Finite Group Databasebeta

← #25103465

Subgroups — #25103465

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583159C211yesmaximal, characteristic
2#19143410C211yesmaximal, characteristic, complemented
3#19143399C211yesmaximal, characteristic
4C2×SD16×Dic43C211yesmaximal, characteristic, complemented
5#19143017C211yesmaximal, characteristic, complemented
6#19135375C211yesmaximal, characteristic, complemented
7#19135260C211yesmaximal, characteristic, complemented
8#19135253C211yesmaximal, characteristic, complemented
9#19135107C211yesmaximal, characteristic, complemented
10#19135100C211yesmaximal, characteristic
11#19134651C211yesmaximal, characteristic, complemented
12#108×Dic43C211yesmaximal, characteristic, complemented
13#101×Dic43C211yesmaximal, characteristic, complemented
14#100×Dic43C211yesmaximal, characteristic, complemented
15C43×#1977C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20#14583367C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583159C418yescomplemented
24#14583008—21no—
25#14583003—21no—
26#14583002—21no—
27#14582996—21no—
28#14582991—21no—
29#14582990—21no—
30SD16×Dic43—21no—
31SD16×Dic43—21no—
32SD16×Dic43—21no—
33SD16×Dic43—21no—
34#14582984—21no—
35#14582979—21no—
36C2×#13063261C2211yescharacteristic
37#14582942C2211yescharacteristic
38#14582942C2211yescharacteristic
39C2×#13063257C2211yescharacteristic
40#14582901C2211yescharacteristic
41#14582901C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063242C2211yescharacteristic
46#14582856—21no—
47#14582855C2211yescharacteristic
48#14582853—21no—
49#14582851—21no—
50M16×Dic43C2211yescharacteristic
51M16×Dic43C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53C2×C8×Dic43C2211yescharacteristic
54C4×C8×D43—21no—
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582663C2211yescharacteristic
61C22×SD16×C43C2211yescharacteristic
62C2×#108×C43C2211yescharacteristic
63C43×#419C2211yescharacteristic
64C43×#418C2211yescharacteristic
65C2×#101×C43C2211yescharacteristic
66C2×#100×C43C2211yescharacteristic
67C43×#405C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C23×Dic43—21no—
70#13063356—22no—
71#13063356C2×C414yescomplemented
72#13063351—22no—
73#13063351C2×C414yes—
74C2×#10621885—21no—
75C2×#10621883—21no—
76C2×#10621884—21no—
77C2×#10621882—21no—
78#13063333—22no—
79#13063333—22no—
80#13063331—22no—
81#13063331C2×C414yescomplemented
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—21no—
87C22×C43⋊C8C2311yescharacteristic
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90Q8×Dic43—21no—
91Q8×Dic43—21no—
92Q8×Dic43—21no—
93Q8×Dic43—21no—
94#13063290D411yescharacteristic
95#13063290D411yescharacteristic
96D4×Dic43—21no—
97D4×Dic43—21no—
98D4×Dic43—21no—
99D4×Dic43—21no—
100#13063287D411yescharacteristic
101#13063287D411yescharacteristic
102(C22⋊D43)⋊C4—21no—
103(C22⋊D43)⋊C4—21no—
104#13063282—21no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C22⋊Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C42×D43—21no—
112#13063261C2×C414yescomplemented
113#13063258—21no—
114#13063258—21no—
115#13063257—21no—
116#13063257—21no—
117#13063256—21no—
118#13063256—21no—
119#13063250—21no—
120#13063250—21no—
121#13063249—21no—
122#13063249—21no—
123#13063247—21no—
124#13063247—21no—
125#13063246—21no—
126#13063246—21no—
127#13063244C2×C414yescomplemented
128#13063242C2×C414yescomplemented
129#13063236—21no—
130#13063235—21no—
131#13063235—21no—
132#13063235—21no—
133C4×C43⋊C8—21no—
134C8×Dic43—21no—
135C8×Dic43—21no—
136C8×Dic43—21no—
137C8×Dic43D411yescharacteristic
138C8×Dic43D411yescharacteristic
139C8×Dic43D411yescharacteristic
140C8×Dic43D411yescharacteristic
141C22×Q8×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143C2×SD16×C43—21no—
144C2×SD16×C43—21no—
145C2×SD16×C43—22no—
146C2×SD16×C43C2×C414yescomplemented
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C2×M16×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151#117×C43C2311yescharacteristic
152#108×C43—22no—
153#103×C43—21no—
154#103×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#101×C43—22no—
158#100×C43—22no—
159#97×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C22×C412yes—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43C22×C412yes—
174C22×C4×C43—21no—
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—41no—
180C22×Dic43—41no—
181C22×Dic43—82no—
182C22×Dic43#4111yescharacteristic
183C22×Dic43#4111yescharacteristic
184#10621898—21no—
185#10621898—21no—
186#10621898C22×C412yes—
187#10621898#4112yes—
188C2×D172C2×D411yescharacteristic
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×Dic86C2×D411yescharacteristic
193SD16×C43—24no—
194SD16×C43—24no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43—21no—
198M16×C43—21no—
199M16×C43—21no—
200M16×C43#4112yes—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43C22×C412yes—
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C2×C8×C43#4112yes—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—21no—
211C42×C43—21no—
212C22⋊Dic43—41no—
213C22⋊Dic43—41no—
214#10621885—24no—
215#10621884—24no—
216#10621883—24no—
217#10621882—24no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—41no—
225C4⋊Dic43—41no—
226Dic43⋊C4—21no—
227Dic43⋊C4—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—41no—
231C4×Dic43—41no—
232C4×Dic43C2×D411yescharacteristic
233C4×Dic43C2×D411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236#10621877—21no—
237#10621877—21no—
238#10621877—21no—
239#10621877C22×C412yes—
240#10621877C22×C412yes—
241#10621877C22×C412yes—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C2×D411yescharacteristic
248C2×C43⋊C8C2×D411yescharacteristic
249#10621872—24no—
250#10621872—24no—
251C8×D43—24no—
252C8×D43—24no—
253C23×C43—22no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—81no—
257C23×C43—81no—
258C23×C43C2×#4111yescharacteristic
259C22×D43—21no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43C23×C411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C22⋊D43—22no—
280C22⋊D43—22no—
281C2×Dic43—21no—
282C2×Dic43—22no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—82no—
287C2×Dic43—82no—
288C2×Dic43—81no—
289C2×Dic43—81no—
290C2×Dic43#12111yescharacteristic
291C2×Dic43#12111yescharacteristic
292C2×Dic43#12111yescharacteristic
293C2×Dic43#12111yescharacteristic
294D172—21no—
295D172C4×D412yes—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—42no—
299C4×D43—42no—
300Dic86—21no—
301Dic86C4×D412yes—
302C8×C43—22no—
303C8×C43—41no—
304C8×C43—41no—
305C8×C43C4×D412yes—
306C8×C43C4×D412yes—
307C43⋊C8—22no—
308C43⋊C8—22no—
309C43⋊C8—22no—
310C43⋊C8—21no—
311C43⋊C8—21no—
312C4×#471—431nomaximal, Sylow
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—42no—
316C22×C43—82no—
317C22×C43—82no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C4×#4111yescharacteristic
321C22×C43C2×#12111yescharacteristic
322C22×C43#52911yescharacteristic
323C2×D43—22no—
324C2×D43—41no—
325C2×D43—41no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—42no—
329C4×C43C2×C4×D411yescharacteristic
330C4×C43C2×C4×D411yescharacteristic
331C4×C43#52511yescharacteristic
332C4×C43#53211yescharacteristic
333Dic43—21no—
334Dic43—21no—
335Dic43—21no—
336Dic43—22no—
337Dic43—81no—
338Dic43—81no—
339Dic43#47112yescomplemented
340C2×#471—431no—
341C4×#137—431no—
342C4×AGL(1,ℤ/8)—431no—
343C2×C4×SD16—431no—
344C4×#131—431no—
345#1977D4311yescharacteristic, complemented
346#1951—431no—
347#1931—431no—
348#1930—431no—
349#1908—431no—
350#1907—431no—
351#1815—431no—
352C4×#108—431no—
353C4×#101—431no—
354C4×#100—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—82no—
358C2×C43C4×#12111yescharacteristic
359C2×C43C2×#47111yescharacteristic
360C2×C43#306711yescharacteristic
361D43—42no—
362C2×#137—431no—
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16C2×D4311yescharacteristic
365C2×#131—431no—
366C2×#131—431no—
367C4×#41—431no—
368C2×C4×Q8—431no—
369C2×C4×D4—431no—
370#471—438no—
371#442—861no—
372#441—861no—
373#440—861no—
374#440—861no—
375C4×Q16—861no—
376C4×SD16—861no—
377C4×SD16—861no—
378C4×SD16—861no—
379C4×SD16—861no—
380C4×SD16—861no—
381C4×SD16—861no—
382C4×D8—861no—
383C2×#108—431no—
384C2×#108C2×D4311yescharacteristic
385#428—431no—
386#428—431no—
387C2×#106—431no—
388#419C2×D4311yescharacteristic
389#418C2×D4311yescharacteristic
390#417—431no—
391#417—431no—
392C2×#103—431no—
393C2×#102—431no—
394C2×#101—431no—
395C2×#101C2×D4311yescharacteristic
396C2×#100—431no—
397C2×#100C2×D4311yescharacteristic
398#405—431no—
399#405—861no—
400#405—861no—
401#405C2×D4311yescharacteristic
402C4×M16—431no—
403C4×M16—431no—
404C4×M16—431no—
405C4×M16—861no—
406C2×C4×C8—431no—
407C2×C4×C8—861no—
408#343—431no—
409#343—431no—
410#343—431no—
411#343—431no—
412#341—431no—
413#341—431no—
414C43C4×#47111yescharacteristic, complemented, Sylow
415C2×#41—431no—
416C22×Q8C22×D4311yescharacteristic
417C22×D4C22×D4311yescharacteristic
418C23×C4—861no—
419#137—434no—
420#137—862no—
421AGL(1,ℤ/8)—434no—
422AGL(1,ℤ/8)—862no—
423C2×Q16—861no—
424C2×SD16—21no—
425C2×SD16—21no—
426C2×SD16—22no—
427C2×SD16—861no—
428C2×SD16—861no—
429C2×SD16C4×D4314yescomplemented
430C2×D8—861no—
431#131—434no—
432#131—862no—
433#131—862no—
434#131—862no—
435C2×M16—431no—
436C2×M16—431no—
437C2×M16—431no—
438C2×M16—861no—
439C2×M16—861no—
440C2×M16C22×D4311yescharacteristic
441C2×M16C22×D4311yescharacteristic
442C2×M16C22×D4311yescharacteristic
443C22×C8—431no—
444C22×C8—861no—
445C22×C8—861no—
446C22×C8C22×D4311yescharacteristic
447C4×Q8—431no—
448C4×Q8—431no—
449C4×Q8—861no—
450C4×Q8—861no—
451C4×Q8—861no—
452C4×Q8—861no—
453C4×D4—431no—
454C4×D4—431no—
455C4×D4—861no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4—861no—
459C4×D4—861no—
460C4×D4—861no—
461#117—861no—
462#117C22×D4311yescharacteristic
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C42—431no—
468C2×C42—861no—
469C2×C42—861no—
470#108—22no—
471#108—434no—
472#107—861no—
473#107—861no—
474#106—861no—
475#106—861no—
476#106—861no—
477#106—861no—
478#103—21no—
479#103—21no—
480#103—861no—
481#103—861no—
482#103—861no—
483#103—861no—
484#102—21no—
485#102—21no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#101—22no—
491#101—434no—
492#100—22no—
493#100—434no—
494#97—21no—
495#97—861no—
496#97—861no—
497#97—861no—
498#97—861no—
499C4×C8—21no—
500C4×C8—431no—
501C4×C8—431no—
502C4×C8—431no—
503C4×C8—431no—
504C4×C8—861no—
505C4×C8—861no—
506C4×C8—861no—
507C4×C8—861no—
508C24—21no—
509#41—432no—
510#41—432no—
511#41—861no—
512#41—861no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—431no—
519C2×Q8C2×C4×D4312yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—431no—
526C2×D4—861no—
527C2×D4C2×C4×D4312yes—
528C22×C4—21no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—3442no—
537C22×C4—1721no—
538C22×C4—1721no—
539C22×C4C23×D4311yescharacteristic
540Q16—864no—
541SD16—24no—
542SD16—24no—
543SD16—864no—
544SD16—864no—
545D8—864no—
546M16—21no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—432no—
552M16—432no—
553M16—432no—
554M16—864no—
555M16—861no—
556M16—861no—
557M16—861no—
558M16—864no—
559M16#1062190012yes—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—431no—
564C2×C8—431no—
565C2×C8—864no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—864no—
572C2×C8C2×C4×D4312yes—
573C2×C8D4×D4311yescharacteristic
574C2×C8D4×D4311yescharacteristic
575C2×C8#1062190012yes—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—1721no—
583C4⋊C4—1721no—
584C4⋊C4D4×D4311yescharacteristic
585C4⋊C4D4×D4311yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—861no—
588C22⋊C4—861no—
589C22⋊C4—1721no—
590C22⋊C4—1721no—
591C42—21no—
592C42—431no—
593C42—431no—
594C42—431no—
595C42—431no—
596C42—861no—
597C42—861no—
598C42—1721no—
599C42—1721no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—81no—
604C23—81no—
605C23—861no—
606C23#41×D4311yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—432no—
612Q8—861no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—432no—
618D4—862no—
619D4—862no—
620D4—861no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—431no—
627C2×C4—431no—
628C2×C4—431no—
629C2×C4—431no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—3442no—
635C2×C4—3442no—
636C2×C4—3441no—
637C2×C4—3441no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4C22×C4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4C2×#1062190011yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—862no—
653C8—862no—
654C8—862no—
655C8—861no—
656C8—861no—
657C8(C22⋊D43)⋊C412yes—
658C8(C22⋊D43)⋊C412yes—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—82no—
663C22—82no—
664C22—81no—
665C22—81no—
666C22—862no—
667C22—1721no—
668C22—1721no—
669C22C4×#1062190011yescharacteristic
670C22#121×D4311yescharacteristic
671C22#1458342811yescharacteristic
672C4—42no—
673C4—41no—
674C4—41no—
675C4—432no—
676C4—862no—
677C4—861no—
678C4—861no—
679C4—861no—
680C4—3441no—
681C4—3441no—
682C4C4×D4×D4311yescharacteristic
683C4C2×(C22⋊D43)⋊C411yescharacteristic
684C4#1458340911yescharacteristic
685C4#1458344711yescharacteristic
686C2—21no—
687C2—21no—
688C2—82no—
689C2—1722no—
690C2#1913711111yescharacteristic
691C2#471×D4311yescharacteristic
692C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1977C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
cosocleC22×C4×C43C24
hypercenter#1977D43
hypocenterC43C4×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1977

Complements

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

NH ≅ G/Ntype
2. #19143410C2semidirect
4. C2×SD16×Dic43C2semidirect
5. #19143017C2semidirect
6. #19135375C2semidirect
7. #19135260C2semidirect
8. #19135253C2semidirect
9. #19135107C2semidirect
11. #19134651C2semidirect
12. #108×Dic43C2semidirect
13. #101×Dic43C2semidirect
14. #100×Dic43C2semidirect
15. C43×#1977C2semidirect
23. #14583159C4semidirect
71. #13063356C2×C4semidirect
81. #13063331C2×C4semidirect
112. #13063261C2×C4semidirect
127. #13063244C2×C4semidirect
128. #13063242C2×C4semidirect
146. C2×SD16×C43C2×C4semidirect
339. Dic43#471semidirect
345. #1977D43semidirect
414. C43C4×#471semidirect
429. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831592
#191434102
#191433992
C2×SD16×Dic432
#191430172
#191353752
#191352602
#191352532
#191351072
#191351002
#191346512
#108×Dic432
#101×Dic432
#100×Dic432
C43×#19772
C4×#47143