Finite Group Databasebeta

← #14680444

Subgroups — #14680444

Order 2816.

1610 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066870C211yesmaximal, characteristic, complemented
5#13066868C212yesmaximal, complemented
6#13066866C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic
8#13066859C212yesmaximal
9#13066853C212yesmaximal
10#13066847C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C2×#66932—24no—
26C2×#66932—24no—
27C2×#66932C418yescomplemented
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4⋊C4×Dic11—24no—
39#10622263—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11C2×C414yes—
67C2×C22⋊Dic11C2×C414yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11C2×C414yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—42no—
79C2×Dic11⋊C4—42no—
80C2×Dic11⋊C4C2×C414yes—
81C2×Dic11⋊C4C2×C414yes—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—42no—
84C2×C4×Dic11—42no—
85C2×C4×Dic11C2×C414yes—
86C2×C4×Dic11D414yes—
87C2×C4×Dic11D414yes—
88#66932—232no—
89C11×#95—22no—
90C11×#95—42no—
91C11⋊#95—22no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#14291—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11—21no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—22no—
110C24×C11C22×C412yes—
111C24×C11C2411yescharacteristic
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
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×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4114yes—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11C22×C412yes—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C412yes—
168C22×Dic11C22×C412yes—
169C22×Dic11C2×D412yes—
170C22×Dic11C2×D412yes—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11#4114yes—
174C11×C4⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—48no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179C22⋊Dic11—48no—
180C4⋊Dic11—28no—
181C4⋊Dic11—28no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—48no—
185C4×Dic11—48no—
186C4×Dic11C22⋊C4116yescomplemented
187C22×#126—111no—
188C2×#382—111no—
189C2×C4×C4⋊C4—111no—
190#1441—112no—
191#1441—111no—
192#1441—111no—
193#1439—112no—
194#1439—111no—
195#1439D1111yescharacteristic
196#1437—112no—
197#1436—112no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11C23×C411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C2×#4112yes—
225C23×C11C2×#4112yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C11H(5,𝔽2)11yescharacteristic
228C23×C11H(5,𝔽2)11yescharacteristic
229C23×C112−1+411yescharacteristic
230C23×C112−1+411yescharacteristic
231C23×C112−1+412yes—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C2×C22⋊C414yes—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11C2×C22⋊C414yes—
293C2×Dic11C2×C22⋊C414yes—
294C2×#126—118no—
295C2×#126—224no—
296C2×#126—224no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4C2×D1111yescharacteristic
307C22×C22⋊C4C2×D1112yes—
308C22×C42—111no—
309C22×C42—112no—
310#382—224no—
311C4×C4⋊C4—224no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—111no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95C2×D1111yescharacteristic
321C2×#95C2×D1112yes—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—42no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11C22×C22⋊C411yescharacteristic
334C22×C11C4×#4112yes—
335C22×C11#52011yescharacteristic
336C22×C11#52011yescharacteristic
337C22×C11#52012yes—
338C22×C11#52511yescharacteristic
339C22×C11#52511yescharacteristic
340C22×C11#53212yes—
341C22×C11#53511yescharacteristic
342C22×C11#53511yescharacteristic
343C22×C11#53611yescharacteristic
344C22×C11#53611yescharacteristic
345C22×C11#53711yescharacteristic
346C22×C11#53712yes—
347C22×C11#53711yescharacteristic
348C22×C11#53812yes—
349C22×C11#53812yes—
350C22×C11#53912yes—
351C22×C11#53912yes—
352C22×C11#54112yes—
353C22×C11#54112yes—
354C22×C11#54212yes—
355C22×C11#54212yes—
356C4×C11—24no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11—82no—
360Dic11—24no—
361Dic11—24no—
362Dic11—42no—
363Dic11—44no—
364Dic11—42no—
365Dic11—82no—
366C25C22×D1111yescharacteristic
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—112no—
372C23×C4—112no—
373C23×C4C22×D1112yes—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377#126—2232no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—442no—
393C2×C4⋊C4—442no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—442no—
407C2×C22⋊C4—442no—
408C2×C22⋊C4C4×D1114yes—
409C2×C42—114no—
410C2×C42—114no—
411C2×C42—114no—
412C2×C42—224no—
413C2×C42—442no—
414C2×C42—442no—
415#95—22no—
416#95—42no—
417#95—224no—
418#95—224no—
419#95—224no—
420#95—222no—
421#95—224no—
422#95—442no—
423#95—442no—
424#95—442no—
425C2×C11—82no—
426C2×C11#229711yescharacteristic
427C2×C11#231111yescharacteristic
428C2×C11#231111yescharacteristic
429C2×C11#233412yes—
430C2×C11#233412yes—
431C2×C11#263611yescharacteristic
432C2×C11#263611yescharacteristic
433C2×C11#263711yescharacteristic
434C2×C11#263711yescharacteristic
435C2×C11#266212yes—
436C2×C11#266412yes—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24C2×C4×D1112yes—
448C24C23×D1111yescharacteristic
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4C2×C4×D1112yes—
507C22×C4C2×C4×D1112yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1112yes—
510C22×C4#434114yes—
511C4⋊C4—28no—
512C4⋊C4—228no—
513C4⋊C4—228no—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C4⋊C4—448no—
517C22⋊C4—28no—
518C22⋊C4—48no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—448no—
522C42—1116no—
523C42—448no—
524C11#1429111yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—22no—
528C23—24no—
529C23—24no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23C22×C4×D1111yescharacteristic
549C23C2×D4×D1111yescharacteristic
550C23C2×D4×D1111yescharacteristic
551C23C2×#434112yes—
552C23#6703712yes—
553C23#6703711yescharacteristic
554C23#6704011yescharacteristic
555C23#41×D1112yes—
556C23#6704211yescharacteristic
557C23#6704311yescharacteristic
558C23#6704312yes—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—114no—
583C2×C4—114no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—442no—
603C2×C4—441no—
604C2×C4—442no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—442no—
609C2×C4—441no—
610C2×C4—442no—
611C2×C4—441no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4C22⋊C4×D1114yes—
621C22—44no—
622C22—44no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—82no—
627C22—81no—
628C22—81no—
629C22—82no—
630C22—81no—
631C22—81no—
632C22C2×C22⋊C4×D1111yescharacteristic
633C22#1062303511yescharacteristic
634C22#1062305411yescharacteristic
635C22C4×#434112yes—
636C22#1062307712yes—
637C22#1062311711yescharacteristic
638C22#1062312412yes—
639C22#1062312712yes—
640C22#1062313312yes—
641C22#1062313811yescharacteristic
642C22#1062313912yes—
643C22#1062313911yescharacteristic
644C22#1062315612yes—
645C22#1062315911yescharacteristic
646C22#1062316011yescharacteristic
647C22#1062316912yes—
648C22#1062318711yescharacteristic
649C22#1062318812yes—
650C22#1062319312yes—
651C22#1062320611yescharacteristic
652C22#1062321312yes—
653C22#1062323212yes—
654C22#1062324611yescharacteristic
655C4—24no—
656C4—44no—
657C4—42no—
658C4—82no—
659C4—224no—
660C4—224no—
661C4—444no—
662C4—442no—
663C4—442no—
664C4—882no—
665C2—82no—
666C2#1307110111yescharacteristic
667C2#1307120511yescharacteristic
668C2#1307120611yescharacteristic
669C2#1307138812yes—
670C2#1307139212yes—
671C2#1307451011yescharacteristic
672C2#1307451411yescharacteristic
673C2#1307452111yescharacteristic
674C2#1307452511yescharacteristic
675C2#1307475212yes—
676C2#1307477612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14291
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
4. #13066870C2semidirect
5. #13066868C2semidirect
6. #13066866C2semidirect
10. #13066847C2semidirect
27. C2×#66932C4semidirect
186. C4×Dic11C22⋊C4semidirect
524. C11#14291semidirect

Maximal subgroups

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

subgroupindex
C22×#669322
C2×#106222632
C2×C4⋊C4×Dic112
#130668702
#130668682
#130668662
#130668612
#130668592
#130668532
#130668472
C11×#14392
#1429111