Finite Group Databasebeta

← #25115112

Subgroups — #25115112

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
1C2×#14583020C211yesmaximal, characteristic
2#19143480C211yesmaximal, characteristic
3#19143469C211yesmaximal, characteristic
4#19143194C211yesmaximal, characteristic, complemented
5#19143189C211yesmaximal, characteristic, complemented
6#19135376C211yesmaximal, characteristic, complemented
7#19134831C211yesmaximal, characteristic, complemented
8#19134825C211yesmaximal, characteristic, complemented
9#19134824C211yesmaximal, characteristic, complemented
10#19134818C211yesmaximal, characteristic, complemented
11#19134762C211yesmaximal, characteristic, complemented
12#19134658C211yesmaximal, characteristic, complemented
13#19134653C211yesmaximal, characteristic, complemented
14#19134480C211yesmaximal, characteristic, complemented
15C43×#1952C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19#14583380C2211yescharacteristic
20#14583380C2211yescharacteristic
21#14583379C2211yescharacteristic
22#14583379C2211yescharacteristic
23#14583020C418yescomplemented
24#14583012—21no—
25#14583007—21no—
26#14582998—21no—
27#14582998—21no—
28#14582993—21no—
29C4×#10621873—21no—
30C4×#10621873—21no—
31#14582981—21no—
32C2×#13063260C2211yescharacteristic
33#14582941C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582940—21no—
36#14582940—21no—
37#14582938—21no—
38#14582938—21no—
39#14582936—21no—
40#14582935C2211yescharacteristic
41#14582934—21no—
42C2×#13063258C2211yescharacteristic
43#107×D43—21no—
44C2×#13063257C2211yescharacteristic
45C2×#13063256C2211yescharacteristic
46#106×D43—21no—
47C2×#13063251C2211yescharacteristic
48C2×#13063251C2211yescharacteristic
49#14582901C2211yescharacteristic
50#14582901C2211yescharacteristic
51#14582898C2211yescharacteristic
52#14582898C2211yescharacteristic
53#14582854C2211yescharacteristic
54C2×#13063235C2211yescharacteristic
55#14582768C2211yescharacteristic
56#14582764C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582660C2211yescharacteristic
60#14582658C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C43×#428C2211yescharacteristic
64C2×#107×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063347C2×C414yes—
71#13063347Q814yes—
72C2×Dic172D411yescharacteristic
73C2×#10621873D411yescharacteristic
74C2×#10621873D411yescharacteristic
75C2×D344D411yescharacteristic
76#13063333—22no—
77#13063333—22no—
78#13063333C2×C414yescomplemented
79#13063333C2×C414yescomplemented
80C2×#10621877C2311yescharacteristic
81C2×#10621872—21no—
82C2×#10621872—21no—
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88#13063290—21no—
89#13063290—21no—
90C4×D172—21no—
91C4×D172—21no—
92#13063287—21no—
93#13063287—21no—
94C4×C22⋊D43—41no—
95C4×C22⋊D43—41no—
96(C22⋊D43)⋊C4—41no—
97(C22⋊D43)⋊C4—41no—
98#13063284C2311yescharacteristic
99#13063283—21no—
100#13063283—21no—
101#13063283—21no—
102#13063283—21no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—41no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063260—22no—
112#13063259—21no—
113#13063259—21no—
114#13063258—21no—
115#13063258—21no—
116#13063258D411yescharacteristic
117#13063258D411yescharacteristic
118#13063257—21no—
119#13063257—21no—
120#13063257—21no—
121#13063257—21no—
122#13063256—21no—
123#13063256—21no—
124#13063256D411yescharacteristic
125#13063256D411yescharacteristic
126#13063251C2×C414yescomplemented
127#13063251C2×C414yescomplemented
128#13063250—21no—
129#13063250—21no—
130#13063248—21no—
131#13063248—21no—
132#13063247—21no—
133#13063247—21no—
134#13063245—21no—
135#13063245—21no—
136#13063235—21no—
137#13063235C2×C414yescomplemented
138C8×Dic43—21no—
139C43⋊#95—41no—
140C2×M16×C43C2311yescharacteristic
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147#108×C43C2×C414yescomplemented
148#107×C43—21no—
149#107×C43—21no—
150#107×C43—21no—
151#107×C43—21no—
152#106×C43—21no—
153#106×C43—21no—
154#97×C43—21no—
155C4×C8×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C2×C22⋊D43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898C22×C412yes—
169#10621898C22×C412yes—
170#10621898C2×Q812yes—
171#10621898C2×Q812yes—
172C2×D172C2×D411yescharacteristic
173C2×D172C2×D411yescharacteristic
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×Dic86C2×D411yescharacteristic
181C2×Dic86C2×D411yescharacteristic
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43C22×C412yes—
187M16×C43C22×C412yes—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C22×C412yes—
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×Q812yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C22⋊C4×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—21no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43C2×D411yescharacteristic
213C4⋊Dic43C2×D411yescharacteristic
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217Dic43⋊C4—41no—
218Dic43⋊C4—82no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—41no—
222C4×Dic43—41no—
223C4×Dic43—41no—
224C4×Dic43—41no—
225C4×Dic43C22×C412yes—
226#10621877—21no—
227#10621877—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8C22×C412yes—
230C2×C43⋊C8C2×D411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C2×C43⋊C8#4112yes—
233Dic172C4⋊C414yescomplemented
234D344C4⋊C414yescomplemented
235#10621873C4⋊C414yescomplemented
236#10621873C4⋊C414yescomplemented
237#10621872—24no—
238#10621872—24no—
239C8×D43—24no—
240C8×D43—24no—
241C23×C43H(5,𝔽2)11yescharacteristic
242C22×D43—21no—
243C22×D43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—81no—
249C2×C4×C43—81no—
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×Q811yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C22⋊D43—22no—
257C22⋊D43—22no—
258C22⋊D43—22no—
259C22⋊D43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—81no—
270C2×Dic43—81no—
271D172—21no—
272D172—21no—
273D172C2×C4⋊C412yes—
274D172C2×C4⋊C412yes—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—161no—
280C4×D43—161no—
281C4×D43—161no—
282C4×D43—161no—
283Dic86—21no—
284Dic86—21no—
285Dic86C2×C4⋊C412yes—
286Dic86C2×C4⋊C412yes—
287C8×C43—22no—
288C8×C43—22no—
289C8×C43—41no—
290C8×C43C2×C4⋊C412yes—
291C8×C43C2×C4⋊C412yes—
292C43⋊C8—41no—
293C43⋊C8C4×D412yes—
294C43⋊C8C4×D412yes—
295#22693—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43#52011yescharacteristic
299C22×C43D4211yescharacteristic
300C22×C43#55411yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C22×C4⋊C411yescharacteristic
312C4×C43C2×C4×D411yescharacteristic
313C4×C43#54711yescharacteristic
314C4×C43D4×Q811yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322C2×#444—431no—
323#2952—431no—
324#2951—431no—
325#2913—431no—
326#2912—431no—
327#1952D4311yescharacteristic, complemented
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×C43D4×C4⋊C411yescharacteristic
340C2×C43#328811yescharacteristic
341C2×C43#328911yescharacteristic
342D43—42no—
343D43—42no—
344C2×#135—431no—
345C2×#131—431no—
346C2×#131—431no—
347#520—431no—
348#520—431no—
349#520—431no—
350#520—431no—
351#444—438no—
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—861no—
365#428—861no—
366#428—861no—
367#428—861no—
368#428C2×D4311yescharacteristic
369#428C2×D4311yescharacteristic
370#427—431no—
371#427—861no—
372#427—861no—
373C2×#107—431no—
374C2×#107—861no—
375C2×#107C2×D4311yescharacteristic
376C2×#106—431no—
377C2×#106—431no—
378C2×#106—861no—
379C2×#104—431no—
380C2×#104—431no—
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#405—431no—
386#405C2×D4311yescharacteristic
387C2×#97—431no—
388#384—431no—
389#382—431no—
390#343—431no—
391#343—431no—
392#343C2×D4311yescharacteristic
393#343C2×D4311yescharacteristic
394#339—431no—
395#339—431no—
396C43#2269311yescharacteristic, complemented, Sylow
397C2×#41—431no—
398C2×#41—431no—
399#135—434no—
400#135—434no—
401C2×Q16—431no—
402C2×SD16—431no—
403C2×SD16—431no—
404C2×D8—431no—
405#131—434no—
406#131—434no—
407#131—862no—
408#131—862no—
409C2×M16—431no—
410C2×M16—861no—
411C2×M16—861no—
412C2×M16C22×D4311yescharacteristic
413C2×M16C22×D4311yescharacteristic
414C2×M16C22×D4311yescharacteristic
415C22×C8—431no—
416C22×C8—861no—
417C22×C8—861no—
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—861no—
433#117—861no—
434#117—861no—
435#117—861no—
436#117C22×D4311yescharacteristic
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—1721no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C42—431no—
447#108—862no—
448#108C4×D4314yescomplemented
449#107—21no—
450#107—21no—
451#107—21no—
452#107—21no—
453#107—431no—
454#107—431no—
455#107—861no—
456#107—861no—
457#107—861no—
458#107—861no—
459#106—21no—
460#106—21no—
461#106—431no—
462#106—431no—
463#106—861no—
464#106—861no—
465#106—861no—
466#106—861no—
467#106—861no—
468#106—861no—
469#104—434no—
470#104—434no—
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—21no—
480#97—434no—
481#97—861no—
482C4×C8—21no—
483C4×C8—861no—
484#95—1721no—
485#41—432no—
486#41—432no—
487#41—432no—
488#41—432no—
489#41—861no—
490#41—861no—
491#41—861no—
492#41—861no—
493C2×Q8—431no—
494C2×Q8—431no—
495C2×D4—431no—
496C2×D4—431no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—861no—
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
511Q16—434no—
512SD16—434no—
513SD16—434no—
514D8—434no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—864no—
520M16—864no—
521M16—861no—
522M16—861no—
523M16C2×C4×D4312yes—
524M16C2×C4×D4312yes—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—432no—
529C2×C8—431no—
530C2×C8—431no—
531C2×C8—432no—
532C2×C8—864no—
533C2×C8—864no—
534C2×C8—861no—
535C2×C8C2×C4×D4312yes—
536C2×C8D4×D4311yescharacteristic
537C2×C8D4×D4311yescharacteristic
538C2×C8Q8×D4312yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—431no—
544C4⋊C4—431no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—3442no—
550C4⋊C4—1721no—
551C4⋊C4—1721no—
552C4⋊C4—1721no—
553C4⋊C4—1721no—
554C4⋊C4D4×D4311yescharacteristic
555C4⋊C4D4×D4311yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—861no—
558C22⋊C4—1721no—
559C22⋊C4—1721no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—21no—
563C42—432no—
564C42—861no—
565C42—861no—
566C42—1721no—
567C42—1721no—
568C42—1721no—
569C42—1721no—
570C23—861no—
571C23—861no—
572C23#1306337111yescharacteristic
573Q8—432no—
574Q8—432no—
575Q8—861no—
576Q8—861no—
577D4—432no—
578D4—432no—
579D4—862no—
580D4—862no—
581D4—862no—
582D4—862no—
583D4—861no—
584D4—861no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
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×C4C22×C4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4C2×Q8×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#1306337311yescharacteristic
616C8—22no—
617C8—22no—
618C8—41no—
619C8—432no—
620C8—432no—
621C8—1721no—
622C8C4⋊C4×D4312yes—
623C8C4⋊C4×D4312yes—
624C22—21no—
625C22—21no—
626C22—862no—
627C22—862no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22—1721no—
632C22#1458338111yescharacteristic
633C22#1458353311yescharacteristic
634C22#1458360511yescharacteristic
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—862no—
640C4—862no—
641C4—3441no—
642C4—3441no—
643C4—1722no—
644C4—1721no—
645C4—1721no—
646C4C2×C4⋊C4×D4311yescharacteristic
647C4C4×D4×D4311yescharacteristic
648C4#1458355111yescharacteristic
649C4#1458356411yescharacteristic
650C2—21no—
651C2—21no—
652C2—1722no—
653C2—1722no—
654C2#1913749611yescharacteristic
655C2#1914635811yescharacteristic
656C2#1914636911yescharacteristic
subgroupG/H
centerC22#14583533
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1952C2
socleC22×C43D42
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1952D43
hypocenterC43#22693
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
4. #19143194C2semidirect
5. #19143189C2semidirect
6. #19135376C2semidirect
7. #19134831C2semidirect
8. #19134825C2semidirect
9. #19134824C2semidirect
10. #19134818C2semidirect
11. #19134762C2semidirect
12. #19134658C2semidirect
13. #19134653C2semidirect
14. #19134480C2semidirect
15. C43×#1952C2semidirect
23. #14583020C4semidirect
78. #13063333C2×C4semidirect
79. #13063333C2×C4semidirect
126. #13063251C2×C4semidirect
127. #13063251C2×C4semidirect
137. #13063235C2×C4semidirect
147. #108×C43C2×C4semidirect
233. Dic172C4⋊C4semidirect
234. D344C4⋊C4semidirect
235. #10621873C4⋊C4semidirect
236. #10621873C4⋊C4semidirect
327. #1952D43semidirect
396. C43#22693semidirect
448. #108C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830202
#191434802
#191434692
#191431942
#191431892
#191353762
#191348312
#191348252
#191348242
#191348182
#191347622
#191346582
#191346532
#191344802
C43×#19522
#2269343