Finite Group Databasebeta

← #25147033

Subgroups — #25147033

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144996C211yesmaximal, characteristic
2C2×#14583207C211yesmaximal, characteristic, complemented
3#19144069C211yesmaximal, characteristic
4#19143338C211yesmaximal, characteristic
5#19136042C211yesmaximal, characteristic, complemented
6#19136037C211yesmaximal, characteristic, complemented
7#19135896C211yesmaximal, characteristic, complemented
8#19135896C211yesmaximal, characteristic, complemented
9#19135587C211yesmaximal, characteristic, complemented
10#19135109C211yesmaximal, characteristic, complemented
11#19135109C211yesmaximal, characteristic, complemented
12#19134656C211yesmaximal, characteristic, complemented
13#19134651C211yesmaximal, characteristic, complemented
14C4×#13063243C211yesmaximal, characteristic, complemented
15C43×#1950C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063358C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20#14583449C2211yescharacteristic
21C2×#13063317C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583268—21no—
24#14583264—21no—
25#14583254—21no—
26#14583254—21no—
27#14583207—21no—
28#14583207—21no—
29#14583207—21no—
30#14583207—21no—
31#14583122—21no—
32#14583122—21no—
33#14583110—21no—
34#14583100—21no—
35#14582976—21no—
36#14582969—21no—
37#14582969—21no—
38#14582964—21no—
39C2×#13063259C2211yescharacteristic
40C2×#13063257C2211yescharacteristic
41#14582901C2211yescharacteristic
42#14582901C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582901C2211yescharacteristic
45#14582901C2211yescharacteristic
46#14582901C2211yescharacteristic
47C2×#13063250C2211yescharacteristic
48C2×#13063250C2211yescharacteristic
49C2×#13063243C2211yescharacteristic
50C2×#13063243C2211yescharacteristic
51#14582865C2211yescharacteristic
52#14582865C2211yescharacteristic
53C4×#10621877C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C2×C4⋊C8×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70#13063358—22no—
71#13063358—22no—
72#13063358—41no—
73#13063358—41no—
74C2×Dic172—21no—
75C2×Dic172—21no—
76C2×#10621873—21no—
77C2×#10621873—21no—
78#13063331—22no—
79#13063331—22no—
80#13063331—41no—
81#13063331—41no—
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063325D411yescharacteristic
89#13063322D411yescharacteristic
90#13063317—21no—
91#13063317—21no—
92#13063317—21no—
93#13063317—21no—
94#13063313D411yescharacteristic
95#13063313D411yescharacteristic
96#13063299—21no—
97#13063299—21no—
98C4×Dic86—21no—
99C4×Dic86—21no—
100C4×Dic86—21no—
101C4×Dic86—21no—
102C4×D172—21no—
103C4×D172—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×C4×Dic43—21no—
111#13063259—21no—
112#13063259—21no—
113#13063257—21no—
114#13063257—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250—21no—
122#13063250—21no—
123#13063250—21no—
124#13063250—21no—
125#13063247—21no—
126#13063247—21no—
127#13063247—21no—
128#13063247—21no—
129#13063247—21no—
130#13063247—21no—
131#13063243—22no—
132#13063243—22no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137#13063236—21no—
138C4×C43⋊C8—21no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#108×C43—41no—
147#108×C43—41no—
148C4⋊C8×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43D411yescharacteristic
151C4⋊C8×C43D411yescharacteristic
152C4⋊C8×C43D411yescharacteristic
153C4⋊C8×C43D411yescharacteristic
154#97×C43—21no—
155C4×C8×C43—21no—
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C2×C22⋊D43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898—21no—
170#10621898—21no—
171#10621898—21no—
172#10621898—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C2×D411yescharacteristic
176C2×D172C2×D411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86C2×D411yescharacteristic
185C2×Dic86C2×D411yescharacteristic
186C2×Dic86#4112yes—
187M16×C43—21no—
188M16×C43—21no—
189M16×C43—21no—
190M16×C43—21no—
191M16×C43—21no—
192M16×C43—21no—
193M16×C43—21no—
194M16×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43C2×D411yescharacteristic
204C2×C8×C43C2×D411yescharacteristic
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—21no—
213(C2×D43)⋊C4—21no—
214(C2×D43)⋊C4—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223Dic43⋊C4—41no—
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226Dic43⋊C4—41no—
227Dic43⋊C4—41no—
228Dic43⋊C4—41no—
229C4×Dic43—41no—
230C4×Dic43—41no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877#4112yes—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237Dic172—42no—
238Dic172—42no—
239#10621873—42no—
240#10621873—42no—
241#10621872—42no—
242#10621872—42no—
243C8×D43—42no—
244C8×D43—42no—
245C23×C43C2×#4111yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43#12111yescharacteristic
251C2×C4×C43#12111yescharacteristic
252C2×C4×C43#12111yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C22⋊D43—41no—
261C22⋊D43—41no—
262C22⋊D43—41no—
263C22⋊D43—41no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—81no—
273C2×Dic43—81no—
274C2×Dic43—81no—
275D172—21no—
276D172—21no—
277D172—21no—
278D172—21no—
279D172—42no—
280D172—81no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285Dic86—22no—
286Dic86—21no—
287Dic86—21no—
288Dic86—21no—
289Dic86—21no—
290Dic86—22no—
291Dic86—41no—
292Dic86—41no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—41no—
298C8×C43—41no—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#25363—431nomaximal, Sylow
304C22×C43—21no—
305C22×C43—21no—
306C22×C43C2×#12111yescharacteristic
307C22×C43#52911yescharacteristic
308C22×C43#54211yescharacteristic
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43#54611yescharacteristic
320C4×C43#54611yescharacteristic
321C4×C43#54711yescharacteristic
322C4×C43#54811yescharacteristic
323Dic43—42no—
324Dic43—41no—
325Dic43—41no—
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329#3142—431no—
330C2×#479—431no—
331#3037—431no—
332#2935—431no—
333#2079—431no—
334#2078—431no—
335#2052—431no—
336#2052—431no—
337#1998—431no—
338#1950D4311yescharacteristic, complemented
339#1908—431no—
340#1908—431no—
341#1816—431no—
342#1815—431no—
343C4×#101—431no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43#242711yescharacteristic
347C2×C43#306711yescharacteristic
348C2×C43#306911yescharacteristic
349D43—81no—
350D43—81no—
351C2×#137—431no—
352C2×#137—431no—
353C2×#131—431no—
354C2×#131—431no—
355#532—431no—
356C2×#125—431no—
357C2×C4×Q8—431no—
358#491—861no—
359#490—861no—
360#488—861no—
361#488—861no—
362#479—861no—
363#479—861no—
364#479—861no—
365#479—861no—
366#464—861no—
367#464—861no—
368#462—861no—
369#460—861no—
370#436—861no—
371#435—861no—
372#435—861no—
373C8×D4—861no—
374C2×#108C2×D4311yescharacteristic
375C2×#108C2×D4311yescharacteristic
376C2×#107—431no—
377C2×#106—431no—
378#423C2×D4311yescharacteristic
379C2×C4⋊C8C2×D4311yescharacteristic
380#417—431no—
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#417—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#101—431no—
389C2×#101—431no—
390#408—431no—
391#408—431no—
392C4×M16—431no—
393C4×M16C2×D4311yescharacteristic
394#343—431no—
395#343—431no—
396#343—431no—
397#343—431no—
398#343—431no—
399#343—431no—
400#341C2×D4311yescharacteristic
401#341C2×D4311yescharacteristic
402C43#2536311yescharacteristic, complemented, Sylow
403C2×#41—431no—
404C2×#41—431no—
405C22×Q8—431no—
406#137—862no—
407#137—862no—
408#137—1721no—
409#137—1721no—
410C2×Q16—861no—
411C2×Q16—861no—
412C2×SD16—861no—
413C2×SD16—861no—
414#131—862no—
415#131—862no—
416#131—1721no—
417#131—1721no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—861no—
421C2×M16—861no—
422C2×M16C22×D4311yescharacteristic
423C2×M16C22×D4311yescharacteristic
424C2×M16C22×D4311yescharacteristic
425C2×M16C22×D4311yescharacteristic
426C22×C8—861no—
427C22×C8—861no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4⋊Q8—431no—
431#127—431no—
432#125—861no—
433#125—861no—
434#125—861no—
435#125—861no—
436#124—431no—
437#124—431no—
438#121—861no—
439#121—861no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×D4—861no—
445C4×D4—861no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#108—41no—
455#108—41no—
456#107—861no—
457#107—861no—
458#106—861no—
459#106—861no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8D17211yescharacteristic
463C4⋊C8D17211yescharacteristic
464C4⋊C8D17211yescharacteristic
465C4⋊C8D17211yescharacteristic
466#103—861no—
467#103—861no—
468#103—861no—
469#103—861no—
470#103—861no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#102—861no—
480#102—861no—
481#102—861no—
482#101—862no—
483#101—862no—
484C22⋊C8—861no—
485C22⋊C8—861no—
486C22⋊C8—861no—
487C22⋊C8—861no—
488#97—21no—
489#97—861no—
490C4×C8—21no—
491C4×C8—861no—
492#41—861no—
493#41—861no—
494#41—861no—
495#41—861no—
496#41—861no—
497#41—861no—
498#41—861no—
499#41—861no—
500C2×Q8—431no—
501C2×Q8—431no—
502C2×Q8—432no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×D4—431no—
509C2×D4—431no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4#1062190211yescharacteristic
521C22×C4#1062190211yescharacteristic
522C22×C4C23×D4311yescharacteristic
523Q16—1722no—
524Q16—1722no—
525SD16—1722no—
526SD16—1722no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—432no—
536M16—861no—
537M16—861no—
538M16—861no—
539M16—1722no—
540M16—1722no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—1722no—
552C2×C8—1722no—
553C2×C8C2×D17211yescharacteristic
554C2×C8C2×D17211yescharacteristic
555C2×C8C2×D17211yescharacteristic
556C2×C8C2×D17211yescharacteristic
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—1721no—
566C4⋊C4—1721no—
567C4⋊C4—1721no—
568C4⋊C4—1721no—
569C4⋊C4—1721no—
570C4⋊C4—1721no—
571C22⋊C4—861no—
572C22⋊C4—861no—
573C22⋊C4—861no—
574C22⋊C4—861no—
575C42—1721no—
576C42—1721no—
577C42C2×D17211yescharacteristic
578C42C2×D17211yescharacteristic
579C42D4×D4311yescharacteristic
580C42D4×D4311yescharacteristic
581C23—861no—
582C23—861no—
583C23C2×#1062190211yescharacteristic
584Q8—862no—
585Q8—862no—
586Q8—861no—
587Q8—861no—
588Q8—861no—
589Q8—861no—
590Q8—1721no—
591Q8—1721no—
592D4—861no—
593D4—861no—
594D4—861no—
595D4—861no—
596D4—3441no—
597D4—1722no—
598D4—1721no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—862no—
607C2×C4—3441no—
608C2×C4—3441no—
609C2×C4—3441no—
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#1306330011yescharacteristic
620C2×C4#1306330011yescharacteristic
621C2×C4#1306330011yescharacteristic
622C2×C4#1306330011yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C22×D17211yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4#1306337011yescharacteristic
628C2×C4#1306337311yescharacteristic
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—41no—
634C8—41no—
635C8—41no—
636C8—41no—
637C8—862no—
638C8—1721no—
639C22—21no—
640C22—21no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22—1721no—
646C22—1721no—
647C22C2×#1306330011yescharacteristic
648C22#1458343411yescharacteristic
649C22#1458352311yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—3441no—
655C4—3441no—
656C4—3441no—
657C4—1721no—
658C4—1721no—
659C4—1722no—
660C4#1458354411yescharacteristic
661C4#1458354611yescharacteristic
662C4#1458355111yescharacteristic
663C4#1458356111yescharacteristic
664C2—21no—
665C2—21no—
666C2—3441no—
667C2—3441no—
668C2#1913817011yescharacteristic
669C2#1914431611yescharacteristic
670C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1950C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenter#1950D43
hypocenterC43#25363
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
5. #19136042C2semidirect
6. #19136037C2semidirect
7. #19135896C2semidirect
8. #19135896C2semidirect
9. #19135587C2semidirect
10. #19135109C2semidirect
11. #19135109C2semidirect
12. #19134656C2semidirect
13. #19134651C2semidirect
14. C4×#13063243C2semidirect
15. C43×#1950C2semidirect
338. #1950D43semidirect
402. C43#25363semidirect

Maximal subgroups

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

subgroupindex
#191449962
C2×#145832072
#191440692
#191433382
#191360422
#191360372
#191358962
#191355872
#191351092
#191346562
#191346512
C4×#130632432
C43×#19502
#2536343