Finite Group Databasebeta

← #14772171

Subgroups — #14772171

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic
3C2×#10622401C211yesmaximal, characteristic
4Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13071517C211yesmaximal, characteristic
6#13069343C211yesmaximal, characteristic, complemented
7#13069341C211yesmaximal, characteristic, complemented
8#13068886C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic
10#13068874C211yesmaximal, characteristic
11#13068771C211yesmaximal, characteristic, complemented
12#13068619C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068477C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C4×#4325—24no—
36#10622602—21no—
37#10622598C2211yescharacteristic
38#10622589—21no—
39#10622589C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622401—24no—
53#10622401C418yescomplemented
54#10622281—21no—
55#10622280—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81Q8×Dic11C2×C414yescomplemented
82C2×#4325C2×C414yes—
83C2×#4325D414yes—
84C2×#4325Q814yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66946—22no—
109#66946—22no—
110#66946—41no—
111#66946C2×C414yes—
112C4⋊C4×D11—44no—
113C4×D44—22no—
114C4×D44—41no—
115C11×#106—41no—
116C11×#103—22no—
117C11×#103C2×C414yescomplemented
118C11×#95—21no—
119#66899—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885C2×C414yes—
127#66881—41no—
128Dic11⋊C8—22no—
129C8×Dic11—22no—
130C8×Dic11C2×C414yescomplemented
131#66873—22no—
132#66872—22no—
133#66872—22no—
134#66872C2×C414yescomplemented
135C4×C11⋊C8—22no—
136C4⋊C4×SD16—111nomaximal, Sylow
137C23×D11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C22×C412yes—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C412yes—
162C2×D44C2×D412yes—
163C2×D44C2×Q812yes—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4C22×C412yes—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190#4325C4⋊C4116yescomplemented
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—24no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203Dic11⋊C4—22no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207Dic11⋊C4—81no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210Dic11⋊C4SD1614yescomplemented
211C4×Dic11—24no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11C22×C412yes—
216C4×Dic11#4112yes—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C2×D412yes—
222C2×C11⋊C8C2×Q812yes—
223C2×C4×SD16—111no—
224C2×C4×SD16—111no—
225C2×C4×SD16—111no—
226Q8×C4⋊C4—111no—
227D4×C4⋊C4—111no—
228#1941—111no—
229#1941—111no—
230#1865—111no—
231#1865D1111yescharacteristic, complemented
232#1864—111no—
233#1864—111no—
234#1844—111no—
235#1803—111no—
236#1802—111no—
237C8×C4⋊C4—111no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11C2×C4⋊C414yescomplemented
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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×C11—41no—
267C2×C4×C11C2×SD1612yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
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×Dic11C4×D412yes—
291C2×Dic11C4×D412yes—
292C2×Dic11C2×SD1612yes—
293C2×Dic11C2×SD1612yes—
294C2×Dic11#13512yes—
295D44—22no—
296D44—22no—
297D44—22no—
298D44C2×C4⋊C414yes—
299C4×D11—48no—
300C4×D11—84no—
301C4×D11—84no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—41no—
305C11⋊C8C2×C4⋊C414yescomplemented
306C22×SD16—111no—
307C2×C4×Q8—111no—
308C2×C4×Q8—111no—
309C2×C4×Q8C2×D1111yescharacteristic
310C2×C4×D4—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C22×C4⋊C4—221no—
314C4×SD16—118no—
315C4×SD16—224no—
316C4×SD16—224no—
317C2×#106—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#106C2×D1111yescharacteristic
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#103C2×D1111yescharacteristic
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332#389—111no—
333#389—111no—
334#389—111no—
335#389—221no—
336#389—221no—
337#389C2×D1111yescharacteristic
338#385—221no—
339#385—221no—
340#384—111no—
341#384—111no—
342#384—221no—
343#380—221no—
344C4×C4⋊C4—111no—
345C4×C4⋊C4—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#336—111no—
351#336C2×D1111yescharacteristic
352C22×C11C2×C4×D411yescharacteristic
353C22×C11D4211yescharacteristic
354C22×C11D4×Q811yescharacteristic
355C22×C11C22×SD1611yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57711yescharacteristic
359C2×D11—24no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C4×C11—24no—
367C4×C11—22no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11C22×C4⋊C411yescharacteristic
373C4×C11#52011yescharacteristic
374C4×C11#54711yescharacteristic
375C4×C11#55411yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—42no—
379Dic11—41no—
380Dic11—81no—
381Dic11—81no—
382Dic11C4×SD1614yescomplemented
383C22×Q8C22×D1111yescharacteristic
384C22×D4—111no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4—221no—
388C2×SD16—114no—
389C2×SD16—114no—
390C2×SD16—114no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4×Q8—22no—
396C4×Q8—41no—
397C4×Q8—114no—
398C4×Q8—222no—
399C4×Q8—222no—
400C4×Q8—441no—
401C4×D4—114no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—441no—
406C4×D4—441no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—444no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436#106—41no—
437#106—114no—
438#106—222no—
439#106—222no—
440#106—441no—
441C4⋊C8—222no—
442#103—22no—
443#103—222no—
444#103C4×D1114yescomplemented
445#102—114no—
446#102—222no—
447#102—222no—
448C4×C8—114no—
449C4×C8—222no—
450C4×C8—222no—
451#95—21no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457C2×C11D4×C4⋊C411yescharacteristic
458C2×C11C2×C4×SD1611yescharacteristic
459C2×C11#295211yescharacteristic
460C2×C11D4×SD1611yescharacteristic
461C2×C11#328411yescharacteristic
462C2×C11Q8×SD1611yescharacteristic
463C2×C11#338111yescharacteristic
464D11—44no—
465C24—221no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8C2×C4×D1112yes—
470C2×Q8D4×D1112yes—
471C2×Q8Q8×D1112yes—
472C2×D4—112no—
473C2×D4—112no—
474C2×D4—112no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—224no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—881no—
497C22×C4—881no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—1116no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—112no—
508C2×C8—112no—
509C2×C8—112no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8C2×C4×D1112yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—114no—
522C4⋊C4—112no—
523C4⋊C4—222no—
524C4⋊C4—224no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C4⋊C4—881no—
538C4⋊C4C2×C4×D1112yes—
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—112no—
546C42—112no—
547C42—224no—
548C42—221no—
549C42—221no—
550C42—442no—
551C11C4⋊C4×SD1611yescharacteristic, complemented, Sylow
552C23—222no—
553C23—222no—
554C23—222no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8C4⋊C4×D1114yescomplemented
564D4—114no—
565D4—222no—
566D4—222no—
567D4—222no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—221no—
598C2×C4—448no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—884no—
608C2×C4—884no—
609C2×C4SD16×D1112yes—
610C2×C4C22×C4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4C2×Q8×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#6704311yescharacteristic
616C8—22no—
617C8—41no—
618C8—114no—
619C8—441no—
620C22—224no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22C4×D4×D1111yescharacteristic
628C22#1062312111yescharacteristic
629C22#1062316311yescharacteristic
630C22C2×SD16×D1111yescharacteristic
631C22D11×#13511yescharacteristic
632C22#1062330911yescharacteristic
633C22#1062330911yescharacteristic
634C4—24no—
635C4—22no—
636C4—41no—
637C4—42no—
638C4—81no—
639C4—81no—
640C4—114no—
641C4—222no—
642C4—222no—
643C4—441no—
644C4—442no—
645C4—881no—
646C4—881no—
647C4C2×C4⋊C4×D1111yescharacteristic
648C4#1062307711yescharacteristic
649C4#1062316711yescharacteristic
650C4#1062318611yescharacteristic
651C2—444no—
652C2#1307151411yescharacteristic
653C2C4×SD16×D1111yescharacteristic
654C2#1307749611yescharacteristic
655C2#1308030511yescharacteristic
656C2#1308033911yescharacteristic
657C2#1308147511yescharacteristic
658C2#1308149411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11C4⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. Q8×Dic11⋊C4C2semidirect
6. #13069343C2semidirect
7. #13069341C2semidirect
8. #13068886C2semidirect
11. #13068771C2semidirect
12. #13068619C2semidirect
14. #13068477C2semidirect
15. C11×#1865C2semidirect
53. #10622401C4semidirect
81. Q8×Dic11C2×C4semidirect
117. C11×#103C2×C4semidirect
130. C8×Dic11C2×C4semidirect
134. #66872C2×C4semidirect
190. #4325C4⋊C4semidirect
210. Dic11⋊C4SD16semidirect
231. #1865D11semidirect
249. Q8×C11C2×C4⋊C4semidirect
305. C11⋊C8C2×C4⋊C4semidirect
382. Dic11C4×SD16semidirect
444. #103C4×D11semidirect
551. C11C4⋊C4×SD16semidirect
563. Q8C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
C2×#106224012
Q8×Dic11⋊C42
#130715172
#130693432
#130693412
#130688862
#130688802
#130688742
#130687712
#130686192
#130686152
#130684772
C11×#18652
C4⋊C4×SD1611