Finite Group Databasebeta

← #14680971

Subgroups — #14680971

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622556C211yesmaximal, characteristic, complemented
3C2×#10622555C211yesmaximal, characteristic, complemented
4#13066868C212yesmaximal, complemented
5#13066863C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066857C211yesmaximal, characteristic
9#13066841C212yesmaximal, complemented
10#13066838C212yesmaximal, complemented
11C11×#1438C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×D4×Dic11—24no—
24C2×D4×Dic11—24no—
25C2×D4×Dic11C418yescomplemented
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622556—24no—
39#10622555—24no—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—24no—
45C22×D4×C11—24no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—42no—
53C23×Dic11—42no—
54C23×Dic11—42no—
55C23×Dic11—42no—
56C23×Dic11C2×C414yes—
57C23×Dic11C2×C414yes—
58C23×Dic11D414yes—
59C23×Dic11D414yes—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11C2×C414yes—
85C2×C22⋊Dic11C2×C414yes—
86D4×Dic11—232no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11C2×C414yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4—42no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11C2×C414yes—
96C11×#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14344—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11C22×C412yes—
120C24×C11C22×C412yes—
121C24×C11C2×D412yes—
122C24×C11C2×D412yes—
123C24×C11#4114yes—
124C24×C11C2411yescharacteristic
125C2×D4×C11—216no—
126C2×D4×C11—216no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11#4114yes—
149C22×Dic11—28no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—48no—
177C22×Dic11—48no—
178C22×Dic11—44no—
179C22×Dic11—44no—
180C22×Dic11—48no—
181C22×Dic11—44no—
182C22×Dic11—48no—
183C22×Dic11—44no—
184C22×Dic11C22⋊C4116yescomplemented
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C2×D412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C11×C22⋊C4—44no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—48no—
196C22⋊Dic11—28no—
197C22⋊Dic11—28no—
198C22⋊Dic11—44no—
199C22⋊Dic11—44no—
200C22⋊Dic11—48no—
201C4⋊Dic11—28no—
202Dic11⋊C4—48no—
203C4×Dic11—28no—
204C22×C4×D4—111no—
205C2×#381—111no—
206C2×#380—111no—
207#1441—112no—
208#1440—111no—
209#1440—111no—
210#1439—112no—
211#1438—111no—
212#1438D1111yescharacteristic
213#1434—112no—
214C22⋊#95—112no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11C2×C22⋊C414yes—
256C23×C11#11714yes—
257C23×C11C23×C411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C2×#4112yes—
261C23×C11C2×#4112yes—
262C23×C11H(5,𝔽2)12yes—
263C23×C11H(5,𝔽2)12yes—
264C23×C11H(5,𝔽2)12yes—
265C23×C112−1+412yes—
266D4×C11—232no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11#11714yes—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—416no—
299C2×Dic11—416no—
300C2×Dic11—41no—
301C2×Dic11—42no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11C2×C22⋊C414yes—
321C2×Dic11C2×C22⋊C414yes—
322C23×D4C2×D1111yescharacteristic
323C24×C4—111no—
324C24×C4—111no—
325C2×C4×D4—118no—
326C2×C4×D4—224no—
327C2×C4×D4—224no—
328C22×C4⋊C4—111no—
329C22×C4⋊C4—112no—
330C22×C22⋊C4—111no—
331C22×C22⋊C4—111no—
332C22×C22⋊C4—112no—
333C22×C22⋊C4—111no—
334C22×C22⋊C4—111no—
335C22×C22⋊C4C2×D1112yes—
336C22×C22⋊C4C2×D1111yescharacteristic
337C22×C22⋊C4C2×D1111yescharacteristic
338C22×C42—111no—
339#381—224no—
340#380—224no—
341C2×#95—112no—
342C2×#95—112no—
343C2×#95—112no—
344C2×#95—112no—
345C2×#95—112no—
346C2×#95—112no—
347C2×#95—112no—
348C2×#95—112no—
349C2×#95C2×D1112yes—
350C22×C11—24no—
351C22×C11—24no—
352C22×C11—28no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—44no—
358C22×C11—44no—
359C22×C11—44no—
360C22×C11—44no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11C22×C22⋊C411yescharacteristic
369C22×C11C2×#11711yescharacteristic
370C22×C11C2×#11711yescharacteristic
371C22×C11#51812yes—
372C22×C11#52012yes—
373C22×C11#52512yes—
374C22×C11#52512yes—
375C22×C11#53411yescharacteristic
376C22×C11#53412yes—
377C22×C11#53411yescharacteristic
378C22×C11#53511yescharacteristic
379C22×C11#53611yescharacteristic
380C22×C11#53712yes—
381C22×C11#53812yes—
382C22×C11#53812yes—
383C22×C11#53912yes—
384C22×C11#53912yes—
385C22×C11#54012yes—
386C22×C11#54012yes—
387C22×C11#54212yes—
388C22×C11#54212yes—
389C4×C11—24no—
390C4×C11—82no—
391C4×C11—82no—
392Dic11—24no—
393Dic11—24no—
394Dic11—42no—
395Dic11—42no—
396Dic11—82no—
397Dic11—82no—
398C25C22×D1111yescharacteristic
399C25C22×D1111yescharacteristic
400C22×D4—22no—
401C22×D4—22no—
402C22×D4—24no—
403C22×D4—24no—
404C22×D4C4×D1114yes—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—114no—
408C23×C4—114no—
409C23×C4—114no—
410C23×C4—111no—
411C23×C4—111no—
412C23×C4—114no—
413C23×C4—112no—
414C23×C4—112no—
415C23×C4—222no—
416C23×C4—222no—
417C23×C4—442no—
418C23×C4—442no—
419C23×C4—442no—
420C23×C4—442no—
421C23×C4C22×D1112yes—
422C23×C4C22×D1112yes—
423C23×C4C22×D1111yescharacteristic
424C4×D4—2232no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—224no—
429C2×C4⋊C4—442no—
430C2×C4⋊C4—442no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—114no—
439C2×C22⋊C4—114no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—222no—
442C2×C22⋊C4—222no—
443C2×C22⋊C4—222no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—222no—
446C2×C22⋊C4—224no—
447C2×C22⋊C4—442no—
448C2×C22⋊C4—442no—
449C2×C22⋊C4—442no—
450C2×C22⋊C4—442no—
451C2×C42—114no—
452C2×C42—222no—
453C2×C42—222no—
454#95—24no—
455#95—224no—
456#95—224no—
457#95—224no—
458#95—224no—
459#95—442no—
460#95—442no—
461#95—442no—
462#95—442no—
463C2×C11—44no—
464C2×C11—44no—
465C2×C11#228011yescharacteristic
466C2×C11#230811yescharacteristic
467C2×C11#231111yescharacteristic
468C2×C11#231812yes—
469C2×C11#231912yes—
470C2×C11#263012yes—
471C2×C11#263012yes—
472C2×C11#263512yes—
473C2×C11#263812yes—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24C2×C4×D1112yes—
488C24C2×C4×D1112yes—
489C24D4×D1112yes—
490C24D4×D1112yes—
491C24#434114yes—
492C24C23×D1111yescharacteristic
493C2×D4—216no—
494C2×D4—216no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—1116no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—228no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—448no—
552C22×C4—448no—
553C22×C4—444no—
554C22×C4—448no—
555C22×C4—444no—
556C22×C4—444no—
557C22×C4—448no—
558C22×C4—444no—
559C22×C4C2×C4×D1112yes—
560C22×C4#434114yes—
561C4⋊C4—228no—
562C4⋊C4—448no—
563C22⋊C4—44no—
564C22⋊C4—44no—
565C22⋊C4—48no—
566C22⋊C4—228no—
567C22⋊C4—228no—
568C22⋊C4—444no—
569C22⋊C4—448no—
570C22⋊C4—444no—
571C42—228no—
572C11#1434411yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23—41no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23#6693014yes—
614C23C22⋊C4×D1114yes—
615C23C22×C4×D1111yescharacteristic
616C23C2×D4×D1111yescharacteristic
617C23C2×D4×D1111yescharacteristic
618C23C2×#434112yes—
619C23C2×#434112yes—
620C23#6703712yes—
621C23#6703712yes—
622C23#6704212yes—
623C23#6704312yes—
624D4—232no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—114no—
644C2×C4—114no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—4416no—
658C2×C4—4416no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—442no—
662C2×C4—442no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—442no—
676C2×C4—442no—
677C2×C4—442no—
678C2×C4—442no—
679C2×C4#6693014yes—
680C22—24no—
681C22—24no—
682C22—28no—
683C22—24no—
684C22—24no—
685C22—44no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—42no—
692C22—42no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C2×#6693011yescharacteristic
699C22C2×#6693011yescharacteristic
700C22C2×C22⋊C4×D1111yescharacteristic
701C22#1062307612yes—
702C22#1062307712yes—
703C22#1062311712yes—
704C22#1062311712yes—
705C22#1062312011yescharacteristic
706C22#1062312311yescharacteristic
707C22#1062312412yes—
708C22#1062312812yes—
709C22#1062313312yes—
710C22#1062313412yes—
711C22#1062313612yes—
712C22#1062314812yes—
713C22#1062315012yes—
714C22#1062317911yescharacteristic
715C22#1062318411yescharacteristic
716C22#1062319612yes—
717C22#1062321312yes—
718C22#1062325012yes—
719C4—24no—
720C4—82no—
721C4—82no—
722C4—224no—
723C4—224no—
724C4—442no—
725C4—442no—
726C4—882no—
727C4—882no—
728C2—44no—
729C2—44no—
730C2#1307099411yescharacteristic
731C2#1307119011yescharacteristic
732C2#1307120311yescharacteristic
733C2#1307124212yes—
734C2#1307125312yes—
735C2#1307445212yes—
736C2#1307445412yes—
737C2#1307449912yes—
738C2#1307453212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622556C2semidirect
3. C2×#10622555C2semidirect
4. #13066868C2semidirect
5. #13066863C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
9. #13066841C2semidirect
10. #13066838C2semidirect
25. C2×D4×Dic11C4semidirect
184. C22×Dic11C22⋊C4semidirect
572. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106225562
C2×#106225552
#130668682
#130668632
#130668592
#130668572
#130668412
#130668382
C11×#14382
#1434411