Finite Group Databasebeta

← #25103487

Subgroups — #25103487

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×#14583173C211yesmaximal, characteristic
2#19143413C211yesmaximal, characteristic
3#19143410C211yesmaximal, characteristic
4C2×#14582991C211yesmaximal, characteristic, complemented
5#19143017C211yesmaximal, characteristic
6#19135509C211yesmaximal, characteristic, complemented
7#19135377C211yesmaximal, characteristic, complemented
8#19135250C211yesmaximal, characteristic, complemented
9#19135113C211yesmaximal, characteristic
10#19135109C211yesmaximal, characteristic
11#19134658C211yesmaximal, characteristic
12#19134496C211yesmaximal, characteristic, complemented
13#101×Dic43C211yesmaximal, characteristic, complemented
14#19134390C211yesmaximal, characteristic, complemented
15C43×#1930C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063356C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21#14583367C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24#14583173C418yescomplemented
25#14583005—21no—
26#14583003—21no—
27#14583002—21no—
28#14582998—21no—
29#14582993—21no—
30#14582991—21no—
31#14582991—21no—
32#14582991—21no—
33#14582991—21no—
34#14582991—21no—
35#14582986—21no—
36#14582984—21no—
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582942C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41#14582907C2211yescharacteristic
42#14582901C2211yescharacteristic
43#14582898C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45C2×#13063244C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063243C2211yescharacteristic
48#14582856—21no—
49#14582855C2211yescharacteristic
50#14582853—21no—
51#14582851—21no—
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55C2×C8×Dic43C2211yescharacteristic
56C4×C8×D43—21no—
57#14582668C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582664C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#419C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#101×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70#13063358—22no—
71#13063358C2×C414yes—
72#13063356—22no—
73#13063356C2×C414yes—
74C2×Dic172—21no—
75C2×#10621885—21no—
76C2×#10621885—21no—
77C2×#10621885—21no—
78C2×#10621885—22no—
79C2×#10621885C2×C414yescomplemented
80C2×#10621873—21no—
81C2×#10621884—21no—
82#13063333—22no—
83#13063333C2×C414yes—
84#13063331—22no—
85#13063331—22no—
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—21no—
93C2×C8×D43—21no—
94Q8×Dic43—21no—
95Q8×Dic43—21no—
96Q8×Dic43—21no—
97Q8×Dic43—21no—
98#13063290—21no—
99#13063290—21no—
100#13063290—21no—
101#13063290—21no—
102#13063290D411yescharacteristic
103#13063290D411yescharacteristic
104#13063287D411yescharacteristic
105#13063287D411yescharacteristic
106(C22⋊D43)⋊C4—21no—
107(C22⋊D43)⋊C4—21no—
108#13063282—21no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43C2311yescharacteristic
115C42×D43—21no—
116#13063260—22no—
117#13063260C2×C414yescomplemented
118#13063258—21no—
119#13063258—21no—
120#13063258—21no—
121#13063256—21no—
122#13063250—21no—
123#13063250—21no—
124#13063250—21no—
125#13063248—21no—
126#13063248—21no—
127#13063248—21no—
128#13063247—21no—
129#13063245—21no—
130#13063244—22no—
131#13063243—22no—
132#13063243C2×C414yescomplemented
133#13063236—21no—
134#13063235—21no—
135#13063235—21no—
136#13063235—21no—
137C4×C43⋊C8—21no—
138C8×Dic43—21no—
139C8×Dic43—21no—
140C8×Dic43—21no—
141C8×Dic43D411yescharacteristic
142C8×Dic43D411yescharacteristic
143C8×Dic43D411yescharacteristic
144C8×Dic43D411yescharacteristic
145C22×Q8×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152#107×C43—21no—
153#106×C43—21no—
154#103×C43—21no—
155#103×C43—21no—
156#103×C43—21no—
157#103×C43—21no—
158#101×C43C2×C414yescomplemented
159#97×C43—21no—
160C4×C8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43C2411yescharacteristic
170C2×C22⋊D43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43#4111yescharacteristic
174C22×Dic43#4111yescharacteristic
175#10621898—21no—
176#10621898—21no—
177#10621898C22×C412yes—
178#10621898#4112yes—
179C2×D172C2×D411yescharacteristic
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86C22×C412yes—
189C2×Dic86C2×D411yescharacteristic
190M16×C43—21no—
191M16×C43—21no—
192M16×C43—21no—
193M16×C43—21no—
194M16×C43C22×C412yes—
195M16×C43C22×C412yes—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C2×D411yescharacteristic
202C2×C8×C43C2×D411yescharacteristic
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C22⋊C4×C43—21no—
208C42×C43—21no—
209#10621885—24no—
210#10621885—24no—
211#10621885—24no—
212#10621884—24no—
213(C2×D43)⋊C4—21no—
214(C2×D43)⋊C4—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—41no—
218C4⋊Dic43—41no—
219Dic43⋊C4—21no—
220Dic43⋊C4—21no—
221Dic43⋊C4—41no—
222Dic43⋊C4—41no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—41no—
226C4×Dic43—41no—
227C4×Dic43—41no—
228C4×Dic43—41no—
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233#10621877—21no—
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877C22×C412yes—
238#10621877#4112yes—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C22×C412yes—
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8#4112yes—
246Dic172—24no—
247#10621873—24no—
248#10621872—24no—
249#10621872—24no—
250C8×D43—24no—
251C8×D43—24no—
252C23×C43C2×#4111yescharacteristic
253C22×D43—21no—
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43—41no—
257Q8×C43—41no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—81no—
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C22⋊D43—22no—
272C22⋊D43—22no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—81no—
281C2×Dic43#12111yescharacteristic
282C2×Dic43#12111yescharacteristic
283C2×Dic43#12111yescharacteristic
284C2×Dic43#12111yescharacteristic
285D172—21no—
286D172C4×D412yes—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—42no—
290C4×D43—42no—
291Dic86—21no—
292Dic86—22no—
293Dic86—22no—
294Dic86—41no—
295Dic86—41no—
296Dic86C4×D412yes—
297C8×C43—22no—
298C8×C43—22no—
299C8×C43—21no—
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×C43C4×#4111yescharacteristic
311C22×C43C2×#12111yescharacteristic
312C22×C43#52911yescharacteristic
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43C2×C4×D411yescharacteristic
321C4×C43C2×C4×D411yescharacteristic
322C4×C43#52511yescharacteristic
323C4×C43#53211yescharacteristic
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—22no—
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#1930D4311yescharacteristic, complemented
340#1908—431no—
341#1908—431no—
342#1816—431no—
343C4×#108—431no—
344C4×#101—431no—
345C4×#101—431no—
346C2×C43—21no—
347C2×C43—21no—
348C2×C43C4×#12111yescharacteristic
349C2×C43C2×#47311yescharacteristic
350C2×C43#306711yescharacteristic
351D43—42no—
352C2×#137—431no—
353C2×#137—431no—
354C22×Q16—431no—
355C2×#131—431no—
356C2×#131—431no—
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#428C2×D4311yescharacteristic
377C2×#107—431no—
378#419—431no—
379#419C2×D4311yescharacteristic
380#417—431no—
381#417—431no—
382C2×#103—431no—
383C2×#103C2×D4311yescharacteristic
384C2×#101—431no—
385C2×#101—431no—
386C2×#101—431no—
387C2×#101C2×D4311yescharacteristic
388#405—431no—
389#405—861no—
390#405—861no—
391#405C2×D4311yescharacteristic
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×#41—431no—
406C22×Q8—431no—
407C22×Q8C22×D4311yescharacteristic
408#137—434no—
409#137—434no—
410#137—862no—
411#137—862no—
412C2×Q16—434no—
413C2×Q16—861no—
414C2×Q16—862no—
415C2×Q16—861no—
416C2×Q16—861no—
417C2×Q16—861no—
418C2×SD16—861no—
419C2×SD16—861no—
420#131—434no—
421#131—862no—
422#131—862no—
423#131—862no—
424C2×M16—431no—
425C2×M16—431no—
426C2×M16—431no—
427C2×M16—861no—
428C2×M16—861no—
429C2×M16C22×D4311yescharacteristic
430C2×M16C22×D4311yescharacteristic
431C2×M16C22×D4311yescharacteristic
432C22×C8—431no—
433C22×C8—861no—
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—861no—
451#117C22×D4311yescharacteristic
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—21no—
463#107—861no—
464#107—861no—
465#107—861no—
466#106—21no—
467#106—861no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—21no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#103—861no—
477#103—861no—
478#102—861no—
479#102—861no—
480#101—434no—
481#101—862no—
482#101—862no—
483#101C4×D4314yescomplemented
484#97—21no—
485#97—861no—
486#97—861no—
487#97—861no—
488#97—861no—
489C4×C8—21no—
490C4×C8—431no—
491C4×C8—431no—
492C4×C8—431no—
493C4×C8—431no—
494C4×C8—861no—
495C4×C8—861no—
496C4×C8—861no—
497C4×C8—861no—
498#41—432no—
499#41—432no—
500#41—861no—
501#41—861no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—432no—
508C2×Q8—431no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8C2×C4×D4312yes—
515C2×D4—431no—
516C2×D4—861no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4C23×D4311yescharacteristic
527Q16—864no—
528Q16—864no—
529Q16—864no—
530Q16—864no—
531SD16—864no—
532SD16—864no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—432no—
538M16—432no—
539M16—864no—
540M16—864no—
541M16—861no—
542M16—861no—
543M16—861no—
544M16—861no—
545M16C2×C4×D4312yes—
546M16C2×C4×D4312yes—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—432no—
553C2×C8—431no—
554C2×C8—431no—
555C2×C8—432no—
556C2×C8—864no—
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—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—1721no—
570C4⋊C4—1721no—
571C4⋊C4—1721no—
572C4⋊C4—1721no—
573C4⋊C4D4×D4311yescharacteristic
574C4⋊C4D4×D4311yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—861no—
577C22⋊C4—861no—
578C42—21no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—431no—
583C42—861no—
584C42—861no—
585C42—1721no—
586C42—1721no—
587C42—1721no—
588C42—1721no—
589C23—861no—
590C23#41×D4311yescharacteristic
591Q8—22no—
592Q8—22no—
593Q8—41no—
594Q8—41no—
595Q8—432no—
596Q8—861no—
597Q8—862no—
598Q8—862no—
599Q8—1721no—
600Q8—1721no—
601D4—432no—
602D4—862no—
603D4—862no—
604D4—861no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—81no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—862no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—3441no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1721no—
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×C4#41×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C8—22no—
635C8—22no—
636C8—21no—
637C8—21no—
638C8—41no—
639C8—432no—
640C8—432no—
641C8—862no—
642C8—862no—
643C8—1721no—
644C22—21no—
645C22—21no—
646C22—862no—
647C22—1721no—
648C22—1721no—
649C22#1458336711yescharacteristic
650C22#121×D4311yescharacteristic
651C22#1458343211yescharacteristic
652C4—42no—
653C4—41no—
654C4—41no—
655C4—81no—
656C4—432no—
657C4—862no—
658C4—861no—
659C4—861no—
660C4—861no—
661C4—3441no—
662C4—1722no—
663C4C4×D4×D4311yescharacteristic
664C4C4×D4×D4311yescharacteristic
665C4#1458340711yescharacteristic
666C4#1458344811yescharacteristic
667C2—21no—
668C2—21no—
669C2—1722no—
670C2#1913710711yescharacteristic
671C2#473×D4311yescharacteristic
672C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1930C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1930D43
hypocenterC43C4×#473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1930

Complements

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

NH ≅ G/Ntype
4. C2×#14582991C2semidirect
6. #19135509C2semidirect
7. #19135377C2semidirect
8. #19135250C2semidirect
12. #19134496C2semidirect
13. #101×Dic43C2semidirect
14. #19134390C2semidirect
15. C43×#1930C2semidirect
24. #14583173C4semidirect
79. C2×#10621885C2×C4semidirect
117. #13063260C2×C4semidirect
132. #13063243C2×C4semidirect
158. #101×C43C2×C4semidirect
330. Dic43#473semidirect
339. #1930D43semidirect
404. C43C4×#473semidirect
483. #101C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831732
#191434132
#191434102
C2×#145829912
#191430172
#191355092
#191353772
#191352502
#191351132
#191351092
#191346582
#191344962
#101×Dic432
#191343902
C43×#19302
C4×#47343