Finite Group Databasebeta

← #25103485

Subgroups — #25103485

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583172C211yesmaximal, characteristic
2#19143419C211yesmaximal, characteristic
3#137×Dic43C211yesmaximal, characteristic
4C2×#14582991C211yesmaximal, characteristic, complemented
5#131×Dic43C211yesmaximal, characteristic
6#19135507C211yesmaximal, characteristic, complemented
7#19135379C211yesmaximal, characteristic, complemented
8#19135251C211yesmaximal, characteristic, complemented
9#19135247C211yesmaximal, characteristic, complemented
10#19135110C211yesmaximal, characteristic
11#19134657C211yesmaximal, characteristic
12#19134496C211yesmaximal, characteristic, complemented
13#101×Dic43C211yesmaximal, characteristic, complemented
14#19134390C211yesmaximal, characteristic, complemented
15C43×#1908C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#41×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22#14583172C418yescomplemented
23#14583006—21no—
24#14583003—21no—
25#14583000—21no—
26#14582996—21no—
27Q16×Dic43—21no—
28#14582991—21no—
29#14582991—21no—
30#14582991—21no—
31#14582991—21no—
32#14582991—21no—
33#14582990—21no—
34SD16×Dic43—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39C2×#13063258C2211yescharacteristic
40#14582909C2211yescharacteristic
41#14582908C2211yescharacteristic
42#14582900C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47#14582857—21no—
48#14582857C2211yescharacteristic
49#14582854—21no—
50#14582854C2211yescharacteristic
51M16×Dic43—21no—
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55C2×C8×Dic43—21no—
56C2×C8×Dic43C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582664C2211yescharacteristic
61C2×#137×C43C2211yescharacteristic
62C2×#131×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C2×#103×C43C2211yescharacteristic
65C2×#101×C43C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C22×Dic86C2311yescharacteristic
69#13063355—22no—
70#13063355C2×C414yes—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621885—21no—
74C2×#10621885—22no—
75C2×#10621885C2×C414yescomplemented
76C2×#10621883—21no—
77#13063332—22no—
78#13063332C2×C414yes—
79C2×#10621877—21no—
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C22×C43⋊C8—21no—
84C22×C43⋊C8C2311yescharacteristic
85Q8×Dic43—21no—
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88Q8×Dic43—21no—
89Q8×Dic43D411yescharacteristic
90Q8×Dic43D411yescharacteristic
91#13063290—21no—
92#13063290—21no—
93#13063290—21no—
94#13063290—21no—
95D4×Dic43—21no—
96D4×Dic43—21no—
97D4×Dic43D411yescharacteristic
98D4×Dic43D411yescharacteristic
99#13063284—21no—
100#13063284C2311yescharacteristic
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108#13063260—22no—
109#13063260C2×C414yescomplemented
110#13063259—21no—
111#13063258—21no—
112#13063258—21no—
113#13063258—21no—
114#13063257—21no—
115#13063256—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063249—21no—
121#13063249—21no—
122#13063249—21no—
123#13063246—21no—
124#13063244C2×C414yescomplemented
125#13063243—22no—
126#13063243C2×C414yescomplemented
127#13063235—21no—
128#13063235—21no—
129#13063235—21no—
130#13063235—21no—
131#13063235—21no—
132C8×Dic43—21no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C8×Dic43—21no—
136C8×Dic43—21no—
137C8×Dic43D411yescharacteristic
138C8×Dic43D411yescharacteristic
139C8×Dic43D411yescharacteristic
140C8×Dic43D411yescharacteristic
141C2×#41×C43C2311yescharacteristic
142C22×Q8×C43C2311yescharacteristic
143#137×C43—22no—
144#137×C43C2×C414yes—
145C2×Q16×C43—21no—
146C2×SD16×C43—21no—
147#131×C43—22no—
148#131×C43—22no—
149C2×M16×C43—21no—
150C2×M16×C43C2311yescharacteristic
151C2×M16×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C22×C8×C43—21no—
154C22×C8×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156#103×C43—21no—
157#103×C43—21no—
158#103×C43—21no—
159#102×C43—21no—
160#101×C43—22no—
161#41×C43—21no—
162#41×C43—21no—
163#41×C43C22×C412yes—
164#41×C43#4112yes—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×D4×C43—21no—
173C2×D4×C43C2×D411yescharacteristic
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43#4111yescharacteristic
183C22×Dic43#4111yescharacteristic
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190Q16×C43—24no—
191SD16×C43—24no—
192M16×C43—24no—
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43C22×C412yes—
198M16×C43#4112yes—
199C2×C8×C43—24no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊Dic43—21no—
210C22⋊Dic43—21no—
211C22⋊Dic43—21no—
212#10621885—24no—
213#10621885—24no—
214#10621885—24no—
215#10621883—24no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—41no—
221C4⋊Dic43—41no—
222C4⋊Dic43C2×D411yescharacteristic
223C4⋊Dic43C2×D411yescharacteristic
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—41no—
230C4×Dic43—41no—
231C4×Dic43—41no—
232C4×Dic43—41no—
233C4×Dic43C2×D411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237#10621877—21no—
238#10621877—21no—
239#10621877—24no—
240#10621877—21no—
241#10621877—21no—
242#10621877C22×C412yes—
243#10621877C22×C412yes—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—24no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8C22×C412yes—
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251C2×C43⋊C8#4112yes—
252C23×C43—21no—
253C23×C43C2×#4111yescharacteristic
254Q8×C43—21no—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43C4×D412yes—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—21no—
263D4×C43C4×D412yes—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—81no—
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—42no—
287C2×Dic43—41no—
288C2×Dic43—81no—
289C2×Dic43#12111yescharacteristic
290C2×Dic43#12111yescharacteristic
291C2×Dic43#12111yescharacteristic
292C2×Dic43#12111yescharacteristic
293Dic86—22no—
294Dic86—22no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—22no—
298C8×C43—21no—
299C8×C43—22no—
300C8×C43—21no—
301C8×C43—41no—
302C43⋊C8—22no—
303C43⋊C8—22no—
304C43⋊C8—41no—
305C43⋊C8C4×D412yes—
306C43⋊C8C4×D412yes—
307C4×#473—431nomaximal, Sylow
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—22no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43C4×#4111yescharacteristic
314C22×C43C2×#12111yescharacteristic
315C22×C43#52911yescharacteristic
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43C2×C4×D411yescharacteristic
320C4×C43C2×C4×D411yescharacteristic
321C4×C43#52511yescharacteristic
322C4×C43#53211yescharacteristic
323Dic43—21no—
324Dic43—21no—
325Dic43—21no—
326Dic43—41no—
327Dic43—41no—
328Dic43—42no—
329Dic43—81no—
330Dic43#47312yescomplemented
331C2×#473—431no—
332C4×#137—431no—
333C4×#137—431no—
334C2×C4×Q16—431no—
335C4×#131—431no—
336#1979—431no—
337#1952—431no—
338#1930—431no—
339#1930—431no—
340#1908—431no—
341#1908D4311yescharacteristic
342#1816—431no—
343C4×#108—431no—
344C4×#101—431no—
345C4×#101—431no—
346C2×C43—21no—
347C2×C43—21no—
348C2×C43—42no—
349C2×C43C4×#12111yescharacteristic
350C2×C43C2×#47311yescharacteristic
351C2×C43#306711yescharacteristic
352C2×#137—431no—
353C2×#137C2×D4311yescharacteristic
354C22×Q16—431no—
355C2×#131—431no—
356C2×#131C2×D4311yescharacteristic
357C4×#41—431no—
358C2×C4×Q8—431no—
359C2×C4×Q8—431no—
360#473—438no—
361#441—861no—
362#441—861no—
363#440—861no—
364#440—861no—
365C4×Q16—861no—
366C4×Q16—861no—
367C4×Q16—861no—
368C4×Q16—861no—
369C4×Q16—861no—
370C4×Q16—861no—
371C4×SD16—861no—
372C4×SD16—861no—
373C2×#108—431no—
374C2×#108—431no—
375#428—431no—
376#428—431no—
377C2×#107—431no—
378#419—431no—
379#419—431no—
380#417—431no—
381#417C2×D4311yescharacteristic
382C2×#103—431no—
383C2×#103C2×D4311yescharacteristic
384C2×#101—431no—
385C2×#101—431no—
386C2×#101—431no—
387C2×#101C2×D4311yescharacteristic
388#405—431no—
389#405—431no—
390#405—861no—
391#405—861no—
392C4×M16—431no—
393C4×M16—431no—
394C4×M16—431no—
395C4×M16—861no—
396C2×C4×C8—431no—
397C2×C4×C8—861no—
398#343—431no—
399#343—431no—
400#343—431no—
401#343C2×D4311yescharacteristic
402#341—431no—
403#341C2×D4311yescharacteristic
404C43C4×#47311yescharacteristic, complemented, Sylow
405C2×#41C22×D4311yescharacteristic
406C22×Q8—431no—
407C22×Q8C22×D4311yescharacteristic
408#137—22no—
409#137—434no—
410#137—862no—
411#137C4×D4314yes—
412C2×Q16—21no—
413C2×Q16—434no—
414C2×Q16—862no—
415C2×Q16—861no—
416C2×Q16—861no—
417C2×Q16—861no—
418C2×SD16—21no—
419C2×SD16—861no—
420#131—22no—
421#131—22no—
422#131—434no—
423#131—862no—
424C2×M16—21no—
425C2×M16—431no—
426C2×M16—431no—
427C2×M16—431no—
428C2×M16—861no—
429C2×M16C22×D4311yescharacteristic
430C2×M16C22×D4311yescharacteristic
431C2×M16C22×D4311yescharacteristic
432C22×C8—21no—
433C22×C8—431no—
434C22×C8—861no—
435C22×C8C22×D4311yescharacteristic
436C4×Q8—431no—
437C4×Q8—431no—
438C4×Q8—861no—
439C4×Q8—861no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×Q8—861no—
445C4×Q8—861no—
446C4×D4—431no—
447C4×D4—431no—
448C4×D4—861no—
449C4×D4—861no—
450#117—431no—
451#117—861no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C42—431no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42—861no—
460#108—434no—
461#108—862no—
462#107—861no—
463#107—861no—
464#107—861no—
465#107—861no—
466#106—861no—
467#106—861no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#103—861no—
477#103—861no—
478#102—21no—
479#102—861no—
480#101—22no—
481#101—434no—
482#101—434no—
483#101—862no—
484#97—861no—
485#97—861no—
486#97—861no—
487#97—861no—
488#97—861no—
489C4×C8—431no—
490C4×C8—431no—
491C4×C8—431no—
492C4×C8—431no—
493C4×C8—861no—
494C4×C8—861no—
495C4×C8—861no—
496C4×C8—861no—
497C4×C8—861no—
498#41—21no—
499#41—21no—
500#41C2×C4×D4312yes—
501#41#1062190012yes—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—432no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8C2×C4×D4312yes—
514C2×Q8D4×D4311yescharacteristic
515C2×D4—21no—
516C2×D4D4×D4311yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4C23×D4311yescharacteristic
527Q16—24no—
528Q16—864no—
529Q16—864no—
530Q16—864no—
531SD16—24no—
532SD16—864no—
533M16—24no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—432no—
539M16—432no—
540M16—864no—
541M16—861no—
542M16—861no—
543M16—861no—
544M16—861no—
545M16C2×C4×D4312yes—
546M16#1062190012yes—
547C2×C8—24no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—432no—
554C2×C8—431no—
555C2×C8—431no—
556C2×C8—432no—
557C2×C8—864no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8D4×D4311yescharacteristic
562C2×C8D4×D4311yescharacteristic
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—431no—
566C4⋊C4—431no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—1721no—
572C4⋊C4—1721no—
573C4⋊C4—1721no—
574C4⋊C4—1721no—
575C22⋊C4—861no—
576C22⋊C4—861no—
577C22⋊C4—861no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—1721no—
586C42—1721no—
587C42—1721no—
588C42—1721no—
589C23—21no—
590C23#41×D4311yescharacteristic
591Q8—21no—
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—862no—
597Q8—862no—
598Q8—1721no—
599Q8—1721no—
600Q8(C22⋊D43)⋊C412yes—
601D4—22no—
602D4—22no—
603D4—21no—
604D4(C22⋊D43)⋊C412yes—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—81no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—431no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—3441no—
622C2×C4—1722no—
623C2×C4—1721no—
624C2×C4—1722no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4C22×C4×D4311yescharacteristic
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4C2×#1062190011yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C8—22no—
635C8—21no—
636C8—22no—
637C8—21no—
638C8—41no—
639C8—432no—
640C8—432no—
641C8—862no—
642C8—862no—
643C8—1721no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22C4×#1062190011yescharacteristic
650C22#121×D4311yescharacteristic
651C22#1458342611yescharacteristic
652C4—22no—
653C4—42no—
654C4—81no—
655C4—432no—
656C4—861no—
657C4—861no—
658C4—861no—
659C4—3441no—
660C4—1722no—
661C4—1721no—
662C4—1721no—
663C4C4×D4×D4311yescharacteristic
664C4C2×(C22⋊D43)⋊C411yescharacteristic
665C4#1458340511yescharacteristic
666C4#1458344411yescharacteristic
667C2—21no—
668C2—21no—
669C2—42no—
670C2#1913710511yescharacteristic
671C2#473×D4311yescharacteristic
672C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1908C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1908D43
hypocenterC43C4×#473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1908

Complements

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

NH ≅ G/Ntype
4. C2×#14582991C2semidirect
6. #19135507C2semidirect
7. #19135379C2semidirect
8. #19135251C2semidirect
9. #19135247C2semidirect
12. #19134496C2semidirect
13. #101×Dic43C2semidirect
14. #19134390C2semidirect
22. #14583172C4semidirect
75. C2×#10621885C2×C4semidirect
109. #13063260C2×C4semidirect
124. #13063244C2×C4semidirect
126. #13063243C2×C4semidirect
330. Dic43#473semidirect
404. C43C4×#473semidirect

Maximal subgroups

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

subgroupindex
C2×#145831722
#191434192
#137×Dic432
C2×#145829912
#131×Dic432
#191355072
#191353792
#191352512
#191352472
#191351102
#191346572
#191344962
#101×Dic432
#191343902
C43×#19082
C4×#47343