Finite Group Databasebeta

← #25165117

Subgroups — #25165117

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139133C211yesmaximal, characteristic, complemented
2#19136008C211yesmaximal, characteristic, complemented
3#19135983C211yesmaximal, characteristic, complemented
4#19135826C211yesmaximal, characteristic
5#19135826C211yesmaximal, characteristic
6#19135281C211yesmaximal, characteristic, complemented
7#19135212C211yesmaximal, characteristic, complemented
8#19135187C211yesmaximal, characteristic, complemented
9#19135173C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#2366C211yesmaximal, characteristic
16C2×#13063258C2211yescharacteristic
17C2×#13063256C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063246C2211yescharacteristic
20C2×#13063246C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582840—21no—
29#14582830—21no—
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582780—21no—
35#14582765C2211yescharacteristic
36#14582763—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#127×C43C2211yescharacteristic
49C2×C4×D4×C43—21no—
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C43×#390—21no—
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#386—21no—
56C43×#386—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×C4×Dic43—21no—
72#13063258—22no—
73#13063256—22no—
74C4⋊(C43⋊C8)—41no—
75#13063246—22no—
76#13063246—22no—
77#13063246—22no—
78#13063246—22no—
79#13063246—22no—
80#13063246—22no—
81#13063246—41no—
82#13063246—41no—
83C4×C43⋊C8—41no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43C2311yescharacteristic
94C22×D4×C43C2311yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97#127×C43—22no—
98#127×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—41no—
102C4×D4×C43—41no—
103C4×D4×C43—44no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43—21no—
122C24×C43—21no—
123C2×D4×C43—24no—
124C2×D4×C43—24no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—81no—
138C2×D4×C43—81no—
139C2×D4×C43#4112yes—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43#4112yes—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—81no—
171C22⋊C4×C43—81no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—42no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C22×D411yescharacteristic
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—22no—
223D4×C43—48no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—84no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—84no—
252C2×C4×C43—84no—
253C2×C4×C43#13512yes—
254C2×C4×C43AGL(1,ℤ/8)12yes—
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#26753—431nomaximal, Sylow
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43#52511yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C43#57611yescharacteristic
298C22×C43#57711yescharacteristic
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#53911yescharacteristic
309C4×C43#55211yescharacteristic
310C4×C43#55311yescharacteristic
311Dic43—42no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315#2508—431no—
316#2366D4311yescharacteristic
317#2073—431no—
318#2067—431no—
319#2041—431no—
320#2041—431no—
321#1934—431no—
322#1925—431no—
323#1921—431no—
324#1919—431no—
325#1916—431no—
326#1864—431no—
327#1864—431no—
328#1804—431no—
329C4×#102—431no—
330C2×C43—82no—
331C2×C43—82no—
332C2×C43#246011yescharacteristic
333C2×C43#310511yescharacteristic
334C2×C43#311811yescharacteristic
335C2×C43#330511yescharacteristic
336C2×C43#331011yescharacteristic
337C2×C43#336511yescharacteristic
338C2×C43#336611yescharacteristic
339C2×#127C2×D4311yescharacteristic
340C2×C4×D4—21no—
341C2×C4×D4C2×D4311yescharacteristic
342C2×C4×D4C2×D4311yescharacteristic
343C2×#107—431no—
344C2×#106—431no—
345C2×C4⋊C8—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×C4×C8—431no—
355#400—861no—
356#398—861no—
357#390—21no—
358#390C2×D4311yescharacteristic
359#390C2×D4311yescharacteristic
360#389—431no—
361#389—431no—
362#389—431no—
363#389—431no—
364#387—861no—
365#386—21no—
366#386—21no—
367#382—431no—
368#382—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4C2×D4311yescharacteristic
371C4×C4⋊C4C2×D4311yescharacteristic
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#336—431no—
379#336—431no—
380#336—431no—
381#336—431no—
382C43#2675311yescharacteristic, complemented, Sylow
383C22×D4—21no—
384C22×D4—21no—
385C22×D4C22×D4311yescharacteristic
386C22×D4C22×D4311yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C22×C8—431no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—431no—
393#127—22no—
394#127—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—41no—
398C4×D4—41no—
399C4×D4—44no—
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×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C42—21no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423#107—862no—
424#106—862no—
425C4⋊C8—1721no—
426#102—862no—
427#102—862no—
428#102—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#102—1721no—
433#102—1721no—
434C4×C8—1721no—
435#95—21no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95C22⋊D4311yescharacteristic
444#95C22⋊D4311yescharacteristic
445C24—21no—
446C24—21no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4#1062189812yes—
464C2×D4#1062189812yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—432no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—3441no—
510C4⋊C4—3441no—
511C4⋊C4—3441no—
512C4⋊C4—1722no—
513C4⋊C4#1062190012yes—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—1722no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23C22×C22⋊D4311yescharacteristic
543D4—22no—
544D4—22no—
545D4—22no—
546D4—22no—
547D4—48no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—84no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4—862no—
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#1306334512yes—
590C2×C4#1306335112yes—
591C2×C4#41×D4311yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C2×C4#1306337011yescharacteristic
596C2×C4#1306337211yescharacteristic
597C8—1721no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1458341011yescharacteristic
616C22#1458354311yescharacteristic
617C22#1458355611yescharacteristic
618C22C2×#1306334511yescharacteristic
619C22C2×#1306335111yescharacteristic
620C22#1458370211yescharacteristic
621C22#1458371011yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—81no—
630C4—3441no—
631C4—3441no—
632C4—3441no—
633C4—1722no—
634C4#1458342911yescharacteristic
635C4#1458349111yescharacteristic
636C4#1458358911yescharacteristic
637C4#1458359811yescharacteristic
638C2—82no—
639C2—82no—
640C2#1913854111yescharacteristic
641C2#1914464211yescharacteristic
642C2#1914477911yescharacteristic
643C2#1914654511yescharacteristic
644C2#1914661611yescharacteristic
645C2#1914728711yescharacteristic
646C2#1914729811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2366C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#2366D43
hypocenterC43#26753
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #19139133C2semidirect
2. #19136008C2semidirect
3. #19135983C2semidirect
6. #19135281C2semidirect
7. #19135212C2semidirect
8. #19135187C2semidirect
9. #19135173C2semidirect
10. #19135154C2semidirect
11. #19134856C2semidirect
12. #19134856C2semidirect
13. #19134605C2semidirect
14. C4×#13063246C2semidirect
382. C43#26753semidirect

Maximal subgroups

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

subgroupindex
#191391332
#191360082
#191359832
#191358262
#191352812
#191352122
#191351872
#191351732
#191351542
#191348562
#191346052
C4×#130632462
C43×#23662
#2675343