—44no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—41no—
185C4⋊Dic43—41no—
186C4⋊Dic43—42no—
187C4⋊Dic43—81no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—22no—
244C2×Dic43—22no—
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—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#29425—431nomaximal, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43#52511yescharacteristic
284C22×C43#52511yescharacteristic
285C22×C43#53411yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57711yescharacteristic
288C22×C43#57811yescharacteristic
289C22×C43#57811yescharacteristic
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#55111yescharacteristic
296C4×C43#55311yescharacteristic
297C4×C43#55311yescharacteristic
298C4×C43#55911yescharacteristic
299Dic43—42no—
300Dic43—42no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307#2323—431no—
308#2323—431no—
309#2077—431no—
310#2036D4311yescharacteristic
311#2035—431no—
312#2001—431no—
313#1928—431no—
314#1927—431no—
315#1921—431no—
316#1920—431no—
317#1878—431no—
318#1878—431no—
319#1865—431no—
320#1865—431no—
321#1818—431no—
322C2×C43—81no—
323C2×C43#260011yescharacteristic
324C2×C43#312011yescharacteristic
325C2×C43#312111yescharacteristic
326C2×C43#312511yescharacteristic
327C2×C43#312711yescharacteristic
328C2×C43#320111yescharacteristic
329C2×C43#320111yescharacteristic
330C22×Q16—431no—
331C2×C22⋊Q8—431no—
332C2×C22⋊Q8C2×D4311yescharacteristic
333C2×C4×Q8—431no—
334C2×C4×Q8—431no—
335C2×#117—431no—
336C2×#107C2×D4311yescharacteristic
337C2×#106—431no—
338C2×#106—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103C2×D4311yescharacteristic
344C2×#103C2×D4311yescharacteristic
345C2×C22⋊C8—431no—
346C2×C22⋊C8C2×D4311yescharacteristic
347#391—431no—
348#391—431no—
349#389—431no—
350#389—431no—
351#389—861no—
352#389—861no—
353#388—861no—
354#388—861no—
355#388—861no—
356#388—861no—
357#387—861no—
358#387—861no—
359#380—431no—
360#380C2×D4311yescharacteristic
361C4×C4⋊C4—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—
371#336—431no—
372#336—431no—
373C43#2942511yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C2×Q16—862no—
378C2×Q16—862no—
379C2×Q16—1721no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C4×Q8—1721no—
391C4×Q8—1721no—
392#117—1721no—
393#117—1721no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—431no—
411C2×C22⋊C4—431no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420#107—22no—
421#106—862no—
422#106—1721no—
423#103—22no—
424#103—41no—
425#103—862no—
426#103—862no—
427#103—862no—
428#103—1721no—
429C22⋊C8—41no—
430C22⋊C8—1721no—
431#95—21no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24D4×D4311yescharacteristic
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—432no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8#1062190012yes—
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—21no—
463C22×C4—21no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4D4×D4311yescharacteristic
473C22×C4C23×D4311yescharacteristic
474Q16—1724no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—432no—
494C4⋊C4—864no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4#1062190012yes—
507C22⋊C4—24no—
508C22⋊C4—81no—
509C22⋊C4—864no—
510C22⋊C4—3441no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—3441no—
518C42—3441no—
519C42—1722no—
520C42—1722no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23C2×D4×D4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—862no—
534Q8—862no—
535Q8—1721no—
536Q8—1721no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
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—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C2×C4#1306337011yescharacteristic
585C2×C4#1306337111yescharacteristic
586C8—41no—
587C8—41no—
588C8—1721no—
589C8—1721no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22#1458340511yescharacteristic
598C22#1458340711yescharacteristic
599C22#1458345711yescharacteristic
600C22#1458370611yescharacteristic
601C22#1458370911yescharacteristic
602C22#1458371211yescharacteristic
603C22#1458371511yescharacteristic
604C4—41no—
605C4—42no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4—1722no—
616C4—1722no—
617C4#1458357211yescharacteristic
618C4#1458359211yescharacteristic
619C4#1458359611yescharacteristic
620C4#1458363111yescharacteristic
621C2—81no—
622C2#1914017811yescharacteristic
623C2#1914480411yescharacteristic
624C2#1914482711yescharacteristic
625C2#1914487311yescharacteristic
626C2#1914488911yescharacteristic
627C2#1914547211yescharacteristic
628C2#1914548011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2036D43
hypocenterC43#29425
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
6. #19135235C2semidirect
7. #19135231C2semidirect
8. #19135189C2semidirect
9. #19135179C2semidirect
10. #19134934C2semidirect
11. #19134933C2semidirect
12. #19134864C2semidirect
13. #19134861C2semidirect
373. C43#29425semidirect

Maximal subgroups

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

subgroupindex
#191372792
#191372732
#191360312
#191357922
#191356032
#191352352
#191352312
#191351892
#191351792
#191349342
#191349332
#191348642
#191348612
#191346642
C43×#20362
#2942543