Finite Group Databasebeta

← #14685099

Subgroups — #14685099

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C23×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622556C211yesmaximal, characteristic, complemented
5#13066853C214yesmaximal, complemented
6#13066847C214yesmaximal, complemented
7#13066839C211yesmaximal, characteristic, complemented
8#13066838C211yesmaximal, characteristic, complemented
9C2×C11×#386C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×#66988—24no—
21C2×#66988—24no—
22C2×#66988C418yescomplemented
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11—24no—
25C22×C4×Dic11—24no—
26C22×C4×Dic11—24no—
27C22×C4×Dic11C2214yes—
28C11×#386—24no—
29C2×C11×#95C2212yes—
30#10622833—24no—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2214yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2214yes—
35#10622556—24no—
36C25×C11C2311yescharacteristic
37C25×C11C2311yescharacteristic
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11C2×C414yes—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—28no—
48C23×C4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—22no—
57C23×Dic11—22no—
58C23×Dic11—28no—
59C23×Dic11C2×C414yes—
60C23×Dic11D414yes—
61C23×Dic11D414yes—
62C23×Dic11D414yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—28no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11C2×C414yes—
82C2×C22⋊Dic11C2×C418yescomplemented
83#66988—232no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4C2×C418yescomplemented
87C2×C4×Dic11—232no—
88C2×C4×Dic11—28no—
89C2×C4×Dic11—28no—
90C2×C4×Dic11—28no—
91C11×#95—24no—
92C11⋊#95—28no—
93C11⋊#95—28no—
94C11⋊#95—24no—
95C11⋊#95—28no—
96#14706—111nomaximal, Sylow
97C24×C11—24no—
98C24×C11—24no—
99C24×C11—21no—
100C24×C11—21no—
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11C22×C412yes—
108C24×C11C22×C412yes—
109C24×C11C2×D412yes—
110C24×C11C2×D412yes—
111C24×C11C2×D412yes—
112C24×C11C2×D412yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11C2411yescharacteristic
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C22×C4×C11—216no—
124C22×C4×C11—216no—
125C22×C4×C11—28no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—216no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11#4118yes—
144C22×Dic11—216no—
145C22×Dic11—216no—
146C22×Dic11—216no—
147C22×Dic11—28no—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—28no—
153C22×Dic11—28no—
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—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—24no—
170C22×Dic11C22⋊C4116yescomplemented
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D414yes—
175C22×Dic11C2×D414yes—
176C22×Dic11#4118yes—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—48no—
179C22⋊Dic11—216no—
180C22⋊Dic11—28no—
181C22⋊Dic11—48no—
182C22⋊Dic11—44no—
183Dic11⋊C4—216no—
184C4×Dic11—232no—
185C22×#123—111no—
186C23×C42—111no—
187C2×#386—111no—
188C2×#386D1111yescharacteristic
189C2×#381—111no—
190#1437—114no—
191#1436—114no—
192C22⋊#95—111no—
193C22⋊#95—111no—
194C23×C11—28no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—28no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11C2×C22⋊C414yes—
222C23×C11C4×D414yes—
223C23×C11C4×D414yes—
224C23×C11#12014yes—
225C23×C11#12114yes—
226C23×C11#12114yes—
227C23×C11#12314yes—
228C23×C11C23×C411yescharacteristic
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4114yes—
236C23×C11C2×#4114yes—
237D4×C11—416no—
238C2×C4×C11—232no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11#12318yescomplemented
256C2×Dic11—232no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—28no—
266C2×Dic11—28no—
267C2×Dic11—232no—
268C2×Dic11—24no—
269C2×Dic11—28no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278C2×Dic11C2×C22⋊C418yes—
279C2×Dic11#12318yescomplemented
280C23×D4C2×D1111yescharacteristic
281C24×C4—111no—
282C24×C4—111no—
283C24×C4C2×D1111yescharacteristic
284C2×#123—118no—
285C2×#123—224no—
286C2×#123—224no—
287C22×C4⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4C2×D1112yes—
294C22×C42—114no—
295C22×C42—224no—
296C22×C42—224no—
297C22×C42—224no—
298#386—24no—
299#386—224no—
300#381—224no—
301C2×#95—114no—
302C2×#95—114no—
303C2×#95—112no—
304C2×#95—114no—
305C2×#95C2×D1112yes—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—28no—
309C22×C11—28no—
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—28no—
314C22×C11—42no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11#38618yes—
324C22×C11C22×C22⋊C411yescharacteristic
325C22×C11C2×C4×D411yescharacteristic
326C22×C11C2×C4×D411yescharacteristic
327C22×C11C4×#4114yes—
328C22×C11C2×#12011yescharacteristic
329C22×C11C2×#12111yescharacteristic
330C22×C11C2×#12111yescharacteristic
331C22×C11C2×#12311yescharacteristic
332C22×C11C2×#12312yes—
333C22×C11C2×#12312yes—
334C22×C11#52512yes—
335C22×C11#52512yes—
336C22×C11#52512yes—
337C22×C11#52512yes—
338C22×C11#52914yes—
339C22×C11#52914yes—
340C22×C11#53214yes—
341C4×C11—28no—
342C4×C11—42no—
343C4×C11—82no—
344Dic11—28no—
345Dic11—28no—
346Dic11—44no—
347Dic11—82no—
348C25C22×D1111yescharacteristic
349C25C22×D1111yescharacteristic
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4C4×D1114yes—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—28no—
360C23×C4—114no—
361C23×C4—114no—
362C23×C4—114no—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—114no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—228no—
369C23×C4—222no—
370C23×C4—222no—
371C23×C4—222no—
372C23×C4—222no—
373C23×C4—222no—
374C23×C4—222no—
375C23×C4C22⋊D1114yes—
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
379#123—2232no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—224no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—228no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—222no—
399C2×C42—228no—
400C2×C42—228no—
401C2×C42—2232no—
402C2×C42—228no—
403#95—24no—
404#95—228no—
405#95—228no—
406#95—224no—
407#95—228no—
408C2×C11—28no—
409C2×C11—82no—
410C2×C11C2×#38611yescharacteristic
411C2×C11#229712yes—
412C2×C11C4×#12312yes—
413C2×C11C4×#12312yes—
414C2×C11#284911yescharacteristic
415C2×C11#284911yescharacteristic
416C2×C11#285312yes—
417C2×C11#285412yes—
418C2×C11#285412yes—
419C24—24no—
420C24—24no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—24no—
426C24—21no—
427C24—24no—
428C24—21no—
429C24C2×C4×D1112yes—
430C24C2×C4×D1112yes—
431C24#433912yes—
432C24D4×D1112yes—
433C24D4×D1112yes—
434C24D4×D1112yes—
435C24#434112yes—
436C24C2×C22⋊D1112yes—
437C24C23×D1111yescharacteristic
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C22×C4—216no—
446C22×C4—216no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—216no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—1116no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—118no—
469C22×C4—114no—
470C22×C4—2216no—
471C22×C4—2216no—
472C22×C4—2216no—
473C22×C4—228no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—228no—
479C22×C4—228no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4C2×C4×D1112yes—
497C22×C4#434118yes—
498C22×C4C2×C22⋊D1114yes—
499C4⋊C4—2216no—
500C22⋊C4—44no—
501C22⋊C4—48no—
502C22⋊C4—2216no—
503C22⋊C4—228no—
504C22⋊C4—448no—
505C22⋊C4—444no—
506C42—2232no—
507C11#1470611yescharacteristic, complemented, Sylow
508C23—28no—
509C23—28no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—28no—
515C23—28no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—28no—
522C23—41no—
523C23—41no—
524C23—44no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—44no—
532C23—44no—
533C23—42no—
534C23—42no—
535C23C22⋊C4×D1114yes—
536C23(C22⋊D11)⋊C414yes—
537C23#6693614yes—
538C23#6693714yes—
539C23C4×C22⋊D1114yes—
540C23#6699014yes—
541C23#6699114yes—
542C23C22×C4×D1111yescharacteristic
543C23C2×#433911yescharacteristic
544C23C2×D4×D1111yescharacteristic
545C23C2×D4×D1111yescharacteristic
546C23C2×D4×D1111yescharacteristic
547C23C2×#434111yescharacteristic
548C23C2×#434114yes—
549C23#41×D1114yes—
550C23C22×C22⋊D1111yescharacteristic
551D4—416no—
552C2×C4—232no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—118no—
570C2×C4—118no—
571C2×C4—2232no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—2232no—
580C2×C4—228no—
581C2×C4—224no—
582C2×C4—228no—
583C2×C4—224no—
584C2×C4—228no—
585C2×C4—442no—
586C2×C4—444no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—444no—
590C2×C4—442no—
591C2×C4—444no—
592C2×C4—442no—
593C2×C4#6698818yescomplemented
594C22—28no—
595C22—28no—
596C22—24no—
597C22—24no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—44no—
606C22—81no—
607C22—81no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22#1062256918yes—
612C22C2×C22⋊C4×D1111yescharacteristic
613C22C2×(C22⋊D11)⋊C411yescharacteristic
614C22C2×#6693611yescharacteristic
615C22C2×#6693711yescharacteristic
616C22C4×#434114yes—
617C22#1062306914yes—
618C22#1062311712yes—
619C22#1062311712yes—
620C22#1062312714yes—
621C22#1062313114yes—
622C22D11×#12312yes—
623C22#1062318712yes—
624C22C2×C4×C22⋊D1111yescharacteristic
625C22C2×#6698812yes—
626C22C2×#6699011yescharacteristic
627C22C2×#6699111yescharacteristic
628C22#1062335912yes—
629C4—28no—
630C4—42no—
631C4—82no—
632C4—228no—
633C4—228no—
634C4—444no—
635C4—882no—
636C2—28no—
637C2—82no—
638C2C2×#1062256911yescharacteristic
639C2#1307110112yes—
640C2C4×#6698812yes—
641C2#1307114112yes—
642C2#1307690511yescharacteristic
643C2#1307690611yescharacteristic
644C2#1307693712yes—
645C2#1307694212yes—
646C2#1307694412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic11C2semidirect
4. C2×#10622556C2semidirect
5. #13066853C2semidirect
6. #13066847C2semidirect
7. #13066839C2semidirect
8. #13066838C2semidirect
22. C2×#66988C4semidirect
82. C2×C22⋊Dic11C2×C4semidirect
86. C2×Dic11⋊C4C2×C4semidirect
170. C22×Dic11C22⋊C4semidirect
255. C2×C4×C11#123semidirect
279. C2×Dic11#123semidirect
507. C11#14706semidirect
593. C2×C4#66988semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C23×C4×Dic112
C2×#106228332
C2×#106225562
#130668532
#130668472
#130668392
#130668382
C2×C11×#3862
#1470611