Finite Group Databasebeta

← #14676658

Subgroups — #14676658

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622586C211yesmaximal, characteristic, complemented
4C2×#10622559C214yesmaximal, complemented
5C2×#10622589C211yesmaximal, characteristic, complemented
6#13066859C214yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2214yes—
17C2×D4×Dic11—24no—
18C2×D4×Dic11—24no—
19C2×D4×Dic11—24no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2214yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#390—24no—
27#10622834C418yescomplemented
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622589—24no—
33#10622586—24no—
34#10622559—216no—
35C25×C11C2312yes—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11C2×C414yes—
41C22×D4×C11D414yes—
42C22×D4×C11Q814yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—24no—
47C23×Dic11—24no—
48C23×Dic11—24no—
49C23×Dic11—28no—
50C23×Dic11—44no—
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C22⋊C4—28no—
60C2×C11×C22⋊C4—28no—
61C2×C11×C22⋊C4—44no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—28no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11C2×C4116yescomplemented
71D4×Dic11—232no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2×C414yescomplemented
77C2×C4⋊Dic11D414yes—
78C2×Dic11⋊C4—28no—
79C2×Dic11⋊C4—28no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—44no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11C2×C414yescomplemented
88C2×C4×Dic11D414yes—
89C11⋊#95—28no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95D418yescomplemented
93#13977—111nomaximal, Sylow
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11C22×C414yes—
103C24×C11C2×D414yes—
104C24×C11C2×Q814yes—
105C24×C11C2411yescharacteristic
106C2×D4×C11—28no—
107C2×D4×C11—28no—
108C2×D4×C11—28no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11C4⋊C4116yescomplemented
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—216no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—416no—
153C22×Dic11—416no—
154C22×Dic11—48no—
155C22×Dic11—48no—
156C22×Dic11C22×C414yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D412yes—
163C22×Dic11#4114yes—
164C11×C4⋊C4—44no—
165C11×C22⋊C4—416no—
166C42×C11—44no—
167C22⋊Dic11—216no—
168C22⋊Dic11—232no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171Dic11⋊C4—416no—
172Dic11⋊C4—48no—
173C4×Dic11—28no—
174C4×Dic11—28no—
175C22×C4×D4—111no—
176C2×#390—111no—
177C2×#390D1111yescharacteristic
178C2×#389—111no—
179C2×#385—114no—
180C2×#384—111no—
181#1439—114no—
182C4⋊#95—111no—
183C4×#95—111no—
184C23×C11—28no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—28no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11C2×C4⋊C418yes—
207C23×C11C23×C411yescharacteristic
208C23×C11C22×D411yescharacteristic
209C23×C11C22×D411yescharacteristic
210C23×C11C22×D412yes—
211C23×C11C22×D411yescharacteristic
212C23×C11C22×Q811yescharacteristic
213C23×C11C2×#4111yescharacteristic
214C23×C11C2×#4111yescharacteristic
215C23×C11C2×#4112yes—
216C23×C11H(5,𝔽2)12yes—
217C23×C112−1+412yes—
218D4×C11—232no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11C2×C4⋊C414yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12014yes—
235C2×C4×C11C22⋊Q814yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11#12314yes—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—28no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—28no—
255C2×Dic11—432no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11C4×D418yescomplemented
265C2×Dic11#12714yes—
266C23×D4C2×D1111yescharacteristic
267C24×C4—112no—
268C2×C4×D4—224no—
269C2×C4×D4—224no—
270C2×C4×D4—224no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—114no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—114no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1114yes—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42C2×D1111yescharacteristic
282#390—24no—
283#390—118no—
284#389—224no—
285#385—2216no—
286#384—224no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—114no—
290C2×#95—112no—
291C22×C11—216no—
292C22×C11—28no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—48no—
297C22×C11—48no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—44no—
302C22×C11C22×C4⋊C411yescharacteristic
303C22×C11C2×C4×D411yescharacteristic
304C22×C11C2×C4×D411yescharacteristic
305C22×C11C2×C4×D412yes—
306C22×C11#52012yes—
307C22×C11C2×#12011yescharacteristic
308C22×C11C2×C22⋊Q811yescharacteristic
309C22×C11C2×C22⋊Q811yescharacteristic
310C22×C11C2×#12311yescharacteristic
311C22×C11C2×#12711yescharacteristic
312C22×C11#53212yes—
313C22×C11#53211yescharacteristic
314C22×C11#53511yescharacteristic
315C22×C11#53611yescharacteristic
316C22×C11#54212yes—
317C22×C11D4212yes—
318C22×C11D4212yes—
319C22×C11#54712yes—
320C22×C11#54712yes—
321C22×C11#54812yes—
322C22×C11D4×Q812yes—
323C22×C11#55312yes—
324C22×C11#55412yes—
325C4×C11—44no—
326C4×C11—82no—
327C4×C11#38518yescomplemented
328Dic11—28no—
329Dic11—24no—
330Dic11—44no—
331Dic11—42no—
332Dic11—44no—
333C25C22×D1112yes—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4Dic2214yes—
339C22×D4C4×D1114yes—
340C22×D4C22⋊D1114yes—
341C23×C4—112no—
342C23×C4—111no—
343C23×C4—112no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—224no—
347C23×C4—224no—
348C23×C4—228no—
349C23×C4—224no—
350C23×C4—444no—
351C23×C4C22×D1112yes—
352C23×C4C22×D1112yes—
353C23×C4C22×D1111yescharacteristic
354C4×D4—2232no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—444no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—1116no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—224no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42—222no—
384C2×C42—222no—
385C2×C42—222no—
386C2×C42—222no—
387#95—118no—
388#95—224no—
389#95—224no—
390#95—228no—
391C2×C11—48no—
392C2×C11C2×#38511yescharacteristic
393C2×C11C4×#12711yescharacteristic
394C2×C11#232611yescharacteristic
395C2×C11D4×C4⋊C412yes—
396C2×C11#236112yes—
397C2×C11#242212yes—
398C2×C11#243211yescharacteristic
399C2×C11#243311yescharacteristic
400C2×C11#245212yes—
401C2×C11#254211yescharacteristic
402C2×C11#256611yescharacteristic
403C24—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24C2×Dic2214yes—
412C24C2×C4×D1114yes—
413C24C2×C22⋊D1114yes—
414C24C23×D1111yescharacteristic
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4Dic11⋊C4116yescomplemented
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—222no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—221no—
448C22×C4—2216no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—224no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4—448no—
462C22×C4—4416no—
463C22×C4—4416no—
464C22×C4—448no—
465C22×C4C2×Dic2212yes—
466C22×C4C2×C4×D1112yes—
467C22×C4D4×D1114yes—
468C22×C4D4×D1112yes—
469C22×C4D4×D1112yes—
470C22×C4#434112yes—
471C22×C4#434112yes—
472C22×C4C2×C22⋊D1112yes—
473C4⋊C4—44no—
474C4⋊C4—228no—
475C4⋊C4—228no—
476C4⋊C4—448no—
477C4⋊C4—4416no—
478C22⋊C4—416no—
479C22⋊C4—2232no—
480C22⋊C4—2216no—
481C42—44no—
482C42—228no—
483C42—228no—
484C11#1397711yescharacteristic, complemented, Sylow
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—28no—
490C23—28no—
491C23—24no—
492C23—24no—
493C23—28no—
494C23—28no—
495C23—28no—
496C23—28no—
497C23—42no—
498C23—42no—
499C23—44no—
500C23—44no—
501C23—44no—
502C23—44no—
503C23—44no—
504C23—42no—
505C23—42no—
506C23—44no—
507C23C2×Dic11⋊C418yes—
508C23C22×Dic2211yescharacteristic
509C23C22×C4×D1111yescharacteristic
510C23C2×D4×D1111yescharacteristic
511C23C2×D4×D1112yes—
512C23C2×D4×D1111yescharacteristic
513C23C2×#434111yescharacteristic
514C23C2×#434111yescharacteristic
515C23#6703712yes—
516C23#41×D1112yes—
517C23#6704312yes—
518C23C22×C22⋊D1111yescharacteristic
519D4—232no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—114no—
533C2×C4—118no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—228no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—4432no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4—442no—
557C2×C4—444no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4#6693114yes—
561C2×C4#6693114yes—
562C2×C4(C22⋊D11)⋊C414yes—
563C2×C4(C22⋊D11)⋊C414yes—
564C2×C4C2×Dic11⋊C414yes—
565C2×C4#6698814yes—
566C2×C4#6699014yes—
567C22—216no—
568C22—28no—
569C22—48no—
570C22—44no—
571C22—48no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—48no—
578C22C2×#6693111yescharacteristic
579C22C2×#6693111yescharacteristic
580C22C2×(C22⋊D11)⋊C411yescharacteristic
581C22C2×(C22⋊D11)⋊C411yescharacteristic
582C22D4×Dic2212yes—
583C22#1062307012yes—
584C22C4×D4×D1112yes—
585C22#1062307712yes—
586C22#1062312712yes—
587C22#1062313412yes—
588C22#1062314212yes—
589C22#1062314512yes—
590C22#1062319911yescharacteristic
591C22#1062320611yescharacteristic
592C22#1062320812yes—
593C22D11×#12711yescharacteristic
594C22#1062324611yescharacteristic
595C22#1062324812yes—
596C22C22×Dic11⋊C411yescharacteristic
597C22C2×#6698811yescharacteristic
598C22C2×#6699011yescharacteristic
599C22D4×C22⋊D1112yes—
600C22#1062335512yes—
601C4—44no—
602C4—82no—
603C4—228no—
604C4—224no—
605C4—444no—
606C4—442no—
607C4—444no—
608C4#1062255918yescomplemented
609C2—48no—
610C2C2×#1062255911yescharacteristic
611C2#1307118011yescharacteristic
612C2#1307132611yescharacteristic
613C2D4×Dic11⋊C412yes—
614C2#1307163712yes—
615C2#1307212612yes—
616C2#1307224711yescharacteristic
617C2#1307225011yescharacteristic
618C2#1307246912yes—
619C2#1307356711yescharacteristic
620C2#1307381911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#13977
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622586C2semidirect
4. C2×#10622559C2semidirect
5. C2×#10622589C2semidirect
6. #13066859C2semidirect
7. #13066846C2semidirect
8. C4×C11⋊#95C2semidirect
27. #10622834C4semidirect
70. C2×C22⋊Dic11C2×C4semidirect
76. C2×C4⋊Dic11C2×C4semidirect
87. C2×C4×Dic11C2×C4semidirect
92. C11⋊#95D4semidirect
112. C2×D4×C11C4⋊C4semidirect
264. C2×Dic11C4×D4semidirect
327. C4×C11#385semidirect
421. C2×D4Dic11⋊C4semidirect
484. C11#13977semidirect
608. C4#10622559semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228342
C2×#106225862
C2×#106225592
C2×#106225892
#130668592
#130668462
C4×C11⋊#952
C2×C11×#3902
#1397711