Finite Group Databasebeta

← #25157138

Subgroups — #25157138

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144564C211yesmaximal, characteristic, complemented
2#19144143C211yesmaximal, characteristic
3#19143193C211yesmaximal, characteristic, complemented
4#19136130C211yesmaximal, characteristic, complemented
5#19136101C211yesmaximal, characteristic, complemented
6#19136038C211yesmaximal, characteristic, complemented
7#19135810C211yesmaximal, characteristic, complemented
8#19135250C211yesmaximal, characteristic, complemented
9#19135194C211yesmaximal, characteristic, complemented
10#19135108C211yesmaximal, characteristic, complemented
11#19134964C211yesmaximal, characteristic, complemented
12#19134924C211yesmaximal, characteristic
13#19134821C211yesmaximal, characteristic, complemented
14#19134819C211yesmaximal, characteristic, complemented
15C43×#2951C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583470C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583240—21no—
21#14583240—21no—
22#14583234—21no—
23#14583229—21no—
24#14583119—21no—
25#14583112—21no—
26#14583107—21no—
27#14583102—21no—
28#14582942—21no—
29#14582942C2211yescharacteristic
30#14582939—21no—
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582935—21no—
34#14582935C2211yescharacteristic
35C2×#13063258—21no—
36C2×#13063258C2211yescharacteristic
37#14582925C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40#14582907C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#135×C43C2211yescharacteristic
57C43×#520C2211yescharacteristic
58C43×#520C2211yescharacteristic
59C43×#440—21no—
60C43×#440—21no—
61C4×Q16×C43—21no—
62C4×D8×C43—21no—
63C2×#107×C43C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72#13063332—22no—
73#13063332—22no—
74C2×#10621877—21no—
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C22×C43⋊C8—21no—
79C22×C43⋊C8C2311yescharacteristic
80#13063323—21no—
81#13063312—21no—
82#13063306—41no—
83#13063304—21no—
84#13063304—21no—
85Q8×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—41no—
88#13063284—21no—
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—41no—
93C2×C4×Dic43C2311yescharacteristic
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258D411yescharacteristic
100#13063258D411yescharacteristic
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256D411yescharacteristic
105#13063256D411yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108#13063252—22no—
109#13063252—22no—
110#13063250—21no—
111#13063250—21no—
112#13063249—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063246—21no—
118#13063243—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121C43⋊#95—41no—
122C2×#41×C43C2311yescharacteristic
123C2×#41×C43C2311yescharacteristic
124#135×C43—22no—
125#135×C43—22no—
126C2×Q16×C43D411yescharacteristic
127C2×SD16×C43D411yescharacteristic
128C2×SD16×C43D411yescharacteristic
129C2×D8×C43D411yescharacteristic
130C2×M16×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—41no—
137C4×D4×C43—41no—
138#117×C43—21no—
139#117×C43—21no—
140#117×C43C2311yescharacteristic
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145#107×C43—21no—
146#107×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#102×C43—21no—
150#102×C43—21no—
151#97×C43—21no—
152C4×C8×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43#4112yes—
160#41×C43#4112yes—
161C2×Q8×C43C2×D411yescharacteristic
162C2×Q8×C43C2×D411yescharacteristic
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—41no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184Q16×C43—22no—
185SD16×C43—22no—
186SD16×C43—22no—
187D8×C43—22no—
188M16×C43—21no—
189M16×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C22⋊C4×C43—21no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C22⋊Dic43—21no—
210C22⋊Dic43—41no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213#10621885—42no—
214#10621883—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—41no—
218C4⋊Dic43C2×D411yescharacteristic
219C4⋊Dic43C2×D411yescharacteristic
220Dic43⋊C4—41no—
221Dic43⋊C4—41no—
222Dic43⋊C4—82no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—41no—
227#10621877—24no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877#4112yes—
234C2×C43⋊C8—24no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8C2×D411yescharacteristic
241C2×C43⋊C8C2×D411yescharacteristic
242C23×C43—21no—
243C23×C43—21no—
244C23×C43H(5,𝔽2)11yescharacteristic
245Q8×C43—21no—
246Q8×C43—21no—
247Q8×C43—21no—
248Q8×C43#12312yes—
249D4×C43—22no—
250D4×C43—22no—
251D4×C43—21no—
252D4×C43—21no—
253D4×C43—21no—
254D4×C43—41no—
255D4×C43—41no—
256D4×C43#12312yes—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—81no—
268C2×C4×C43—81no—
269C2×C4×C43—161no—
270C2×C4×C43—161no—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—81no—
287C2×Dic43—161no—
288Dic86—41no—
289Dic86—41no—
290Dic86—41no—
291Dic86—41no—
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—41no—
295C43⋊C8—21no—
296C43⋊C8—22no—
297C43⋊C8—21no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#26196—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—22no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43#53911yescharacteristic
310C22×C43D4211yescharacteristic
311C22×C43#55311yescharacteristic
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43C2×#12311yescharacteristic
319C4×C43#52511yescharacteristic
320C4×C43#54711yescharacteristic
321C4×C43#54811yescharacteristic
322Dic43—42no—
323Dic43—41no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327#3097—431no—
328#3046—431no—
329#2951D4311yescharacteristic
330#2913—431no—
331#2095—431no—
332#2089—431no—
333#2078—431no—
334#2038—431no—
335#1930—431no—
336#1922—431no—
337#1908—431no—
338#1882—431no—
339#1876—431no—
340#1859—431no—
341#1859—431no—
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—42no—
345C2×C43—81no—
346C2×C43#244311yescharacteristic
347C2×C43#328811yescharacteristic
348C2×C43#329311yescharacteristic
349C2×#137—431no—
350C2×#135C2×D4311yescharacteristic
351C2×#131—431no—
352#536—431no—
353#520—431no—
354#520C2×D4311yescharacteristic
355#520C2×D4311yescharacteristic
356#485—861no—
357#485—861no—
358#484—861no—
359#483—861no—
360#464—861no—
361#463—861no—
362#462—861no—
363#461—861no—
364#440—21no—
365#440—21no—
366C4×Q16—21no—
367C4×D8—21no—
368#428—431no—
369#428—431no—
370#428—431no—
371#428—861no—
372#428—861no—
373#427—431no—
374#427—861no—
375C2×#107—431no—
376C2×#107—861no—
377C2×#107C2×D4311yescharacteristic
378#424—431no—
379C2×#104—431no—
380C2×#104—431no—
381#419—431no—
382#417—431no—
383#417C2×D4311yescharacteristic
384#417C2×D4311yescharacteristic
385C2×#103—431no—
386C2×#103—431no—
387C2×#101—431no—
388#408—431no—
389#405C2×D4311yescharacteristic
390#391—431no—
391#384—431no—
392#343—431no—
393#343—431no—
394#343—431no—
395#341—431no—
396#341—431no—
397#339—431no—
398#339—431no—
399#336—431no—
400C43#2619611yescharacteristic, complemented, Sylow
401C2×#41C22×D4311yescharacteristic
402C2×#41C22×D4311yescharacteristic
403C22×Q8—431no—
404#137—862no—
405#137—862no—
406#135—22no—
407#135—22no—
408C2×Q16—861no—
409C2×Q16C22⋊D4311yescharacteristic
410C2×SD16—861no—
411C2×SD16C22⋊D4311yescharacteristic
412C2×SD16C22⋊D4311yescharacteristic
413C2×D8C22⋊D4311yescharacteristic
414#131—862no—
415#131—862no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—431no—
419C2×M16—861no—
420C2×M16C22×D4311yescharacteristic
421C22×C8—431no—
422C22×C8—861no—
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8—861no—
425#124—861no—
426#123—1721no—
427C22⋊Q8—861no—
428C22⋊Q8—861no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—861no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—861no—
437C4×D4—1721no—
438#117—21no—
439#117—21no—
440#117—431no—
441#117—861no—
442#117C22×D4311yescharacteristic
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—1721no—
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C42—431no—
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#107—861no—
460#106—431no—
461#106—431no—
462#106—861no—
463#106—861no—
464#106—861no—
465C4⋊C8—861no—
466C4⋊C8—861no—
467#104—862no—
468#104—862no—
469#103—21no—
470#103—21no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#103—861no—
477#103—861no—
478#102—21no—
479#102—21no—
480#102—861no—
481#101—862no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484#97—21no—
485C4×C8—21no—
486#95—1721no—
487#41—21no—
488#41—21no—
489#41—21no—
490#41—21no—
491#41—21no—
492#41—21no—
493#41#1062189812yes—
494#41#1062189812yes—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8C2×C22⋊D4311yescharacteristic
502C2×Q8C2×C22⋊D4311yescharacteristic
503C2×D4—21no—
504C2×D4—21no—
505C2×D4C2×C22⋊D4311yescharacteristic
506C2×D4C2×C22⋊D4311yescharacteristic
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—1721no—
517C22×C4C23×D4311yescharacteristic
518Q16—22no—
519Q16—1722no—
520SD16—22no—
521SD16—22no—
522SD16—1722no—
523D8—22no—
524M16—21no—
525M16—21no—
526M16—432no—
527M16—864no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—431no—
537C2×C8—431no—
538C2×C8—864no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8C2×C22⋊D4311yescharacteristic
545C2×C8C2×C22⋊D4311yescharacteristic
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—431no—
553C4⋊C4—431no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—3442no—
557C4⋊C4—1721no—
558C4⋊C4—1721no—
559C4⋊C4—1721no—
560C4⋊C4D4×D4311yescharacteristic
561C4⋊C4D4×D4311yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—861no—
566C22⋊C4—1721no—
567C22⋊C4—1721no—
568C22⋊C4—1721no—
569C42—21no—
570C42—41no—
571C42—41no—
572C42—861no—
573C42—861no—
574C42—861no—
575C42—1721no—
576C23—21no—
577C23—21no—
578C23#1306337011yescharacteristic
579Q8—21no—
580Q8—21no—
581Q8—21no—
582Q8—1721no—
583Q8—1721no—
584Q8—1721no—
585Q8—1721no—
586Q8#1306330812yes—
587D4—22no—
588D4—22no—
589D4—21no—
590D4—21no—
591D4—21no—
592D4—41no—
593D4—41no—
594D4#1306330812yes—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—161no—
608C2×C4—161no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3441no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—6881no—
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C22×C22⋊D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4#1306337211yescharacteristic
626C8—21no—
627C8—21no—
628C8—41no—
629C8—861no—
630C8—861no—
631C8—862no—
632C8—1721no—
633C8—1721no—
634C22—21no—
635C22—21no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22#1458349111yescharacteristic
643C22D4×C22⋊D4311yescharacteristic
644C22#1458359811yescharacteristic
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—3441no—
652C4—3441no—
653C4—1722no—
654C4—1721no—
655C4—1721no—
656C4C2×#1306330811yescharacteristic
657C4#1458340811yescharacteristic
658C4#1458354811yescharacteristic
659C4#1458355811yescharacteristic
660C2—21no—
661C2—21no—
662C2—42no—
663C2—81no—
664C2#1913832411yescharacteristic
665C2#1914635911yescharacteristic
666C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2951C2
socleC22×C43D42
prime radicalC2×#135×C43C22
hypercenter#2951D43
hypocenterC43#26196
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #19144564C2semidirect
3. #19143193C2semidirect
4. #19136130C2semidirect
5. #19136101C2semidirect
6. #19136038C2semidirect
7. #19135810C2semidirect
8. #19135250C2semidirect
9. #19135194C2semidirect
10. #19135108C2semidirect
11. #19134964C2semidirect
13. #19134821C2semidirect
14. #19134819C2semidirect
400. C43#26196semidirect

Maximal subgroups

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

subgroupindex
#191445642
#191441432
#191431932
#191361302
#191361012
#191360382
#191358102
#191352502
#191351942
#191351082
#191349642
#191349242
#191348212
#191348192
C43×#29512
#2619643