Finite Group Databasebeta

← #14797644

Subgroups — #14797644

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×Dic11C211yesmaximal, characteristic, complemented
2#13072115C211yesmaximal, characteristic
3Q8×C22⋊Dic11C211yesmaximal, characteristic
4#13070162C211yesmaximal, characteristic, complemented
5#13070039C211yesmaximal, characteristic
6#13069936C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic
8#13069289C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic, complemented
11#13068959C211yesmaximal, characteristic, complemented
12#13068882C211yesmaximal, characteristic, complemented
13#13068629C211yesmaximal, characteristic, complemented
14#13068551C211yesmaximal, characteristic
15C2×C11×#451C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C11×#451—24no—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843—21no—
28#10622843—21no—
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825—21no—
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic
41C4×C22⋊Dic11—21no—
42C4×C22⋊Dic11C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44Q16×Dic11—24no—
45C2×#66882C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48#10622599—21no—
49#10622591—21no—
50#10622590C2211yescharacteristic
51#10622586C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53#10622566—21no—
54#10622557—21no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C2×C11×Q16—22no—
74C2×C11×Q16—22no—
75C2×C11×Q16—22no—
76C2×C11×Q16—22no—
77C2×C11×Q16—41no—
78C2×C11×Q16D414yes—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—41no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—22no—
92Q8×Dic11—22no—
93Q8×Dic11—41no—
94Q8×Dic11—41no—
95Q8×Dic11—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#103—22no—
112C11×#103—22no—
113C11×C22⋊C8—22no—
114#66899—22no—
115#66899—22no—
116#66899—22no—
117#66899—22no—
118#66899—41no—
119#66899—41no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95D411yescharacteristic
132C11⋊#95D411yescharacteristic
133C22⋊(C11⋊C8)—41no—
134#66882—22no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137#66872—41no—
138#24902—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—42no—
155C2×Q8×C11—42no—
156C2×Q8×C11—44no—
157C2×Q8×C11—44no—
158C2×Q8×C11—44no—
159C2×Q8×C11—44no—
160C2×Q8×C11C2×D412yes—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×Q8×C11#4112yes—
164C2×Q8×C11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C11×Q16—28no—
189C11×Q16—44no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C2×D412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—42no—
199C11×C22⋊C4—42no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—42no—
203C22⋊Dic11—42no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215Dic11⋊C4—42no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×#451D1111yescharacteristic
230C2×C4×Q16—111no—
231#2421—111no—
232Q8×C22⋊C4—111no—
233#2097—111no—
234#2075—111no—
235#2056—111no—
236#2035—111no—
237#1933—111no—
238#1923—111no—
239#1878—111no—
240#1878—111no—
241#1865—111no—
242#1805—111no—
243#1787—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11#13512yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—48no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11#12314yes—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—48no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11#13712yes—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C23×Q8C2×D1111yescharacteristic
320C22×Q16C2×D1111yescharacteristic
321C22×Q16C2×D1111yescharacteristic
322C2×C22⋊Q8C2×D1111yescharacteristic
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326#451—24no—
327C4×Q16—224no—
328C2×#107—111no—
329C2×#106—111no—
330C2×C4⋊C8—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×C22⋊C8—111no—
340C2×C22⋊C8C2×D1111yescharacteristic
341C2×C4×C8—111no—
342#400—221no—
343#397—221no—
344#391—111no—
345#391—111no—
346#391—111no—
347#391—221no—
348#391—221no—
349#389—111no—
350#388—221no—
351#387—221no—
352#382—111no—
353#380—111no—
354#380—111no—
355#380—221no—
356C4×C22⋊C4—111no—
357C4×C22⋊C4—221no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#336—111no—
363#336—111no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11#52511yescharacteristic
372C22×C11D4211yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11C2×#13511yescharacteristic
375C22×C11C2×#13711yescharacteristic
376C22×C11#57811yescharacteristic
377C22×C11#57811yescharacteristic
378C4×C11—24no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11C2×#12311yescharacteristic
384C4×C11#53811yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#55111yescharacteristic
387Dic11—22no—
388Dic11—41no—
389Dic11—41no—
390Dic11—41no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8C22×D1111yescharacteristic
403C22×Q8C22×D1111yescharacteristic
404C22×Q8C22×D1111yescharacteristic
405C23×C4—21no—
406C23×C4C22×D1111yescharacteristic
407C2×Q16—22no—
408C2×Q16—22no—
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—41no—
412C2×Q16C22⋊D1114yes—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—22no—
418C22⋊Q8—41no—
419C4×Q8—222no—
420C4×Q8—222no—
421C4×Q8—222no—
422C4×Q8—441no—
423C4×Q8—441no—
424C4×Q8—441no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445#107—222no—
446#106—441no—
447C4⋊C8—441no—
448#103—22no—
449#103—22no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103—222no—
454#103—441no—
455#103—441no—
456C22⋊C8—22no—
457C22⋊C8—441no—
458C4×C8—222no—
459#95—111no—
460#95—111no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472C2×C11—42no—
473C2×C11#241811yescharacteristic
474C2×C11#310811yescharacteristic
475C2×C11#312711yescharacteristic
476C2×C11#327011yescharacteristic
477C2×C11#328511yescharacteristic
478C2×C11#330011yescharacteristic
479C2×C11#332811yescharacteristic
480C24D4×D1111yescharacteristic
481C2×Q8—24no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8#434112yes—
502C2×Q8#434112yes—
503C2×Q8#434112yes—
504C2×Q8C2×C22⋊D1112yes—
505C2×Q8C2×C22⋊D1112yes—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4D4×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529Q16—28no—
530Q16—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8C2×C22⋊D1112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C22⋊C4—42no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C42—221no—
564C42—221no—
565C42—221no—
566C42—221no—
567C42—442no—
568C42—442no—
569C42—442no—
570C11#2490211yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#6697212yes—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8#6698814yes—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
601C2×C4—41no—
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—41no—
611C2×C4—41no—
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—221no—
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—441no—
636C2×C4C2×#434111yescharacteristic
637C2×C4C2×#434111yescharacteristic
638C2×C4C2×#434111yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#6703711yescharacteristic
641C2×C4C22×C22⋊D1111yescharacteristic
642C8—22no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#1062311711yescharacteristic
654C22#1062312211yescharacteristic
655C22C2×#6697211yescharacteristic
656C22#1062329711yescharacteristic
657C22D11×#13711yescharacteristic
658C22#1062331011yescharacteristic
659C22D4×C22⋊D1111yescharacteristic
660C4—24no—
661C4—41no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—222no—
666C4—441no—
667C4—441no—
668C4—441no—
669C4—881no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4#1062311811yescharacteristic
674C4#1062312411yescharacteristic
675C4C2×#6698811yescharacteristic
676C4#1062333711yescharacteristic
677C2—42no—
678C2#1307207411yescharacteristic
679C2#1307869711yescharacteristic
680C2#1307891011yescharacteristic
681C2#1308018011yescharacteristic
682C2#1308035711yescharacteristic
683C2#1308050711yescharacteristic
684C2#1308089211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#451D11
hypocenterC11#24902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×Q16×Dic11C2semidirect
4. #13070162C2semidirect
6. #13069936C2semidirect
8. #13069289C2semidirect
10. #13068959C2semidirect
11. #13068959C2semidirect
12. #13068882C2semidirect
13. #13068629C2semidirect
570. C11#24902semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×Dic112
#130721152
Q8×C22⋊Dic112
#130701622
#130700392
#130699362
#130698092
#130692892
#130692192
#130689592
#130688822
#130686292
#130685512
C2×C11×#4512
#2490211