Finite Group Databasebeta

← #14675673

Subgroups — #14675673

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622825C212yesmaximal, complemented
4#13066865C212yesmaximal, complemented
5#13066857C212yesmaximal
6#13066853C212yesmaximal, complemented
7#13066848C212yesmaximal, complemented
8#13066846C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C4×D4×C11—24no—
14C2×C4×D4×C11—24no—
15C2×C4×D4×C11C418yescomplemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2214yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66979—24no—
24C2×#66979—28no—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28#10622825—24no—
29#10622825—28no—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2214yes—
33C2×C11⋊#95C2214yes—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2×C414yes—
49C23×C4×C11D414yes—
50C23×C4×C11D414yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2314yes—
57C23×Dic11C2314yes—
58C4×D4×C11—232no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2×C414yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4C2×C414yes—
67C2×C11×C22⋊C4C2×C414yes—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11C2×C414yes—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—28no—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—44no—
77C2×C22⋊Dic11—44no—
78#66979—232no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11D418yescomplemented
85C2×C4×Dic11—24no—
86C2×C4×Dic11—28no—
87C11⋊#95—24no—
88C11⋊#95—28no—
89C11⋊#95—28no—
90C11⋊#95—44no—
91#13871—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C22×C412yes—
107C24×C11C2×D412yes—
108C24×C11C2×D412yes—
109C24×C11#4114yes—
110C24×C11C2411yescharacteristic
111C2×D4×C11—216no—
112C2×D4×C11—216no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—216no—
122C22×C4×C11—28no—
123C22×C4×C11—216no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—28no—
134C22×C4×C11—216no—
135C22×C4×C11—44no—
136C22×C4×C11—48no—
137C22×C4×C11—44no—
138C22×C4×C11C22⋊C4116yescomplemented
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11#4114yes—
150C22×C4×C11#4114yes—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11C2×D418yes—
165C11×C4⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C42×C11—28no—
169C22⋊Dic11—216no—
170C22⋊Dic11—416no—
171C22⋊Dic11—48no—
172C4⋊Dic11—216no—
173C4⋊Dic11—48no—
174C4×Dic11—216no—
175C22×C4×D4D1111yescharacteristic
176C22×#117—111no—
177C2×#380—112no—
178C2×#380—111no—
179#1440—112no—
180#1438—112no—
181#1437—112no—
182#1436—112no—
183C4⋊#95—112no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—24no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11C2×C22⋊C414yes—
225C23×C11#11714yescomplemented
226C23×C11C23×C411yescharacteristic
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229C23×C11C22×D411yescharacteristic
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C23×C11C2×#4112yes—
233C23×C11H(5,𝔽2)12yes—
234C23×C112−1+412yes—
235D4×C11—232no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—232no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—416no—
256C2×C4×C11C2×C22⋊C414yes—
257C2×C4×C11C2×C22⋊C414yes—
258C2×C4×C11#11714yescomplemented
259C2×C4×C11C4×D418yes—
260C2×C4×C11#12014yes—
261C2×C4×C11#12118yes—
262C2×C4×C11#12314yes—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—28no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C23×D4C2×D1111yescharacteristic
278C24×C4C2×D1111yescharacteristic
279C24×C4C2×D1111yescharacteristic
280C2×C4×D4—24no—
281C2×C4×D4—24no—
282C2×C4×D4Dic1118yescomplemented
283C2×#117—228no—
284C2×#117—224no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—112no—
289C22×C22⋊C4—114no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C42—112no—
294C22×C42C2×D1111yescharacteristic
295#380—228no—
296#380—224no—
297C2×#95—114no—
298C2×#95—112no—
299C2×#95—114no—
300C2×#95—114no—
301C22×C11—24no—
302C22×C11—28no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11C22×C22⋊C411yescharacteristic
320C22×C11C2×#11711yescharacteristic
321C22×C11C2×#11711yescharacteristic
322C22×C11C2×C4×D412yes—
323C22×C11#52012yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12112yes—
326C22×C11C2×#12311yescharacteristic
327C22×C11#52512yes—
328C22×C11#52512yes—
329C22×C11#53511yescharacteristic
330C22×C11#53611yescharacteristic
331C22×C11#53712yes—
332C22×C11#54612yes—
333C22×C11#54712yes—
334C22×C11#54812yes—
335C22×C11#55012yes—
336C22×C11#55212yes—
337C22×C11#55312yes—
338C22×C11#55512yes—
339C22×C11#55612yes—
340C4×C11—24no—
341C4×C11—24no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#38618yes—
345Dic11—48no—
346Dic11—84no—
347C25C22×D1111yescharacteristic
348C25C22×D1111yescharacteristic
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4C2×Dic1114yes—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—114no—
361C23×C4—114no—
362C23×C4C2×Dic1114yes—
363C23×C4C2×Dic1114yes—
364C23×C4C22⋊D1114yes—
365C23×C4C22⋊D1114yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C4×D4—232no—
372#117—2232no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—118no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4C2×Dic1114yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—444no—
392C2×C22⋊C4—444no—
393C2×C22⋊C4C2×Dic1114yes—
394C2×C22⋊C4C2×Dic1114yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—228no—
398C2×C42—224no—
399C2×C42C2×Dic1114yes—
400#95—228no—
401#95—228no—
402#95—224no—
403#95—444no—
404C2×C11—44no—
405C2×C11—44no—
406C2×C11#228011yescharacteristic
407C2×C11C2×#38611yescharacteristic
408C2×C11#231111yescharacteristic
409C2×C11#235212yes—
410C2×C11#235412yes—
411C2×C11#240712yes—
412C2×C11#241412yes—
413C2×C11#241512yes—
414C2×C11#248512yes—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24#433914yes—
429C24C22×Dic1112yes—
430C24C22×Dic1112yes—
431C24C2×C22⋊D1112yes—
432C24C2×C22⋊D1112yes—
433C24C23×D1111yescharacteristic
434C2×D4—216no—
435C2×D4—216no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—28no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—216no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—216no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—216no—
457C22×C4—28no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—48no—
461C22×C4—118no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4C22⋊Dic11116yescomplemented
476C22×C4#433914yes—
477C22×C4D4×D1114yes—
478C22×C4#434114yes—
479C22×C4C22×Dic1112yes—
480C22×C4C22×Dic1112yes—
481C22×C4C22×Dic1112yes—
482C22×C4C22×Dic1112yes—
483C22×C4C22×Dic1112yes—
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C2×C22⋊D1112yes—
487C22×C4C2×C22⋊D1112yes—
488C4⋊C4—28no—
489C4⋊C4—2216no—
490C4⋊C4—448no—
491C22⋊C4—28no—
492C22⋊C4—28no—
493C22⋊C4—2216no—
494C22⋊C4—4416no—
495C22⋊C4—448no—
496C42—28no—
497C42—2216no—
498C11#1387111yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23#6697914yescomplemented
540C23C2×C22⋊Dic1114yes—
541C23C2×#433912yes—
542C23C2×#433912yes—
543C23C2×D4×D1112yes—
544C23C2×#434112yes—
545C23#6704212yes—
546C23#6704312yes—
547C23C23×Dic1111yescharacteristic
548C23C22×C22⋊D1111yescharacteristic
549C23C22×C22⋊D1111yescharacteristic
550D4—232no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—232no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—416no—
571C2×C4—228no—
572C2×C4—228no—
573C2×C4—228no—
574C2×C4—444no—
575C2×C4—444no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—444no—
585C2×C4#6697914yescomplemented
586C2×C4D4×Dic1118yes—
587C2×C4#6698814yes—
588C2×C4#6699014yes—
589C2×C4#6699218yes—
590C2×C4C2×C22⋊Dic1114yes—
591C2×C4C2×C22⋊Dic1114yes—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—28no—
596C22—24no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22#1062307212yes—
611C22#1062307312yes—
612C22#1062308112yes—
613C22#1062308212yes—
614C22#1062308312yes—
615C22#1062308412yes—
616C22#1062309412yes—
617C22#1062309612yes—
618C22C2×#6697911yescharacteristic
619C22C2×#6697911yescharacteristic
620C22#1062332212yes—
621C22#1062332212yes—
622C22C2×D4×Dic1112yes—
623C22C2×#6698811yescharacteristic
624C22C2×#6699011yescharacteristic
625C22C2×#6699212yes—
626C22#1062335611yescharacteristic
627C22#1062335812yes—
628C22#1062336111yescharacteristic
629C22#1062336412yes—
630C22C22×C22⋊Dic1111yescharacteristic
631C4—24no—
632C4—24no—
633C4—42no—
634C4—42no—
635C4—448no—
636C4—884no—
637C4#1062283318yes—
638C2—44no—
639C2—44no—
640C2#1307099911yescharacteristic
641C2C2×#1062283311yescharacteristic
642C2#1307120811yescharacteristic
643C2#1307154512yes—
644C2#1307156512yes—
645C2#1307196112yes—
646C2#1307203412yes—
647C2#1307204512yes—
648C2#1307291312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13871
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. C2×#10622825C2semidirect
3. C2×#10622825C2semidirect
4. #13066865C2semidirect
6. #13066853C2semidirect
7. #13066848C2semidirect
8. #13066846C2semidirect
15. C2×C4×D4×C11C4semidirect
84. C2×C4⋊Dic11D4semidirect
138. C22×C4×C11C22⋊C4semidirect
225. C23×C11#117semidirect
258. C2×C4×C11#117semidirect
282. C2×C4×D4Dic11semidirect
475. C22×C4C22⋊Dic11semidirect
498. C11#13871semidirect
539. C23#66979semidirect
585. C2×C4#66979semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106228252
#130668652
#130668572
#130668532
#130668482
#130668462
C22×C4×D4×C112
#1387111