Finite Group Databasebeta

← #25164715

Subgroups — #25164715

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138965C211yesmaximal, characteristic
2#19137600C211yesmaximal, characteristic
3#19135919C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic
5#19135735C211yesmaximal, characteristic, complemented
6#19135605C211yesmaximal, characteristic
7#19135541C211yesmaximal, characteristic, complemented
8#19135269C211yesmaximal, characteristic, complemented
9#19135234C211yesmaximal, characteristic, complemented
10#19135198C211yesmaximal, characteristic
11#19135185C211yesmaximal, characteristic, complemented
12#19134937C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1824C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582840—21no—
32#14582811—21no—
33#14582804C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582803—21no—
37#14582795C2211yescharacteristic
38#14582794—21no—
39#14582787—21no—
40#14582780—21no—
41#14582772—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×Dic172—22no—
63C2×Dic172—41no—
64C2×Dic172—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324—41no—
69#13063304—22no—
70#13063304—22no—
71#13063304—22no—
72#13063304—41no—
73#13063290—22no—
74#13063290—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43D411yescharacteristic
85C2×C22⋊Dic43D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—22no—
92Dic43⋊C8—41no—
93#13063250—22no—
94#13063250—22no—
95#13063248—22no—
96#13063248—22no—
97#13063248—41no—
98#13063248—41no—
99C22⋊(C43⋊C8)—41no—
100C8×Dic43—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C23×C4×C43—21no—
113C23×C4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—41no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C22⋊C8×C43—41no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—42no—
162C2×Dic86—42no—
163C2×Dic86—81no—
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—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43#4112yes—
180C22⋊C4×C43—81no—
181C22⋊Dic43—24no—
182C22⋊Dic43—41no—
183C22⋊Dic43—42no—
184C22⋊Dic43Q1614yescomplemented
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43#4112yes—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—81no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207Dic172—44no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C2×Q1612yes—
215C23×C43C22×D411yescharacteristic
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
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—84no—
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
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×Q1612yes—
265C2×Dic43C2×Q1612yes—
266Dic86—22no—
267Dic86—22no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—84no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26726—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43C22×Q1611yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C4×C43—41no—
295C4×C43—42no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#52911yescharacteristic
300C4×C43#53811yescharacteristic
301C4×C43#55511yescharacteristic
302C4×C43#55911yescharacteristic
303Dic43—22no—
304Dic43—22no—
305Dic43—42no—
306Dic43—42no—
307Dic43—41no—
308Dic43—41no—
309Dic43—42no—
310Dic43—81no—
311#2492—431no—
312#2360—431no—
313#2056—431no—
314#2036—431no—
315#2024—431no—
316#2001—431no—
317#1987—431no—
318#1933—431no—
319#1928—431no—
320#1923—431no—
321#1921—431no—
322#1878—431no—
323#1872—431no—
324#1824D4311yescharacteristic
325C4×#103—431no—
326C2×C43—42no—
327C2×C43#245911yescharacteristic
328C2×C43#310411yescharacteristic
329C2×C43#312511yescharacteristic
330C2×C43#329911yescharacteristic
331C2×C43#329911yescharacteristic
332C2×C43#331111yescharacteristic
333C2×C43#332311yescharacteristic
334C22×Q16—431no—
335C2×C4⋊Q8—431no—
336C2×C22⋊Q8—431no—
337C2×C22⋊Q8—431no—
338C2×C4×Q8—431no—
339C22×C4⋊C4C2×D4311yescharacteristic
340C2×#107—431no—
341C2×C4⋊C8—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8—431no—
349C2×C22⋊C8C2×D4311yescharacteristic
350C2×C4×C8—431no—
351#400—861no—
352#393—861no—
353#391—431no—
354#391—431no—
355#391—431no—
356#391—861no—
357#389—431no—
358#389—861no—
359#388—861no—
360#387—861no—
361#385—861no—
362#380C2×D4311yescharacteristic
363C4×C4⋊C4—431no—
364C4×C4⋊C4—431no—
365C4×C22⋊C4—431no—
366C4×C22⋊C4—861no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375#336—431no—
376#336—431no—
377C43#2672611yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8—431no—
380C22×Q8—861no—
381C23×C4—21no—
382C23×C4C22×D4311yescharacteristic
383C2×Q16—862no—
384C2×Q16—1721no—
385C2×Q16—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—862no—
391C4⋊Q8—1721no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—1721no—
396C4×Q8—862no—
397C4×Q8—1721no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
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⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—431no—
414C2×C22⋊C4—431no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422#107—862no—
423C4⋊C8—1721no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—862no—
428#103—1721no—
429#103—1721no—
430C22⋊C8—41no—
431C22⋊C8—1721no—
432C4×C8—1721no—
433#95—21no—
434#95—431no—
435#95—431no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24D4×D4311yescharacteristic
446C2×Q8—432no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—3441no—
459C2×Q8—1722no—
460C2×Q8—1722no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484Q16—1724no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—864no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4#1062189812yes—
515C22⋊C4—81no—
516C22⋊C4—434no—
517C22⋊C4—864no—
518C22⋊C4—1721no—
519C22⋊C4—1722no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—3441no—
525C42—3441no—
526C42—1722no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23Q16×D4312yes—
534C23C2×D4×D4311yescharacteristic
535Q8—862no—
536Q8—862no—
537Q8—3444no—
538Q8—1721no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543Q8—1721no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
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—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—84no—
564C2×C4—432no—
565C2×C4—432no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—862no—
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#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C2×C4#1306337011yescharacteristic
593C2×C4#1306337111yescharacteristic
594C8—41no—
595C8—41no—
596C8—1721no—
597C8—1721no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1458340711yescharacteristic
606C22#1458353911yescharacteristic
607C22#1458354111yescharacteristic
608C22C2×Q16×D4311yescharacteristic
609C22#1458369511yescharacteristic
610C22#1458370511yescharacteristic
611C22#1458370911yescharacteristic
612C4—42no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—862no—
618C4—862no—
619C4—3441no—
620C4—1721no—
621C4—1722no—
622C4—1721no—
623C4—1722no—
624C4—1722no—
625C4#1458342711yescharacteristic
626C4#1458348511yescharacteristic
627C4#1458361211yescharacteristic
628C4#1458363311yescharacteristic
629C2—42no—
630C2#1913852911yescharacteristic
631C2#1914463111yescharacteristic
632C2#1914487511yescharacteristic
633C2#1914646711yescharacteristic
634C2#1914646911yescharacteristic
635C2#1914663211yescharacteristic
636C2#1914681411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1824C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1824D43
hypocenterC43#26726
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #19135919C2semidirect
5. #19135735C2semidirect
7. #19135541C2semidirect
8. #19135269C2semidirect
9. #19135234C2semidirect
11. #19135185C2semidirect
12. #19134937C2semidirect
14. #19134414C2semidirect
184. C22⋊Dic43Q16semidirect
377. C43#26726semidirect

Maximal subgroups

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

subgroupindex
#191389652
#191376002
#191359192
#191357982
#191357352
#191356052
#191355412
#191352692
#191352342
#191351982
#191351852
#191349372
#191349022
#191344142
C43×#18242
#2672643