Finite Group Databasebeta

← #25147026

Subgroups — #25147026

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
1C2×#14583196C211yesmaximal, characteristic, complemented
2#19144055C211yesmaximal, characteristic
3#19143339C211yesmaximal, characteristic, complemented
4#19136043C211yesmaximal, characteristic, complemented
5#19136038C211yesmaximal, characteristic, complemented
6#19135885C211yesmaximal, characteristic, complemented
7#19135885C211yesmaximal, characteristic, complemented
8#19135589C211yesmaximal, characteristic, complemented
9#19135370C211yesmaximal, characteristic, complemented
10#19135101C211yesmaximal, characteristic, complemented
11#19135101C211yesmaximal, characteristic, complemented
12#19134657C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C43×#3142C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063350C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583196—21no—
22#14583196—21no—
23#14583196—21no—
24#14583196—21no—
25#14583111—21no—
26#14583111—21no—
27#14583101—21no—
28#14583091—21no—
29#14582977—21no—
30#14582971—21no—
31#14582971—21no—
32D4×C43⋊C8—21no—
33C2×#13063260C2211yescharacteristic
34C2×#13063260C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37#14582923C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39#14582900C2211yescharacteristic
40#14582900C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063241C2211yescharacteristic
44C2×#13063241C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582866C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C2×#125×C43C2211yescharacteristic
58C43×#491—21no—
59C43×#490—21no—
60C43×#488—21no—
61C43×#488—21no—
62C43×#417C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#417C2211yescharacteristic
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—
77#13063332—22no—
78#13063332—22no—
79#13063332—41no—
80#13063332—41no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C22×C43⋊C8—21no—
88C22×C43⋊C8—21no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C4×D172—21no—
92C4×D172—21no—
93C4×D172—21no—
94C4×D172—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×(C2×D43)⋊C4—21no—
97#13063260—41no—
98#13063260—41no—
99#13063258—21no—
100#13063258—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)D411yescharacteristic
106C4⋊(C43⋊C8)D411yescharacteristic
107C4⋊(C43⋊C8)D411yescharacteristic
108C4⋊(C43⋊C8)D411yescharacteristic
109#13063249—21no—
110#13063249—21no—
111#13063246—21no—
112#13063246—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117#13063241—22no—
118#13063241—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125C2×#41×C43C2311yescharacteristic
126C2×#41×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C4⋊Q8×C43D411yescharacteristic
130#127×C43D411yescharacteristic
131#125×C43—21no—
132#125×C43—21no—
133#125×C43—21no—
134#125×C43—21no—
135#124×C43D411yescharacteristic
136#124×C43D411yescharacteristic
137#121×C43—21no—
138#121×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×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—21no—
176C22×C4×C43—21no—
177C22×C4×C43#4111yescharacteristic
178C22×C4×C43#4111yescharacteristic
179C22×C4×C43C2411yescharacteristic
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—21no—
194C2×C8×C43—21no—
195C2×C8×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—21no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C42×C43C2×D411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214#10621884—42no—
215#10621884—42no—
216#10621882—42no—
217#10621882—42no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—42no—
230#10621877—42no—
231#10621877#4112yes—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—42no—
241C2×C43⋊C8—42no—
242C2×C43⋊C8C2×D411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
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—41no—
277C2×C4×C43—41no—
278C2×C4×C43—81no—
279C2×C4×C43—81no—
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43#12111yescharacteristic
283C2×C4×C43#12111yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C2×C4×C432−1+411yescharacteristic
290C2×Dic43—41no—
291C2×Dic43—81no—
292D172—22no—
293D172—22no—
294D172—41no—
295D172—41no—
296C4×D43—82no—
297C4×D43—82no—
298C8×C43—41no—
299C8×C43—41no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—21no—
304C43⋊C8—22no—
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—81no—
332C4×C43—81no—
333C4×C43#54611yescharacteristic
334C4×C43#54611yescharacteristic
335C4×C43#54711yescharacteristic
336C4×C43#54811yescharacteristic
337Dic43—81no—
338#3142D4311yescharacteristic, complemented
339C2×#478—431no—
340#3036—431no—
341#2935—431no—
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×#131—431no—
364C2×#131—431no—
365#532C2×D4311yescharacteristic
366C2×#125C2×D4311yescharacteristic
367C2×C4×D4—431no—
368#491—21no—
369#490—21no—
370#488—21no—
371#488—21no—
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—861no—
381#435—861no—
382#435—861no—
383C8×D4—861no—
384C2×#108—431no—
385C2×#108—431no—
386C2×#107—431no—
387C2×#106—431no—
388#423—431no—
389C2×C4⋊C8—431no—
390#417—431no—
391#417—431no—
392#417C2×D4311yescharacteristic
393#417C2×D4311yescharacteristic
394#417C2×D4311yescharacteristic
395#417C2×D4311yescharacteristic
396C2×#102—431no—
397C2×#102—431no—
398C2×#100—431no—
399C2×#100—431no—
400#408—431no—
401#408—431no—
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—862no—
426#131—862no—
427#131—1721no—
428#131—1721no—
429C2×M16—431no—
430C2×M16—431no—
431C2×M16—431no—
432C2×M16—431no—
433C2×M16—861no—
434C2×M16—861no—
435C2×M16C22×D4311yescharacteristic
436C2×M16C22×D4311yescharacteristic
437C22×C8—431no—
438C22×C8—431no—
439C22×C8—861no—
440C22×C8—861no—
441C4⋊Q8C22⋊D4311yescharacteristic
442#127C22⋊D4311yescharacteristic
443#125—21no—
444#125—21no—
445#125—21no—
446#125—21no—
447#124C22⋊D4311yescharacteristic
448#124C22⋊D4311yescharacteristic
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—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
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—431no—
471C4⋊C8—431no—
472C4⋊C8—431no—
473C4⋊C8—431no—
474C4⋊C8—861no—
475C4⋊C8—861no—
476#103—21no—
477#103—21no—
478#103—21no—
479#103—21no—
480#103—861no—
481#103—861no—
482#102—21no—
483#102—21no—
484#102—21no—
485#102—21no—
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—861no—
495C22⋊C8—861no—
496C22⋊C8—861no—
497C22⋊C8—861no—
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×C22⋊D4311yescharacteristic
512C2×Q8C2×C22⋊D4311yescharacteristic
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×C22⋊D4311yescharacteristic
524C2×D4C2×C22⋊D4311yescharacteristic
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—861no—
530C22×C4—3442no—
531C22×C4—1721no—
532C22×C4—1721no—
533C22×C4#1062190011yescharacteristic
534C22×C4#1062190011yescharacteristic
535C22×C4C23×D4311yescharacteristic
536SD16—1722no—
537SD16—1722no—
538D8—1722no—
539D8—1722no—
540M16—21no—
541M16—21no—
542M16—21no—
543M16—21no—
544M16—432no—
545M16—861no—
546M16—861no—
547M16—861no—
548M16—861no—
549M16—861no—
550M16—861no—
551M16—861no—
552M16—1722no—
553M16—1722no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—431no—
557C2×C8—431no—
558C2×C8—431no—
559C2×C8—431no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—1722no—
569C2×C8—1722no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—21no—
586C22⋊C4—1721no—
587C22⋊C4—1721no—
588C42D4×D4311yescharacteristic
589C42D4×D4311yescharacteristic
590C42C2×C22⋊D4311yescharacteristic
591C42C2×C22⋊D4311yescharacteristic
592C23—21no—
593C23—21no—
594C23—862no—
595C23—3441no—
596C23—3441no—
597C23—1721no—
598C23—1721no—
599C23C2×#1062190011yescharacteristic
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—41no—
627C2×C4—41no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—3442no—
631C2×C4—3442no—
632C2×C4—3441no—
633C2×C4—1721no—
634C2×C4#1306329711yescharacteristic
635C2×C4#1306329711yescharacteristic
636C2×C4#1306329711yescharacteristic
637C2×C4#1306329711yescharacteristic
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4C22×C22⋊D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4#1306337111yescharacteristic
643C2×C4#1306337211yescharacteristic
644C8—41no—
645C8—41no—
646C8—861no—
647C8—861no—
648C8—861no—
649C8—861no—
650C8—862no—
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×#1306329711yescharacteristic
668C22#1458342811yescharacteristic
669C22#1458351811yescharacteristic
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4—41no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—3441no—
679C4#1458353711yescharacteristic
680C4#1458354211yescharacteristic
681C4#1458354811yescharacteristic
682C4#1458355711yescharacteristic
683C2—21no—
684C2—21no—
685C2—81no—
686C2—81no—
687C2—3442no—
688C2#1913817511yescharacteristic
689C2#1914431211yescharacteristic
690C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3142C2
socleC22×C43C2×#121
prime radical#19144055C2
hypercenter#3142D43
hypocenterC43#25362
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
3. #19143339C2semidirect
4. #19136043C2semidirect
5. #19136038C2semidirect
6. #19135885C2semidirect
7. #19135885C2semidirect
8. #19135589C2semidirect
9. #19135370C2semidirect
10. #19135101C2semidirect
11. #19135101C2semidirect
12. #19134657C2semidirect
13. #19134652C2semidirect
14. C4×#13063241C2semidirect
15. C43×#3142C2semidirect
338. #3142D43semidirect
412. C43#25362semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
#191440552
#191433392
#191360432
#191360382
#191358852
#191355892
#191353702
#191351012
#191346572
#191346522
C4×#130632412
C43×#31422
#2536243