Finite Group Databasebeta

← #25147031

Subgroups — #25147031

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#19144998C211yesmaximal, characteristic
2#19144067C211yesmaximal, characteristic
3#19143338C211yesmaximal, characteristic
4#19136041C211yesmaximal, characteristic, complemented
5#19136036C211yesmaximal, characteristic, complemented
6#19135895C211yesmaximal, characteristic, complemented
7#19135895C211yesmaximal, characteristic, complemented
8#19135589C211yesmaximal, characteristic, complemented
9#19135371C211yesmaximal, characteristic, complemented
10#19135113C211yesmaximal, characteristic, complemented
11#19135113C211yesmaximal, characteristic, complemented
12#19134660C211yesmaximal, characteristic, complemented
13#19134655C211yesmaximal, characteristic, complemented
14C4×#13063244C211yesmaximal, characteristic, complemented
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063356C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20#14583449C2211yescharacteristic
21#14583269—21no—
22#14583265—21no—
23#14583256—21no—
24#14583256—21no—
25#14583121—21no—
26#14583121—21no—
27#14583109—21no—
28#14583099—21no—
29#14582976—21no—
30#14582969—21no—
31#14582969—21no—
32#14582964—21no—
33C2×#13063261C2211yescharacteristic
34C2×#13063261C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582898C2211yescharacteristic
37#14582898C2211yescharacteristic
38#14582898C2211yescharacteristic
39#14582898C2211yescharacteristic
40#14582898C2211yescharacteristic
41#14582898C2211yescharacteristic
42C2×#13063244C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582865C2211yescharacteristic
46C4×#10621877C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C43×#479—21no—
59C43×#479—21no—
60C43×#479—21no—
61C43×#479—21no—
62C2×#107×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#103×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063356—22no—
70#13063356—22no—
71#13063356—41no—
72#13063356—41no—
73C2×#10621885—21no—
74C2×#10621885—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77#13063331—22no—
78#13063331—22no—
79#13063331—41no—
80#13063331—41no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91#13063325D411yescharacteristic
92#13063322D411yescharacteristic
93#13063313D411yescharacteristic
94#13063313D411yescharacteristic
95#13063299—21no—
96#13063299—21no—
97C4×D172—21no—
98C4×D172—21no—
99#13063261—41no—
100#13063261—41no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063244—22no—
116#13063244—22no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236—21no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C22×Q8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128#125×C43—21no—
129#125×C43—21no—
130#125×C43—21no—
131#125×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#107×C43—21no—
145#107×C43—21no—
146#106×C43—21no—
147#106×C43—21no—
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150C4⋊C8×C43D411yescharacteristic
151C4⋊C8×C43D411yescharacteristic
152#103×C43—21no—
153#103×C43—21no—
154#103×C43—21no—
155#103×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43#4111yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—21no—
170C2×C22⋊D43—21no—
171#10621898—21no—
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176#10621898—21no—
177#10621898—21no—
178#10621898—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172C2×D411yescharacteristic
182C2×D172C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×Dic86C2×D411yescharacteristic
186C2×Dic86C2×D411yescharacteristic
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213#10621885—42no—
214#10621885—42no—
215#10621884—42no—
216#10621884—42no—
217(C2×D43)⋊C4—21no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220(C2×D43)⋊C4—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877#4112yes—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241#10621872—42no—
242#10621872—42no—
243C8×D43—42no—
244C8×D43—42no—
245C23×C43C2×#4111yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248Q8×C43—22no—
249Q8×C43—22no—
250Q8×C43—41no—
251Q8×C43—41no—
252C2×C4×C43—22no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—81no—
261C2×C4×C43—81no—
262C2×C4×C43—81no—
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43#12111yescharacteristic
266C2×C4×C43#12111yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C22⋊D43—41no—
274C22⋊D43—41no—
275C22⋊D43—41no—
276C22⋊D43—41no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279D172—21no—
280D172—21no—
281D172—21no—
282D172—21no—
283D172—42no—
284D172—81no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288C4×D43—41no—
289Dic86—21no—
290Dic86—21no—
291Dic86—21no—
292Dic86—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301C43⋊C8—41no—
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—42no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43#54611yescharacteristic
324C4×C43#54611yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#54811yescharacteristic
327Dic43—41no—
328Dic43—41no—
329#3142—431no—
330C2×#479D4311yescharacteristic, complemented
331#3037—431no—
332#2935—431no—
333#2079—431no—
334#2078—431no—
335#2052—431no—
336#2052—431no—
337#1998—431no—
338#1950—431no—
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×#125C2×D4311yescharacteristic
357C2×C4×Q8C2×D4311yescharacteristic
358#491—861no—
359#490—861no—
360#488—861no—
361#488—861no—
362#479—21no—
363#479—21no—
364#479—21no—
365#479—21no—
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×#108—431no—
375C2×#108—431no—
376C2×#107C2×D4311yescharacteristic
377C2×#106C2×D4311yescharacteristic
378#423—431no—
379C2×C4⋊C8C2×D4311yescharacteristic
380#417—431no—
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#417—431no—
386C2×#103C2×D4311yescharacteristic
387C2×#103C2×D4311yescharacteristic
388C2×#101—431no—
389C2×#101—431no—
390#408—431no—
391#408—431no—
392C4×M16—431no—
393C4×M16—431no—
394#343—431no—
395#343—431no—
396#343—431no—
397#343—431no—
398#343—431no—
399#343—431no—
400#341—431no—
401#341—431no—
402C43#2536311yescharacteristic, complemented, Sylow
403C2×#41—431no—
404C2×#41—431no—
405C22×Q8C22×D4311yescharacteristic
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—431no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16—431no—
424C2×M16—861no—
425C2×M16—861no—
426C22×C8—861no—
427C22×C8—861no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4⋊Q8—431no—
431#127—431no—
432#125—21no—
433#125—21no—
434#125—21no—
435#125—21no—
436#124—431no—
437#124—431no—
438#121—861no—
439#121—861no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×D4—861no—
445C4×D4—861no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C42—21no—
453C2×C42C22×D4311yescharacteristic
454#108—1721no—
455#108—1721no—
456#107—21no—
457#107—21no—
458#106—21no—
459#106—21no—
460C4⋊C8—861no—
461C4⋊C8—861no—
462C4⋊C8C22⋊D4311yescharacteristic
463C4⋊C8C22⋊D4311yescharacteristic
464C4⋊C8C22⋊D4311yescharacteristic
465C4⋊C8C22⋊D4311yescharacteristic
466#103—21no—
467#103—21no—
468#103—21no—
469#103—21no—
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—861no—
489#97—861no—
490C4×C8—861no—
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—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—431no—
506C2×Q8—431no—
507C2×Q8#1062190212yes—
508C2×D4—431no—
509C2×D4—431no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4#1062190011yescharacteristic
521C22×C4#1062190011yescharacteristic
522C22×C4C23×D4311yescharacteristic
523Q16—1722no—
524Q16—1722no—
525SD16—1722no—
526SD16—1722no—
527M16—432no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16—861no—
536M16—861no—
537M16—861no—
538M16—861no—
539M16—1722no—
540M16—1722no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—1722no—
552C2×C8—1722no—
553C2×C8C2×C22⋊D4311yescharacteristic
554C2×C8C2×C22⋊D4311yescharacteristic
555C2×C8C2×C22⋊D4311yescharacteristic
556C2×C8C2×C22⋊D4311yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C22⋊C4—861no—
572C22⋊C4—861no—
573C22⋊C4—861no—
574C22⋊C4—861no—
575C42—41no—
576C42—41no—
577C42D4×D4311yescharacteristic
578C42D4×D4311yescharacteristic
579C42C2×C22⋊D4311yescharacteristic
580C42C2×C22⋊D4311yescharacteristic
581C23—861no—
582C23—861no—
583C23C2×#1062190011yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588Q8—861no—
589Q8—861no—
590Q8—861no—
591Q8—861no—
592D4—861no—
593D4—861no—
594D4—861no—
595D4—861no—
596D4—3441no—
597D4—1722no—
598D4—1721no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306329611yescharacteristic
620C2×C4#1306329611yescharacteristic
621C2×C4#1306329611yescharacteristic
622C2×C4#1306329611yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C22×C22⋊D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4C2×#1062190211yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337311yescharacteristic
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—862no—
634C8—1721no—
635C8—1721no—
636C8—1721no—
637C8—1721no—
638C8—1721no—
639C22—21no—
640C22—21no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22—1721no—
646C22—1721no—
647C22C2×#1306329611yescharacteristic
648C22#1458343511yescharacteristic
649C22#1458352211yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—1721no—
659C4—1721no—
660C4#1458353711yescharacteristic
661C4#1458354011yescharacteristic
662C4#1458355111yescharacteristic
663C4#1458356011yescharacteristic
664C2—21no—
665C2—21no—
666C2—3441no—
667C2—3441no—
668C2#1913816811yescharacteristic
669C2#1914431111yescharacteristic
670C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenterC2×#479D43
hypocenterC43#25363
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #19136041C2semidirect
5. #19136036C2semidirect
6. #19135895C2semidirect
7. #19135895C2semidirect
8. #19135589C2semidirect
9. #19135371C2semidirect
10. #19135113C2semidirect
11. #19135113C2semidirect
12. #19134660C2semidirect
13. #19134655C2semidirect
14. C4×#13063244C2semidirect
15. C2×C43×#479C2semidirect
330. C2×#479D43semidirect
402. C43#25363semidirect

Maximal subgroups

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

subgroupindex
#191449982
#191440672
#191433382
#191360412
#191360362
#191358952
#191355892
#191353712
#191351132
#191346602
#191346552
C4×#130632442
C2×C43×#4792
#2536343