Finite Group Databasebeta

← #14690484

Subgroups — #14690484

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622269C212yesmaximal
3C2×#10622592C212yesmaximal
4C2×#10622260C211yesmaximal, characteristic
5C2×#10622589C212yesmaximal
6#13066881C211yesmaximal, characteristic
7#13066880C211yesmaximal, characteristic
8#13066879C211yesmaximal, characteristic
9Dic11⋊#95C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic
11C11×#1444C211yesmaximal, characteristic
12C23×Dic22C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2212yes—
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C2×#66941—28no—
27C2×#66941—24no—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622592—28no—
38#10622589—28no—
39#10622269—28no—
40#10622260—24no—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C22×Dic22—24no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22—24no—
56C22×Dic22—24no—
57C22×Dic22—42no—
58C22×Dic22—42no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—42no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—24no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—42no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
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⋊C4D418yes—
86C2×Dic11⋊C4Q814yescomplemented
87C2×C4×Dic11—24no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11D414yes—
91C2×C4×Dic11Q818yescomplemented
92#66941—232no—
93C11×#95—22no—
94C11×#95—24no—
95C11×#95Q814yescomplemented
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95D418yes—
101C11⋊#95Q814yescomplemented
102#15143—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—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×Q812yes—
129C22×C4×C11C2×Q812yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11C2×Q814yes—
132C22×C4×C11C2×Q814yes—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11C2×D412yes—
158C22×Dic11C2×D414yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×Q812yes—
162C22×Dic11C2×Q814yes—
163C22×Dic11C2×Q814yes—
164C22×Dic11C2×Q814yes—
165C22×Dic11C2×Q812yes—
166C22×Dic11#4112yes—
167C2×Dic22—216no—
168C2×Dic22—48no—
169C2×Dic22—48no—
170C2×Dic22—48no—
171C2×Dic22—48no—
172C2×Dic22—48no—
173C2×Dic22—48no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—48no—
176C4⋊Dic11—28no—
177C4⋊Dic11—48no—
178C4⋊Dic11—44no—
179Dic11⋊C4—216no—
180Dic11⋊C4—28no—
181Dic11⋊C4—48no—
182Dic11⋊C4—48no—
183Dic11⋊C4—44no—
184Dic11⋊C4—44no—
185C4×Dic11—28no—
186C4×Dic11—216no—
187C22×C4⋊Q8—111no—
188C2×#395—112no—
189C2×#395—112no—
190C2×#389—111no—
191C2×#384—112no—
192#1444—111no—
193#1444—111no—
194#1444—111no—
195#1444D1111yescharacteristic
196C4⋊#95—112no—
197C4×#95—111no—
198C23×C11C22×D411yescharacteristic
199C23×C11C22×D412yes—
200C23×C11C22×D412yes—
201C23×C11C22×Q811yescharacteristic
202C23×C11C22×Q812yes—
203C23×C11C22×Q811yescharacteristic
204C23×C11C22×Q811yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C112−1+412yes—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C4⋊Q814yes—
237C2×C4×C11C4⋊Q818yescomplemented
238C2×Dic11—22no—
239C2×Dic11—24no—
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—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11#12014yes—
266C2×Dic11C22⋊Q818yes—
267C2×Dic11C22⋊Q814yes—
268C2×Dic11#12714yes—
269C2×Dic11C4⋊Q814yes—
270C2×Dic11C4⋊Q818yes—
271C2×Dic11C4⋊Q818yescomplemented
272Dic22—432no—
273C23×Q8—112no—
274C2×C4⋊Q8—224no—
275C2×C4⋊Q8—228no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C4⋊C4C2×D1112yes—
287C22×C42—111no—
288C22×C42—112no—
289#395—228no—
290#395—228no—
291#389—224no—
292#384—228no—
293C2×#95—112no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—111no—
299C2×#95C2×D1112yes—
300C2×#95C2×D1111yescharacteristic
301C2×#95C2×D1111yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×C22⋊Q811yescharacteristic
304C22×C11C2×C22⋊Q812yes—
305C22×C11C2×#12711yescharacteristic
306C22×C11C2×C4⋊Q811yescharacteristic
307C22×C11C2×C4⋊Q812yes—
308C22×C11C2×C4⋊Q812yes—
309C22×C11C2×C4⋊Q811yescharacteristic
310C22×C11C2×C4⋊Q812yes—
311C22×C11#53511yescharacteristic
312C22×C11#53611yescharacteristic
313C22×C11#54412yes—
314C22×C11#54412yes—
315C22×C11D4212yes—
316C22×C11D4212yes—
317C22×C11#54712yes—
318C22×C11D4×Q812yes—
319C22×C11D4×Q812yes—
320C22×C11D4×Q812yes—
321C22×C11#55411yescharacteristic
322C22×C11#55411yescharacteristic
323C22×C11Q8211yescharacteristic
324C22×C11Q8211yescharacteristic
325C4×C11—24no—
326C4×C11—28no—
327C4×C11—44no—
328C4×C11—42no—
329C4×C11—81no—
330Dic11—24no—
331Dic11—28no—
332Dic11—44no—
333Dic11—42no—
334Dic11—81no—
335Dic11#39518yescomplemented
336C22×Q8—224no—
337C22×Q8—224no—
338C22×Q8—224no—
339C22×Q8—224no—
340C22×Q8—224no—
341C22×Q8—442no—
342C22×Q8—442no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1112yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C4⋊Q8—2232no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4—442no—
382C2×C4⋊C4—442no—
383C2×C42—114no—
384C2×C42—118no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—224no—
388#95—22no—
389#95—24no—
390#95—118no—
391#95—114no—
392#95—224no—
393#95—224no—
394#95—222no—
395#95—224no—
396#95Dic2214yescomplemented
397C2×C11C2×#39511yescharacteristic
398C2×C11#243311yescharacteristic
399C2×C11#243411yescharacteristic
400C2×C11#244012yes—
401C2×C11#244012yes—
402C2×C11#254211yescharacteristic
403C2×C11#255112yes—
404C2×C11#255112yes—
405C2×C11#256711yescharacteristic
406C2×C11#266011yescharacteristic
407C2×C11#286811yescharacteristic
408C24C23×D1111yescharacteristic
409C2×Q8—2216no—
410C2×Q8—448no—
411C2×Q8—448no—
412C2×Q8—448no—
413C2×Q8—448no—
414C2×Q8—448no—
415C2×Q8—448no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4C2×Dic2212yes—
472C22×C4C2×Dic2214yes—
473C22×C4D4×D1114yes—
474C22×C4D4×D1112yes—
475C22×C4D4×D1114yes—
476C22×C4Q8×D1112yes—
477C22×C4Q8×D1112yes—
478C22×C4Q8×D1114yes—
479C4⋊C4—28no—
480C4⋊C4—48no—
481C4⋊C4—2216no—
482C4⋊C4—228no—
483C4⋊C4—228no—
484C4⋊C4—448no—
485C4⋊C4—448no—
486C4⋊C4—444no—
487C4⋊C4—444no—
488C4⋊C4—444no—
489C4⋊C4—448no—
490C42—228no—
491C42—2216no—
492C11#1514311yescharacteristic, complemented, Sylow
493C23C22×Dic2211yescharacteristic
494C23C2×D4×D1111yescharacteristic
495C23C2×D4×D1112yes—
496C23C2×D4×D1112yes—
497C23#6703711yescharacteristic
498C23C2×Q8×D1111yescharacteristic
499C23C2×Q8×D1111yescharacteristic
500C23C2×Q8×D1112yes—
501C23#41×D1111yescharacteristic
502C23#6704211yescharacteristic
503C23#6704312yes—
504Q8—4432no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—114no—
533C2×C4—118no—
534C2×C4—114no—
535C2×C4—118no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—118no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—222no—
553C2×C4—224no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—441no—
560C2×C4—442no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—442no—
564C2×C4—441no—
565C2×C4—442no—
566C2×C4#6694114yes—
567C2×C4#6694118yescomplemented
568C22C2×#6694111yescharacteristic
569C22C2×#6694112yes—
570C22D4×Dic2212yes—
571C22#1062307011yescharacteristic
572C22Q8×Dic2211yescharacteristic
573C22D11×#12011yescharacteristic
574C22#1062312112yes—
575C22#1062313811yescharacteristic
576C22#1062314012yes—
577C22#1062315412yes—
578C22D11×C22⋊Q811yescharacteristic
579C22D11×C22⋊Q812yes—
580C22#1062316312yes—
581C22#1062316312yes—
582C22#1062317911yescharacteristic
583C22#1062318612yes—
584C22#1062322012yes—
585C22#1062322111yescharacteristic
586C22D11×#12711yescharacteristic
587C22#1062325311yescharacteristic
588C22D11×C4⋊Q811yescharacteristic
589C22D11×C4⋊Q812yes—
590C22D11×C4⋊Q812yes—
591C4—24no—
592C4—28no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4—118no—
597C4—224no—
598C4—228no—
599C4—444no—
600C4—442no—
601C4—881no—
602C2D11×#39511yescharacteristic
603C2#1307224811yescharacteristic
604C2#1307225811yescharacteristic
605C2#1307231312yes—
606C2#1307231712yes—
607C2#1307356411yescharacteristic
608C2#1307364112yes—
609C2#1307364412yes—
610C2#1307382311yescharacteristic
611C2#1307473911yescharacteristic
612C2#1307701311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1444C2
hypercenter#1444D11
hypocenterC11#15143
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
86. C2×Dic11⋊C4Q8semidirect
91. C2×C4×Dic11Q8semidirect
95. C11×#95Q8semidirect
101. C11⋊#95Q8semidirect
237. C2×C4×C11C4⋊Q8semidirect
271. C2×Dic11C4⋊Q8semidirect
335. Dic11#395semidirect
396. #95Dic22semidirect
492. C11#15143semidirect
567. C2×C4#66941semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106222692
C2×#106225922
C2×#106222602
C2×#106225892
#130668812
#130668802
#130668792
Dic11⋊#952
#95×Dic112
C11×#14442
#1514311