Finite Group Databasebeta

← #25200189

Subgroups — #25200189

Order 11008.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142921C211yesmaximal, characteristic
2#19137123C211yesmaximal, characteristic, complemented
3#19136032C211yesmaximal, characteristic, complemented
4#19135792C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic
6#19135450C211yesmaximal, characteristic, complemented
7#19135321C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19135269C211yesmaximal, characteristic, complemented
10#19135224C211yesmaximal, characteristic, complemented
11#19135171C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic, complemented
13#19134860C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063306—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582787—21no—
37#14582787—21no—
38#14582781—21no—
39#14582779—21no—
40#14582771—21no—
41#14582759C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582750—21no—
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063306—44no—
68#13063304—22no—
69#13063304—22no—
70#13063290—41no—
71#13063290—41no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—41no—
89C2×C4×Dic43—41no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063257—22no—
95#13063256—22no—
96#13063250—22no—
97#13063250—22no—
98#13063248—41no—
99#13063246—22no—
100C22⋊(C43⋊C8)—22no—
101C8×Dic43—41no—
102C8×Dic43—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43—21no—
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#121×C43—41no—
116#121×C43—41no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122#106×C43—41no—
123#102×C43—22no—
124#102×C43—41no—
125C22⋊C8×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
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—42no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43SD1614yescomplemented
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86#4112yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43#4112yes—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊Dic43—24no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189#10621883—44no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—41no—
206C4×Dic43—41no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8#4112yes—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C2×SD1612yes—
229C23×C43C22×D411yescharacteristic
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—84no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—44no—
269C2×Dic43—44no—
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—41no—
280C2×Dic43C2×SD1612yes—
281C2×Dic43C2×SD1612yes—
282C2×Dic43#13512yes—
283Dic86—22no—
284Dic86—22no—
285Dic86—41no—
286Dic86—41no—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#29466—431nomaximal, Sylow
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43#52511yescharacteristic
307C22×C43#53211yescharacteristic
308C22×C43#53411yescharacteristic
309C22×C43C22×SD1611yescharacteristic
310C22×C43C2×#13511yescharacteristic
311C22×C43#57511yescharacteristic
312C22×C43#57511yescharacteristic
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#55111yescharacteristic
318C4×C43#55311yescharacteristic
319C4×C43#55311yescharacteristic
320C4×C43#55911yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—22no—
324Dic43—42no—
325Dic43—42no—
326Dic43—41no—
327Dic43—81no—
328Dic43—81no—
329#2854—431no—
330C4×C22⋊Q8—431no—
331#2077—431no—
332#2035—431no—
333#2034D4311yescharacteristic
334#2000—431no—
335#1968—431no—
336#1941—431no—
337#1934—431no—
338#1933—431no—
339#1926—431no—
340#1919—431no—
341#1880—431no—
342#1865—431no—
343C4×C22⋊C8—431no—
344C2×C43—42no—
345C2×C43—161no—
346C2×C43#260211yescharacteristic
347C2×C43#310211yescharacteristic
348C2×C43#310311yescharacteristic
349C2×C43#316711yescharacteristic
350C2×C43#318311yescharacteristic
351C2×C43#318711yescharacteristic
352C2×C43#319111yescharacteristic
353C22×SD16—431no—
354C2×#123—861no—
355C2×C22⋊Q8—431no—
356C2×#121C2×D4311yescharacteristic
357C2×C4×Q8—431no—
358C22×C42—431no—
359C2×#106—431no—
360C2×#106—431no—
361C2×#106C2×D4311yescharacteristic
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×#102C2×D4311yescharacteristic
368C2×C22⋊C8—431no—
369C2×C22⋊C8C2×D4311yescharacteristic
370C2×C4×C8—431no—
371C2×C4×C8—431no—
372#391—431no—
373#390—431no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—431no—
378#388—861no—
379#388—861no—
380#387—861no—
381#386—861no—
382#385—861no—
383#380—431no—
384#380C2×D4311yescharacteristic
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396C43#2946611yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×D4—21no—
399C22×D4C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—431no—
402C23×C4C22×D4311yescharacteristic
403C2×SD16—862no—
404C2×SD16—862no—
405C2×SD16—1721no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#123—1724no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413#121—41no—
414#121—41no—
415C4×Q8—1721no—
416C4×Q8—1721no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—1721no—
443C2×C42—1721no—
444#106—41no—
445#106—862no—
446#106—862no—
447#103—862no—
448#103—862no—
449#103—1721no—
450#102—22no—
451#102—41no—
452#102—862no—
453C22⋊C8—22no—
454C22⋊C8—862no—
455C4×C8—1721no—
456C4×C8—1721no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—21no—
466C24D4×D4311yescharacteristic
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—434no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1721no—
504C22×C4—1721no—
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507SD16—1724no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8#1062190012yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—432no—
527C4⋊C4—864no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—864no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—1721no—
550C42—1721no—
551C42—1722no—
552C42—1722no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23SD16×D4312yes—
567C23C2×D4×D4311yescharacteristic
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—1724no—
608C2×C4—1724no—
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—1721no—
618C2×C4—1721no—
619C2×C4#41×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337011yescharacteristic
625C8—22no—
626C8—41no—
627C8—862no—
628C8—1721no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#1458340711yescharacteristic
644C22#1458344411yescharacteristic
645C22#1458345911yescharacteristic
646C22C2×SD16×D4311yescharacteristic
647C22#135×D4311yescharacteristic
648C22#1458369511yescharacteristic
649C22#1458369511yescharacteristic
650C4—41no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—862no—
655C4—862no—
656C4—862no—
657C4—3441no—
658C4—3441no—
659C4—1722no—
660C4—1722no—
661C4—1721no—
662C4#1458357911yescharacteristic
663C4#1458359211yescharacteristic
664C4#1458359611yescharacteristic
665C4#1458363311yescharacteristic
666C2—42no—
667C2—161no—
668C2#1914021011yescharacteristic
669C2#1914460811yescharacteristic
670C2#1914462311yescharacteristic
671C2#1914514911yescharacteristic
672C2#1914531911yescharacteristic
673C2#1914534911yescharacteristic
674C2#1914538511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#29466
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. #19137123C2semidirect
3. #19136032C2semidirect
4. #19135792C2semidirect
6. #19135450C2semidirect
7. #19135321C2semidirect
8. #19135275C2semidirect
9. #19135269C2semidirect
10. #19135224C2semidirect
11. #19135171C2semidirect
12. #19134947C2semidirect
13. #19134860C2semidirect
14. C22⋊C8×Dic43C2semidirect
158. C22×Dic43SD16semidirect
396. C43#29466semidirect

Maximal subgroups

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

subgroupindex
#191429212
#191371232
#191360322
#191357922
#191355982
#191354502
#191353212
#191352752
#191352692
#191352242
#191351712
#191349472
#191348602
C22⋊C8×Dic432
C43×#20342
#2946643