Finite Group Databasebeta

← #25165137

Subgroups — #25165137

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139125C211yesmaximal, characteristic, complemented
2#19137659C211yesmaximal, characteristic
3#19136002C211yesmaximal, characteristic, complemented
4#19135964C211yesmaximal, characteristic, complemented
5#19135830C211yesmaximal, characteristic
6#19135829C211yesmaximal, characteristic
7#19135279C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19135180C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134857C211yesmaximal, characteristic, complemented
12#19134857C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1920C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×C4×D172—21no—
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582832—21no—
32#14582831—21no—
33#14582801—21no—
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795—21no—
40#14582782—21no—
41#14582777—21no—
42#14582777—21no—
43#14582768C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063322—22no—
68#13063322—22no—
69C4×D172—44no—
70#13063287—22no—
71#13063287—22no—
72#13063287—41no—
73#13063287—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063256—22no—
93Dic43⋊C8—41no—
94#13063247—22no—
95#13063247—22no—
96#13063247—41no—
97#13063247—41no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063245—22no—
102C8×Dic43—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#106×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43—21no—
122C23×D43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×D172—24no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—24no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172—81no—
151C2×D172—81no—
152C2×D172#4112yes—
153C2×D172#4112yes—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—81no—
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—
172C4⋊C4×C43—81no—
173C4⋊C4×C43#4112yes—
174C4⋊C4×C43#4112yes—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43—42no—
190C4⋊Dic43—81no—
191C4⋊Dic43SD1614yes—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
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×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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×C43C2×SD1612yes—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
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—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43C2×SD1612yes—
262C2×Dic43C2×SD1612yes—
263D172—22no—
264D172—22no—
265D172—22no—
266D172—22no—
267D172—48no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—41no—
272D172—84no—
273C4×D43—84no—
274C4×D43—84no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26754—431nomaximal, Sylow
280C22×C43#52511yescharacteristic
281C22×C43#54611yescharacteristic
282C22×C43#54811yescharacteristic
283C22×C43C22×SD1611yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57611yescharacteristic
286C22×C43#57611yescharacteristic
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#53911yescharacteristic
309C4×C43#55211yescharacteristic
310C4×C43#55311yescharacteristic
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317#2507—431no—
318#2366—431no—
319#2071—431no—
320#2065—431no—
321#2041—431no—
322#2041—431no—
323#1934—431no—
324#1926—431no—
325#1920—431no—
326#1920D4311yescharacteristic, complemented
327#1916—431no—
328#1864—431no—
329#1864—431no—
330#1802—431no—
331C4×#102—431no—
332C2×C43#246011yescharacteristic
333C2×C43#310111yescharacteristic
334C2×C43#312211yescharacteristic
335C2×C43#329511yescharacteristic
336C2×C43#330911yescharacteristic
337C2×C43#336211yescharacteristic
338C2×C43#337011yescharacteristic
339D43—82no—
340D43—82no—
341C2×#127—431no—
342C2×C4×D4—431no—
343C2×C4×D4—431no—
344C2×C4×D4—861no—
345C2×#106—431no—
346C2×#106C2×D4311yescharacteristic
347C2×C4⋊C8—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×C4×C8—431no—
357#398—861no—
358#398—861no—
359#390—431no—
360#390—431no—
361#390—861no—
362#389—431no—
363#389—431no—
364#389—431no—
365#389—861no—
366#389C2×D4311yescharacteristic
367#387—861no—
368#386—861no—
369#386—861no—
370#384—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4C2×D4311yescharacteristic
374#340—431no—
375#340—431no—
376#340—431no—
377#340C2×D4311yescharacteristic
378#340C2×D4311yescharacteristic
379#340C2×D4311yescharacteristic
380#336—431no—
381#336—431no—
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2675411yescharacteristic, complemented, Sylow
385C22×D4—431no—
386C22×D4—431no—
387C22×D4—861no—
388C22×D4—861no—
389C23×C4—861no—
390C23×C4—861no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395#127—862no—
396#127—862no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—1724no—
400C4×D4—1721no—
401C4×D4—1721no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—21no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427#106—22no—
428#106—862no—
429C4⋊C8—1721no—
430#102—862no—
431#102—862no—
432#102—862no—
433#102—862no—
434#102—862no—
435#102—862no—
436#102—1721no—
437#102—1721no—
438C4×C8—1721no—
439#95—21no—
440#95—21no—
441#95—431no—
442#95—431no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24—861no—
448C24—861no—
449C2×D4—432no—
450C2×D4—432no—
451C2×D4—864no—
452C2×D4—864no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—3441no—
464C2×D4—3441no—
465C2×D4—1722no—
466C2×D4—1722no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—81no—
505C4⋊C4—434no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—3441no—
512C4⋊C4—3441no—
513C4⋊C4—3441no—
514C4⋊C4—1721no—
515C4⋊C4—1722no—
516C4⋊C4#1062189812yes—
517C4⋊C4#1062190212yes—
518C22⋊C4—3441no—
519C22⋊C4—3441no—
520C22⋊C4—1722no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—861no—
528C42—861no—
529C42—861no—
530C42—861no—
531C42—3441no—
532C23—862no—
533C23—862no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23C2×D4×D4311yescharacteristic
547D4—862no—
548D4—862no—
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1728no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3444no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4SD16×D4312yes—
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062189811yescharacteristic
598C2×C4C2×#1062190211yescharacteristic
599C2×C4#1306337111yescharacteristic
600C2×C4#1306337211yescharacteristic
601C8—41no—
602C8—41no—
603C8—1721no—
604C8—1721no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—1722no—
614C22—1722no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22#1458340711yescharacteristic
620C22#1458354011yescharacteristic
621C22#1458355811yescharacteristic
622C22C2×SD16×D4311yescharacteristic
623C22#1458369811yescharacteristic
624C22#1458370111yescharacteristic
625C22#1458370311yescharacteristic
626C4—22no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—862no—
633C4—862no—
634C4—3441no—
635C4—3441no—
636C4—1721no—
637C4—1721no—
638C4#1458343611yescharacteristic
639C4#1458349011yescharacteristic
640C4#1458358711yescharacteristic
641C4#1458359311yescharacteristic
642C2—3442no—
643C2—3442no—
644C2#1913854611yescharacteristic
645C2#1914460011yescharacteristic
646C2#1914483411yescharacteristic
647C2#1914641611yescharacteristic
648C2#1914659811yescharacteristic
649C2#1914726411yescharacteristic
650C2#1914734911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#1920D43
hypocenterC43#26754
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #19139125C2semidirect
3. #19136002C2semidirect
4. #19135964C2semidirect
7. #19135279C2semidirect
8. #19135221C2semidirect
9. #19135180C2semidirect
10. #19135151C2semidirect
11. #19134857C2semidirect
12. #19134857C2semidirect
13. #19134594C2semidirect
14. #19134409C2semidirect
15. C43×#1920C2semidirect
326. #1920D43semidirect
384. C43#26754semidirect

Maximal subgroups

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

subgroupindex
#191391252
#191376592
#191360022
#191359642
#191358302
#191358292
#191352792
#191352212
#191351802
#191351512
#191348572
#191345942
#191344092
C43×#19202
#2675443