Finite Group Databasebeta

← #14801962

Subgroups — #14801962

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C211yesmaximal, characteristic
2#13073095C211yesmaximal, characteristic, complemented
3#13071636C211yesmaximal, characteristic
4#13070095C211yesmaximal, characteristic, complemented
5#13070022C211yesmaximal, characteristic, complemented
6#13069993C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069376C211yesmaximal, characteristic, complemented
9#13069253C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C2×C11×#465C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11—21no—
21C2×D4×Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C11×#465—24no—
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622647—24no—
41#10622598C2211yescharacteristic
42#10622596—21no—
43#10622596—21no—
44#10622589C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49#10622564—21no—
50#10622563—21no—
51#10622559—21no—
52#10622559—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×#121—22no—
79C11×#121D414yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90D4×Dic11—22no—
91D4×Dic11—41no—
92D4×Dic11—44no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C11×#106—22no—
114C11×#103—22no—
115C11×#102—22no—
116#66899—22no—
117#66899—41no—
118#66896—22no—
119#66896—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128C22⋊(C11⋊C8)—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—41no—
131#66872—22no—
132#66872—22no—
133#25202—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—81no—
172C22×Dic11—81no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C11×SD16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—44no—
186C2×C8×C11#4112yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—81no—
198C22⋊Dic11SD1614yescomplemented
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×#481—111no—
226C2×#465D1111yescharacteristic
227#2502—111no—
228#2361—111no—
229#2084—111no—
230#2071—111no—
231#2066—111no—
232#2055—111no—
233#1948—111no—
234#1927—111no—
235#1877—111no—
236#1872—111no—
237#1850—111no—
238#1802—111no—
239C2×#340—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11#12112yes—
252C23×C11C2×SD1612yes—
253C23×C11#13712yes—
254C23×C11C22×D411yescharacteristic
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—48no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11#12112yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C112−1+411yescharacteristic
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—84no—
309C2×Dic11—84no—
310C2×Dic11—84no—
311C2×Dic11C2×SD1612yes—
312C2×Dic11C2×SD1612yes—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C22×SD16C2×D1111yescharacteristic
318C23×C8C2×D1111yescharacteristic
319C2×C22⋊Q8C2×D1111yescharacteristic
320C2×#121C2×D1111yescharacteristic
321C2×C4×D4—111no—
322C2×C4×D4—221no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325#481—224no—
326#465—24no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103C2×D1111yescharacteristic
335C2×#102—111no—
336C2×#102—111no—
337C2×#102C2×D1111yescharacteristic
338C2×C22⋊C8—111no—
339#398—221no—
340#398—221no—
341#391—111no—
342#391—111no—
343#390—111no—
344#389—111no—
345#388—221no—
346#386—221no—
347#385—221no—
348#385—221no—
349#385—221no—
350#384—111no—
351#384—111no—
352C4×C4⋊C4—111no—
353C4×C22⋊C4—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#336—111no—
361#336—111no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11#46114yes—
376C22×C11C2×#12111yescharacteristic
377C22×C11#54611yescharacteristic
378C22×C11#54711yescharacteristic
379C22×C11C22×SD1611yescharacteristic
380C22×C11C2×#13711yescharacteristic
381C22×C11#57611yescharacteristic
382C22×C11#57711yescharacteristic
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11#52911yescharacteristic
388C4×C11#53911yescharacteristic
389C4×C11#54611yescharacteristic
390C4×C11#54711yescharacteristic
391Dic11—22no—
392Dic11—22no—
393Dic11—41no—
394Dic11—42no—
395Dic11—41no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—21no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—221no—
403C23×C4—221no—
404C23×C4—221no—
405C23×C4C22×D1111yescharacteristic
406C2×SD16—22no—
407C2×SD16—22no—
408C2×SD16—41no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418#121—22no—
419#121C22⋊D1114yes—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—444no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—441no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—221no—
451#106—22no—
452#106—222no—
453#106—222no—
454C4⋊C8—222no—
455C4⋊C8—441no—
456#103—22no—
457#103—222no—
458#103—441no—
459#102—22no—
460#102—222no—
461#102—222no—
462C22⋊C8—222no—
463#95—111no—
464#95—111no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—24no—
472C2×C11—82no—
473C2×C11#242511yescharacteristic
474C2×C11C2×#46111yescharacteristic
475C2×C11#304511yescharacteristic
476C2×C11#329511yescharacteristic
477C2×C11#331611yescharacteristic
478C2×C11#333511yescharacteristic
479C2×C11#334611yescharacteristic
480C24—21no—
481C24D4×D1111yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4C2×C22⋊D1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4D4×D1111yescharacteristic
522C22×C4#434112yes—
523C22×C4C2×C22⋊D1112yes—
524C22×C4C23×D1111yescharacteristic
525SD16—44no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—44no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8#434112yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—112no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—881no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C4⋊C4C2×C22⋊D1112yes—
559C22⋊C4—24no—
560C22⋊C4—42no—
561C22⋊C4—114no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—881no—
566C42—221no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—442no—
571C11#2520211yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23SD16×D1112yes—
584C23#6696812yes—
585C23#6699212yes—
586C23C2×D4×D1111yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—221no—
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—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—884no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4#6699212yes—
639C2×C4C2×#434111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#6704311yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C8—22no—
646C8—41no—
647C8—441no—
648C8—441no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22#1062277514yes—
663C22#1062314111yescharacteristic
664C22#1062314211yescharacteristic
665C22C2×SD16×D1111yescharacteristic
666C22C2×#6696811yescharacteristic
667C22#1062330011yescharacteristic
668C22#1062330111yescharacteristic
669C22C2×#6699211yescharacteristic
670C4—22no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—222no—
675C4—222no—
676C4—441no—
677C4—442no—
678C4—441no—
679C4—881no—
680C4—881no—
681C4—881no—
682C4#1062313111yescharacteristic
683C4#1062313311yescharacteristic
684C4#1062333711yescharacteristic
685C4#1062335511yescharacteristic
686C2—24no—
687C2—82no—
688C2#1307217311yescharacteristic
689C2C2×#1062277511yescharacteristic
690C2#1307815311yescharacteristic
691C2#1308043511yescharacteristic
692C2#1308073311yescharacteristic
693C2#1308096811yescharacteristic
694C2#1308110711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#465D11
hypocenterC11#25202
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. #13073095C2semidirect
4. #13070095C2semidirect
5. #13070022C2semidirect
6. #13069993C2semidirect
7. #13069929C2semidirect
8. #13069376C2semidirect
9. #13069253C2semidirect
10. #13068952C2semidirect
11. #13068924C2semidirect
12. #13068794C2semidirect
13. #13068614C2semidirect
14. C2×#10622189C2semidirect
198. C22⋊Dic11SD16semidirect
571. C11#25202semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
#130730952
#130716362
#130700952
#130700222
#130699932
#130699292
#130693762
#130692532
#130689522
#130689242
#130687942
#130686142
C2×#106221892
C2×C11×#4652
#2520211