Finite Group Databasebeta

← #14758746

Subgroups — #14758746

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623069C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3C2×M16×Dic11C211yesmaximal, characteristic, complemented
4#13069554C212yesmaximal, complemented
5#13069412C212yesmaximal, complemented
6#13068914C211yesmaximal, characteristic, complemented
7#13068913C211yesmaximal, characteristic, complemented
8#13068911C211yesmaximal, characteristic, complemented
9#13068384C212yesmaximal, complemented
10#13068381C212yesmaximal, complemented
11C11×#1870C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66992C411yescharacteristic
15C2×#66988C411yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21#10623069—24no—
22#10623069—24no—
23C2×#66951C411yescharacteristic
24C2×#66942C411yescharacteristic
25C2×#66939C411yescharacteristic
26C2×#66938C411yescharacteristic
27C2×#66932C411yescharacteristic
28C2×#66931C411yescharacteristic
29C2×#66925C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C2×C11×C22⋊C8C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35M16×Dic11—24no—
36C2×(C2×D11)⋊C8C2212yes—
37C2×(C2×D11)⋊C8C2212yes—
38C2×#66879C2212yes—
39C2×#66879C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622332—24no—
43C11×#336C2212yes—
44#10622188C2212yes—
45#10622188C2212yes—
46#10622162C2212yes—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11C2×C411yescharacteristic
51C22×C22⋊D11C2×C411yescharacteristic
52C23×Dic11C2×C411yescharacteristic
53C23×Dic11C2×C411yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C2×C11×M16—22no—
57C2×C11×M16—24no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C411yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70#66992—24no—
71#66988—24no—
72C4×C22⋊D11—22no—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C4×C22⋊D11—22no—
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80#66979—22no—
81#66979—22no—
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11D414yes—
94C2×C4×Dic11D414yes—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×#4318—22no—
99C2×#4318—24no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102#66951—24no—
103#66942—24no—
104#66939—24no—
105#66938—24no—
106#66932—24no—
107#66931—24no—
108#66925—22no—
109#66925—22no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—24no—
114C22⋊(C11⋊C8)—22no—
115C22⋊(C11⋊C8)—24no—
116(C2×D11)⋊C8—24no—
117(C2×D11)⋊C8—24no—
118#66879—24no—
119#66879—24no—
120Dic11⋊C8—24no—
121C8×Dic11—24no—
122#21376—111nomaximal, Sylow
123C24×C11C22×C411yescharacteristic
124C24×C11C22×C411yescharacteristic
125C23×D11C22×C411yescharacteristic
126C2×D4×C11—22no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—22no—
143C2×C22⋊D11—22no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—42no—
147C22×Dic11—41no—
148C22×Dic11—41no—
149C22×Dic11—42no—
150C22×Dic11C22⋊C414yes—
151C22×Dic11C22⋊C414yes—
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×Dic22—22no—
164C2×Dic22—42no—
165C11×M16—28no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11#4114yes—
172C11×C4⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192Dic11⋊C4—22no—
193Dic11⋊C4—22no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22⋊C414yes—
197C4×Dic11C22⋊C414yes—
198C4×Dic11C2×D412yes—
199C4×Dic11C2×D412yes—
200C4×Dic11C2×D412yes—
201C4×Dic11C2×D412yes—
202#4318—28no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8#4114yes—
209C2×#529—111no—
210C2×#432—111no—
211C2×C4×M16—111no—
212#1985—112no—
213#1955—112no—
214#1870—111no—
215#1870—111no—
216#1870—111no—
217#1870D1111yescharacteristic, complemented
218#1750—112no—
219#1750—112no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C2×C22⋊C412yes—
230C23×C11C23×C411yescharacteristic
231C22×D11—21no—
232C22×D11—22no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—22no—
236D4×C11—44no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11C2×#4112yes—
256C22⋊D11—44no—
257C22⋊D11—44no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275C2×Dic11C2×C22⋊C412yes—
276C2×Dic11C2×C22⋊C412yes—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—42no—
280Dic22—44no—
281C8×C11—24no—
282C8×C11—42no—
283C11⋊C8—24no—
284C11⋊C8—42no—
285C22×M16—111no—
286C22×M16C2×D1111yescharacteristic
287#529—224no—
288#529—224no—
289C2×#126—111no—
290C2×#126—111no—
291C2×#125—111no—
292C2×#124—111no—
293C2×#123—111no—
294C2×#123—111no—
295C2×C22⋊Q8—111no—
296C2×#121—111no—
297C2×C4×Q8—111no—
298C2×C4×D4—111no—
299C2×C4×D4—111no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×#117—111no—
302C2×#117—111no—
303C22×C42—111no—
304#432—224no—
305C2×C4⋊C8—112no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8—112no—
308C2×C22⋊C8—112no—
309C2×C22⋊C8—112no—
310C2×C22⋊C8C2×D1111yescharacteristic
311C2×C22⋊C8C2×D1112yes—
312C4×M16—224no—
313C2×#97—112no—
314C2×#97—112no—
315C2×C4×C8—112no—
316#336—112no—
317#336—112no—
318#336—112no—
319#336C2×D1112yes—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—41no—
330C22×C11C22×C22⋊C411yescharacteristic
331C22×C11C4×#4112yes—
332C22×C11#56811yescharacteristic
333C22×C11#56811yescharacteristic
334C22×C11#56812yes—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—41no—
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11#52511yescharacteristic
345C4×C11#52511yescharacteristic
346C4×C11#53212yes—
347Dic11—22no—
348Dic11—22no—
349Dic11—22no—
350Dic11—22no—
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354C22×Q8—111no—
355C22×D4—111no—
356C22×D4—111no—
357C22×D4C4×D1111yescharacteristic
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C2×M16—22no—
364C2×M16—24no—
365C2×M16—224no—
366C2×M16—222no—
367C22×C8—112no—
368C22×C8—112no—
369C22×C8C22×D1112yes—
370C22×C8C22×D1112yes—
371#126—224no—
372#126—224no—
373#125—224no—
374#124—224no—
375#123—224no—
376#123—224no—
377C22⋊Q8—224no—
378#121—224no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—222no—
384C4×D4—222no—
385C4×D4—222no—
386C4×D4—222no—
387#117—222no—
388#117—222no—
389#117—222no—
390#117—222no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4C4×D1111yescharacteristic
401C2×C22⋊C4—111no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4C4×D1111yescharacteristic
410C2×C22⋊C4C4×D1111yescharacteristic
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—114no—
414C2×C42—114no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42C22×D1111yescharacteristic
419C4⋊C8—224no—
420C22⋊C8—22no—
421C22⋊C8—24no—
422C22⋊C8—224no—
423C22⋊C8—224no—
424C22⋊C8—222no—
425C22⋊C8—224no—
426#97—224no—
427#97—224no—
428C4×C8—224no—
429C2×C11—42no—
430C2×C11—81no—
431C2×C11#229711yescharacteristic
432C2×C11#287911yescharacteristic
433C2×C11#287911yescharacteristic
434C2×C11#296712yes—
435C2×C11#296712yes—
436D11—81no—
437C24—111no—
438C24C2×C4×D1111yescharacteristic
439C24C2×C4×D1111yescharacteristic
440C2×Q8—222no—
441C2×Q8—442no—
442C2×D4—22no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—442no—
448C2×D4—441no—
449C2×D4—441no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—441no—
470C22×C4—441no—
471C22×C4—442no—
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4C2×C4×D1111yescharacteristic
474C22×C4C2×C4×D1111yescharacteristic
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4D4×D1112yes—
477C22×C4D4×D1112yes—
478C22×C4C23×D1111yescharacteristic
479M16—28no—
480M16—228no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—114no—
487C2×C8—222no—
488C2×C8—222no—
489C2×C8—222no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8#434114yes—
493C4⋊C4—22no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C42—21no—
514C42—21no—
515C42—114no—
516C42—114no—
517C42—112no—
518C42—112no—
519C42—112no—
520C42—112no—
521C42—221no—
522C42—221no—
523C11#2137611yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—22no—
527C23—22no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—22no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23—222no—
537C23—222no—
538C23C22⋊C4×D1112yes—
539C23C22×C4×D1111yescharacteristic
540Q8—444no—
541D4—44no—
542D4—444no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—444no—
576C2×C4—444no—
577C2×C4—441no—
578C2×C4—442no—
579C2×C4—441no—
580C2×C4C22⋊C4×D1112yes—
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×#434112yes—
584C2×C4#41×D1112yes—
585C8—24no—
586C8—42no—
587C8—224no—
588C8—442no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—42no—
593C22—42no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—42no—
598C22—41no—
599C22—441no—
600C22—441no—
601C22—442no—
602C22—442no—
603C22—441no—
604C22C2×C22⋊C4×D1111yescharacteristic
605C22C4×#434112yes—
606C22#1062327611yescharacteristic
607C22#1062327611yescharacteristic
608C22#1062328112yes—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—222no—
614C4—222no—
615C4—222no—
616C4—222no—
617C4—441no—
618C4—441no—
619C4—441no—
620C4#1062311711yescharacteristic
621C4#1062312712yes—
622C4#1062318711yescharacteristic
623C2—42no—
624C2—81no—
625C2—881no—
626C2#1307110111yescharacteristic
627C2#1307705811yescharacteristic
628C2#1307705911yescharacteristic
629C2#1307759512yes—
630C2#1307760212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#21376
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. C2×M16×Dic11C2semidirect
4. #13069554C2semidirect
5. #13069412C2semidirect
6. #13068914C2semidirect
7. #13068913C2semidirect
8. #13068911C2semidirect
9. #13068384C2semidirect
10. #13068381C2semidirect
11. C11×#1870C2semidirect
217. #1870D11semidirect
523. C11#21376semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
C2×#106223322
C2×M16×Dic112
#130695542
#130694122
#130689142
#130689132
#130689112
#130683842
#130683812
C11×#18702
#2137611