Finite Group Databasebeta

← #25200298

Subgroups — #25200298

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#19137286C211yesmaximal, characteristic
3#19136034C211yesmaximal, characteristic, complemented
4#19135796C211yesmaximal, characteristic, complemented
5#19135780C211yesmaximal, characteristic
6#19135597C211yesmaximal, characteristic
7#19135452C211yesmaximal, characteristic, complemented
8#19135325C211yesmaximal, characteristic, complemented
9#19135292C211yesmaximal, characteristic, complemented
10#19135239C211yesmaximal, characteristic, complemented
11#19135183C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063300C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582840—21no—
32#14582833—21no—
33#14582828—21no—
34#14582826—21no—
35#14582806C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582800—21no—
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582788—21no—
41#14582777—21no—
42#14582770—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#103×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621884—22no—
64C2×#10621884—22no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063301—41no—
69#13063301—41no—
70#13063300—22no—
71#13063300—22no—
72#13063287—41no—
73#13063287—41no—
74#13063282—41no—
75#13063282—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
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×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063258—41no—
97#13063256—22no—
98#13063249—22no—
99#13063247—22no—
100#13063247—41no—
101#13063245—22no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—22no—
104C4×C43⋊C8—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#103×C43—22no—
121#103×C43—41no—
122#97×C43—41no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—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—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172—24no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—81no—
154C2×D172—81no—
155C2×D172#4112yes—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43#4112yes—
178C42×C43—21no—
179C42×C43—21no—
180#10621884—44no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—81no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—42no—
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#4112yes—
209C2×C43⋊C8#4112yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—22no—
272D172—22no—
273D172—41no—
274D172—41no—
275D172—84no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—84no—
281C8×C43—41no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—22no—
285#29473—431nomaximal, Sylow
286C22×C43#52511yescharacteristic
287C22×C43#53211yescharacteristic
288C22×C43#53411yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57811yescharacteristic
293C2×D43—41no—
294C2×D43—42no—
295C2×D43—41no—
296C2×D43—42no—
297C2×D43—41no—
298C2×D43—42no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43#55111yescharacteristic
314C4×C43#55311yescharacteristic
315C4×C43#55311yescharacteristic
316C4×C43#55911yescharacteristic
317Dic43—41no—
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#1935D4311yescharacteristic, complemented
333#1928—431no—
334#1920—431no—
335#1877—431no—
336#1862—431no—
337#1750—431no—
338C2×C43#260211yescharacteristic
339C2×C43#311811yescharacteristic
340C2×C43#312011yescharacteristic
341C2×C43#317411yescharacteristic
342C2×C43#317511yescharacteristic
343C2×C43#319811yescharacteristic
344C2×C43#320111yescharacteristic
345D43—81no—
346D43—82no—
347C22×SD16—431no—
348C2×C22⋊Q8—431no—
349C2×#121—431no—
350C2×C4×D4—431no—
351C2×#117—431no—
352C2×#107—431no—
353C2×#107—431no—
354C2×#106—431no—
355C2×#103—431no—
356C2×#103C2×D4311yescharacteristic
357C2×#103C2×D4311yescharacteristic
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8—431no—
363C2×#97C2×D4311yescharacteristic
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#389C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#336—431no—
389#336—431no—
390C43#2947311yescharacteristic, complemented, Sylow
391C22×Q8C22×D4311yescharacteristic
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—431no—
395C23×C4—861no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—1721no—
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—1721no—
408C4×D4—1721no—
409#117—1721no—
410#117—1721no—
411C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—431no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—861no—
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—22no—
439#103—41no—
440#103—862no—
441#102—862no—
442#102—862no—
443#102—1721no—
444C22⋊C8—862no—
445C22⋊C8—862no—
446#97—41no—
447C4×C8—1721no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—431no—
459C24—861no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—432no—
467C2×D4—864no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—3441no—
474C2×D4—3441no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1724no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—81no—
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—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1722no—
527C4⋊C4#1062189812yes—
528C22⋊C4—864no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—861no—
540C42—861no—
541C42—3441no—
542C23—862no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23—861no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23C2×D4×D4311yescharacteristic
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561D4—862no—
562D4—862no—
563D4—3444no—
564D4—1721no—
565D4—1721no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
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—41no—
582C2×C4—41no—
583C2×C4—41no—
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—861no—
593C2×C4—3444no—
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×C4#41×D4311yescharacteristic
610C2×C4C2×#1062189811yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337111yescharacteristic
613C8—41no—
614C8—41no—
615C8—862no—
616C8—862no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—1721no—
622C22—1721no—
623C22—1721no—
624C22—1721no—
625C22—1722no—
626C22—1721no—
627C22—1722no—
628C22—1721no—
629C22—1722no—
630C22—1721no—
631C22#1458340811yescharacteristic
632C22#1458344811yescharacteristic
633C22#1458345711yescharacteristic
634C22#1458370311yescharacteristic
635C22#1458370811yescharacteristic
636C22#1458370811yescharacteristic
637C22#1458371511yescharacteristic
638C4—41no—
639C4—42no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1721no—
648C4—1721no—
649C4—1721no—
650C4#1458357411yescharacteristic
651C4#1458359311yescharacteristic
652C4#1458359411yescharacteristic
653C4#1458363211yescharacteristic
654C2—3442no—
655C2—3441no—
656C2#1914021411yescharacteristic
657C2#1914478311yescharacteristic
658C2#1914480711yescharacteristic
659C2#1914522611yescharacteristic
660C2#1914523311yescharacteristic
661C2#1914544811yescharacteristic
662C2#1914547811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1935D43
hypocenterC43#29473
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. #19140395C2semidirect
3. #19136034C2semidirect
4. #19135796C2semidirect
7. #19135452C2semidirect
8. #19135325C2semidirect
9. #19135292C2semidirect
10. #19135239C2semidirect
11. #19135183C2semidirect
12. #19134926C2semidirect
13. #19134843C2semidirect
14. #19134364C2semidirect
15. C43×#1935C2semidirect
332. #1935D43semidirect
390. C43#29473semidirect

Maximal subgroups

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

subgroupindex
#191403952
#191372862
#191360342
#191357962
#191357802
#191355972
#191354522
#191353252
#191352922
#191352392
#191351832
#191349262
#191348432
#191343642
C43×#19352
#2947343