Finite Group Databasebeta

← #14801987

Subgroups — #14801987

Order 2816.

940 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×#10622418C211yesmaximal, characteristic, complemented
2C2×#10622784C211yesmaximal, characteristic
3#13073086C211yesmaximal, characteristic
4#13071626C211yesmaximal, characteristic, complemented
5#13070096C211yesmaximal, characteristic, complemented
6#13070024C211yesmaximal, characteristic, complemented
7#13069988C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069240C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068930C211yesmaximal, characteristic
12#13068792C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66936—21no—
24C2×#66936—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622784—24no—
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622562—21no—
44#10622562—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46#10622548C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622418—24no—
49#10622281—21no—
50#10622279—21no—
51#10622265—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66999—22no—
81#66999D414yes—
82Q8×Dic11—22no—
83Q8×Dic11—41no—
84#66991—22no—
85#66991—22no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—41no—
110C4⋊C4×D11—22no—
111C4⋊C4×D11—22no—
112C4⋊C4×D11—22no—
113C4⋊C4×D11—41no—
114#66936—44no—
115#66936—44no—
116C11×C4⋊C8—22no—
117C11×#103—22no—
118C11×#102—41no—
119C11×#95—21no—
120C11×#95—21no—
121#66899—22no—
122#66899—22no—
123#66896—22no—
124#66896—22no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129(C2×D11)⋊C8—22no—
130#66881—22no—
131#66881—22no—
132Dic11⋊C8—41no—
133#66872—22no—
134#25204—111nomaximal, Sylow
135C24×C11—21no—
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—81no—
175C2×C4×D11C2×D412yes—
176C2×C4×D11#4112yes—
177C11×SD16—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11#4112yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C42×C11—21no—
191C42×C11—21no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4SD1614yescomplemented
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C4×Dic11—81no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C8×D11—44no—
226C2×#483—111no—
227C2×#465—111no—
228#2501—111no—
229#2360—111no—
230#2084—111no—
231#2072—111no—
232#2065—111no—
233#2055D1111yescharacteristic, complemented
234#1948—111no—
235#1926—111no—
236#1880—111no—
237#1874—111no—
238#1850—111no—
239#1803—111no—
240C2×#340—111no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11#12112yes—
254C22×D11C2×SD1612yes—
255C22×D11AGL(1,ℤ/8)12yes—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
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×C11C2×SD1612yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C22⋊D11—84no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
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#12112yes—
306C2×Dic11C2×SD1612yes—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—84no—
312C4×D11—84no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C22×SD16C2×D1111yescharacteristic
318C23×C8—111no—
319C2×#123—221no—
320C2×#123—221no—
321C2×C22⋊Q8—111no—
322C2×#121—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325C22×C4⋊C4—111no—
326#483—224no—
327#465—224no—
328C2×#106—111no—
329C2×#106—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#103—111no—
334C2×#103—111no—
335C2×#103C2×D1111yescharacteristic
336C2×#102—111no—
337C2×#102—111no—
338C2×#102C2×D1111yescharacteristic
339C2×C22⋊C8—111no—
340#399—221no—
341#399—221no—
342#391C2×D1111yescharacteristic
343#390—111no—
344#390C2×D1111yescharacteristic
345#389—111no—
346#389—221no—
347#387—221no—
348#385—221no—
349#384—111no—
350#384—111no—
351C4×C4⋊C4—111no—
352C4×C22⋊C4—111no—
353C4×C22⋊C4—221no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#336—111no—
361#336—111no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×#12111yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C22×SD1611yescharacteristic
373C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57811yescharacteristic
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11#46014yes—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11#52911yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54611yescharacteristic
391C4×C11#54711yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—42no—
395Dic11—42no—
396Dic11—41no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—111no—
403C23×C4—221no—
404C23×C4—221no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—41no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—222no—
411C22×C8—222no—
412C22×C8—441no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415#123—444no—
416#123—444no—
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—222no—
420#121—222no—
421C4×Q8—222no—
422C4×Q8—441no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
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—221no—
439C2×C4⋊C4—441no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—111no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454#106—222no—
455#106—222no—
456#106—222no—
457C4⋊C8—22no—
458C4⋊C8—441no—
459#103—22no—
460#103—222no—
461#103—222no—
462#102—41no—
463#102—222no—
464#102—222no—
465C22⋊C8—222no—
466#95—21no—
467#95—21no—
468#95—111no—
469#95—111no—
470#95—221no—
471#95—221no—
472C2×C11—161no—
473C2×C11#242511yescharacteristic
474C2×C11C2×#46011yescharacteristic
475C2×C11#304611yescharacteristic
476C2×C11#329811yescharacteristic
477C2×C11#330611yescharacteristic
478C2×C11#333511yescharacteristic
479C2×C11#334311yescharacteristic
480D11—24no—
481C24—21no—
482C24—111no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8D4×D1112yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—442no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—111no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—881no—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4C23×D1111yescharacteristic
523SD16—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—444no—
536C2×C8#434112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—112no—
542C4⋊C4—112no—
543C4⋊C4—224no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—881no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—114no—
561C22⋊C4—222no—
562C22⋊C4—224no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C42—21no—
567C42—21no—
568C42—221no—
569C42—221no—
570C42—442no—
571C42—881no—
572C11#2520411yescharacteristic, complemented, Sylow
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—112no—
581C23—112no—
582C23—112no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23C2×D4×D1111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—884no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
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—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—222no—
624C2×C4—221no—
625C2×C4—222no—
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—441no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4SD16×D1112yes—
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704311yescharacteristic
645C8—22no—
646C8—41no—
647C8—441no—
648C8—441no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—114no—
657C22—222no—
658C22—222no—
659C22—222no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22D11×#12111yescharacteristic
664C22#1062314211yescharacteristic
665C22#1062314311yescharacteristic
666C22C2×SD16×D1111yescharacteristic
667C22#1062330111yescharacteristic
668C22D11×AGL(1,ℤ/8)11yescharacteristic
669C22#1062331011yescharacteristic
670C4—22no—
671C4—42no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—222no—
676C4—222no—
677C4—441no—
678C4—442no—
679C4—442no—
680C4—881no—
681C4—881no—
682C4#1062312211yescharacteristic
683C4#1062318611yescharacteristic
684C4#1062319111yescharacteristic
685C4#1062321111yescharacteristic
686C2—161no—
687C2—224no—
688C2#1307216811yescharacteristic
689C2D11×#46011yescharacteristic
690C2#1307816911yescharacteristic
691C2#1308048411yescharacteristic
692C2#1308058411yescharacteristic
693C2#1308096811yescharacteristic
694C2#1308105111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2055D11
hypocenterC11#25204
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. C2×#10622418C2semidirect
4. #13071626C2semidirect
5. #13070096C2semidirect
6. #13070024C2semidirect
7. #13069988C2semidirect
8. #13069380C2semidirect
9. #13069240C2semidirect
10. #13068973C2semidirect
12. #13068792C2semidirect
13. #13068619C2semidirect
14. D11×#340C2semidirect
15. C11×#2055C2semidirect
197. (C2×D11)⋊C4SD16semidirect
233. #2055D11semidirect
572. C11#25204semidirect

Maximal subgroups

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

subgroupindex
C2×#106224182
C2×#106227842
#130730862
#130716262
#130700962
#130700242
#130699882
#130693802
#130692402
#130689732
#130689302
#130687922
#130686192
D11×#3402
C11×#20552
#2520411