Finite Group Databasebeta

← #25147014

Subgroups — #25147014

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144995C211yesmaximal, characteristic, complemented
2C2×#14583200C211yesmaximal, characteristic, complemented
3#19144055C211yesmaximal, characteristic
4#19136040C211yesmaximal, characteristic, complemented
5#19136035C211yesmaximal, characteristic, complemented
6#19135886C211yesmaximal, characteristic, complemented
7#19135886C211yesmaximal, characteristic, complemented
8#19135588C211yesmaximal, characteristic, complemented
9#19135371C211yesmaximal, characteristic, complemented
10#19135103C211yesmaximal, characteristic, complemented
11#19135103C211yesmaximal, characteristic, complemented
12#19134659C211yesmaximal, characteristic, complemented
13#19134654C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C43×#2935C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063350C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583267—21no—
21#14583263—21no—
22#14583253—21no—
23#14583253—21no—
24#14583200—21no—
25#14583200—21no—
26#14583200—21no—
27#14583200—21no—
28#14583111—21no—
29#14583111—21no—
30#14583101—21no—
31#14583091—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063261C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582900C2211yescharacteristic
38#14582900C2211yescharacteristic
39#14582900C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42#14582900C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063241C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582667C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#131×C43C2211yescharacteristic
57C2×#131×C43C2211yescharacteristic
58C43×#532C2211yescharacteristic
59C43×#436—21no—
60C43×#435—21no—
61C43×#435—21no—
62C8×D4×C43—21no—
63C2×C4⋊C8×C43C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69#13063350—22no—
70#13063350—22no—
71#13063350—41no—
72#13063350—41no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81#13063317—21no—
82#13063317—21no—
83#13063317—21no—
84#13063317—21no—
85C4×D172—21no—
86C4×D172—21no—
87C4×D172—21no—
88C4×D172—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95#13063261—41no—
96#13063261—41no—
97#13063259—21no—
98#13063259—21no—
99#13063257—21no—
100#13063257—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063247—21no—
110#13063247—21no—
111#13063247—21no—
112#13063247—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063241—22no—
120#13063241—22no—
121#13063236—21no—
122C4×C43⋊C8—21no—
123C2×#41×C43C2311yescharacteristic
124C2×#41×C43C2311yescharacteristic
125#131×C43—22no—
126#131×C43—22no—
127#131×C43—41no—
128#131×C43—41no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C22×C8×C43—21no—
134C22×C8×C43—21no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C4⋊Q8×C43D411yescharacteristic
138#127×C43D411yescharacteristic
139#124×C43D411yescharacteristic
140#124×C43D411yescharacteristic
141#121×C43—21no—
142#121×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150C22⋊C8×C43—21no—
151C22⋊C8×C43—21no—
152C22⋊C8×C43—21no—
153C22⋊C8×C43—21no—
154#97×C43—21no—
155C4×C8×C43—21no—
156C23×D43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43—21no—
161#41×C43—21no—
162#41×C43—21no—
163#41×C43—21no—
164#41×C43—21no—
165C2×Q8×C43C2×D411yescharacteristic
166C2×Q8×C43C2×D411yescharacteristic
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43C2×D411yescharacteristic
172C2×D4×C43C2×D411yescharacteristic
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43#4111yescharacteristic
176C22×C4×C43#4111yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172#4112yes—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—82no—
190M16×C43—21no—
191M16×C43—21no—
192M16×C43—21no—
193M16×C43—42no—
194M16×C43—42no—
195M16×C43#4112yes—
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—42no—
203C2×C8×C43—42no—
204C2×C8×C43C2×D411yescharacteristic
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C2×C8×C43C2×D411yescharacteristic
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43C2×D411yescharacteristic
217C42×C43C2×D411yescharacteristic
218#10621884—42no—
219#10621884—42no—
220#10621882—42no—
221#10621882—42no—
222(C2×D43)⋊C4—41no—
223(C2×D43)⋊C4—41no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230Dic43⋊C4—41no—
231Dic43⋊C4—41no—
232Dic43⋊C4—41no—
233Dic43⋊C4—41no—
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877—21no—
238#10621877—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43C2×#4111yescharacteristic
249C22×D43—22no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—81no—
253C22×D43—81no—
254Q8×C43—21no—
255Q8×C43—21no—
256Q8×C43—21no—
257Q8×C43—21no—
258D4×C43—21no—
259D4×C43—21no—
260D4×C43—21no—
261D4×C43—21no—
262D4×C43—42no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—81no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—81no—
290C2×Dic43—81no—
291C2×Dic43—81no—
292D172—22no—
293D172—22no—
294D172—41no—
295D172—41no—
296C4×D43—82no—
297C4×D43—82no—
298C8×C43—21no—
299C8×C43—21no—
300C8×C43—21no—
301C8×C43—21no—
302C8×C43—22no—
303C8×C43—41no—
304C43⋊C8—41no—
305C43⋊C8—41no—
306C43⋊C8—41no—
307C43⋊C8—41no—
308#25362—431nomaximal, Sylow
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43C2×#12111yescharacteristic
318C22×C43#52911yescharacteristic
319C22×C43#54211yescharacteristic
320C2×D43—42no—
321C2×D43—82no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—82no—
325C4×C43—21no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43#54611yescharacteristic
332C4×C43#54611yescharacteristic
333C4×C43#54711yescharacteristic
334C4×C43#54811yescharacteristic
335Dic43—81no—
336Dic43—81no—
337Dic43—81no—
338#3142—431no—
339C2×#478—431no—
340#3036—431no—
341#2935D4311yescharacteristic, complemented
342#2079—431no—
343#2078—431no—
344#2051—431no—
345#2051—431no—
346#1998—431no—
347#1950—431no—
348#1907—431no—
349#1907—431no—
350#1816—431no—
351#1815—431no—
352C4×#100—431no—
353C2×C43—21no—
354C2×C43—21no—
355C2×C43—81no—
356C2×C43—81no—
357C2×C43#242711yescharacteristic
358C2×C43#306711yescharacteristic
359C2×C43#306811yescharacteristic
360D43—82no—
361C2×AGL(1,ℤ/8)—431no—
362C2×AGL(1,ℤ/8)—431no—
363C2×#131C2×D4311yescharacteristic
364C2×#131C2×D4311yescharacteristic
365#532C2×D4311yescharacteristic
366C2×#125—431no—
367C2×C4×D4—431no—
368#491—861no—
369#490—861no—
370#488—861no—
371#488—861no—
372#478—861no—
373#478—861no—
374#478—861no—
375#478—861no—
376#463—861no—
377#463—861no—
378#461—861no—
379#459—861no—
380#436—21no—
381#435—21no—
382#435—21no—
383C8×D4—21no—
384C2×#108—431no—
385C2×#108—431no—
386C2×#107—431no—
387C2×#106—431no—
388#423—431no—
389C2×C4⋊C8C2×D4311yescharacteristic
390#417—431no—
391#417—431no—
392#417—431no—
393#417—431no—
394#417—431no—
395#417—431no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#100—431no—
399C2×#100—431no—
400#408C2×D4311yescharacteristic
401#408C2×D4311yescharacteristic
402C4×M16—431no—
403C4×M16C2×D4311yescharacteristic
404#343—431no—
405#343—431no—
406#343—431no—
407#343—431no—
408#343—431no—
409#343—431no—
410#341—431no—
411#341—431no—
412C43#2536211yescharacteristic, complemented, Sylow
413C2×#41C22×D4311yescharacteristic
414C2×#41C22×D4311yescharacteristic
415C22×D4—431no—
416C23×C4—861no—
417AGL(1,ℤ/8)—862no—
418AGL(1,ℤ/8)—862no—
419AGL(1,ℤ/8)—1721no—
420AGL(1,ℤ/8)—1721no—
421C2×SD16—861no—
422C2×SD16—861no—
423C2×D8—861no—
424C2×D8—861no—
425#131—22no—
426#131—22no—
427#131—41no—
428#131—41no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—431no—
432C2×M16—431no—
433C2×M16—431no—
434C2×M16—431no—
435C2×M16C22×D4311yescharacteristic
436C2×M16C22×D4311yescharacteristic
437C22×C8—21no—
438C22×C8—21no—
439C22×C8C22×D4311yescharacteristic
440C22×C8C22×D4311yescharacteristic
441C4⋊Q8D17211yescharacteristic
442#127D17211yescharacteristic
443#125—861no—
444#125—861no—
445#125—861no—
446#125—861no—
447#124D17211yescharacteristic
448#124D17211yescharacteristic
449#121—21no—
450#121—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—861no—
454C4×D4—861no—
455C4×D4—861no—
456C4×D4—861no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C42C22×D4311yescharacteristic
464#108—1721no—
465#108—1721no—
466#107—861no—
467#107—861no—
468#106—861no—
469#106—861no—
470C4⋊C8—861no—
471C4⋊C8—861no—
472C4⋊C8C22⋊D4311yescharacteristic
473C4⋊C8C22⋊D4311yescharacteristic
474C4⋊C8C22⋊D4311yescharacteristic
475C4⋊C8C22⋊D4311yescharacteristic
476#103—861no—
477#103—861no—
478#103—861no—
479#103—861no—
480#103—861no—
481#103—861no—
482#102—861no—
483#102—861no—
484#102—861no—
485#102—861no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#102—861no—
491#102—861no—
492#100—862no—
493#100—862no—
494C22⋊C8—21no—
495C22⋊C8—21no—
496C22⋊C8—21no—
497C22⋊C8—21no—
498#97—21no—
499#97—861no—
500C4×C8—21no—
501C4×C8—861no—
502C24—861no—
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—21no—
511C2×Q8C2×D17211yescharacteristic
512C2×Q8C2×D17211yescharacteristic
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—432no—
518C2×D4—861no—
519C2×D4—861no—
520C2×D4—861no—
521C2×D4—861no—
522C2×D4—861no—
523C2×D4C2×D17211yescharacteristic
524C2×D4C2×D17211yescharacteristic
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—3442no—
531C22×C4—1721no—
532C22×C4—1721no—
533C22×C4#1062189811yescharacteristic
534C22×C4#1062189811yescharacteristic
535C22×C4C23×D4311yescharacteristic
536SD16—1722no—
537SD16—1722no—
538D8—1722no—
539D8—1722no—
540M16—21no—
541M16—21no—
542M16—21no—
543M16—42no—
544M16—42no—
545M16—861no—
546M16—861no—
547M16—861no—
548M16—861no—
549M16—861no—
550M16—861no—
551M16—861no—
552M16—861no—
553M16#1062190012yes—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8C2×C22⋊D4311yescharacteristic
567C2×C8C2×C22⋊D4311yescharacteristic
568C2×C8C2×C22⋊D4311yescharacteristic
569C2×C8C2×C22⋊D4311yescharacteristic
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—1721no—
579C4⋊C4—1721no—
580C4⋊C4—1721no—
581C4⋊C4—1721no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—21no—
586C22⋊C4—1721no—
587C22⋊C4—1721no—
588C42C2×D17211yescharacteristic
589C42C2×D17211yescharacteristic
590C42C2×C22⋊D4311yescharacteristic
591C42C2×C22⋊D4311yescharacteristic
592C23—21no—
593C23—21no—
594C23—862no—
595C23—3441no—
596C23—3441no—
597C23—1721no—
598C23—1721no—
599C23C2×#1062189811yescharacteristic
600Q8—21no—
601Q8—21no—
602Q8—21no—
603Q8—21no—
604D4—21no—
605D4—21no—
606D4—21no—
607D4—21no—
608D4—42no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—81no—
614D4—862no—
615D4—862no—
616D4—1721no—
617D4—1721no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—3442no—
627C2×C4—3442no—
628C2×C4—3441no—
629C2×C4—3441no—
630C2×C4—3441no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4#1306329911yescharacteristic
635C2×C4#1306329911yescharacteristic
636C2×C4#1306329911yescharacteristic
637C2×C4#1306329911yescharacteristic
638C2×C4C22×C22⋊D4311yescharacteristic
639C2×C4C22×D17211yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4C2×#1062190011yescharacteristic
642C2×C4#1306337011yescharacteristic
643C2×C4#1306337211yescharacteristic
644C8—21no—
645C8—21no—
646C8—21no—
647C8—21no—
648C8—22no—
649C8—41no—
650C8—1721no—
651C8—1721no—
652C8—1721no—
653C8—1721no—
654C22—21no—
655C22—21no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—3442no—
663C22—3442no—
664C22—3441no—
665C22—3441no—
666C22—1722no—
667C22C2×#1306329911yescharacteristic
668C22#1458343111yescharacteristic
669C22#1458351411yescharacteristic
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4—41no—
675C4—41no—
676C4—3441no—
677C4—3441no—
678C4—3441no—
679C4#1458354311yescharacteristic
680C4#1458354411yescharacteristic
681C4#1458355311yescharacteristic
682C4#1458355611yescharacteristic
683C2—21no—
684C2—21no—
685C2—81no—
686C2—81no—
687C2—3442no—
688C2#1913816611yescharacteristic
689C2#1914431511yescharacteristic
690C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2935C2
socleC22×C43C2×#121
prime radical#19144055C2
hypercenter#2935D43
hypocenterC43#25362
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #19144995C2semidirect
2. C2×#14583200C2semidirect
4. #19136040C2semidirect
5. #19136035C2semidirect
6. #19135886C2semidirect
7. #19135886C2semidirect
8. #19135588C2semidirect
9. #19135371C2semidirect
10. #19135103C2semidirect
11. #19135103C2semidirect
12. #19134659C2semidirect
13. #19134654C2semidirect
14. C4×#13063241C2semidirect
15. C43×#2935C2semidirect
341. #2935D43semidirect
412. C43#25362semidirect

Maximal subgroups

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

subgroupindex
#191449952
C2×#145832002
#191440552
#191360402
#191360352
#191358862
#191355882
#191353712
#191351032
#191346592
#191346542
C4×#130632412
C43×#29352
#2536243