Finite Group Databasebeta

← #25200287

Subgroups — #25200287

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140395C211yesmaximal, characteristic, complemented
2#19137282C211yesmaximal, characteristic
3#19136030C211yesmaximal, characteristic, complemented
4#19135796C211yesmaximal, characteristic, complemented
5#19135775C211yesmaximal, characteristic
6#19135595C211yesmaximal, characteristic
7#19135451C211yesmaximal, characteristic, complemented
8#19135327C211yesmaximal, characteristic, complemented
9#19135294C211yesmaximal, characteristic, complemented
10#19135282C211yesmaximal, characteristic, complemented
11#19135233C211yesmaximal, characteristic, complemented
12#19135181C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582840—21no—
31#14582833—21no—
32#14582828—21no—
33#14582826—21no—
34#14582806C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582799—21no—
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582793—21no—
41#14582778—21no—
42#14582772—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063301—41no—
64#13063301—41no—
65#13063296—22no—
66#13063296—22no—
67#13063282—41no—
68#13063282—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063258—22no—
90#13063258—41no—
91#13063257—22no—
92#13063249—22no—
93#13063249—22no—
94#13063246—22no—
95#13063246—41no—
96(C2×D43)⋊C8—22no—
97(C2×D43)⋊C8—22no—
98#13063235—41no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×D4×C43—41no—
117C4×D4×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#103×C43—41no—
123#102×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—24no—
150C2×C22⋊D43—81no—
151C2×C22⋊D43—81no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165SD16×C43—44no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43#4112yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C22⋊C4×C43—42no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—24no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—81no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200Dic43⋊C4—81no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8#4112yes—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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—84no—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—84no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C8×C43—22no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285#29473—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43#52511yescharacteristic
294C22×C43#53211yescharacteristic
295C22×C43#53411yescharacteristic
296C22×C43#57611yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57811yescharacteristic
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43#55111yescharacteristic
313C4×C43#55311yescharacteristic
314C4×C43#55311yescharacteristic
315C4×C43#55911yescharacteristic
316Dic43—41no—
317Dic43—42no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323#2625—431no—
324#2324—431no—
325#2077—431no—
326#2036—431no—
327#2033—431no—
328#2000—431no—
329#1968—431no—
330#1942—431no—
331#1936—431no—
332#1935—431no—
333#1928—431no—
334#1920—431no—
335#1877D4311yescharacteristic, complemented
336#1862—431no—
337#1750—431no—
338C2×C43—82no—
339C2×C43#260211yescharacteristic
340C2×C43#311811yescharacteristic
341C2×C43#312011yescharacteristic
342C2×C43#317411yescharacteristic
343C2×C43#317511yescharacteristic
344C2×C43#319811yescharacteristic
345C2×C43#320111yescharacteristic
346D43—81no—
347C22×SD16C2×D4311yescharacteristic
348C2×C22⋊Q8—431no—
349C2×#121—431no—
350C2×C4×D4C2×D4311yescharacteristic
351C2×#117—431no—
352C2×#107—431no—
353C2×#107—431no—
354C2×#106—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103C2×D4311yescharacteristic
358C2×#102—431no—
359C2×#102—431no—
360C2×#102C2×D4311yescharacteristic
361C2×C22⋊C8—431no—
362C2×C22⋊C8—431no—
363C2×#97—431no—
364C2×C4×C8—431no—
365#400—861no—
366#398—861no—
367#397—861no—
368#397—861no—
369#391—431no—
370#391C2×D4311yescharacteristic
371#390—431no—
372#390—861no—
373#389—431no—
374#389—431no—
375#389—431no—
376#388—861no—
377#386—861no—
378#385—861no—
379#380—431no—
380#380—431no—
381C4×C4⋊C4—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340C2×D4311yescharacteristic
388#336—431no—
389#336C2×D4311yescharacteristic
390C43#2947311yescharacteristic, complemented, Sylow
391C22×Q8C22×D4311yescharacteristic
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—431no—
396C2×SD16—22no—
397C2×SD16—22no—
398C2×SD16—41no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C22⋊Q8—1721no—
404C22⋊Q8—1721no—
405#121—862no—
406#121—862no—
407C4×D4—41no—
408C4×D4—41no—
409#117—1721no—
410#117—1721no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—862no—
436#107—1721no—
437#106—862no—
438#103—41no—
439#103—862no—
440#103—862no—
441#102—22no—
442#102—862no—
443#102—1721no—
444C22⋊C8—862no—
445C22⋊C8—862no—
446#97—1721no—
447C4×C8—1721no—
448#95—21no—
449#95—21no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24—431no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—864no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4#1062190012yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—44no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—432no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8#1062189812yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—432no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3441no—
523C4⋊C4—3441no—
524C4⋊C4—3441no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4—1722no—
528C22⋊C4—42no—
529C22⋊C4—864no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—3441no—
534C22⋊C4—1721no—
535C22⋊C4—1721no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—861no—
540C42—861no—
541C42—3441no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23C2×D4×D4311yescharacteristic
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—3444no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062190011yescharacteristic
610C2×C4C2×#1062189811yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337011yescharacteristic
613C8—22no—
614C8—41no—
615C8—862no—
616C8—1721no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—1721no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22#1458340911yescharacteristic
632C22#1458344611yescharacteristic
633C22#1458345911yescharacteristic
634C22#1458370311yescharacteristic
635C22#1458370511yescharacteristic
636C22#1458370611yescharacteristic
637C22#1458371511yescharacteristic
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—1721no—
647C4—1722no—
648C4—1721no—
649C4—1721no—
650C4#1458357511yescharacteristic
651C4#1458359211yescharacteristic
652C4#1458359411yescharacteristic
653C4#1458363211yescharacteristic
654C2—82no—
655C2—3441no—
656C2#1914020311yescharacteristic
657C2#1914477811yescharacteristic
658C2#1914480611yescharacteristic
659C2#1914521911yescharacteristic
660C2#1914523211yescharacteristic
661C2#1914545111yescharacteristic
662C2#1914547411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1877D43
hypocenterC43#29473
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. #19140395C2semidirect
3. #19136030C2semidirect
4. #19135796C2semidirect
7. #19135451C2semidirect
8. #19135327C2semidirect
9. #19135294C2semidirect
10. #19135282C2semidirect
11. #19135233C2semidirect
12. #19135181C2semidirect
13. #19134842C2semidirect
14. #19134360C2semidirect
15. C43×#1877C2semidirect
335. #1877D43semidirect
390. C43#29473semidirect

Maximal subgroups

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

subgroupindex
#191403952
#191372822
#191360302
#191357962
#191357752
#191355952
#191354512
#191353272
#191352942
#191352822
#191352332
#191351812
#191348422
#191343602
C43×#18772
#2947343