Finite Group Databasebeta

← #14813823

Subgroups — #14813823

Order 2816.

918 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×#10622776C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic, complemented
3#13072379C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13070148C211yesmaximal, characteristic, complemented
6#13070116C211yesmaximal, characteristic, complemented
7#13070019C211yesmaximal, characteristic, complemented
8#13069849C211yesmaximal, characteristic
9#13069300C211yesmaximal, characteristic, complemented
10#13069174C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic, complemented
12#13068969C211yesmaximal, characteristic, complemented
13#13068886C211yesmaximal, characteristic, complemented
14#13068879C211yesmaximal, characteristic, complemented
15C11×#1880C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×#66939—21no—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622776—24no—
31SD16×Dic11—24no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622598—21no—
40#10622598—21no—
41#10622598C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622598C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45#10622574—21no—
46#10622574—21no—
47#10622571—21no—
48#10622552C2211yescharacteristic
49#10622548—21no—
50#10622548C2211yescharacteristic
51C4×C4⋊Dic11—21no—
52C4×C4⋊Dic11C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C22×D44C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16D414yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325—22no—
89#66993—22no—
90#66993—41no—
91D4×Dic11—22no—
92D4×Dic11—41no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11D411yescharacteristic
105C2×C4⋊Dic11D411yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115#66939—44no—
116C11×#103—22no—
117C11×#102—22no—
118#66899—22no—
119#66896—22no—
120#66896—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885—22no—
127#66885—41no—
128#66881—22no—
129#66881—41no—
130Dic11⋊C8—22no—
131C8×Dic11—22no—
132#66873—22no—
133#26163—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11#4112yes—
141C2×Q8×C11#4112yes—
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×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—81no—
159C2×C22⋊D11—81no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C11×SD16—28no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4#4112yes—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—81no—
190C42×C11—24no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—42no—
194#4325—44no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—41no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—81no—
211C4⋊Dic11—81no—
212C4⋊Dic11—81no—
213C4⋊Dic11SD1614yescomplemented
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—42no—
219C4×Dic11—42no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×#460—111no—
227C2×C4×SD16—111no—
228#2445—111no—
229Q8×C4⋊C4—111no—
230#2094—111no—
231#2088—111no—
232#2071—111no—
233#2041—111no—
234#1934—111no—
235#1916—111no—
236#1880—111no—
237#1880—111no—
238#1880D1111yescharacteristic, complemented
239#1865—111no—
240#1864—111no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11#12314yescomplemented
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
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—
286C22⋊D11—84no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
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—84no—
307C2×Dic11C2×SD1612yes—
308C2×Dic11C2×SD1612yes—
309D44—41no—
310D44—41no—
311D44—41no—
312D44—41no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C22×SD16—111no—
318C22×SD16C2×D1111yescharacteristic
319C2×#127—111no—
320C2×#123—221no—
321C2×C4×Q8—111no—
322C2×C4×Q8—111no—
323C2×C4×Q8C2×D1111yescharacteristic
324C2×C4×D4—111no—
325#460—224no—
326C4×SD16—224no—
327C2×#106—111no—
328C2×#106—111no—
329C2×C4⋊C8—111no—
330C2×#103—111no—
331C2×#103C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102C2×D1111yescharacteristic
338C2×C4×C8—111no—
339#394—221no—
340#394—221no—
341#390—111no—
342#390—111no—
343#390C2×D1111yescharacteristic
344#389—111no—
345#389—111no—
346#389—111no—
347#389—221no—
348#389—221no—
349#386—221no—
350#384—111no—
351#384—221no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—221no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
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×C11#52511yescharacteristic
370C22×C11D4211yescharacteristic
371C22×C11#54811yescharacteristic
372C22×C11C22×SD1611yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—22no—
384C4×C11—24no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11C2×#12311yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54711yescharacteristic
391C4×C11#55311yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—41no—
395Dic11—41no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—111no—
401C22×D4—221no—
402C22×D4—221no—
403C22×D4C22×D1111yescharacteristic
404C23×C4—221no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—222no—
408C2×SD16—222no—
409C2×SD16—222no—
410C2×SD16D4414yes—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415#127—222no—
416#127—441no—
417#123—444no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—222no—
421C4×Q8—222no—
422C4×Q8—441no—
423C4×Q8—441no—
424C4×D4—222no—
425C4×D4—441no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—21no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454#106—222no—
455#106—441no—
456C4⋊C8—222no—
457#103—22no—
458#103—222no—
459#102—22no—
460#102—222no—
461#102—222no—
462#102—222no—
463#102—222no—
464#102—441no—
465C4×C8—222no—
466#95—111no—
467#95—111no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—82no—
472C2×C11#244311yescharacteristic
473C2×C11#310311yescharacteristic
474C2×C11#311911yescharacteristic
475C2×C11#326811yescharacteristic
476C2×C11D4×SD1611yescharacteristic
477C2×C11#336211yescharacteristic
478C2×C11#337111yescharacteristic
479D11—161no—
480C24—21no—
481C24—221no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×D4412yes—
486C2×Q8#434112yes—
487C2×Q8#434112yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—442no—
503C2×D4—881no—
504C2×D4—881no—
505C2×D4C2×D4412yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522SD16—28no—
523SD16—444no—
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×C8C2×D4412yes—
536C4⋊C4—24no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—114no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—441no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—881no—
553C4⋊C4—881no—
554C4⋊C4—881no—
555C4⋊C4#434112yes—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—221no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—442no—
571C42—442no—
572C11#2616311yescharacteristic, complemented, Sylow
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23C2×D4×D1111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8#6693914yescomplemented
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4—441no—
597D4—441no—
598D4—441no—
599D4—441no—
600D4—884no—
601D4—884no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
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—441no—
637C2×C4—884no—
638C2×C4SD16×D1112yes—
639C2×C4C22×D4411yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4C2×#434111yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4#6704211yescharacteristic
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—881no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22—881no—
662C22—881no—
663C22D4×D4411yescharacteristic
664C22#1062311711yescharacteristic
665C22#1062312911yescharacteristic
666C22C2×SD16×D1111yescharacteristic
667C22#1062330111yescharacteristic
668C22#1062330511yescharacteristic
669C22#1062330811yescharacteristic
670C4—22no—
671C4—24no—
672C4—41no—
673C4—42no—
674C4—81no—
675C4—222no—
676C4—222no—
677C4—441no—
678C4—441no—
679C4—881no—
680C4—881no—
681C4—881no—
682C4C2×#6693911yescharacteristic
683C4#1062308611yescharacteristic
684C4#1062314911yescharacteristic
685C4#1062319611yescharacteristic
686C2—82no—
687C2—1761no—
688C2#1307234911yescharacteristic
689C2#1307864211yescharacteristic
690C2#1307881611yescharacteristic
691C2#1308015811yescharacteristic
692C2SD16×D4411yescharacteristic
693C2#1308128211yescharacteristic
694C2#1308138111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1880D11
hypocenterC11#26163
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic11C2semidirect
4. Q8×C4⋊Dic11C2semidirect
5. #13070148C2semidirect
6. #13070116C2semidirect
7. #13070019C2semidirect
9. #13069300C2semidirect
10. #13069174C2semidirect
11. #13068971C2semidirect
12. #13068969C2semidirect
13. #13068886C2semidirect
14. #13068879C2semidirect
15. C11×#1880C2semidirect
213. C4⋊Dic11SD16semidirect
238. #1880D11semidirect
259. Q8×C11#123semidirect
572. C11#26163semidirect
591. Q8#66939semidirect

Maximal subgroups

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

subgroupindex
C2×#106227762
C2×SD16×Dic112
#130723792
Q8×C4⋊Dic112
#130701482
#130701162
#130700192
#130698492
#130693002
#130691742
#130689712
#130689692
#130688862
#130688792
C11×#18802
#2616311