Finite Group Databasebeta

← #14780902

Subgroups — #14780902

Order 2816.

1986 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic
3C2×#10622845C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5#13071204C211yesmaximal, characteristic, complemented
6#13069716C212yesmaximal, complemented
7#13069710C212yesmaximal, complemented
8#13069699C212yesmaximal, complemented
9#13069693C212yesmaximal, complemented
10#13068313C211yesmaximal, characteristic, complemented
11C2×C11×#536C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C11×#536—24no—
16C11×#536—24no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×#124C2212yes—
19C2×C11×#123—22no—
20C2×C11×C22⋊Q8—22no—
21C2×C11×#117C2211yescharacteristic
22C2×#67003—24no—
23C2×#67003—24no—
24C2×#67003—24no—
25C22×#4326C2212yes—
26C22×#4326C2211yescharacteristic
27C2×#66995—24no—
28C2×#66995—24no—
29C2×#66995—24no—
30C22×#4325C2212yes—
31C22×#4325C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×#4318C2211yescharacteristic
36C23×C11⋊C8C2211yescharacteristic
37#10622845—24no—
38C2×#66899—24no—
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43#10622600—22no—
44#10622571—22no—
45#10622552C2212yes—
46#10622542C2212yes—
47#10622162C2212yes—
48#10622162C2212yes—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41D414yes—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11D414yes—
62C22×Q8×C11C2312yes—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339D414yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×Dic22C2311yescharacteristic
80C11×C4⋊Q8—24no—
81C11×C4⋊Q8—24no—
82C11×#124—24no—
83C11×#124—24no—
84C11×#123—216no—
85C11×C22⋊Q8—216no—
86C11×#117—22no—
87C11×#117—22no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4D412yes—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11C2312yes—
93#67003—232no—
94C2×#4326—24no—
95C2×#4326—22no—
96C2×#4326—24no—
97C2×#4326—22no—
98C2×#4326—24no—
99C2×#4326—22no—
100#66995—232no—
101C2×#4325—24no—
102C2×#4325—22no—
103C2×#4325—24no—
104C2×#4325—22no—
105C2×#4325—24no—
106C2×#4325—22no—
107C2×#4324—22no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×(C2×D11)⋊C4—24no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11C2312yes—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318D414yes—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8D414yes—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2312yes—
127#66899—24no—
128#66899—24no—
129#66899—24no—
130#66896—24no—
131C11⋊#95—24no—
132#23427—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C11×#41—28no—
137C11×#41—28no—
138C11×#41—44no—
139C11×#41—44no—
140C2×Q8×C11—24no—
141C2×Q8×C11—22no—
142C2×Q8×C11—21no—
143C2×Q8×C11—28no—
144C2×Q8×C11—28no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—44no—
154C2×Q8×C11—42no—
155C2×Q8×C11—44no—
156C2×Q8×C11—42no—
157C2×Q8×C11C2×D414yes—
158C2×Q8×C11C2×D412yes—
159C2×D4×C11—24no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11C2×D412yes—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—24no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—42no—
191C22×Dic11—82no—
192#4339—28no—
193#4339—28no—
194#4339—44no—
195#4339—44no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44C2×D412yes—
202C2×C4×D11—24no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22C2×D412yes—
211C11×C4⋊C4—216no—
212C11×C4⋊C4—24no—
213C11×C22⋊C4—216no—
214C11×C22⋊C4—24no—
215C42×C11—22no—
216C42×C11—22no—
217#4326—216no—
218#4326—28no—
219#4325—216no—
220#4325—28no—
221#4324—28no—
222#4323—28no—
223(C2×D11)⋊C4—84no—
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—42no—
227#4318—28no—
228C2×C11⋊C8—28no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8C2×D414yes—
236C2×C11⋊C8C2×D412yes—
237C2×C11⋊C8C2×D412yes—
238C22×#137—111no—
239C22×#135—111no—
240C2×#536D1111yescharacteristic, complemented
241C2×#417—111no—
242C22×#103—111no—
243#2311—111no—
244#2016—112no—
245#2015—112no—
246#2013—112no—
247#2012—112no—
248#1729—111no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11#12012yes—
257C23×C11#12112yes—
258C23×C11#12712yes—
259C23×C11C22×D411yescharacteristic
260C22×D11—22no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—42no—
264C22×D11—42no—
265Q8×C11—24no—
266Q8×C11—22no—
267Q8×C11—24no—
268Q8×C11—22no—
269Q8×C11—42no—
270Q8×C11—41no—
271Q8×C11—42no—
272Q8×C11—41no—
273Q8×C11—48no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—48no—
277D4×C11—41no—
278D4×C11—41no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—41no—
287C2×C4×C11—42no—
288C2×C4×C11—48no—
289C2×C4×C11—48no—
290C2×C4×C11#12014yes—
291C2×C4×C11#12014yes—
292C2×C4×C11#12012yes—
293C2×C4×C11#12112yes—
294C2×C4×C11#12114yes—
295C2×C4×C11#12114yes—
296C2×C4×C11#12712yes—
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C22⋊D11—48no—
304C2×Dic11—22no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—42no—
308C2×Dic11—44no—
309C2×Dic11—84no—
310D44—22no—
311D44—22no—
312D44—41no—
313D44—41no—
314C4×D11—48no—
315Dic22—22no—
316Dic22—22no—
317Dic22—41no—
318Dic22—41no—
319C11⋊C8—22no—
320C11⋊C8—22no—
321C11⋊C8—24no—
322C22×#41—111no—
323C22×#41C2×D1111yescharacteristic
324C23×Q8C2×D1111yescharacteristic
325C2×#137—224no—
326C2×#137—224no—
327C2×#137—224no—
328C2×#135—224no—
329C2×#135—224no—
330C2×#135—224no—
331C22×Q16—112no—
332C22×Q16—111no—
333C22×SD16—112no—
334C22×SD16—111no—
335C22×SD16—111no—
336C22×D8—111no—
337C22×M16—111no—
338C23×C8—111no—
339#536—24no—
340#536—24no—
341C2×C4⋊Q8C2×D1112yes—
342C2×#124C2×D1112yes—
343C2×#123—22no—
344C2×C22⋊Q8—22no—
345C2×#117C2×D1111yescharacteristic
346C22×C4⋊C4—111no—
347#417—224no—
348C2×#103—112no—
349C2×#103—112no—
350C2×#103—112no—
351C2×#103—224no—
352C2×#102—112no—
353#391—112no—
354#390—112no—
355#386—222no—
356#380—222no—
357#336—112no—
358#336—112no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—42no—
364C22×C11—44no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—82no—
368C22×C11#39214yes—
369C22×C11C2×#12011yescharacteristic
370C22×C11C2×#12111yescharacteristic
371C22×C11C2×#12711yescharacteristic
372C22×C11#57712yes—
373C22×C11#57812yes—
374C2×D11—42no—
375C2×D11—44no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—82no—
379C4×C11—42no—
380C4×C11—44no—
381C4×C11—44no—
382C4×C11#39214yes—
383C4×C11C2×#12011yescharacteristic
384C4×C11C2×#12011yescharacteristic
385C4×C11C2×#12111yescharacteristic
386C4×C11C2×#12111yescharacteristic
387Dic11—42no—
388Dic11—82no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—114no—
395C2×#41—222no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41—222no—
399C2×#41—222no—
400C2×#41C22⋊D1114yes—
401C22×Q8—21no—
402C22×Q8—22no—
403C22×Q8—22no—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—111no—
408C22×Q8C22⋊D1114yes—
409C22×Q8C22×D1112yes—
410C22×Q8C22×D1111yescharacteristic
411C22×D4—21no—
412C22×D4—111no—
413C22×D4—221no—
414C22×D4C22×D1111yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—221no—
418C23×C4—221no—
419C23×C4C22×D1111yescharacteristic
420#137—2232no—
421#135—2232no—
422C2×Q16—222no—
423C2×Q16—224no—
424C2×Q16—222no—
425C2×Q16—224no—
426C2×Q16—222no—
427C2×Q16—224no—
428C2×SD16—222no—
429C2×SD16—222no—
430C2×SD16—224no—
431C2×SD16—222no—
432C2×SD16—222no—
433C2×SD16—224no—
434C2×SD16—222no—
435C2×SD16—224no—
436C2×SD16—222no—
437C2×D8—222no—
438C2×D8—222no—
439C2×D8—222no—
440C2×M16—114no—
441C2×M16—222no—
442C2×M16—222no—
443C22×C8—114no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—112no—
447C22×C8—222no—
448C22×C8—222no—
449C4⋊Q8—24no—
450C4⋊Q8—24no—
451#124—24no—
452#124—24no—
453#123—216no—
454C22⋊Q8—216no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4C22⋊D1112yes—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4C22⋊D1112yes—
466C2×C42C22×D1112yes—
467#103—224no—
468#103—224no—
469#103—224no—
470#102—224no—
471#95—224no—
472C2×C11—24no—
473C2×C11—82no—
474C2×C11C2×#39211yescharacteristic
475C2×C11#301312yes—
476C2×C11#304612yes—
477C2×C11#315411yescharacteristic
478C2×C11#315611yescharacteristic
479D11—82no—
480C24—21no—
481C24—221no—
482C24C2×C22⋊D1111yescharacteristic
483#41—28no—
484#41—28no—
485#41—44no—
486#41—44no—
487#41—228no—
488#41—228no—
489#41—444no—
490#41—444no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—22no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—22no—
503C2×Q8—21no—
504C2×Q8—44no—
505C2×Q8—42no—
506C2×Q8—44no—
507C2×Q8—42no—
508C2×Q8—112no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×Q8C2×C22⋊D1114yes—
515C2×Q8C2×C22⋊D1112yes—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—112no—
525C2×D4—224no—
526C2×D4—221no—
527C2×D4—221no—
528C2×D4—221no—
529C2×D4—221no—
530C2×D4—221no—
531C2×D4—442no—
532C2×D4—442no—
533C2×D4C2×C22⋊D1112yes—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—221no—
543C22×C4—224no—
544C22×C4—222no—
545C22×C4—442no—
546C22×C4—442no—
547C22×C4—442no—
548C22×C4—882no—
549C22×C4D4×D1112yes—
550C22×C4D4×D1112yes—
551C22×C4D4×D1112yes—
552C22×C4#434112yes—
553C22×C4C2×C22⋊D1114yes—
554C22×C4C2×C22⋊D1112yes—
555C22×C4C2×C22⋊D1112yes—
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C23×D1111yescharacteristic
558Q16—228no—
559Q16—2216no—
560SD16—228no—
561SD16—228no—
562SD16—2216no—
563D8—228no—
564M16—228no—
565C2×C8—114no—
566C2×C8—112no—
567C2×C8—112no—
568C2×C8—228no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—222no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—222no—
575C4⋊C4—216no—
576C4⋊C4—24no—
577C4⋊C4—222no—
578C4⋊C4—222no—
579C4⋊C4—442no—
580C22⋊C4—216no—
581C22⋊C4—24no—
582C22⋊C4—884no—
583C42—22no—
584C42—22no—
585C11#2342711yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—42no—
592C23—42no—
593C23—222no—
594C23—441no—
595C23—442no—
596C23—442no—
597C23—441no—
598C23#6699112yes—
599C23#6699312yes—
600C23#6700612yes—
601C23C22×C22⋊D1111yescharacteristic
602Q8—24no—
603Q8—22no—
604Q8—24no—
605Q8—22no—
606Q8—42no—
607Q8—41no—
608Q8—42no—
609Q8—41no—
610Q8—48no—
611Q8—222no—
612Q8—222no—
613Q8—441no—
614Q8—441no—
615D4—22no—
616D4—22no—
617D4—48no—
618D4—41no—
619D4—41no—
620D4—222no—
621D4—222no—
622D4—448no—
623D4—441no—
624D4—441no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—48no—
635C2×C4—48no—
636C2×C4—222no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—448no—
640C2×C4—442no—
641C2×C4—444no—
642C2×C4—884no—
643C2×C4#6699014yes—
644C2×C4#6699014yes—
645C2×C4#6699112yes—
646C2×C4#6699214yes—
647C2×C4#6699214yes—
648C2×C4#6699312yes—
649C2×C4#6700612yes—
650C2×C4C2×D4×D1111yescharacteristic
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4C2×D4×D1111yescharacteristic
653C2×C4C2×#434111yescharacteristic
654C2×C4C22×C22⋊D1111yescharacteristic
655C2×C4C22×C22⋊D1111yescharacteristic
656C8—222no—
657C8—222no—
658C8—224no—
659C22—22no—
660C22—22no—
661C22—24no—
662C22—24no—
663C22—44no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—82no—
668C22—444no—
669C22—442no—
670C22—881no—
671C22—881no—
672C22—882no—
673C22#1062283614yes—
674C22C2×#6699111yescharacteristic
675C22C2×#6699311yescharacteristic
676C22#1062336812yes—
677C22#1062336912yes—
678C22C2×#6700611yescharacteristic
679C4—44no—
680C4—42no—
681C4—44no—
682C4—442no—
683C4—882no—
684C4#1062283614yes—
685C4C2×#6699011yescharacteristic
686C4C2×#6699011yescharacteristic
687C4C2×#6699211yescharacteristic
688C4C2×#6699211yescharacteristic
689C2—24no—
690C2—82no—
691C2—882no—
692C2C2×#1062283611yescharacteristic
693C2#1307793112yes—
694C2#1307816212yes—
695C2#1307909411yescharacteristic
696C2#1307910711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
hypercenterC2×#536D11
hypocenterC11#23427
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C2×#10622845C2semidirect
4. C22×#66899C2semidirect
5. #13071204C2semidirect
6. #13069716C2semidirect
7. #13069710C2semidirect
8. #13069699C2semidirect
9. #13069693C2semidirect
10. #13068313C2semidirect
11. C2×C11×#536C2semidirect
240. C2×#536D11semidirect
585. C11#23427semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C22×#670032
C2×#106228452
C22×#668992
#130712042
#130697162
#130697102
#130696992
#130696932
#130683132
C2×C11×#5362
#2342711