Finite Group Databasebeta

← #14690495

Subgroups — #14690495

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622274C211yesmaximal, characteristic
2C2×#10622593C211yesmaximal, characteristic
3C2×#10622596C211yesmaximal, characteristic
4C2×#10622585C211yesmaximal, characteristic
5C2×#10622589C211yesmaximal, characteristic
6C2×#10622589C212yesmaximal
7#13066880C212yesmaximal
8#13066879C212yesmaximal
9Dic11⋊#95C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic
11C2×C11×#398C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C11×#398—24no—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36#10622596—24no—
37#10622593—24no—
38#10622589—28no—
39#10622589—24no—
40#10622585—24no—
41#10622274—24no—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—42no—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—42no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—42no—
84C2×Dic11⋊C4—42no—
85C2×Dic11⋊C4—42no—
86C2×Dic11⋊C4—42no—
87C2×Dic11⋊C4D414yes—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11D414yes—
92C2×C4×Dic11Q818yes—
93C11×#95—24no—
94C11×#95D414yes—
95C11⋊#95—24no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95D414yes—
101C11⋊#95Q818yes—
102#15145—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2×Q814yes—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×Q814yes—
166C22×Dic11C2×Q814yes—
167C22×Dic11C2×Q814yes—
168C22×Dic11C2×Q814yes—
169C22×Dic11#4112yes—
170C22×Dic11#4114yes—
171C11×C4⋊C4—48no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4—44no—
174C4⋊Dic11—48no—
175C4⋊Dic11—44no—
176Dic11⋊C4—28no—
177Dic11⋊C4—48no—
178Dic11⋊C4—48no—
179Dic11⋊C4—48no—
180Dic11⋊C4—48no—
181Dic11⋊C4—44no—
182Dic11⋊C4—44no—
183C4×Dic11—216no—
184C4×Dic11—28no—
185C2×#398—111no—
186C2×#398—111no—
187C2×#398—111no—
188C2×#398D1111yescharacteristic
189C2×#389—111no—
190C2×#384—112no—
191C2×#384—111no—
192#1444—112no—
193#1444—112no—
194C4⋊#95—112no—
195C4×#95—111no—
196C23×C11C22×D411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×Q812yes—
201C23×C11C22×Q812yes—
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4112yes—
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C11H(5,𝔽2)11yescharacteristic
206C23×C112−1+412yes—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12714yes—
237C2×C4×C11C4⋊Q818yes—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11#12114yes—
268C2×Dic11C22⋊Q818yes—
269C2×Dic11#12314yes—
270C2×Dic11#12518yes—
271C2×Dic11C4⋊Q818yes—
272C2×Dic11C4⋊Q814yes—
273C2×Dic11C4⋊Q814yes—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1112yes—
286C22×C42—112no—
287C22×C42—111no—
288#398—24no—
289#398—224no—
290#398—224no—
291#398—224no—
292#389—224no—
293#384—224no—
294#384—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—111no—
301C2×#95—111no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1111yescharacteristic
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×C22⋊Q812yes—
306C22×C11C2×#12311yescharacteristic
307C22×C11C2×#12512yes—
308C22×C11C2×#12711yescharacteristic
309C22×C11C2×C4⋊Q811yescharacteristic
310C22×C11C2×C4⋊Q812yes—
311C22×C11C2×C4⋊Q811yescharacteristic
312C22×C11C2×C4⋊Q812yes—
313C22×C11#53511yescharacteristic
314C22×C11#53611yescharacteristic
315C22×C11#54412yes—
316C22×C11#54412yes—
317C22×C11D4211yescharacteristic
318C22×C11D4211yescharacteristic
319C22×C11#54712yes—
320C22×C11#54712yes—
321C22×C11D4×Q812yes—
322C22×C11#55011yescharacteristic
323C22×C11#55011yescharacteristic
324C22×C11#55412yes—
325C22×C11#55412yes—
326C22×C11#55712yes—
327C4×C11—28no—
328C4×C11—24no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—82no—
332Dic11—28no—
333Dic11—24no—
334Dic11—42no—
335Dic11—81no—
336Dic11—82no—
337Dic11#39818yescomplemented
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—112no—
343C23×C4—111no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—442no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4—442no—
382C2×C4⋊C4—442no—
383C2×C4⋊C4—442no—
384C2×C42—114no—
385C2×C42—118no—
386C2×C42—224no—
387C2×C42—224no—
388C2×C42—224no—
389#95—24no—
390#95—114no—
391#95—118no—
392#95—222no—
393#95—222no—
394#95—224no—
395#95—224no—
396#95—224no—
397#95C22⋊D1114yes—
398C2×C11C2×#39811yescharacteristic
399C2×C11#244012yes—
400C2×C11#244012yes—
401C2×C11#250111yescharacteristic
402C2×C11#250211yescharacteristic
403C2×C11#254111yescharacteristic
404C2×C11#254611yescharacteristic
405C2×C11#255212yes—
406C2×C11#255212yes—
407C2×C11#266011yescharacteristic
408C2×C11#286811yescharacteristic
409C24C23×D1111yescharacteristic
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—221no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—221no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—221no—
469C22×C4—222no—
470C22×C4D4×D1112yes—
471C22×C4D4×D1112yes—
472C22×C4D4×D1112yes—
473C22×C4Q8×D1114yes—
474C22×C4Q8×D1114yes—
475C22×C4C2×C22⋊D1112yes—
476C22×C4C2×C22⋊D1114yes—
477C4⋊C4—48no—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C4⋊C4—228no—
481C4⋊C4—448no—
482C4⋊C4—448no—
483C4⋊C4—448no—
484C4⋊C4—444no—
485C4⋊C4—448no—
486C4⋊C4—448no—
487C4⋊C4—444no—
488C4⋊C4—444no—
489C42—2216no—
490C42—228no—
491C11#1514511yescharacteristic, complemented, Sylow
492C23C2×D4×D1111yescharacteristic
493C23C2×D4×D1111yescharacteristic
494C23C2×D4×D1111yescharacteristic
495C23#6703711yescharacteristic
496C23C2×Q8×D1112yes—
497C23C2×Q8×D1112yes—
498C23#41×D1112yes—
499C23#41×D1111yescharacteristic
500C23#6704211yescharacteristic
501C23#6704312yes—
502C23C22×C22⋊D1111yescharacteristic
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—114no—
533C2×C4—114no—
534C2×C4—118no—
535C2×C4—114no—
536C2×C4—118no—
537C2×C4—118no—
538C2×C4—114no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—441no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—442no—
568C2×C4#6699314yes—
569C2×C4#6699718yes—
570C22#1062313011yescharacteristic
571C22D11×#12111yescharacteristic
572C22#1062313811yescharacteristic
573C22#1062314011yescharacteristic
574C22#1062315412yes—
575C22D11×C22⋊Q812yes—
576C22#1062316312yes—
577C22#1062316712yes—
578C22#1062317911yescharacteristic
579C22D11×#12311yescharacteristic
580C22#1062318612yes—
581C22#1062321612yes—
582C22D11×#12512yes—
583C22#1062322012yes—
584C22#1062322112yes—
585C22D11×C4⋊Q811yescharacteristic
586C22D11×C4⋊Q812yes—
587C22D11×C4⋊Q811yescharacteristic
588C22D4×C22⋊D1111yescharacteristic
589C22C2×#6699311yescharacteristic
590C22C2×#6699712yes—
591C22#1062335512yes—
592C22#1062336511yescharacteristic
593C4—28no—
594C4—24no—
595C4—42no—
596C4—82no—
597C4—81no—
598C4—118no—
599C4—228no—
600C4—224no—
601C4—442no—
602C4—882no—
603C4—881no—
604C2D11×#39811yescharacteristic
605C2#1307231312yes—
606C2#1307231512yes—
607C2#1307308511yescharacteristic
608C2#1307308911yescharacteristic
609C2#1307355911yescharacteristic
610C2#1307360011yescharacteristic
611C2#1307364612yes—
612C2#1307364812yes—
613C2#1307473911yescharacteristic
614C2#1307701211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC2×C11×#398C2
hypercenterC2×#398D11
hypocenterC11#15145
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
337. Dic11#398semidirect
491. C11#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#106222742
C2×#106225932
C2×#106225962
C2×#106225852
C2×#106225892
#130668802
#130668792
Dic11⋊#952
#95×Dic112
C2×C11×#3982
#1514511