Finite Group Databasebeta

← #25165154

Subgroups — #25165154

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#19139140C211yesmaximal, characteristic, complemented
2#19137656C211yesmaximal, characteristic
3#19135969C211yesmaximal, characteristic, complemented
4#19135827C211yesmaximal, characteristic
5#19135827C211yesmaximal, characteristic
6#19135279C211yesmaximal, characteristic, complemented
7#19135220C211yesmaximal, characteristic, complemented
8#19135186C211yesmaximal, characteristic, complemented
9#19135171C211yesmaximal, characteristic, complemented
10#19135155C211yesmaximal, characteristic, complemented
11#19134845C211yesmaximal, characteristic, complemented
12#19134844C211yesmaximal, characteristic, complemented
13#19134602C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2073C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063259C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582840—21no—
31#14582840—21no—
32#14582800C2211yescharacteristic
33#14582799—21no—
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582796—21no—
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582784—21no—
40#14582776—21no—
41#14582775—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#382C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C22⋊D43—21no—
62C23×Dic43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063321—22no—
67#13063321—22no—
68C4×D172—22no—
69C4×D172—41no—
70D4×Dic43—22no—
71D4×Dic43—41no—
72(C22⋊D43)⋊C4—44no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
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×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063256—22no—
92C4⋊(C43⋊C8)—41no—
93#13063247—22no—
94#13063247—41no—
95#13063246—22no—
96#13063246—41no—
97#13063245—22no—
98#13063245—22no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#102×C43—22no—
118#102×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C24×C43—21no—
122C23×D43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43#4112yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—81no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172#4112yes—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
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—21no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43#4112yes—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
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—21no—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C22×D411yescharacteristic
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—41no—
222D4×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C22⋊D43—48no—
245C22⋊D43—84no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—84no—
266C2×Dic43#13512yes—
267C2×Dic43AGL(1,ℤ/8)12yes—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—84no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#26755—431nomaximal, Sylow
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43#52511yescharacteristic
286C22×C43#54611yescharacteristic
287C22×C43#54811yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57711yescharacteristic
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52911yescharacteristic
305C4×C43#53911yescharacteristic
306C4×C43#55211yescharacteristic
307C4×C43#55311yescharacteristic
308Dic43—22no—
309Dic43—22no—
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313Dic43—42no—
314Dic43—81no—
315#2509—431no—
316#2366—431no—
317#2073D4311yescharacteristic, complemented
318#2065—431no—
319#2041—431no—
320#2041—431no—
321#1934—431no—
322#1926—431no—
323#1921—431no—
324#1919—431no—
325#1916—431no—
326#1862—431no—
327#1862—431no—
328#1804—431no—
329C4×#102—431no—
330C2×C43—82no—
331C2×C43#246011yescharacteristic
332C2×C43#310511yescharacteristic
333C2×C43#311811yescharacteristic
334C2×C43#330411yescharacteristic
335C2×C43#331811yescharacteristic
336C2×C43#336111yescharacteristic
337C2×C43#336811yescharacteristic
338D43—82no—
339C2×#127—431no—
340C2×C4×D4—431no—
341C2×C4×D4—431no—
342C2×C4×D4—861no—
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×#102C2×D4311yescharacteristic
353C2×#102C2×D4311yescharacteristic
354C2×C4×C8—431no—
355#400—861no—
356#400—861no—
357#390—431no—
358#390—861no—
359#390C2×D4311yescharacteristic
360#389—431no—
361#389—431no—
362#389—431no—
363#389—431no—
364#389—861no—
365#387—861no—
366#386—861no—
367#386—861no—
368#382C2×D4311yescharacteristic
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340C2×D4311yescharacteristic
377#340C2×D4311yescharacteristic
378#336—431no—
379#336—431no—
380#336—431no—
381#336C2×D4311yescharacteristic
382C43#2675511yescharacteristic, complemented, Sylow
383C22×D4—431no—
384C22×D4—861no—
385C22×D4—861no—
386C22×D4C22×D4311yescharacteristic
387C23×C4—861no—
388C23×C4—861no—
389C22×C8—431no—
390C22×C8—431no—
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393#127—862no—
394#127—862no—
395C4×D4—862no—
396C4×D4—862no—
397C4×D4—1721no—
398C4×D4—1721no—
399C4×D4—1724no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423#107—862no—
424#106—862no—
425C4⋊C8—1721no—
426#102—22no—
427#102—22no—
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—21no—
437#95—431no—
438#95—431no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—21no—
446C24—861no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—432no—
453C2×D4—864no—
454C2×D4—864no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1722no—
463C2×D4—1722no—
464C2×D4#1062190012yes—
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×C4—3441no—
476C22×C4—3441no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—432no—
503C4⋊C4—432no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—3441no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—3441no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C22⋊C4—1722no—
520C42—21no—
521C42—21no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—861no—
526C42—3441no—
527C42—1722no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—862no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23C2×D4×D4311yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—862no—
548D4—862no—
549D4—3444no—
550D4—1728no—
551D4—1721no—
552D4—1721no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—3444no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4#41×D4311yescharacteristic
594C2×C4C2×#1062190011yescharacteristic
595C2×C4#1306337111yescharacteristic
596C2×C4#1306337211yescharacteristic
597C8—41no—
598C8—41no—
599C8—1721no—
600C8—1721no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22#1458340911yescharacteristic
616C22#1458354111yescharacteristic
617C22#1458355711yescharacteristic
618C22#135×D4311yescharacteristic
619C22AGL(1,ℤ/8)×D4311yescharacteristic
620C22#1458370111yescharacteristic
621C22#1458370911yescharacteristic
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—862no—
628C4—862no—
629C4—3441no—
630C4—1721no—
631C4—1721no—
632C4—1722no—
633C4—1722no—
634C4#1458342611yescharacteristic
635C4#1458349311yescharacteristic
636C4#1458358511yescharacteristic
637C4#1458360011yescharacteristic
638C2—82no—
639C2—3442no—
640C2#1913854811yescharacteristic
641C2#1914464111yescharacteristic
642C2#1914477611yescharacteristic
643C2#1914653211yescharacteristic
644C2#1914673911yescharacteristic
645C2#1914725211yescharacteristic
646C2#1914732111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2073C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#2073D43
hypocenterC43#26755
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
1. #19139140C2semidirect
3. #19135969C2semidirect
6. #19135279C2semidirect
7. #19135220C2semidirect
8. #19135186C2semidirect
9. #19135171C2semidirect
10. #19135155C2semidirect
11. #19134845C2semidirect
12. #19134844C2semidirect
13. #19134602C2semidirect
14. #102×Dic43C2semidirect
15. C43×#2073C2semidirect
317. #2073D43semidirect
382. C43#26755semidirect

Maximal subgroups

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

subgroupindex
#191391402
#191376562
#191359692
#191358272
#191352792
#191352202
#191351862
#191351712
#191351552
#191348452
#191348442
#191346022
#102×Dic432
C43×#20732
#2675543