Finite Group Databasebeta

← #14660250

Subgroups — #14660250

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66897C211yesmaximal, characteristic
2C2×M16×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622192C211yesmaximal, characteristic, complemented
5C2×#10622192C211yesmaximal, characteristic, complemented
6#13068309C211yesmaximal, characteristic, complemented
7C22×C11×#100C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C22⋊Dic11C414yes—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×C11×#100—22no—
17C2×C11×#100—22no—
18C2×C11×#100C414yescomplemented
19#10622834—22no—
20#10622834—21no—
21#10622834—21no—
22C2×#66897—22no—
23C2×#66897—22no—
24C2×#66897C414yescomplemented
25M16×Dic11—22no—
26M16×Dic11—22no—
27C2×#66879—21no—
28C2×C8×Dic11—21no—
29#10622192—22no—
30#10622192—22no—
31#10622188—22no—
32C25×C11C2×C412yes—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2×C412yes—
46C22×D4×C11C2×C412yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2×C412yes—
49C23×Dic11C2×C412yes—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16C2×C412yes—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—48no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11D412yes—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318C2×C412yes—
89C2×#4318C2×C412yes—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C11×#100—28no—
95#66897—28no—
96#66879—24no—
97C8×Dic11—24no—
98#10962—111nomaximal, Sylow
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—44no—
106C24×C11—44no—
107C24×C11C4214yes—
108C24×C11C22×C411yescharacteristic
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—42no—
158C22×Dic11—44no—
159C22×Dic11C22⋊C412yes—
160C22×Dic11C22⋊C412yes—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16C22⋊C414yescomplemented
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C22⋊Dic11—48no—
176C22⋊Dic11—48no—
177C4⋊Dic11—41no—
178C4⋊Dic11—41no—
179C4⋊Dic11—41no—
180C4⋊Dic11—41no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—41no—
193#4318—41no—
194#4318C22⋊C414yescomplemented
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—41no—
200C2×C11⋊C8—41no—
201C22×#100—111no—
202C22×#100D1111yescharacteristic
203C2×C4×M16—111no—
204C2×#390—111no—
205C2×#343—111no—
206C2×#343—111no—
207#1728—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—84no—
222C23×C11—84no—
223C23×C11—82no—
224C23×C11—82no—
225C23×C11—82no—
226C23×C11—82no—
227C23×C11C2×C4211yescharacteristic
228C23×C11C2×C22⋊C411yescharacteristic
229C23×C11#11711yescharacteristic
230C23×C11C4×D411yescharacteristic
231C23×C11C4×D411yescharacteristic
232C23×C11C4×D411yescharacteristic
233C23×C11C4×D411yescharacteristic
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—42no—
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11C2×C22⋊C411yescharacteristic
244C2×C4×C11#11711yescharacteristic
245C2×C4×C11#11711yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12611yescharacteristic
268C2×C4×C11#12611yescharacteristic
269C2×C4×C11#12711yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278C2×Dic11—44no—
279C2×Dic11—82no—
280C2×Dic11—82no—
281C2×Dic11#10014yescomplemented
282C8×C11—24no—
283C8×C11—42no—
284C11⋊C8—24no—
285C11⋊C8—42no—
286C23×D4C2×D1111yescharacteristic
287C22×M16—111no—
288C22×M16—111no—
289C22×M16C2×D1111yescharacteristic
290C22×M16C2×D1111yescharacteristic
291C22×C4⋊C4—111no—
292C22×C22⋊C4—114no—
293C22×C42—111no—
294C2×#100—22no—
295C2×#100—22no—
296C2×#100—114no—
297C2×#100—222no—
298C2×#100—222no—
299C2×#100Dic1114yescomplemented
300C4×M16—222no—
301C4×M16—222no—
302C2×#97—221no—
303C2×C4×C8—221no—
304#390—222no—
305#390—221no—
306#390—221no—
307#343—222no—
308#343—222no—
309#336—222no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—44no—
319C22×C11—48no—
320C22×C11—84no—
321C22×C11—84no—
322C22×C11—84no—
323C22×C11—84no—
324C22×C11—84no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11C4×C22⋊C411yescharacteristic
328C22×C11C4×C22⋊C411yescharacteristic
329C22×C11C4×C22⋊C411yescharacteristic
330C22×C11#38611yescharacteristic
331C22×C11#38811yescharacteristic
332C22×C11#38811yescharacteristic
333C22×C11#39011yescharacteristic
334C22×C11C2×#10012yes—
335C22×C11#41312yes—
336C4×C11#38611yescharacteristic
337C4×C11#38611yescharacteristic
338C4×C11#38811yescharacteristic
339C4×C11#38811yescharacteristic
340C4×C11#38811yescharacteristic
341C4×C11#38811yescharacteristic
342C4×C11#39011yescharacteristic
343C4×C11#39011yescharacteristic
344Dic11—24no—
345Dic11—42no—
346Dic11—82no—
347C25C4×D1112yes—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4C4×D1112yes—
361C22×D4C2×Dic1112yes—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—112no—
374C2×M16—112no—
375C2×M16—112no—
376C2×M16—112no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16C2×Dic1112yes—
386C2×M16C2×Dic1112yes—
387C2×M16C22⋊D1112yes—
388C2×M16C22⋊D1112yes—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—221no—
392C22×C8—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—448no—
402C2×C42—112no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409#100—28no—
410#100—228no—
411#97—224no—
412C4×C8—224no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—84no—
418C2×C11#143711yescharacteristic
419C2×C11C4×#10012yes—
420C2×C11#190012yes—
421C2×C11#196511yescharacteristic
422C2×C11#196711yescharacteristic
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—44no—
430C24—44no—
431C24C4×Dic1114yes—
432C24C2×C4×D1111yescharacteristic
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—224no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—442no—
470C22×C4—444no—
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4#433911yescharacteristic
473C22×C4#433911yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4#434111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4#434111yescharacteristic
481C22×C4#434111yescharacteristic
482C22×C4C22×Dic1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—114no—
493M16—222no—
494M16—222no—
495M16—222no—
496M16—222no—
497M16—222no—
498M16—441no—
499M16—441no—
500M16C22⋊Dic1114yescomplemented
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—441no—
512C2×C8—441no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C4⋊C4—441no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C42—221no—
520C42—221no—
521C42—222no—
522C42—221no—
523C42—221no—
524C42—222no—
525C11#1096211yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—48no—
532C23—48no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—44no—
538C23—44no—
539C23—84no—
540C23—84no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23#6693011yescharacteristic
546C23C22⋊C4×D1111yescharacteristic
547C23(C22⋊D11)⋊C411yescharacteristic
548C23(C22⋊D11)⋊C411yescharacteristic
549C23C2×C4×Dic1111yescharacteristic
550C23C4×C22⋊D1111yescharacteristic
551C23C4×C22⋊D1111yescharacteristic
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—42no—
560C2×C4—114no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—444no—
567C2×C4—444no—
568C2×C4—442no—
569C2×C4—444no—
570C2×C4—882no—
571C2×C4—882no—
572C2×C4#6693011yescharacteristic
573C2×C4#6693211yescharacteristic
574C2×C4#6693211yescharacteristic
575C2×C4C22⋊C4×D1111yescharacteristic
576C2×C4(C22⋊D11)⋊C411yescharacteristic
577C2×C4(C22⋊D11)⋊C411yescharacteristic
578C2×C4#6693611yescharacteristic
579C2×C4#6693611yescharacteristic
580C2×C4#6693711yescharacteristic
581C2×C4#6693711yescharacteristic
582C2×C4#6693811yescharacteristic
583C2×C4#6693811yescharacteristic
584C2×C4#6697911yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4C4×C22⋊D1111yescharacteristic
587C2×C4D4×Dic1111yescharacteristic
588C2×C4D4×Dic1111yescharacteristic
589C2×C4D4×Dic1111yescharacteristic
590C2×C4D4×Dic1111yescharacteristic
591C2×C4#6698811yescharacteristic
592C2×C4#6698911yescharacteristic
593C2×C4#6699011yescharacteristic
594C2×C4#6699111yescharacteristic
595C2×C4#6699111yescharacteristic
596C2×C4#6699211yescharacteristic
597C2×C4#6699211yescharacteristic
598C2×C4#6699311yescharacteristic
599C2×C4C2×C22⋊Dic1111yescharacteristic
600C8—24no—
601C8—42no—
602C8—224no—
603C8—442no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—44no—
613C22—48no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—84no—
619C22—82no—
620C22—82no—
621C22D11×#10012yes—
622C22#1062235812yes—
623C22C22⋊C4×Dic1111yescharacteristic
624C22C22⋊C4×Dic1111yescharacteristic
625C22#1062255711yescharacteristic
626C22#1062255811yescharacteristic
627C22#1062256911yescharacteristic
628C22#1062257011yescharacteristic
629C22C4×C22⋊Dic1111yescharacteristic
630C4—224no—
631C4—442no—
632C4—882no—
633C4#1062255711yescharacteristic
634C4#1062255811yescharacteristic
635C4#1062256411yescharacteristic
636C4#1062256411yescharacteristic
637C4#1062256911yescharacteristic
638C4#1062257011yescharacteristic
639C4#1062283311yescharacteristic
640C4#1062283411yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—84no—
646C2#1306685311yescharacteristic
647C2#100×Dic1112yes—
648C2#1306907612yes—
649C2#1306945411yescharacteristic
650C2#1306946211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC22×C11×#100C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C22
cosocleC23×C4×C11C23
hypercenterC22×#100D11
hypocenterC11#10962
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic11C2semidirect
4. C2×#10622192C2semidirect
5. C2×#10622192C2semidirect
6. #13068309C2semidirect
18. C2×C11×#100C4semidirect
24. C2×#66897C4semidirect
168. C11×M16C22⋊C4semidirect
194. #4318C22⋊C4semidirect
281. C2×Dic11#100semidirect
299. C2×#100Dic11semidirect
500. M16C22⋊Dic11semidirect
525. C11#10962semidirect

Maximal subgroups

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

subgroupindex
C22×#668972
C2×M16×Dic112
C2×#106228342
C2×#106221922
#130683092
C22×C11×#1002
#1096211