Finite Group Databasebeta

← #25115105

Subgroups — #25115105

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143479C211yesmaximal, characteristic
2#19143471C211yesmaximal, characteristic
3#19143195C211yesmaximal, characteristic, complemented
4#19143190C211yesmaximal, characteristic, complemented
5#19135381C211yesmaximal, characteristic, complemented
6#19135376C211yesmaximal, characteristic, complemented
7#19134830C211yesmaximal, characteristic, complemented
8#19134830C211yesmaximal, characteristic, complemented
9#19134823C211yesmaximal, characteristic, complemented
10#19134823C211yesmaximal, characteristic, complemented
11#19134763C211yesmaximal, characteristic, complemented
12#19134659C211yesmaximal, characteristic, complemented
13#19134654C211yesmaximal, characteristic, complemented
14#19134479C211yesmaximal, characteristic, complemented
15C2×C43×#444C211yesmaximal, characteristic
16#14583382C2211yescharacteristic
17#14583382C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583011—21no—
21#14583006—21no—
22#14583000—21no—
23#14583000—21no—
24Q16×Dic43—21no—
25SD16×Dic43—21no—
26SD16×Dic43—21no—
27D8×Dic43—21no—
28C2×#13063261C2211yescharacteristic
29#14582941—21no—
30#14582941—21no—
31#14582941—21no—
32#14582941—21no—
33#14582941C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582937—21no—
38#14582937—21no—
39#14582937C2211yescharacteristic
40C2×#13063259—21no—
41C2×#13063259C2211yescharacteristic
42C2×#13063259C2211yescharacteristic
43C2×#13063257—21no—
44C2×#13063257C2211yescharacteristic
45C2×#13063257C2211yescharacteristic
46#14582900C2211yescharacteristic
47#14582900C2211yescharacteristic
48#14582900C2211yescharacteristic
49#14582900C2211yescharacteristic
50#14582854C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582769C2211yescharacteristic
53#14582765C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C2×#135×C43C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic
62C2×#131×C43C2211yescharacteristic
63C43×#444C418yescomplemented
64C2×#108×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#97×C43C2211yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70Q8×Dic43—21no—
71Q8×Dic43—21no—
72Q8×Dic43—21no—
73Q8×Dic43—21no—
74D4×Dic43—21no—
75D4×Dic43—21no—
76D4×Dic43—21no—
77D4×Dic43—21no—
78D4×Dic43—41no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81D4×Dic43—41no—
82#13063284—21no—
83#13063284—21no—
84#13063284—21no—
85#13063284—21no—
86#13063284C2311yescharacteristic
87#13063284C2311yescharacteristic
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97#13063261—22no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063259—21no—
106#13063259D411yescharacteristic
107#13063259D411yescharacteristic
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257—21no—
113#13063257—21no—
114#13063257—21no—
115#13063257—21no—
116#13063257D411yescharacteristic
117#13063257D411yescharacteristic
118#13063249—21no—
119#13063249—21no—
120#13063249—21no—
121#13063249—21no—
122#13063246—21no—
123#13063246—21no—
124#13063246—21no—
125#13063246—21no—
126#13063235—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C43⋊#95—41no—
131C2×#41×C43C2311yescharacteristic
132C2×#41×C43C2311yescharacteristic
133#135×C43C2×C414yes—
134#135×C43Q814yes—
135C2×Q16×C43D411yescharacteristic
136C2×SD16×C43D411yescharacteristic
137C2×SD16×C43D411yescharacteristic
138C2×D8×C43D411yescharacteristic
139#131×C43—22no—
140#131×C43—22no—
141#131×C43C2×C414yescomplemented
142#131×C43C2×C414yescomplemented
143C2×M16×C43—21no—
144C2×M16×C43—21no—
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C22×C8×C43—21no—
148C22×C8×C43—21no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
152#108×C43C2×C414yescomplemented
153#104×C43C2×C414yescomplemented
154#104×C43C2×C414yescomplemented
155#97×C43C2×C414yescomplemented
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43C22×C412yes—
161#41×C43C22×C412yes—
162#41×C43C2×Q812yes—
163#41×C43C2×Q812yes—
164C2×Q8×C43C2×D411yescharacteristic
165C2×Q8×C43C2×D411yescharacteristic
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C2×D411yescharacteristic
169C2×D4×C43C2×D411yescharacteristic
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—41no—
179C22×Dic43—41no—
180C22×Dic43—41no—
181C22×Dic43—41no—
182Q16×C43C4⋊C414yescomplemented
183SD16×C43C4⋊C414yescomplemented
184SD16×C43C4⋊C414yescomplemented
185D8×C43C4⋊C414yescomplemented
186M16×C43—21no—
187M16×C43—21no—
188M16×C43—24no—
189M16×C43—24no—
190M16×C43C22×C412yes—
191M16×C43C22×C412yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—24no—
195C2×C8×C43—24no—
196C2×C8×C43C22×C412yes—
197C2×C8×C43C22×C412yes—
198C2×C8×C43C2×D411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C2×C8×C43C2×D411yescharacteristic
201C2×C8×C43C2×D411yescharacteristic
202C2×C8×C43C2×Q812yes—
203C2×C8×C43#4112yes—
204C42×C43—21no—
205C42×C43C22×C412yes—
206C22⋊Dic43—21no—
207C22⋊Dic43—21no—
208C22⋊Dic43—41no—
209C22⋊Dic43—41no—
210C22⋊Dic43—41no—
211C22⋊Dic43—41no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—41no—
221C4⋊Dic43—41no—
222C4⋊Dic43—41no—
223C4⋊Dic43—41no—
224C4⋊Dic43—82no—
225C4⋊Dic43C2×D411yescharacteristic
226C4⋊Dic43C2×D411yescharacteristic
227C4⋊Dic43C2×D411yescharacteristic
228C4⋊Dic43C2×D411yescharacteristic
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—41no—
232C4×Dic43—41no—
233C4×Dic43—41no—
234C4×Dic43—41no—
235#10621877—21no—
236#10621877—21no—
237#10621877—21no—
238#10621877—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43H(5,𝔽2)11yescharacteristic
244Q8×C43—21no—
245Q8×C43—21no—
246Q8×C43C2×C4⋊C412yes—
247Q8×C43C2×C4⋊C412yes—
248D4×C43—22no—
249D4×C43—22no—
250D4×C43—22no—
251D4×C43—22no—
252D4×C43—21no—
253D4×C43—21no—
254D4×C43C2×C4⋊C412yes—
255D4×C43C2×C4⋊C412yes—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×Q811yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—81no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43—81no—
283C2×Dic43—161no—
284C2×Dic43—161no—
285C2×Dic43—161no—
286C2×Dic43—161no—
287C8×C43—22no—
288C8×C43—22no—
289C8×C43C2×C4⋊C412yes—
290C8×C43C2×C4⋊C412yes—
291C8×C43C4×D412yes—
292C8×C43C4×D412yes—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#22693—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43#52011yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#55411yescharacteristic
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—42no—
310C4×C43C22×C4⋊C411yescharacteristic
311C4×C43C2×C4×D411yescharacteristic
312C4×C43#54711yescharacteristic
313C4×C43D4×Q811yescharacteristic
314Dic43—41no—
315Dic43—41no—
316Dic43—41no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322C2×#444D4311yescharacteristic
323#2952—431no—
324#2951—431no—
325#2913—431no—
326#2912—431no—
327#1952—431no—
328#1951—431no—
329#1860—431no—
330#1860—431no—
331#1859—431no—
332#1859—431no—
333#1847—431no—
334#1816—431no—
335#1815—431no—
336#1773—431no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—42no—
340C2×C43—42no—
341C2×C43D4×C4⋊C411yescharacteristic
342C2×C43#328811yescharacteristic
343C2×C43#328911yescharacteristic
344C2×#135C2×D4311yescharacteristic
345C2×#131C2×D4311yescharacteristic
346C2×#131C2×D4311yescharacteristic
347#520—431no—
348#520—431no—
349#520—431no—
350#520—431no—
351#444Dic4318yescomplemented
352#442—861no—
353#441—861no—
354#440—861no—
355#440—861no—
356C4×Q16—861no—
357C4×SD16—861no—
358C4×SD16—861no—
359C4×D8—861no—
360C2×#108—431no—
361C2×#108C2×D4311yescharacteristic
362#428—431no—
363#428—431no—
364#428—431no—
365#428—431no—
366#428—861no—
367#428—861no—
368#428—861no—
369#428—861no—
370#427—431no—
371#427—861no—
372#427—861no—
373C2×#107—431no—
374C2×#107—431no—
375C2×#107—861no—
376C2×#106—431no—
377C2×#106—431no—
378C2×#106—861no—
379C2×#104C2×D4311yescharacteristic
380C2×#104C2×D4311yescharacteristic
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#405—431no—
386#405—431no—
387C2×#97C2×D4311yescharacteristic
388#384—431no—
389#382—431no—
390#343—431no—
391#343—431no—
392#343—431no—
393#343—431no—
394#339—431no—
395#339—431no—
396C43#2269311yescharacteristic, complemented, Sylow
397C2×#41C22×D4311yescharacteristic
398C2×#41C22×D4311yescharacteristic
399#135Dic8614yes—
400#135C2×Dic4314yes—
401C2×Q16D17211yescharacteristic
402C2×SD16D17211yescharacteristic
403C2×SD16D17211yescharacteristic
404C2×D8D17211yescharacteristic
405#131—22no—
406#131—22no—
407#131C2×Dic4314yescomplemented
408#131C2×Dic4314yescomplemented
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—431no—
412C2×M16—431no—
413C2×M16C22×D4311yescharacteristic
414C2×M16C22×D4311yescharacteristic
415C22×C8—21no—
416C22×C8—21no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—1721no—
428C4×D4—1721no—
429C4×D4—1721no—
430C4×D4—1721no—
431#117—431no—
432#117—431no—
433#117—861no—
434#117—861no—
435#117—861no—
436#117—861no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1721no—
446C2×C42C22×D4311yescharacteristic
447#108—862no—
448#108C2×Dic4314yescomplemented
449#107—431no—
450#107—431no—
451#107—861no—
452#107—861no—
453#107—861no—
454#107—861no—
455#107—861no—
456#107—861no—
457#107—861no—
458#107—861no—
459#106—431no—
460#106—431no—
461#106—861no—
462#106—861no—
463#106—861no—
464#106—861no—
465#106—861no—
466#106—861no—
467#106—861no—
468#106—861no—
469#104C2×Dic4314yescomplemented
470#104C2×Dic4314yescomplemented
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#97—861no—
480#97—861no—
481#97C2×Dic4314yescomplemented
482C4×C8—861no—
483C4×C8—861no—
484#95—1721no—
485#41—21no—
486#41—21no—
487#41—21no—
488#41—21no—
489#41C2×Dic8612yes—
490#41C2×Dic8612yes—
491#41C22×Dic4312yes—
492#41C22×Dic4312yes—
493C2×Q8C2×D17211yescharacteristic
494C2×Q8C2×D17211yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4C2×D17211yescharacteristic
498C2×D4C2×D17211yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4C23×D4311yescharacteristic
511Q16C4⋊Dic4314yescomplemented
512SD16C4⋊Dic4314yescomplemented
513SD16C4⋊Dic4314yescomplemented
514D8C4⋊Dic4314yescomplemented
515M16—21no—
516M16—21no—
517M16—24no—
518M16—24no—
519M16—861no—
520M16—861no—
521M16—861no—
522M16—861no—
523M16C22×Dic4312yes—
524M16C22×Dic4312yes—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8C2×Dic8612yes—
532C2×C8C2×D17211yescharacteristic
533C2×C8C2×D17211yescharacteristic
534C2×C8D4×D4311yescharacteristic
535C2×C8D4×D4311yescharacteristic
536C2×C8#1062190012yes—
537C2×C8C22×Dic4312yes—
538C2×C8C22×Dic4312yes—
539C4⋊C4—431no—
540C4⋊C4—431no—
541C4⋊C4—431no—
542C4⋊C4—431no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—3442no—
552C4⋊C4—1721no—
553C4⋊C4—1721no—
554C4⋊C4—1721no—
555C4⋊C4—1721no—
556C22⋊C4—861no—
557C22⋊C4—861no—
558C22⋊C4—1721no—
559C22⋊C4—1721no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—21no—
563C42—861no—
564C42—861no—
565C42—1721no—
566C42—1721no—
567C42—1721no—
568C42—1721no—
569C42C22×Dic4312yes—
570C23—21no—
571C23—21no—
572C23#1306337111yescharacteristic
573Q8—21no—
574Q8—21no—
575Q8C2×C4⋊Dic4312yes—
576Q8C2×C4⋊Dic4312yes—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4—21no—
582D4—21no—
583D4C2×C4⋊Dic4312yes—
584D4C2×C4⋊Dic4312yes—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—3441no—
599C2×C4—3441no—
600C2×C4—3441no—
601C2×C4—3441no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—6881no—
607C2×C4—6881no—
608C2×C4—6881no—
609C2×C4—6881no—
610C2×C4C23×Dic4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C22×D17211yescharacteristic
613C2×C4C22×Dic8611yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337211yescharacteristic
616C8—22no—
617C8—22no—
618C8—1721no—
619C8—1721no—
620C8C2×C4⋊Dic4312yes—
621C8C2×C4⋊Dic4312yes—
622C8D4×Dic4312yes—
623C8D4×Dic4312yes—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22#1458338211yescharacteristic
633C22D4×D17211yescharacteristic
634C22#1458360611yescharacteristic
635C4—22no—
636C4—22no—
637C4—42no—
638C4—3441no—
639C4—3441no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4—1721no—
644C4—1721no—
645C4—1721no—
646C4C22×C4⋊Dic4311yescharacteristic
647C4C2×D4×Dic4311yescharacteristic
648C4#1458355311yescharacteristic
649C4D4×Dic8611yescharacteristic
650C2—21no—
651C2—21no—
652C2—42no—
653C2—42no—
654C2D4×C4⋊Dic4311yescharacteristic
655C2#1914636211yescharacteristic
656C2#1914637111yescharacteristic
subgroupG/H
centerC22D4×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#444C2
socleC22×C43D42
prime radicalC2×#135×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#444D43
hypocenterC43#22693
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
3. #19143195C2semidirect
4. #19143190C2semidirect
5. #19135381C2semidirect
6. #19135376C2semidirect
7. #19134830C2semidirect
8. #19134830C2semidirect
9. #19134823C2semidirect
10. #19134823C2semidirect
11. #19134763C2semidirect
12. #19134659C2semidirect
13. #19134654C2semidirect
14. #19134479C2semidirect
63. C43×#444C4semidirect
141. #131×C43C2×C4semidirect
142. #131×C43C2×C4semidirect
152. #108×C43C2×C4semidirect
153. #104×C43C2×C4semidirect
154. #104×C43C2×C4semidirect
155. #97×C43C2×C4semidirect
182. Q16×C43C4⋊C4semidirect
183. SD16×C43C4⋊C4semidirect
184. SD16×C43C4⋊C4semidirect
185. D8×C43C4⋊C4semidirect
351. #444Dic43semidirect
396. C43#22693semidirect
407. #131C2×Dic43semidirect
408. #131C2×Dic43semidirect
448. #108C2×Dic43semidirect
469. #104C2×Dic43semidirect
470. #104C2×Dic43semidirect
481. #97C2×Dic43semidirect
511. Q16C4⋊Dic43semidirect
512. SD16C4⋊Dic43semidirect
513. SD16C4⋊Dic43semidirect
514. D8C4⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191434792
#191434712
#191431952
#191431902
#191353812
#191353762
#191348302
#191348232
#191347632
#191346592
#191346542
#191344792
C2×C43×#4442
#2269343