Finite Group Databasebeta

← #14680414

Subgroups — #14680414

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C2×#10622555C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066867C212yesmaximal, complemented
5#13066863C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C212yesmaximal, complemented
10#13066847C212yesmaximal, complemented
11C11×#1438C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66988—24no—
24C2×#66988—24no—
25C2×#66988C418yescomplemented
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
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#10622555—24no—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11—42no—
51C23×Dic11—42no—
52C23×Dic11C2×C414yes—
53C23×Dic11D414yes—
54C23×Dic11D414yes—
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11C2×C414yes—
82C2×C22⋊Dic11C2×C414yes—
83C2×C22⋊Dic11C2×C414yes—
84#66988—232no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4C2×C414yes—
93C2×Dic11⋊C4C2×C414yes—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11—42no—
97C11×#95—42no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14287—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11C22×C412yes—
121C24×C11C22×C412yes—
122C24×C11C2×D412yes—
123C24×C11C2×D412yes—
124C24×C11C2411yescharacteristic
125C2×D4×C11—28no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—48no—
129C2×D4×C11—48no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
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—22no—
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—44no—
175C22×Dic11—44no—
176C22×Dic11—48no—
177C22×Dic11—48no—
178C22×Dic11C22⋊C4116yescomplemented
179C22×Dic11C22×C412yes—
180C22×Dic11C22×C412yes—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C2×D412yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11#4114yes—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—48no—
190C11×C22⋊C4—44no—
191C22⋊Dic11—28no—
192C22⋊Dic11—28no—
193C22⋊Dic11—28no—
194C22⋊Dic11—28no—
195C22⋊Dic11—44no—
196C22⋊Dic11—48no—
197Dic11⋊C4—28no—
198Dic11⋊C4—28no—
199Dic11⋊C4—48no—
200C4×Dic11—48no—
201C22×#123—111no—
202C2×#380—111no—
203C2×C4×C22⋊C4—111no—
204#1441—112no—
205#1440—111no—
206#1440—111no—
207#1439—112no—
208#1438—111no—
209#1438D1111yescharacteristic
210#1437—112no—
211#1436—112no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—24no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—41no—
243C23×C11—41no—
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×C11C2×C22⋊C414yes—
254C23×C11C23×C411yescharacteristic
255C23×C11C22×D411yescharacteristic
256C23×C11C22×D411yescharacteristic
257C23×C11C2×#4112yes—
258C23×C11C2×#4112yes—
259C23×C11H(5,𝔽2)12yes—
260C23×C11H(5,𝔽2)12yes—
261C23×C11H(5,𝔽2)12yes—
262C23×C112−1+412yes—
263D4×C11—416no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—42no—
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×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—416no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—42no—
302C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
317C2×Dic11C2×C22⋊C414yes—
318C23×D4C2×D1111yescharacteristic
319C24×C4—111no—
320C2×#123—118no—
321C2×#123—224no—
322C2×#123—224no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325C22×C4⋊C4—112no—
326C22×C22⋊C4—111no—
327C22×C22⋊C4—111no—
328C22×C22⋊C4—111no—
329C22×C22⋊C4—111no—
330C22×C22⋊C4—112no—
331C22×C22⋊C4—111no—
332C22×C22⋊C4C2×D1111yescharacteristic
333C22×C22⋊C4C2×D1112yes—
334C22×C22⋊C4C2×D1111yescharacteristic
335C22×C42—112no—
336#380—224no—
337C4×C22⋊C4—224no—
338C2×#95—112no—
339C2×#95—112no—
340C2×#95—112no—
341C2×#95—112no—
342C2×#95—112no—
343C2×#95—112no—
344C2×#95—112no—
345C2×#95C2×D1112yes—
346C22×C11—24no—
347C22×C11—24no—
348C22×C11—24no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11—44no—
353C22×C11—44no—
354C22×C11—44no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—44no—
358C22×C11—44no—
359C22×C11—42no—
360C22×C11—82no—
361C22×C11—82no—
362C22×C11—82no—
363C22×C11—82no—
364C22×C11C22×C22⋊C411yescharacteristic
365C22×C11C4×#4112yes—
366C22×C11#51811yescharacteristic
367C22×C11#51811yescharacteristic
368C22×C11#52012yes—
369C22×C11#52511yescharacteristic
370C22×C11#52511yescharacteristic
371C22×C11#53212yes—
372C22×C11#53412yes—
373C22×C11#53412yes—
374C22×C11#53511yescharacteristic
375C22×C11#53611yescharacteristic
376C22×C11#53712yes—
377C22×C11#53812yes—
378C22×C11#53812yes—
379C22×C11#53912yes—
380C22×C11#53912yes—
381C22×C11#54012yes—
382C22×C11#54012yes—
383C22×C11#54212yes—
384C22×C11#54212yes—
385C4×C11—42no—
386C4×C11—44no—
387C4×C11—82no—
388Dic11—24no—
389Dic11—24no—
390Dic11—42no—
391Dic11—44no—
392Dic11—42no—
393Dic11—82no—
394C25C22×D1111yescharacteristic
395C25C22×D1111yescharacteristic
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4C4×D1114yes—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—114no—
404C23×C4—114no—
405C23×C4—114no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—112no—
409C23×C4—112no—
410C23×C4—442no—
411C23×C4—442no—
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1112yes—
415#123—2232no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—224no—
423C2×C4⋊C4—442no—
424C2×C4⋊C4—442no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—224no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—222no—
442C2×C22⋊C4—222no—
443C2×C22⋊C4—224no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—442no—
446C2×C22⋊C4—442no—
447C2×C22⋊C4—442no—
448C2×C42—224no—
449C2×C42—442no—
450C2×C42—442no—
451#95—42no—
452#95—224no—
453#95—224no—
454#95—224no—
455#95—224no—
456#95—442no—
457#95—442no—
458#95—442no—
459C2×C11—44no—
460C2×C11—82no—
461C2×C11#229711yescharacteristic
462C2×C11#230811yescharacteristic
463C2×C11#231111yescharacteristic
464C2×C11#233512yes—
465C2×C11#233512yes—
466C2×C11#263012yes—
467C2×C11#263012yes—
468C2×C11#266112yes—
469C2×C11#266312yes—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×C4×D1112yes—
485C24C2×C4×D1112yes—
486C24D4×D1112yes—
487C24D4×D1112yes—
488C24C23×D1111yescharacteristic
489C2×D4—28no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—48no—
493C2×D4—48no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
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—112no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—1116no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
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—444no—
547C22×C4—444no—
548C22×C4—448no—
549C22×C4—448no—
550C22×C4C2×C4×D1112yes—
551C22×C4#434114yes—
552C4⋊C4—228no—
553C4⋊C4—228no—
554C4⋊C4—448no—
555C22⋊C4—28no—
556C22⋊C4—48no—
557C22⋊C4—44no—
558C22⋊C4—228no—
559C22⋊C4—228no—
560C22⋊C4—228no—
561C22⋊C4—228no—
562C22⋊C4—448no—
563C22⋊C4—444no—
564C42—448no—
565C11#1428711yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—24no—
569C23—24no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—24no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23C22⋊C4×D1114yes—
608C23C22×C4×D1111yescharacteristic
609C23C2×D4×D1111yescharacteristic
610C23C2×D4×D1111yescharacteristic
611C23C2×#434112yes—
612C23#6703712yes—
613C23#6703712yes—
614C23#6703712yes—
615C23#41×D1112yes—
616C23#6704312yes—
617D4—416no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
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—114no—
638C2×C4—114no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—4416no—
655C2×C4—441no—
656C2×C4—442no—
657C2×C4—441no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—442no—
661C2×C4—442no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C22—24no—
673C22—24no—
674C22—24no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22C2×C22⋊C4×D1111yescharacteristic
691C22#1062301711yescharacteristic
692C22#1062301711yescharacteristic
693C22C4×#434112yes—
694C22#1062307712yes—
695C22#1062311711yescharacteristic
696C22#1062312012yes—
697C22#1062312012yes—
698C22#1062312311yescharacteristic
699C22#1062312412yes—
700C22#1062312712yes—
701C22#1062312812yes—
702C22#1062313312yes—
703C22#1062313412yes—
704C22#1062314412yes—
705C22#1062314612yes—
706C22#1062317911yescharacteristic
707C22#1062318711yescharacteristic
708C22#1062319112yes—
709C22#1062320012yes—
710C22#1062325012yes—
711C4—44no—
712C4—42no—
713C4—82no—
714C4—224no—
715C4—224no—
716C4—444no—
717C4—442no—
718C4—442no—
719C4—882no—
720C2—44no—
721C2—82no—
722C2#1307110111yescharacteristic
723C2#1307119211yescharacteristic
724C2#1307120311yescharacteristic
725C2#1307140312yes—
726C2#1307140712yes—
727C2#1307445212yes—
728C2#1307445612yes—
729C2#1307474112yes—
730C2#1307476312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622555C2semidirect
3. C2×C22⋊C4×Dic11C2semidirect
4. #13066867C2semidirect
5. #13066863C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066847C2semidirect
25. C2×#66988C4semidirect
178. C22×Dic11C22⋊C4semidirect
565. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106225552
C2×C22⋊C4×Dic112
#130668672
#130668632
#130668592
#130668572
#130668532
#130668472
C11×#14382
#1428711