Finite Group Databasebeta

← #25200812

Subgroups — #25200812

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140558C211yesmaximal, characteristic, complemented
2#19137309C211yesmaximal, characteristic, complemented
3#19136075C211yesmaximal, characteristic, complemented
4#19136002C211yesmaximal, characteristic, complemented
5#19135832C211yesmaximal, characteristic, complemented
6#19135673C211yesmaximal, characteristic
7#19135471C211yesmaximal, characteristic
8#19135452C211yesmaximal, characteristic, complemented
9#19135277C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic, complemented
11#19134944C211yesmaximal, characteristic
12#19134865C211yesmaximal, characteristic, complemented
13#19134857C211yesmaximal, characteristic, complemented
14#19134348C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582828—21no—
31#14582826—21no—
32#14582825—21no—
33#14582821—21no—
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582788—21no—
41#14582788—21no—
42#14582773—21no—
43#14582773—21no—
44#14582768C2211yescharacteristic
45#14582745C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#103×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C2×D344—22no—
66C2×D344—22no—
67C2×D344—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063314—22no—
71#13063314—22no—
72Q8×Dic43—41no—
73Q8×Dic43—41no—
74#13063287—41no—
75#13063287—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
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×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063257—41no—
98#13063256—41no—
99#13063249—41no—
100#13063247—41no—
101#13063247—41no—
102#13063245—22no—
103#13063245—22no—
104#13063245—41no—
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
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—22no—
122#97×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
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×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172#4112yes—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—81no—
175C42×C43—21no—
176C42×C43—21no—
177#10621884—44no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43—81no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8#4112yes—
209D344—44no—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
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—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—22no—
226Q8×C43—22no—
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—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
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—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279C4×D43—84no—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#29510—431nomaximal, Sylow
285C22×C43#52511yescharacteristic
286C22×C43#53211yescharacteristic
287C22×C43#53511yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57711yescharacteristic
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43#55111yescharacteristic
313C4×C43#55111yescharacteristic
314C4×C43#55311yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322#2644—431no—
323#2326—431no—
324#2084—431no—
325#2071—431no—
326#2042—431no—
327#2012—431no—
328#1972—431no—
329#1968—431no—
330#1935D4311yescharacteristic, complemented
331#1934—431no—
332#1880—431no—
333#1879—431no—
334#1865—431no—
335#1864—431no—
336#1746—431no—
337C2×C43#260311yescharacteristic
338C2×C43#311911yescharacteristic
339C2×C43#312511yescharacteristic
340C2×C43#317311yescharacteristic
341C2×C43#317911yescharacteristic
342C2×C43#322111yescharacteristic
343C2×C43#322411yescharacteristic
344D43—82no—
345D43—161no—
346C22×SD16—431no—
347C22×D8—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#103—431no—
354C2×#103C2×D4311yescharacteristic
355C2×#103C2×D4311yescharacteristic
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#97C2×D4311yescharacteristic
362C2×C4×C8—431no—
363#397—861no—
364#397—861no—
365#397—861no—
366#396—861no—
367#391C2×D4311yescharacteristic
368#390—431no—
369#390—431no—
370#390—431no—
371#390—431no—
372#389—431no—
373#389—431no—
374#389C2×D4311yescharacteristic
375#388—861no—
376#388—861no—
377#385—861no—
378#385—861no—
379#384—431no—
380#376—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#340C2×D4311yescharacteristic
385#336—431no—
386#336—431no—
387#336—431no—
388#336—431no—
389C43#2951011yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C22×D4—431no—
393C23×C4—861no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C2×D8—862no—
398C2×D8—862no—
399C2×D8—1721no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#124—862no—
405#124—862no—
406C4×Q8—1721no—
407C4×Q8—1721no—
408C4×D4—1721no—
409C4×D4—1721no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
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—431no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436#106—1721no—
437#106—1721no—
438#103—22no—
439#103—22no—
440#103—1721no—
441#102—862no—
442#102—862no—
443#102—1721no—
444#102—1721no—
445#102—1721no—
446#97—22no—
447C4×C8—862no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—431no—
452#95—431no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457C24—861no—
458C24—861no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8#1062189812yes—
465C2×D4—432no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—1722no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494D8—1724no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8#1062190012yes—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C42—21no—
535C42—21no—
536C42—861no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—1722no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—862no—
561D4—862no—
562D4—1721no—
563D4—1721no—
564D4—1721no—
565D4—1721no—
566D4—1721no—
567D4—1721no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
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—41no—
585C2×C4—41no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—3444no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337111yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—22no—
612C8—41no—
613C8—862no—
614C8—1721no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22#1458340811yescharacteristic
630C22#1458344411yescharacteristic
631C22#1458346711yescharacteristic
632C22#1458370311yescharacteristic
633C22#1458370811yescharacteristic
634C22#1458370811yescharacteristic
635C22#1458370811yescharacteristic
636C4—41no—
637C4—42no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—3441no—
643C4—3441no—
644C4—1721no—
645C4—1721no—
646C4—1721no—
647C4—1721no—
648C4#1458357211yescharacteristic
649C4#1458357311yescharacteristic
650C4#1458359511yescharacteristic
651C4#1458360011yescharacteristic
652C2—3442no—
653C2—6881no—
654C2#1914022011yescharacteristic
655C2#1914479211yescharacteristic
656C2#1914487011yescharacteristic
657C2#1914521311yescharacteristic
658C2#1914527111yescharacteristic
659C2#1914565711yescharacteristic
660C2#1914569011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1935D43
hypocenterC43#29510
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. #19140558C2semidirect
2. #19137309C2semidirect
3. #19136075C2semidirect
4. #19136002C2semidirect
5. #19135832C2semidirect
8. #19135452C2semidirect
9. #19135277C2semidirect
10. #19134948C2semidirect
12. #19134865C2semidirect
13. #19134857C2semidirect
14. #19134348C2semidirect
15. C43×#1935C2semidirect
330. #1935D43semidirect
389. C43#29510semidirect

Maximal subgroups

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

subgroupindex
#191405582
#191373092
#191360752
#191360022
#191358322
#191356732
#191354712
#191354522
#191352772
#191349482
#191349442
#191348652
#191348572
#191343482
C43×#19352
#2951043