Finite Group Databasebeta

← #14811330

Subgroups — #14811330

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078482C211yesmaximal, characteristic, complemented
2#13078471C211yesmaximal, characteristic, complemented
3#13077142C211yesmaximal, characteristic
4#13077142C211yesmaximal, characteristic
5#13070137C211yesmaximal, characteristic, complemented
6#13069972C211yesmaximal, characteristic, complemented
7#13069972C211yesmaximal, characteristic, complemented
8#13069772C211yesmaximal, characteristic, complemented
9#13068889C211yesmaximal, characteristic, complemented
10#13068889C211yesmaximal, characteristic, complemented
11#13068851C211yesmaximal, characteristic, complemented
12#13068851C211yesmaximal, characteristic, complemented
13#13068678C211yesmaximal, characteristic, complemented
14#13068673C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17#10623358C2211yescharacteristic
18#10623358C2211yescharacteristic
19C2×#67001C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21#10623031C2211yescharacteristic, complemented
22C2×C11×#104C2211yescharacteristic
23C2×C11×#104C2211yescharacteristic
24C11×#417C2211yescharacteristic
25C11×#417C2211yescharacteristic
26C2×C11×#100C2211yescharacteristic
27C11×#390C2211yescharacteristic
28#10622846—21no—
29#10622846—21no—
30#10622846C2211yescharacteristic
31#10622846C2211yescharacteristic
32#10622845—21no—
33#10622845—21no—
34#10622845C2211yescharacteristic
35#10622845C2211yescharacteristic
36#10622828—21no—
37#10622828—21no—
38#10622828C2211yescharacteristic
39#10622828C2211yescharacteristic
40C2×#66896—21no—
41C2×#66896—21no—
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66886C2211yescharacteristic, complemented
45C2×#66886C2211yescharacteristic, complemented
46#10622734C2211yescharacteristic, complemented
47#10622734C2211yescharacteristic, complemented
48#10622732C2211yescharacteristic, complemented
49#10622732C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52#10622549C2211yescharacteristic, complemented
53#10622412—21no—
54#10622409—21no—
55#10622407—21no—
56#10622404—21no—
57#10622379—21no—
58#10622376—21no—
59#10622374—21no—
60#10622372—21no—
61#10622192C2211yescharacteristic, complemented
62#10622192C2211yescharacteristic, complemented
63#10622168C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65#10622161C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, complemented
67C11×H(5,𝔽2)—22no—
68C11×H(5,𝔽2)—22no—
69C11×H(5,𝔽2)—41no—
70C11×H(5,𝔽2)Q814yescomplemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41C2311yescharacteristic
74C2×C11×#41C2311yescharacteristic
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—41no—
78C22×D4×C11C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—41no—
83C2×C42×C11C2311yescharacteristic
84#67001—22no—
85#67001—22no—
86#67001—41no—
87#67001—41no—
88Q8×Dic11—21no—
89Q8×Dic11—21no—
90D4×Dic11—21no—
91D4×Dic11—21no—
92D4×Dic11—41no—
93D4×Dic11—41no—
94#66979—21no—
95#66979—21no—
96#66979C2311yescharacteristic
97#66979C2311yescharacteristic
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—41no—
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318C2311yescharacteristic
106C2×#4318C2311yescharacteristic
107C22×C11⋊C8—21no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66943—21no—
112#66943—21no—
113#66941—21no—
114#66941—21no—
115C11×#104—22no—
116C11×#104—22no—
117C11×#103—21no—
118C11×#103—21no—
119C11×#102—21no—
120C11×#102—21no—
121C11×#100—41no—
122#66899—21no—
123#66899—21no—
124#66899D411yescharacteristic
125#66899D411yescharacteristic
126#66899D411yescharacteristic
127#66899D411yescharacteristic
128#66896—21no—
129#66896—21no—
130#66896—21no—
131#66896—21no—
132#66896—21no—
133#66896—21no—
134#66896—21no—
135#66896—21no—
136#66896—21no—
137#66896—21no—
138#66896D411yescharacteristic
139#66896D411yescharacteristic
140#66896D411yescharacteristic
141#66896D411yescharacteristic
142C11⋊#95—41no—
143#66886—41no—
144#66886—41no—
145#66882—21no—
146#66882—21no—
147#66881—21no—
148#66881—21no—
149Dic11⋊C8—21no—
150Dic11⋊C8—21no—
151Dic11⋊C8—21no—
152Dic11⋊C8—21no—
153#66872—21no—
154#66872—21no—
155#66871—21no—
156#66871—21no—
157#25984—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—41no—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—21no—
163C11×#41—21no—
164C11×#41—24no—
165C11×#41—24no—
166C11×#41—42no—
167C11×#41—42no—
168C11×#41C2×Q812yes—
169C11×#41C2×Q812yes—
170C11×#41#4112yes—
171C11×#41#4112yes—
172C2×Q8×C11C2×D411yescharacteristic
173C2×Q8×C11C2×D411yescharacteristic
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—41no—
186C2×D4×C11—41no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11C2×D411yescharacteristic
190C2×D4×C11C2×D411yescharacteristic
191C2×D4×C11C2×Q812yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—41no—
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—41no—
201C22×Dic11—41no—
202C2×Dic22—41no—
203C11×M16—21no—
204C11×M16—21no—
205C11×M16—21no—
206C11×M16—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C22⋊C4—82no—
212C42×C11—21no—
213C42×C11—21no—
214C22⋊Dic11—21no—
215C22⋊Dic11—21no—
216C22⋊Dic11—41no—
217C22⋊Dic11—41no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—41no—
223C4⋊Dic11—41no—
224C4⋊Dic11—41no—
225C4⋊Dic11C2×D411yescharacteristic
226C4⋊Dic11C2×D411yescharacteristic
227C4⋊Dic11C2×D411yescharacteristic
228C4⋊Dic11C2×D411yescharacteristic
229Dic11⋊C4—41no—
230Dic11⋊C4—41no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—41no—
234C4×Dic11—41no—
235#4318—21no—
236#4318—21no—
237#4318—21no—
238#4318—21no—
239#4318—42no—
240#4318—42no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—42no—
248C2×C11⋊C8—42no—
249C2×C11⋊C8C2×D411yescharacteristic
250C2×C11⋊C8C2×D411yescharacteristic
251C2×C11⋊C8C2×D411yescharacteristic
252C2×C11⋊C8C2×D411yescharacteristic
253#3084—111no—
254#3083—111no—
255#2897—111no—
256#2897—111no—
257#2092—111no—
258#2063—111no—
259#2063—111no—
260#2027—111no—
261#1866—111no—
262#1866—111no—
263#1860—111no—
264#1860—111no—
265#1816—111no—
266#1815—111no—
267#1792D1111yescharacteristic
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—22no—
271C23×C11—44no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—81no—
275C23×C11—81no—
276C23×C11—161no—
277C23×C11—161no—
278C23×C11H(5,𝔽2)11yescharacteristic
279Q8×C11—21no—
280Q8×C11—21no—
281Q8×C11C22⋊Q812yes—
282Q8×C11C22⋊Q812yes—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—21no—
290D4×C11—21no—
291D4×C11—44no—
292D4×C11—44no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11C22⋊Q812yes—
296D4×C11C22⋊Q812yes—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—44no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—81no—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×Q811yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—81no—
322C2×Dic11—81no—
323C2×Dic11—161no—
324C2×Dic11—161no—
325Dic22—161no—
326C8×C11—41no—
327C8×C11—41no—
328C11⋊C8—21no—
329C11⋊C8—21no—
330C11⋊C8—21no—
331C11⋊C8—21no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C2×H(5,𝔽2)C2×D1111yescharacteristic
335C2×#131—111no—
336C2×#131—111no—
337#544—111no—
338#520—111no—
339#520—111no—
340#479—221no—
341#479—221no—
342#478—221no—
343#478—221no—
344#477—221no—
345#476—221no—
346#475—221no—
347#474—221no—
348C2×#108—111no—
349C2×#108—111no—
350#428—111no—
351#428—111no—
352C2×#107—111no—
353C2×#106—111no—
354#424—111no—
355#424—111no—
356C2×#104C2×D1111yescharacteristic
357C2×#104C2×D1111yescharacteristic
358#418—111no—
359#418—111no—
360#418—221no—
361#418—221no—
362#417—111no—
363#417—111no—
364#417—221no—
365#417—221no—
366#417C2×D1111yescharacteristic
367#417C2×D1111yescharacteristic
368#416—111no—
369#416—111no—
370#416—221no—
371#416—221no—
372C2×#102—111no—
373C2×#102—111no—
374C2×#102—221no—
375C2×#102—221no—
376C2×#100C2×D1111yescharacteristic
377#390C2×D1111yescharacteristic
378#382—111no—
379#343—111no—
380#343—111no—
381#343—111no—
382#339—111no—
383#339—111no—
384#336—111no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—82no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—161no—
398C22×C11—164no—
399C22×C11#54311yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11#55111yescharacteristic
402C4×C11—22no—
403C4×C11—22no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11C2×C22⋊Q811yescharacteristic
407C4×C11C2×C22⋊Q811yescharacteristic
408C4×C11#54611yescharacteristic
409C4×C11#54611yescharacteristic
410Dic11—41no—
411Dic11—41no—
412Dic11—41no—
413Dic11—41no—
414Dic11—81no—
415Dic11—81no—
416H(5,𝔽2)—22no—
417H(5,𝔽2)—22no—
418H(5,𝔽2)—41no—
419H(5,𝔽2)Dic2214yescomplemented
420C2×#41—21no—
421C2×#41—21no—
422C2×#41C22×D1111yescharacteristic
423C2×#41C22×D1111yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—41no—
427C22×D4C22×D1111yescharacteristic
428#131—222no—
429#131—222no—
430#131—441no—
431#131—441no—
432C2×M16—111no—
433C2×M16—111no—
434C2×M16—221no—
435C2×M16—221no—
436C2×M16C22×D1111yescharacteristic
437C2×M16C22×D1111yescharacteristic
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—221no—
441C22×C8—221no—
442C4⋊Q8—221no—
443C4⋊Q8—221no—
444#125—221no—
445#125—221no—
446C22⋊Q8—441no—
447C4×Q8—221no—
448C4×Q8—221no—
449C4×D4—221no—
450C4×D4—221no—
451C4×D4—441no—
452C4×D4—441no—
453#117—111no—
454#117—111no—
455#117—221no—
456#117—221no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—221no—
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C22⋊C4—41no—
463C2×C42C22×D1111yescharacteristic
464#108—441no—
465#108—441no—
466#107—221no—
467#107—221no—
468#107—221no—
469#107—221no—
470#106—221no—
471#106—221no—
472#106—221no—
473#106—221no—
474C4⋊C8—221no—
475C4⋊C8—221no—
476C4⋊C8—221no—
477C4⋊C8—221no—
478#104—22no—
479#104—22no—
480#103—21no—
481#103—21no—
482#103—111no—
483#103—111no—
484#103—111no—
485#103—111no—
486#103—221no—
487#103—221no—
488#102—21no—
489#102—21no—
490#102—111no—
491#102—111no—
492#102—111no—
493#102—111no—
494#102—221no—
495#102—221no—
496#102—221no—
497#102—221no—
498#102—221no—
499#102—221no—
500#102—221no—
501#102—221no—
502#102—221no—
503#102—221no—
504#100—41no—
505#95—441no—
506C2×C11—21no—
507C2×C11—21no—
508C2×C11—42no—
509C2×C11—42no—
510C2×C11—82no—
511C2×C11#243711yescharacteristic
512C2×C11#328811yescharacteristic
513C2×C11#329011yescharacteristic
514C24—21no—
515C24—41no—
516#41—21no—
517#41—21no—
518#41—21no—
519#41—21no—
520#41—24no—
521#41—24no—
522#41—42no—
523#41—42no—
524#41C2×Dic2212yes—
525#41C2×Dic2212yes—
526#41#434112yes—
527#41#434112yes—
528C2×Q8—441no—
529C2×Q8D4×D1111yescharacteristic
530C2×Q8D4×D1111yescharacteristic
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4C2×Dic2212yes—
547C2×D4D4×D1111yescharacteristic
548C2×D4D4×D1111yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—441no—
557C22×C4—441no—
558C22×C4C23×D1111yescharacteristic
559M16—21no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—221no—
564M16—221no—
565M16—221no—
566M16—221no—
567M16—442no—
568M16—442no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—111no—
572C2×C8—111no—
573C2×C8—111no—
574C2×C8—111no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—442no—
582C2×C8—442no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—111no—
586C4⋊C4—111no—
587C4⋊C4—111no—
588C4⋊C4—111no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—441no—
594C4⋊C4—441no—
595C4⋊C4—441no—
596C4⋊C4—441no—
597C4⋊C4—441no—
598C22⋊C4—82no—
599C22⋊C4—221no—
600C22⋊C4—221no—
601C22⋊C4—441no—
602C22⋊C4—441no—
603C42—21no—
604C42—21no—
605C42—221no—
606C42—221no—
607C42—441no—
608C42—441no—
609C11#2598411yescharacteristic, complemented, Sylow
610C23—21no—
611C23—21no—
612C23—22no—
613C23—44no—
614C23—41no—
615C23—41no—
616C23—81no—
617C23—81no—
618C23—161no—
619C23—161no—
620C23#6703711yescharacteristic
621Q8—21no—
622Q8—21no—
623Q8—1761no—
624Q8#6693112yes—
625Q8#6693112yes—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—21no—
633D4—21no—
634D4—44no—
635D4—44no—
636D4—41no—
637D4—41no—
638D4#6693112yes—
639D4#6693112yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—81no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—881no—
659C2×C4—881no—
660C2×C4—1761no—
661C2×C4—1761no—
662C2×C4C22×Dic2211yescharacteristic
663C2×C4C2×D4×D1111yescharacteristic
664C2×C4C2×D4×D1111yescharacteristic
665C2×C4C2×#434111yescharacteristic
666C2×C4C2×#434111yescharacteristic
667C2×C4#6703711yescharacteristic
668C8—41no—
669C8—41no—
670C8—221no—
671C8—221no—
672C8—221no—
673C8—221no—
674C8—441no—
675C8—441no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—82no—
686C22—81no—
687C22—81no—
688C22—161no—
689C22—164no—
690C22#1062301411yescharacteristic
691C22#1062311811yescharacteristic
692C22#1062312111yescharacteristic
693C4—22no—
694C4—22no—
695C4—81no—
696C4—81no—
697C4—441no—
698C4—441no—
699C4—441no—
700C4—441no—
701C4—881no—
702C4—881no—
703C4C2×#6693111yescharacteristic
704C4C2×#6693111yescharacteristic
705C4#1062312211yescharacteristic
706C4#1062312211yescharacteristic
707C2—21no—
708C2—21no—
709C2—42no—
710C2—42no—
711C2—82no—
712C2#1307228211yescharacteristic
713C2#1308037711yescharacteristic
714C2#1308040011yescharacteristic
subgroupG/H
centerC22#10623121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1792C2
socleC22×C11D42
prime radicalC2×C11×H(5,𝔽2)C22
hypercenter#1792D11
hypocenterC11#25984
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1792

Complements

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

NH ≅ G/Ntype
1. #13078482C2semidirect
2. #13078471C2semidirect
5. #13070137C2semidirect
6. #13069972C2semidirect
7. #13069972C2semidirect
8. #13069772C2semidirect
9. #13068889C2semidirect
10. #13068889C2semidirect
11. #13068851C2semidirect
12. #13068851C2semidirect
13. #13068678C2semidirect
14. #13068673C2semidirect
21. #10623031C22semidirect
44. C2×#66886C22semidirect
45. C2×#66886C22semidirect
46. #10622734C22semidirect
47. #10622734C22semidirect
48. #10622732C22semidirect
49. #10622732C22semidirect
50. C2×#66872C22semidirect
51. C2×#66871C22semidirect
52. #10622549C22semidirect
61. #10622192C22semidirect
62. #10622192C22semidirect
63. #10622168C22semidirect
64. #10622162C22semidirect
65. #10622161C22semidirect
66. #10622161C22semidirect
70. C11×H(5,𝔽2)Q8semidirect
419. H(5,𝔽2)Dic22semidirect
609. C11#25984semidirect

Maximal subgroups

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

subgroupindex
#130784822
#130784712
#130771422
#130701372
#130699722
#130697722
#130688892
#130688512
#130686782
#130686732
C11×#17922
#2598411