Finite Group Databasebeta

← #14660286

Subgroups — #14660286

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C212yesmaximal, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic
4C2×#10622167C212yesmaximal, complemented
5C22×C11×C22⋊Q8C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C24×C4×C11C2211yescharacteristic
8C2×C11×C22⋊Q8—24no—
9C2×C11×C22⋊Q8—22no—
10C2×C11×C22⋊Q8—24no—
11C2×C11×C22⋊Q8C414yescomplemented
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4—21no—
15C22×C22⋊Dic11—21no—
16C22×C4⋊Dic11C2212yes—
17C23×C11⋊C8C2212yes—
18C2×#66899—24no—
19C2×#66899—24no—
20C2×#66899—24no—
21#10622825—24no—
22C2×C11⋊#95—21no—
23C2×C22⋊(C11⋊C8)—22no—
24C2×C22⋊(C11⋊C8)—24no—
25#10622167—24no—
26C25×C11D411yescharacteristic
27C22×Q8×C11—21no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—22no—
33C22×Q8×C11C2×C412yes—
34C22×Q8×C11D414yes—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11C2×C412yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D412yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—22no—
48C11×C22⋊Q8—216no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—28no—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2×C412yes—
56C2×C11×C4⋊C4D414yes—
57C2×C11×C22⋊C4—28no—
58C2×C11×C22⋊C4—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—42no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11D414yes—
68C22×C11⋊C8—22no—
69C22×C11⋊C8—22no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8—22no—
74C22×C11⋊C8D414yes—
75#66899—216no—
76C11⋊#95—24no—
77C22⋊(C11⋊C8)—28no—
78#10970—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—22no—
81C24×C11—22no—
82C24×C11—21no—
83C24×C11—22no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11C22⋊C412yes—
88C24×C11SD1612yes—
89C24×C11Q1612yes—
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—22no—
92C2×Q8×C11—24no—
93C2×Q8×C11—24no—
94C2×Q8×C11—24no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11—24no—
98C2×Q8×C11—24no—
99C2×Q8×C11—41no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×Q8×C11C22⋊C414yescomplemented
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—41no—
124C22×C4×C11—42no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C22⋊C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×Dic11—24no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C11×C4⋊C4—216no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C22⋊C414yescomplemented
157C11×C22⋊C4—216no—
158C22⋊Dic11—48no—
159C4⋊Dic11—24no—
160C4⋊Dic11—24no—
161C4⋊Dic11—42no—
162C4⋊Dic11—42no—
163C2×C11⋊C8—24no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—42no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8—42no—
170C22×C22⋊Q8D1111yescharacteristic
171C22×#103—112no—
172C22×C22⋊C8—111no—
173C2×#380—111no—
174C2×#340—112no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—22no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11#10314yescomplemented
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11#12011yescharacteristic
200C23×C11#12012yes—
201C23×C11#12112yes—
202C23×C11#12311yescharacteristic
203C23×C11C2×SD1611yescharacteristic
204C23×C11C2×Q1611yescharacteristic
205C23×C11#13512yes—
206C23×C11AGL(1,ℤ/8)11yescharacteristic
207C23×C11#13712yes—
208C23×C11#13711yescharacteristic
209Q8×C11—28no—
210Q8×C11—44no—
211Q8×C11—44no—
212Q8×C11—44no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C4×D412yes—
235C2×C4×C11C4×D412yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12012yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#12112yes—
242C2×C4×C11#12112yes—
243C2×C4×C11#12112yes—
244C2×C4×C11#12312yes—
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12412yes—
247C2×C4×C11#12712yes—
248C2×Dic11—44no—
249C2×Dic11—44no—
250C2×Dic11—44no—
251C2×Dic11—82no—
252C2×Dic11—82no—
253C2×Dic11—82no—
254C2×Dic11—82no—
255C11⋊C8—44no—
256C23×Q8C2×D1111yescharacteristic
257C24×C4C2×D1111yescharacteristic
258C23×C8—112no—
259C2×C22⋊Q8—24no—
260C2×C22⋊Q8—22no—
261C2×C22⋊Q8—24no—
262C2×C22⋊Q8Dic1114yescomplemented
263C22×C4⋊C4—21no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4C2×D1111yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—221no—
268C2×#103—224no—
269C2×#103—224no—
270C2×#103—224no—
271C2×C22⋊C8—224no—
272C2×C22⋊C8—222no—
273#380—224no—
274C2×#95—221no—
275#340—224no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11#37911yescharacteristic
288C22×C11#38611yescharacteristic
289C22×C11#38611yescharacteristic
290C22×C11#39212yes—
291C22×C11#39412yes—
292C22×C11C2×#10311yescharacteristic
293C22×C11#41611yescharacteristic
294C22×C11#41711yescharacteristic
295C22×C11#41911yescharacteristic
296C22×C11#44812yes—
297C22×C11#44912yes—
298C22×C11#45011yescharacteristic
299C22×C11#45112yes—
300C22×C11#45111yescharacteristic
301C22×C11#45212yes—
302C22×C11#45212yes—
303C22×C11#46512yes—
304C22×C11#46712yes—
305C22×C11#46812yes—
306C22×C11#47012yes—
307C22×C11#48311yescharacteristic
308C22×C11#48411yescharacteristic
309C22×C11#48512yes—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11—44no—
313C4×C11#38612yes—
314C4×C11#39012yes—
315C4×C11#39212yes—
316C4×C11#39412yes—
317Dic11—84no—
318C25C22⋊D1111yescharacteristic
319C22×Q8—21no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8C2×Dic1112yes—
326C22×Q8C22⋊D1114yes—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—222no—
336C23×C4C2×Dic1112yes—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1112yes—
339C23×C4C22×D1111yescharacteristic
340C22×C8—114no—
341C22×C8—222no—
342C22×C8—222no—
343C22×C8—222no—
344C22×C8—222no—
345C22×C8—222no—
346C22×C8—222no—
347C22⋊Q8—216no—
348C22⋊Q8—28no—
349C22⋊Q8—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4C2×Dic1112yes—
361C2×C4⋊C4C22⋊D1114yes—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367#103—2216no—
368C22⋊C8—228no—
369#95—224no—
370C2×C11—44no—
371C2×C11#143811yescharacteristic
372C2×C11#178711yescharacteristic
373C2×C11#178811yescharacteristic
374C2×C11#187211yescharacteristic
375C2×C11#187311yescharacteristic
376C2×C11#189211yescharacteristic
377C2×C11#189411yescharacteristic
378C2×C11#200012yes—
379C2×C11#200112yes—
380C2×C11#203512yes—
381C2×C11#203612yes—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—22no—
390C24#432512yes—
391C24#432612yes—
392C24C22⋊Dic1112yes—
393C24C2×C22⋊D1111yescharacteristic
394C2×Q8—22no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—41no—
403C2×Q8—42no—
404C2×Q8—41no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8C22⋊Dic1114yescomplemented
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—224no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4C22⋊Dic1112yes—
448C22×C4D4×D1112yes—
449C22×C4D4×D1112yes—
450C22×C4#434112yes—
451C22×C4#434112yes—
452C22×C4C22×Dic1111yescharacteristic
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1112yes—
456C2×C8—224no—
457C2×C8—224no—
458C2×C8—224no—
459C2×C8—442no—
460C2×C8—442no—
461C2×C8—442no—
462C2×C8—442no—
463C4⋊C4—216no—
464C4⋊C4—22no—
465C4⋊C4—24no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4C22⋊Dic1114yescomplemented
471C22⋊C4—216no—
472C22⋊C4—448no—
473C11#1097011yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—22no—
487C23—24no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23#6689914yescomplemented
497C23#6698811yescharacteristic
498C23#6699011yescharacteristic
499C23#6699212yes—
500C23C2×#432511yescharacteristic
501C23#6699512yes—
502C23C2×#432611yescharacteristic
503C23#6700211yescharacteristic
504C23#6700312yes—
505C23#6700411yescharacteristic
506C23C2×C22⋊Dic1111yescharacteristic
507C23#6700612yes—
508Q8—28no—
509Q8—44no—
510Q8—44no—
511Q8—44no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—444no—
532C2×C4—444no—
533C2×C4—444no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4—882no—
537C2×C4—882no—
538C2×C4D4×Dic1112yes—
539C2×C4D4×Dic1112yes—
540C2×C4#6698812yes—
541C2×C4#6698811yescharacteristic
542C2×C4#6698912yes—
543C2×C4#6699012yes—
544C2×C4#6699011yescharacteristic
545C2×C4#6699112yes—
546C2×C4#6699112yes—
547C2×C4#6699212yes—
548C2×C4#6699212yes—
549C2×C4#6699212yes—
550C2×C4#6699312yes—
551C2×C4C2×C22⋊Dic1111yescharacteristic
552C2×C4C2×C22⋊Dic1111yescharacteristic
553C2×C4#6700612yes—
554C8—444no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—42no—
559C22—44no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—42no—
566C22#1062265611yescharacteristic
567C22#1062265711yescharacteristic
568C22#1062265812yes—
569C22#1062265911yescharacteristic
570C22#1062266012yes—
571C22#1062266112yes—
572C22#1062266212yes—
573C22#1062266311yescharacteristic
574C22#1062266412yes—
575C22#1062266512yes—
576C22#1062283311yescharacteristic
577C22#1062283311yescharacteristic
578C22#1062283512yes—
579C22#1062283612yes—
580C22C2×#6689911yescharacteristic
581C22#1062283811yescharacteristic
582C22#1062284012yes—
583C22#1062284112yes—
584C22#1062284511yescharacteristic
585C22#1062284611yescharacteristic
586C22#1062285112yes—
587C22#1062285212yes—
588C22#1062286011yescharacteristic
589C4—44no—
590C4—42no—
591C4—44no—
592C4—884no—
593C4#1062283312yes—
594C4#1062283412yes—
595C4#1062283512yes—
596C4#1062283612yes—
597C2—44no—
598C2#1306685711yescharacteristic
599C2#1306855111yescharacteristic
600C2#1306855611yescharacteristic
601C2#1306892411yescharacteristic
602C2#1306892911yescharacteristic
603C2#1306904011yescharacteristic
604C2#1306905011yescharacteristic
605C2#1306961712yes—
606C2#1306962412yes—
607C2#1306980912yes—
608C2#1306981612yes—
subgroupG/H
centerC24C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11#10970
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66899C2semidirect
4. C2×#10622167C2semidirect
11. C2×C11×C22⋊Q8C4semidirect
106. C2×Q8×C11C22⋊C4semidirect
156. C11×C4⋊C4C22⋊C4semidirect
197. C23×C11#103semidirect
262. C2×C22⋊Q8Dic11semidirect
409. C2×Q8C22⋊Dic11semidirect
470. C4⋊C4C22⋊Dic11semidirect
473. C11#10970semidirect
496. C23#66899semidirect

Maximal subgroups

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

subgroupindex
C22×#668992
C22×C22⋊(C11⋊C8)2
C2×#106228252
C2×#106221672
C22×C11×C22⋊Q82
#1097011