Finite Group Databasebeta

← #25115102

Subgroups — #25115102

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×#14583022C211yesmaximal, characteristic
2#19143478C211yesmaximal, characteristic
3#19143469C211yesmaximal, characteristic
4#19143191C211yesmaximal, characteristic, complemented
5#19143186C211yesmaximal, characteristic, complemented
6#19135378C211yesmaximal, characteristic, complemented
7#19135373C211yesmaximal, characteristic, complemented
8#19134827C211yesmaximal, characteristic, complemented
9#19134827C211yesmaximal, characteristic, complemented
10#19134820C211yesmaximal, characteristic, complemented
11#19134820C211yesmaximal, characteristic, complemented
12#19134660C211yesmaximal, characteristic, complemented
13#19134655C211yesmaximal, characteristic, complemented
14#19134479C211yesmaximal, characteristic, complemented
15C43×#1847C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#14583380C2211yescharacteristic
20#14583380C2211yescharacteristic
21#14583380C2211yescharacteristic
22#14583380C2211yescharacteristic
23#14583022C418yescomplemented
24#14583010—21no—
25#14583005—21no—
26#14582998—21no—
27#14582998—21no—
28#14582993—21no—
29#14582986—21no—
30#14582986—21no—
31#14582981—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063261C2211yescharacteristic
34#14582940—21no—
35#14582940—21no—
36#14582939C2211yescharacteristic
37#14582939C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582938—21no—
41#14582938—21no—
42#14582937C2211yescharacteristic
43#14582936—21no—
44#14582934—21no—
45#107×D43—21no—
46#106×D43—21no—
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49#14582898C2211yescharacteristic
50#14582898C2211yescharacteristic
51#14582898C2211yescharacteristic
52#14582898C2211yescharacteristic
53#14582854C2211yescharacteristic
54#14582854C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582668C2211yescharacteristic
59#14582659C2211yescharacteristic
60#14582659C2211yescharacteristic
61C2×#107×C43C2211yescharacteristic
62C2×#107×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C2×#106×C43C2211yescharacteristic
65C2×#97×C43C2211yescharacteristic
66C43×#384C2211yescharacteristic
67C43×#382C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063347C2×C414yes—
71#13063347Q814yes—
72C2×Dic172D411yescharacteristic
73C2×#10621873D411yescharacteristic
74C2×#10621873D411yescharacteristic
75C2×D344D411yescharacteristic
76#13063331—22no—
77#13063331—22no—
78#13063331C2×C414yescomplemented
79#13063331C2×C414yescomplemented
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063290—21no—
89#13063290—21no—
90#13063290—21no—
91#13063290—21no—
92#13063287—21no—
93#13063287—21no—
94#13063287—21no—
95#13063287—21no—
96C4×C22⋊D43—41no—
97C4×C22⋊D43—41no—
98C4×C22⋊D43—41no—
99C4×C22⋊D43—41no—
100#13063284C2311yescharacteristic
101#13063284C2311yescharacteristic
102#13063283—21no—
103#13063283—21no—
104#13063283—21no—
105#13063283—21no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—21no—
110#13063261—22no—
111#13063261C2×C414yescomplemented
112#13063259D411yescharacteristic
113#13063259D411yescharacteristic
114#13063258—21no—
115#13063258—21no—
116#13063258—21no—
117#13063258—21no—
118#13063257D411yescharacteristic
119#13063257D411yescharacteristic
120#13063256—21no—
121#13063256—21no—
122#13063256—21no—
123#13063256—21no—
124#13063253C2×C414yescomplemented
125#13063253C2×C414yescomplemented
126#13063248—21no—
127#13063248—21no—
128#13063248—21no—
129#13063248—21no—
130#13063245—21no—
131#13063245—21no—
132#13063245—21no—
133#13063245—21no—
134#13063235—21no—
135#13063235—21no—
136C8×Dic43—21no—
137C8×Dic43—21no—
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#107×C43—21no—
147#107×C43—21no—
148#107×C43—21no—
149#107×C43—21no—
150#106×C43—21no—
151#106×C43—21no—
152#106×C43—21no—
153#106×C43—21no—
154#97×C43C2×C414yescomplemented
155#95×C43—41no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—21no—
163C2×C22⋊D43—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
182C2×C8×C43C22×C412yes—
183C2×C8×C43C22×C412yes—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×Q812yes—
189C2×C8×C43#4112yes—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—82no—
199C42×C43—21no—
200C42×C43C22×C412yes—
201C22⋊Dic43—21no—
202C22⋊Dic43—21no—
203(C2×D43)⋊C4—41no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209C4⋊Dic43C2×D411yescharacteristic
210C4⋊Dic43C2×D411yescharacteristic
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—41no—
218C4×Dic43—41no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877C22×C412yes—
228#10621877C22×C412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
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—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—81no—
252C2×C4×C43—81no—
253C2×C4×C43—81no—
254C2×C4×C43—81no—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C22⋊D43—22no—
262C22⋊D43—22no—
263C22⋊D43—22no—
264C22⋊D43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
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×C43C2×C4⋊C412yes—
288C8×C43C2×C4⋊C412yes—
289C8×C43C4×D412yes—
290C8×C43C4×D412yes—
291C43⋊C8—22no—
292C43⋊C8—22no—
293C43⋊C8—41no—
294C43⋊C8—41no—
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—42no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C22×C4⋊C411yescharacteristic
313C4×C43C2×C4×D411yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43D4×Q811yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—41no—
319Dic43—41no—
320Dic43—41no—
321Dic43—41no—
322C2×#444—431no—
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#1847D4311yescharacteristic, complemented
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×#108—431no—
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—861no—
374C2×#107C2×D4311yescharacteristic
375C2×#107C2×D4311yescharacteristic
376C2×#106—861no—
377C2×#106C2×D4311yescharacteristic
378C2×#106C2×D4311yescharacteristic
379C2×#104—431no—
380C2×#104—431no—
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#405—431no—
386#405—431no—
387C2×#97C2×D4311yescharacteristic
388#384C2×D4311yescharacteristic
389#382C2×D4311yescharacteristic
390#343—431no—
391#343—431no—
392#343—431no—
393#343—431no—
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—431no—
411C2×M16—431no—
412C2×M16—431no—
413C2×M16—861no—
414C2×M16—861no—
415C22×C8—861no—
416C22×C8—861no—
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—41no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C42C22×D4311yescharacteristic
447#108—434no—
448#108—862no—
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—21no—
462#106—21no—
463#106—431no—
464#106—431no—
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—861no—
480#97—861no—
481#97C4×D4314yescomplemented
482C4×C8—861no—
483C4×C8—861no—
484#95—41no—
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—21no—
502C22×C4—21no—
503C22×C4—21no—
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—432no—
516M16—432no—
517M16—861no—
518M16—861no—
519M16—864no—
520M16—864no—
521M16—861no—
522M16—861no—
523M16—861no—
524M16—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—864no—
528C2×C8—864no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8C2×C4×D4312yes—
532C2×C8C2×C4×D4312yes—
533C2×C8D4×D4311yescharacteristic
534C2×C8D4×D4311yescharacteristic
535C2×C8D4×D4311yescharacteristic
536C2×C8D4×D4311yescharacteristic
537C2×C8Q8×D4312yes—
538C2×C8#1062190212yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—82no—
548C4⋊C4—431no—
549C4⋊C4—431no—
550C4⋊C4—431no—
551C4⋊C4—431no—
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—
569C42C2×C4×D4312yes—
570C23—861no—
571C23—861no—
572C23#1306337011yescharacteristic
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—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
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×C4C2×#1062190211yescharacteristic
615C2×C4#1306337311yescharacteristic
616C8—862no—
617C8—862no—
618C8—1721no—
619C8—1721no—
620C8C4⋊C4×D4312yes—
621C8C4⋊C4×D4312yes—
622C8#1306328712yes—
623C8#1306328712yes—
624C22—21no—
625C22—21no—
626C22—862no—
627C22—862no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22—1721no—
632C22#1458338011yescharacteristic
633C22#1458353411yescharacteristic
634C22#1458361011yescharacteristic
635C4—42no—
636C4—81no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—862no—
641C4—862no—
642C4—1721no—
643C4—1721no—
644C4—1721no—
645C4—1721no—
646C4C2×C4⋊C4×D4311yescharacteristic
647C4C2×#1306328711yescharacteristic
648C4#1458355211yescharacteristic
649C4#1458356411yescharacteristic
650C2—21no—
651C2—21no—
652C2—1722no—
653C2—1722no—
654C2#1913749511yescharacteristic
655C2#1914636111yescharacteristic
656C2#1914637011yescharacteristic
subgroupG/H
centerC22#14583534
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1847C2
socleC22×C43D42
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1847D43
hypocenterC43#22693
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #19143191C2semidirect
5. #19143186C2semidirect
6. #19135378C2semidirect
7. #19135373C2semidirect
8. #19134827C2semidirect
9. #19134827C2semidirect
10. #19134820C2semidirect
11. #19134820C2semidirect
12. #19134660C2semidirect
13. #19134655C2semidirect
14. #19134479C2semidirect
15. C43×#1847C2semidirect
23. #14583022C4semidirect
78. #13063331C2×C4semidirect
79. #13063331C2×C4semidirect
111. #13063261C2×C4semidirect
124. #13063253C2×C4semidirect
125. #13063253C2×C4semidirect
154. #97×C43C2×C4semidirect
233. Dic172C4⋊C4semidirect
234. D344C4⋊C4semidirect
235. #10621873C4⋊C4semidirect
236. #10621873C4⋊C4semidirect
333. #1847D43semidirect
396. C43#22693semidirect
481. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830222
#191434782
#191434692
#191431912
#191431862
#191353782
#191353732
#191348272
#191348202
#191346602
#191346552
#191344792
C43×#18472
#2269343