Finite Group Databasebeta

← #14810906

Subgroups — #14810906

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2C2×D11×#103C211yesmaximal, characteristic
3#13072320C211yesmaximal, characteristic
4#13071450C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13069995C211yesmaximal, characteristic, complemented
7#13069757C211yesmaximal, characteristic, complemented
8#13068883C211yesmaximal, characteristic, complemented
9#13068881C211yesmaximal, characteristic, complemented
10#13068810C211yesmaximal, characteristic
11#13068792C211yesmaximal, characteristic
12#13068638C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C11×#2066C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66949—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622592—21no—
41#10622589C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622464—24no—
48D11×#103—24no—
49#10622281—21no—
50#10622280—21no—
51#10622279—21no—
52#10622270—21no—
53#10622259—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—41no—
66C2×Q8×D11—41no—
67C2×Q8×D11Q814yescomplemented
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22—21no—
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11—41no—
103#66949—44no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106#66940—22no—
107#66940—41no—
108#66922—22no—
109#66922—41no—
110C4×Dic22—22no—
111C4×Dic22—41no—
112C11×#106—41no—
113C11×C4⋊C8—22no—
114C11×#103—22no—
115C11×#103—41no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—22no—
120#66899—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128(C2×D11)⋊C8—22no—
129#66881—22no—
130#66881—22no—
131#66880—22no—
132#66880D414yes—
133Dic11⋊C8—41no—
134#66874—22no—
135#66874—22no—
136#66872—41no—
137#25955—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C2×Q812yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159Q8×D11—28no—
160Q8×D11—44no—
161Q8×D11—44no—
162Q8×D11—44no—
163C2×C4×D11—24no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11C2×Q812yes—
174C2×C4×D11#4112yes—
175C2×Dic22—24no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—42no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22—81no—
184C2×Dic22C2×D412yes—
185C2×Dic22C2×Q812yes—
186C2×Dic22#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11C2×D412yes—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—42no—
200C42×C11—21no—
201C42×C11—21no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4SD1614yes—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—42no—
212C4⋊Dic11C2×D412yes—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—42no—
218Dic11⋊C4—81no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C8×D11—44no—
230C2×#475—111no—
231C22×#103—111no—
232#2440—111no—
233Q8×C22⋊C4—111no—
234#2096—111no—
235#2066—111no—
236#2066D1111yescharacteristic, complemented
237#2024—111no—
238#1865—111no—
239#1865—111no—
240#1853—111no—
241#1850—111no—
242#1807—111no—
243#1803—111no—
244#1787—111no—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11C22⋊Q812yes—
251C22×D11C2×SD1612yes—
252C22×D11#13712yes—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—41no—
256Q8×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C2×SD1612yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×Q811yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11C22⋊Q812yes—
301C2×Dic11C2×SD1612yes—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—48no—
307C4×D11—84no—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22—48no—
312Dic22—84no—
313Dic22C22⋊Q814yescomplemented
314C8×C11—22no—
315C8×C11—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C23×C8—111no—
320C2×C4⋊Q8—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325#475—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—224no—
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342#398—221no—
343#395—221no—
344#391—111no—
345#391—221no—
346#391—221no—
347#391C2×D1111yescharacteristic
348#389—111no—
349#389C2×D1111yescharacteristic
350#385—221no—
351#384—111no—
352#380—111no—
353#380—111no—
354#380—221no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340C2×D1111yescharacteristic
361#336—111no—
362#336—111no—
363C22×C11C2×C22⋊Q811yescharacteristic
364C22×C11D4211yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C22×SD1611yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11#47514yescomplemented
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11C2×C22⋊Q811yescharacteristic
384C4×C11#54311yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#55111yescharacteristic
387Dic11—24no—
388Dic11—22no—
389Dic11—22no—
390Dic11—42no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—114no—
395C22×Q8—111no—
396C22×Q8—221no—
397C22×Q8—222no—
398C22×Q8—221no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—441no—
402C22×Q8—441no—
403C22×Q8C22×D1111yescharacteristic
404C23×C4—111no—
405C23×C4—221no—
406C23×C4—221no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—441no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—222no—
415C4⋊Q8—441no—
416C22⋊Q8—444no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—441no—
420C4×Q8—441no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—441no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445#106—41no—
446#106—222no—
447#106—222no—
448#106—441no—
449C4⋊C8—22no—
450C4⋊C8—441no—
451#103—22no—
452#103—41no—
453#103—114no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458#103—441no—
459C22⋊C8—222no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—111no—
464#95—111no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#243711yescharacteristic
471C2×C11C2×#47511yescharacteristic
472C2×C11#308211yescharacteristic
473C2×C11#327011yescharacteristic
474C2×C11D4×SD1611yescharacteristic
475C2×C11#329811yescharacteristic
476C2×C11#331611yescharacteristic
477D11—24no—
478C24—111no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—112no—
485C2×Q8—112no—
486C2×Q8—112no—
487C2×Q8—224no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—228no—
492C2×Q8—442no—
493C2×Q8—442no—
494C2×Q8—442no—
495C2×Q8—444no—
496C2×Q8—444no—
497C2×Q8—444no—
498C2×Q8—442no—
499C2×Q8—881no—
500C2×Q8Q8×D1112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—224no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4—881no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—444no—
539C2×C8D4×D1112yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—112no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—881no—
560C22⋊C4—114no—
561C22⋊C4—222no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C42—21no—
565C42—21no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—442no—
570C11#2595511yescharacteristic, complemented, Sylow
571C23—112no—
572C23—112no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—114no—
584Q8—222no—
585Q8—222no—
586Q8—222no—
587Q8—448no—
588Q8—884no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—221no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4SD16×D1112yes—
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C2×Q8×D1111yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—22no—
641C8—41no—
642C8—441no—
643C8—441no—
644C22—114no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—222no—
651C22#1062314011yescharacteristic
652C22#1062314311yescharacteristic
653C22D11×C22⋊Q811yescharacteristic
654C22C2×SD16×D1111yescharacteristic
655C22#1062330111yescharacteristic
656C22D11×#13711yescharacteristic
657C22#1062331011yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—224no—
666C4—222no—
667C4—441no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4#1062314111yescharacteristic
672C4D11×C22⋊Q811yescharacteristic
673C4#1062316511yescharacteristic
674C4#1062323611yescharacteristic
675C2—224no—
676C2#1307227811yescharacteristic
677C2D11×#47511yescharacteristic
678C2#1307845511yescharacteristic
679C2#1308019311yescharacteristic
680C2#1308030911yescharacteristic
681C2#1308048411yescharacteristic
682C2#1308073411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2066C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2066D11
hypocenterC11#25955
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
5. #13070157C2semidirect
6. #13069995C2semidirect
7. #13069757C2semidirect
8. #13068883C2semidirect
9. #13068881C2semidirect
13. #13068620C2semidirect
15. C11×#2066C2semidirect
67. C2×Q8×D11Q8semidirect
236. #2066D11semidirect
313. Dic22C22⋊Q8semidirect
376. C2×D11#475semidirect
570. C11#25955semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C2×D11×#1032
#130723202
#130714502
#130701572
#130699952
#130697572
#130688832
#130688812
#130688102
#130687922
#130686382
#130686202
#130685492
C11×#20662
#2595511