Finite Group Databasebeta

← #25169754

Subgroups — #25169754

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139205C211yesmaximal, characteristic, complemented
2#19137657C211yesmaximal, characteristic
3#19136115C211yesmaximal, characteristic, complemented
4#19135910C211yesmaximal, characteristic, complemented
5#19135827C211yesmaximal, characteristic
6#19135681C211yesmaximal, characteristic
7#19135451C211yesmaximal, characteristic, complemented
8#19135238C211yesmaximal, characteristic, complemented
9#19135217C211yesmaximal, characteristic, complemented
10#19135172C211yesmaximal, characteristic, complemented
11#19135155C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C43⋊#401—21no—
31#14582840—21no—
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582799—21no—
37#14582795C2211yescharacteristic
38#14582781—21no—
39#14582778—21no—
40#14582775—21no—
41#14582766—21no—
42#14582765C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063321—22no—
69#13063321—22no—
70#13063287—22no—
71#13063287—41no—
72C4×C22⋊D43—44no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063259—41no—
89#13063257—22no—
90C4⋊(C43⋊C8)—41no—
91#13063249—41no—
92#13063247—22no—
93#13063247—41no—
94#13063246—41no—
95#13063246—41no—
96#13063245—22no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43—41no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4×D4×C43—22no—
118C4×D4×C43—41no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#103×C43—22no—
124#102×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—81no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—24no—
152C2×C22⋊D43—42no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—81no—
155C2×C22⋊D43—81no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172#4112yes—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—81no—
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43#4112yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43#4112yes—
183C22⋊C4×C43—42no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188#10621884—44no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221C22×D43—22no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—48no—
259C22⋊D43—84no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43#13512yes—
280C2×Dic43AGL(1,ℤ/8)12yes—
281D172—22no—
282D172—22no—
283D172—41no—
284D172—41no—
285C4×D43—84no—
286C8×C43—22no—
287C8×C43—41no—
288C43⋊C8—41no—
289C43⋊C8—41no—
290#27063—431nomaximal, Sylow
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43#52511yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43#55011yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57711yescharacteristic
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#52911yescharacteristic
318C4×C43#53811yescharacteristic
319C4×C43#55111yescharacteristic
320C4×C43#55311yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—41no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328#2514—431no—
329#2366—431no—
330#2092—431no—
331#2055—431no—
332#2041—431no—
333#2014—431no—
334#1968—431no—
335#1928—431no—
336#1925—431no—
337#1919—431no—
338#1916—431no—
339#1877—431no—
340#1877D4311yescharacteristic, complemented
341#1804—431no—
342C4×#102—431no—
343C2×C43—82no—
344C2×C43#246711yescharacteristic
345C2×C43#310511yescharacteristic
346C2×C43#312311yescharacteristic
347C2×C43#330411yescharacteristic
348C2×C43#331011yescharacteristic
349C2×C43#339411yescharacteristic
350C2×C43#339711yescharacteristic
351D43—82no—
352C22×SD16—431no—
353C22×SD16C2×D4311yescharacteristic
354C2×#127—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357C2×C4×D4C2×D4311yescharacteristic
358C2×#107—431no—
359C2×#106—431no—
360C2×C4⋊C8—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102C2×D4311yescharacteristic
369C2×C4×C8—431no—
370#401—861no—
371#400—861no—
372#391—431no—
373#391—431no—
374#391C2×D4311yescharacteristic
375#390—431no—
376#390—431no—
377#390—861no—
378#389—431no—
379#387—861no—
380#386—861no—
381#386—861no—
382#383—861no—
383#382—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2706311yescharacteristic, complemented, Sylow
396C22×Q8C22×D4311yescharacteristic
397C22×D4—431no—
398C22×D4—861no—
399C22×D4—861no—
400C22×D4C22×D4311yescharacteristic
401C23×C4—21no—
402C23×C4—861no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—41no—
406C2×SD16—862no—
407C2×SD16—1721no—
408C2×SD16—1721no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413#127—862no—
414#127—862no—
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—862no—
418C4×D4—1721no—
419C4×D4—1724no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439#107—1721no—
440#106—862no—
441C4⋊C8—1721no—
442#103—22no—
443#103—1721no—
444#102—22no—
445#102—862no—
446#102—862no—
447#102—1721no—
448#102—1721no—
449#102—1721no—
450C4×C8—1721no—
451#95—21no—
452#95—21no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—21no—
465C24—861no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—432no—
478C2×D4—864no—
479C2×D4—864no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—3441no—
486C2×D4—3441no—
487C2×D4—1722no—
488C2×D4—1722no—
489C2×D4#1062190012yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—3441no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509SD16—44no—
510SD16—1724no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8#1062189812yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4#1062190012yes—
536C22⋊C4—42no—
537C22⋊C4—3441no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C42—21no—
543C42—21no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—1722no—
549C42—1722no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—862no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569D4—22no—
570D4—22no—
571D4—41no—
572D4—41no—
573D4—862no—
574D4—862no—
575D4—3444no—
576D4—1728no—
577D4—1721no—
578D4—1721no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—84no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—3444no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4#41×D4311yescharacteristic
618C2×C4C2×#1062190011yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4#1306337011yescharacteristic
622C2×C4#1306337111yescharacteristic
623C8—22no—
624C8—41no—
625C8—1721no—
626C8—1721no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22#1458340911yescharacteristic
642C22#1458353611yescharacteristic
643C22#1458357011yescharacteristic
644C22#135×D4311yescharacteristic
645C22AGL(1,ℤ/8)×D4311yescharacteristic
646C22#1458370511yescharacteristic
647C22#1458370811yescharacteristic
648C4—41no—
649C4—41no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—862no—
654C4—862no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—1721no—
659C4—1721no—
660C4#1458343111yescharacteristic
661C4#1458348511yescharacteristic
662C4#1458357511yescharacteristic
663C4#1458360111yescharacteristic
664C2—82no—
665C2—3442no—
666C2#1913865111yescharacteristic
667C2#1914464111yescharacteristic
668C2#1914484511yescharacteristic
669C2#1914652711yescharacteristic
670C2#1914660911yescharacteristic
671C2#1914759211yescharacteristic
672C2#1914761611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1877D43
hypocenterC43#27063
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
1. #19139205C2semidirect
3. #19136115C2semidirect
4. #19135910C2semidirect
7. #19135451C2semidirect
8. #19135238C2semidirect
9. #19135217C2semidirect
10. #19135172C2semidirect
11. #19135155C2semidirect
12. #19134926C2semidirect
13. #19134605C2semidirect
14. #19134409C2semidirect
15. C43×#1877C2semidirect
340. #1877D43semidirect
395. C43#27063semidirect

Maximal subgroups

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

subgroupindex
#191392052
#191376572
#191361152
#191359102
#191358272
#191356812
#191354512
#191352382
#191352172
#191351722
#191351552
#191349262
#191346052
#191344092
C43×#18772
#2706343