Finite Group Databasebeta

← #14770835

Subgroups — #14770835

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#103C211yesmaximal, characteristic
2#13071484C211yesmaximal, characteristic
3Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069305C211yesmaximal, characteristic, complemented
6#13069258C211yesmaximal, characteristic, complemented
7#13069256C211yesmaximal, characteristic, complemented
8#13068872C211yesmaximal, characteristic, complemented
9#13068701C211yesmaximal, characteristic
10#13068642C211yesmaximal, characteristic
11#13068549C211yesmaximal, characteristic
12#13068448C211yesmaximal, characteristic, complemented
13#13068446C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66945—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33#10622600—21no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622591—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39#10622587—21no—
40#10622587C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C4×(C2×D11)⋊C4—21no—
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542—21no—
47#10622542C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49D11×#103C418yescomplemented
50#10622277—21no—
51#10622268—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C2×Q8×D11—22no—
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—41no—
65C2×Q8×D11—41no—
66C2×Q8×D11C2×C414yes—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×Q8×C11—22no—
75C4×Q8×C11—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—41no—
102C2×C8×D11—41no—
103C2×C8×D11C2×C414yes—
104#66945—44no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11C2×C414yes—
107C11×#107—41no—
108C11×#103—22no—
109C11×#103C2×C414yes—
110C11×#95—21no—
111#66899—22no—
112#66899C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124(C2×D11)⋊C8—22no—
125#66882—41no—
126#66880—41no—
127#66880C2×C414yes—
128#66879—41no—
129#66874—41no—
130#66874C2×C414yes—
131#66867—41no—
132#22563—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C22×C412yes—
138C2×Q8×C11#4112yes—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154Q8×D11—28no—
155Q8×D11—44no—
156Q8×D11—44no—
157Q8×D11—44no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11C22×C412yes—
169C2×C4×D11#4112yes—
170C2×Dic22—24no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22C22×C412yes—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4C22×C412yes—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207C4⋊Dic11C22×C412yes—
208Dic11⋊C4—24no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8C22×C412yes—
220C8×D11—44no—
221C22×#103—111no—
222#2344—111no—
223Q8×C22⋊C4—111no—
224#1935—111no—
225#1935—111no—
226#1928—111no—
227#1928—111no—
228#1863—111no—
229#1863D1111yescharacteristic, complemented
230#1823—111no—
231#1808—111no—
232#1787—111no—
233#1763—111no—
234#1763—111no—
235#1752—111no—
236C23×C11C22×D411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11C4×D412yes—
242C22×D11AGL(1,ℤ/8)12yes—
243C22×D11#13712yes—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11#11714yescomplemented
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11C4×D412yes—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—48no—
298C4×D11—48no—
299Dic22—22no—
300Dic22—22no—
301Dic22—48no—
302Dic22—41no—
303Dic22—41no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C23×Q8—111no—
309C23×C8—111no—
310C2×C4×Q8—111no—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×#117—221no—
313C22×C4⋊C4—111no—
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—118no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103C2×D1111yescharacteristic
324C2×#103C2×D1111yescharacteristic
325C2×C22⋊C8—111no—
326C2×#97—111no—
327C2×#97—111no—
328#391—111no—
329#391—111no—
330#391—221no—
331#391—221no—
332#389—111no—
333#389C2×D1111yescharacteristic
334#387—221no—
335#387—221no—
336#381—221no—
337#380—111no—
338#380—111no—
339#380—221no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4—111no—
342C4×C22⋊C4—111no—
343C4×C22⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#336—111no—
351#336C2×D1111yescharacteristic
352C22×C11C2×C4×D411yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57811yescharacteristic
358C22×C11#57811yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11#44014yes—
366C4×C11—24no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11C2×#11711yescharacteristic
373C4×C11#51811yescharacteristic
374C4×C11#55111yescharacteristic
375C4×C11#55111yescharacteristic
376Dic11—22no—
377Dic11—42no—
378Dic11—42no—
379Dic11—41no—
380Dic11—41no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8—114no—
384C22×Q8—111no—
385C22×Q8—221no—
386C22×Q8—222no—
387C22×Q8—222no—
388C22×Q8—222no—
389C22×Q8—441no—
390C22×Q8—441no—
391C22×Q8C22×D1111yescharacteristic
392C23×C4—111no—
393C23×C4—221no—
394C23×C4—221no—
395C22×C8—111no—
396C22×C8—114no—
397C22×C8—111no—
398C22×C8—441no—
399C22×C8—441no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4×Q8—22no—
403C4×Q8—41no—
404C4×Q8—222no—
405C4×Q8—441no—
406#117—444no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—21no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430#107—41no—
431#107—441no—
432#103—22no—
433#103—114no—
434#103—114no—
435#103—114no—
436#103—222no—
437#103—441no—
438#103—441no—
439#103C4×D1114yes—
440C22⋊C8—222no—
441#97—441no—
442#97—441no—
443#95—21no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11#234211yescharacteristic
456C2×C11C2×#44011yescharacteristic
457C2×C11#295011yescharacteristic
458C2×C11#330811yescharacteristic
459C2×C11#330811yescharacteristic
460C2×C11#331211yescharacteristic
461C2×C11#331211yescharacteristic
462D11—24no—
463C24—111no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—112no—
468C2×Q8—224no—
469C2×Q8—221no—
470C2×Q8—228no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—442no—
476C2×Q8—442no—
477C2×Q8—444no—
478C2×Q8—444no—
479C2×Q8—444no—
480C2×Q8C2×C4×D1112yes—
481C2×Q8#434112yes—
482C2×Q8#434312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—111no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—444no—
521C2×C8C2×C4×D1112yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—112no—
530C4⋊C4—224no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4C2×C4×D1112yes—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—221no—
547C42—221no—
548C42—442no—
549C42—442no—
550C42—442no—
551C11#2256311yescharacteristic, complemented, Sylow
552C23—112no—
553C23—112no—
554C23—112no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—222no—
564Q8—222no—
565Q8—448no—
566Q8—441no—
567Q8—441no—
568Q8#6694514yescomplemented
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—112no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—448no—
603C2×C4—448no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4C22×C4×D1111yescharacteristic
615C2×C4C2×#434111yescharacteristic
616C2×C4#6703711yescharacteristic
617C2×C4C2×#434311yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C2×C4#6704211yescharacteristic
620C8—22no—
621C8—41no—
622C8—222no—
623C8—441no—
624C22—114no—
625C22—222no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22C4×D4×D1111yescharacteristic
632C22#1062312211yescharacteristic
633C22#1062316111yescharacteristic
634C22#1062329711yescharacteristic
635C22#1062330211yescharacteristic
636C22D11×AGL(1,ℤ/8)11yescharacteristic
637C22D11×#13711yescharacteristic
638C4—24no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—222no—
645C4—441no—
646C4—441no—
647C4—442no—
648C4—442no—
649C4—881no—
650C4—881no—
651C4C2×#6694511yescharacteristic
652C4#1062307611yescharacteristic
653C4#1062316811yescharacteristic
654C4#1062318911yescharacteristic
655C2—224no—
656C2#1307146311yescharacteristic
657C2D11×#44011yescharacteristic
658C2#1307747911yescharacteristic
659C2#1308060011yescharacteristic
660C2#1308060411yescharacteristic
661C2#1308066011yescharacteristic
662C2#1308066411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1863D11
hypocenterC11#22563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069305C2semidirect
6. #13069258C2semidirect
7. #13069256C2semidirect
8. #13068872C2semidirect
12. #13068448C2semidirect
13. #13068446C2semidirect
15. C11×#1863C2semidirect
49. D11×#103C4semidirect
229. #1863D11semidirect
247. Q8×C11#117semidirect
551. C11#22563semidirect
568. Q8#66945semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1032
#130714842
Q8×(C2×D11)⋊C42
#130693072
#130693052
#130692582
#130692562
#130688722
#130687012
#130686422
#130685492
#130684482
#130684462
#130683912
C11×#18632
#2256311