Finite Group Databasebeta

← #14816883

Subgroups — #14816883

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic, complemented
2#13072482C211yesmaximal, characteristic
3Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13070142C211yesmaximal, characteristic
5#13070095C211yesmaximal, characteristic, complemented
6#13070002C211yesmaximal, characteristic
7#13069956C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic
11#13068973C211yesmaximal, characteristic
12#13068877C211yesmaximal, characteristic
13#13068872C211yesmaximal, characteristic, complemented
14#13068870C211yesmaximal, characteristic, complemented
15C2×C4×C11×SD16C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C4×C11×SD16—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825—21no—
34#10622823—21no—
35C2×#66882C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622589—21no—
40#10622589C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622562—21no—
46#10622561—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622409—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×SD16Q814yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83Q8×Dic11—22no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86Q8×Dic11—41no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66943—22no—
110#66943—41no—
111C11×#106—22no—
112C11×#103D414yes—
113C11×#102—22no—
114C4×C8×C11—22no—
115#66899—22no—
116#66899—22no—
117#66896—22no—
118#66896—41no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66882—22no—
126#66882—22no—
127Dic11⋊C8—22no—
128#66872—22no—
129#66871—41no—
130#26379—111nomaximal, Sylow
131C24×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×Q812yes—
137C2×Q8×C11#4112yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C11×SD16—28no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C2×C8×C11C2×Q812yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—42no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180C22⋊Dic11—81no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—22no—
194Dic11⋊C4—22no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—24no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×#479—111no—
214C2×C4×SD16D1111yescharacteristic
215#2454—111no—
216Q8×C4⋊C4—111no—
217#2093—111no—
218#2084—111no—
219#2067—111no—
220#2059—111no—
221#1942—111no—
222#1916—111no—
223#1880—111no—
224#1880—111no—
225#1864—111no—
226#1863—111no—
227#1863—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11C22⋊Q814yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—84no—
259C2×C4×C11#13712yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11#13512yes—
290C8×C11—22no—
291C8×C11—22no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C22×SD16C2×D1111yescharacteristic
295C2×#125—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8C2×D1111yescharacteristic
299C2×C4×D4C2×D1111yescharacteristic
300#479—224no—
301C4×SD16—24no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103C2×D1111yescharacteristic
311C2×#102—111no—
312C2×#102—111no—
313C2×#102C2×D1111yescharacteristic
314C2×C4×C8C2×D1111yescharacteristic
315#399—221no—
316#396—221no—
317#390—111no—
318#390—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—111no—
323#389—221no—
324#389—221no—
325#385—221no—
326#384—111no—
327#384—221no—
328#380—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#52511yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11D4×Q811yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C4×C11—24no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11C2×C22⋊Q811yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#54711yescharacteristic
361C4×C11#55411yescharacteristic
362Dic11—22no—
363Dic11—41no—
364Dic11—42no—
365Dic11—41no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370C22×Q8C22×D1111yescharacteristic
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16Dic2214yes—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#125—222no—
381#125—441no—
382C4×Q8—22no—
383C4×Q8—41no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—441no—
388C4×D4—22no—
389C4×D4—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—21no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#107—222no—
422#107—441no—
423#106—22no—
424#106—222no—
425C4⋊C8—222no—
426#103—222no—
427#103—222no—
428#103C22⋊D1114yes—
429#102—22no—
430#102—222no—
431#102—441no—
432C4×C8—22no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—82no—
440C2×C11#244911yescharacteristic
441C2×C11#310811yescharacteristic
442C2×C11#311911yescharacteristic
443C2×C11#326611yescharacteristic
444C2×C11#328711yescharacteristic
445C2×C11#338111yescharacteristic
446C2×C11#338511yescharacteristic
447C24—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×Dic2212yes—
452C2×Q8#433912yes—
453C2×Q8C2×C22⋊D1112yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4C2×Dic2212yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—28no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8C2×Dic2212yes—
489C2×C8C2×C22⋊D1112yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—112no—
495C4⋊C4—222no—
496C4⋊C4—224no—
497C4⋊C4—222no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C4⋊C4—881no—
511C4⋊C4—881no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4C2×C22⋊D1112yes—
515C22⋊C4—42no—
516C22⋊C4—442no—
517C22⋊C4—881no—
518C22⋊C4—881no—
519C22⋊C4—881no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—224no—
524C42—221no—
525C42—221no—
526C42—221no—
527C42—221no—
528C42—442no—
529C11#2637911yescharacteristic, complemented, Sylow
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C2×D4×D1111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—22no—
541Q8#6697714yes—
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—221no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4#6696812yes—
586C2×C4C22×Dic2211yescharacteristic
587C2×C4C2×#433911yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#6704311yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—22no—
593C8—22no—
594C8—441no—
595C8—441no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22D4×Dic2211yescharacteristic
604C22#1062307811yescharacteristic
605C22C2×#6696811yescharacteristic
606C22#1062329311yescharacteristic
607C22D11×#13511yescharacteristic
608C22#1062330011yescharacteristic
609C22D4×C22⋊D1111yescharacteristic
610C4—24no—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—81no—
615C4—222no—
616C4—441no—
617C4—442no—
618C4—441no—
619C4—441no—
620C4—881no—
621C4—881no—
622C4—881no—
623C4#1062307011yescharacteristic
624C4#1062309511yescharacteristic
625C4C2×#6697711yescharacteristic
626C4#1062335511yescharacteristic
627C2—82no—
628C2#1307241911yescharacteristic
629C2#1307869411yescharacteristic
630C2#1307882111yescharacteristic
631C2#1308012611yescharacteristic
632C2#1308037011yescharacteristic
633C2#1308149211yescharacteristic
634C2#1308152411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#26379
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622409C2semidirect
3. Q8×Dic11⋊C4C2semidirect
5. #13070095C2semidirect
7. #13069956C2semidirect
8. #13069349C2semidirect
9. #13069173C2semidirect
13. #13068872C2semidirect
14. #13068870C2semidirect
529. C11#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
#130724822
Q8×Dic11⋊C42
#130701422
#130700952
#130700022
#130699562
#130693492
#130691732
#130689732
#130688772
#130688722
#130688702
C2×C4×C11×SD162
#2637911