Finite Group Databasebeta

← #14801955

Subgroups — #14801955

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×#10622390C211yesmaximal, characteristic
2C2×#10622784C211yesmaximal, characteristic
3#13073093C211yesmaximal, characteristic, complemented
4#13071628C211yesmaximal, characteristic
5#13070094C211yesmaximal, characteristic, complemented
6#13070022C211yesmaximal, characteristic, complemented
7#13069997C211yesmaximal, characteristic, complemented
8#13069929C211yesmaximal, characteristic, complemented
9#13069378C211yesmaximal, characteristic, complemented
10#13069252C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1877C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C22×C8×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#391C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622823—21no—
34#10622784—24no—
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622589C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622569—21no—
43#10622558—21no—
44C4×(C2×D11)⋊C4C2211yescharacteristic
45#10622548C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622390—24no—
49#10622281—21no—
50#10622281—21no—
51#10622270—21no—
52#10622270—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11C2311yescharacteristic
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66999—22no—
83#66999—22no—
84#66991—22no—
85#66991D414yes—
86C4×C22⋊D11—44no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×(C2×D11)⋊C4D411yescharacteristic
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×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×C8×D11—22no—
107C2×C8×D11—22no—
108C2×C8×D11—41no—
109C4⋊C4×D11—22no—
110C4⋊C4×D11—22no—
111C4⋊C4×D11—22no—
112C4⋊C4×D11—41no—
113C11×#103—22no—
114C11×#102—22no—
115C11×#95—21no—
116C11×#95—21no—
117#66899—22no—
118#66899—41no—
119#66896—22no—
120#66896—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127(C2×D11)⋊C8—22no—
128#66881—22no—
129#66881—22no—
130Dic11⋊C8—22no—
131#66872—22no—
132C4⋊(C11⋊C8)—41no—
133#25202—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11C2×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—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×D412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—81no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×C4×D11C2×D412yes—
178C2×C4×D11#4112yes—
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#4112yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4#4112yes—
190C11×C22⋊C4—42no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—24no—
194C22⋊Dic11—42no—
195C22⋊Dic11—81no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4SD1614yescomplemented
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—81no—
207C4⋊Dic11—81no—
208C4⋊Dic11C2×D412yes—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—81no—
214Dic11⋊C4—81no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C8×D11—44no—
225C2×#481—111no—
226C2×#465—111no—
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#1877D1111yescharacteristic, complemented
236#1872—111no—
237#1850—111no—
238#1802—111no—
239C2×#340—111no—
240C23×C11—22no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C22×D411yescharacteristic
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11#12112yes—
253C22×D11C2×SD1612yes—
254C22×D11#13712yes—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
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—84no—
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—48no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—41no—
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×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×D4—221no—
322C2×C4×D4C2×D1111yescharacteristic
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325#481—224no—
326#465—224no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
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#391C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
360#336—111no—
361#336C2×D1111yescharacteristic
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
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×#13711yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11#46114yes—
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11#52911yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54611yescharacteristic
391C4×C11#54711yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—41no—
395Dic11—42no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—21no—
403C23×C4—111no—
404C23×C4—221no—
405C23×C4—221no—
406C2×SD16—22no—
407C2×SD16—22no—
408C2×SD16—41no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—222no—
412C22×C8—222no—
413C22×C8—441no—
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22⋊Q8—222no—
417C22⋊Q8—222no—
418#121—114no—
419#121—222no—
420C4×D4—22no—
421C4×D4—41no—
422C4×D4—444no—
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—441no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42C22×D1111yescharacteristic
451#106—222no—
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—21no—
464#95—21no—
465#95—111no—
466#95—111no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—82no—
472C2×C11#242511yescharacteristic
473C2×C11C2×#46111yescharacteristic
474C2×C11#304511yescharacteristic
475C2×C11#329511yescharacteristic
476C2×C11#331611yescharacteristic
477C2×C11#333511yescharacteristic
478C2×C11#334611yescharacteristic
479D11—24no—
480C24—21no—
481C24—111no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—224no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4D4×D1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4—881no—
522C22×C4D4×D1111yescharacteristic
523C22×C4D4×D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525SD16—44no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—444no—
538C2×C8#433912yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—112no—
543C4⋊C4—221no—
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—881no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C4⋊C4#434112yes—
559C22⋊C4—42no—
560C22⋊C4—114no—
561C22⋊C4—222no—
562C22⋊C4—224no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—881no—
566C42—21no—
567C42—21no—
568C42—221no—
569C42—221no—
570C42—442no—
571C11#2520211yescharacteristic, complemented, Sylow
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—112no—
580C23—112no—
581C23—112no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23C2×D4×D1111yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—448no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
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—221no—
624C2×C4—222no—
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—441no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4SD16×D1112yes—
639C2×C4C2×#433911yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4C2×#434111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704311yescharacteristic
645C8—22no—
646C8—41no—
647C8—441no—
648C8—441no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—114no—
657C22—222no—
658C22—222no—
659C22—222no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22#1062308211yescharacteristic
664C22#1062312211yescharacteristic
665C22D11×#12111yescharacteristic
666C22C2×SD16×D1111yescharacteristic
667C22#1062330111yescharacteristic
668C22#1062330511yescharacteristic
669C22D11×#13711yescharacteristic
670C4—22no—
671C4—42no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—222no—
676C4—222no—
677C4—442no—
678C4—441no—
679C4—881no—
680C4—881no—
681C4—881no—
682C4#1062302111yescharacteristic
683C4#1062308811yescharacteristic
684C4#1062314211yescharacteristic
685C4#1062319111yescharacteristic
686C2—82no—
687C2—224no—
688C2#1307216611yescharacteristic
689C2D11×#46111yescharacteristic
690C2#1307815611yescharacteristic
691C2#1308043311yescharacteristic
692C2#1308072011yescharacteristic
693C2#1308097511yescharacteristic
694C2#1308110611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1877D11
hypocenterC11#25202
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #13073093C2semidirect
5. #13070094C2semidirect
6. #13070022C2semidirect
7. #13069997C2semidirect
8. #13069929C2semidirect
9. #13069378C2semidirect
10. #13069252C2semidirect
11. #13068920C2semidirect
12. #13068795C2semidirect
13. #13068616C2semidirect
14. D11×#340C2semidirect
15. C11×#1877C2semidirect
198. (C2×D11)⋊C4SD16semidirect
235. #1877D11semidirect
571. C11#25202semidirect

Maximal subgroups

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

subgroupindex
C2×#106223902
C2×#106227842
#130730932
#130716282
#130700942
#130700222
#130699972
#130699292
#130693782
#130692522
#130689202
#130687952
#130686162
D11×#3402
C11×#18772
#2520211