Finite Group Databasebeta

← #14685102

Subgroups — #14685102

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×#66939C211yesmaximal, characteristic
2C23×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622556C211yesmaximal, characteristic, complemented
6#13066852C214yesmaximal, complemented
7#13066850C214yesmaximal, complemented
8#13066838C211yesmaximal, characteristic, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11—24no—
22C22×C4×Dic11—24no—
23C22×C4×Dic11—24no—
24C22×C4×Dic11C2214yes—
25C2×#66939—24no—
26C2×#66939—24no—
27C2×#66939C418yescomplemented
28C2×C11×#95C2214yes—
29#10622826—24no—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2214yes—
34#10622571—24no—
35#10622556—24no—
36C25×C11C2311yescharacteristic
37C24×D11C2311yescharacteristic
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—28no—
41C23×C4×C11D414yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11C2×C414yes—
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×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4C2×C414yes—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4C2×C418yescomplemented
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11C2×C418yescomplemented
86C2×C4×Dic11—232no—
87C2×C4×Dic11—28no—
88C2×C4×Dic11—28no—
89C2×C4×Dic11—28no—
90#66939—232no—
91C11×#95—28no—
92C11⋊#95—24no—
93C11⋊#95—28no—
94C11⋊#95—24no—
95C11⋊#95—28no—
96#14706—111nomaximal, Sylow
97C24×C11—24no—
98C24×C11—24no—
99C24×C11C22×C412yes—
100C24×C11C2×D412yes—
101C24×C11C2×D412yes—
102C24×C11C2×D412yes—
103C24×C11C2×D412yes—
104C24×C11#4112yes—
105C24×C11#4112yes—
106C24×C11C2411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11C22×C412yes—
116C22×C4×C11—216no—
117C22×C4×C11—216no—
118C22×C4×C11—28no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—216no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11#4118yes—
135C2×C22⋊D11—28no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—44no—
140C2×C22⋊D11—44no—
141C2×C22⋊D11—44no—
142C22×Dic11—216no—
143C22×Dic11—216no—
144C22×Dic11—216no—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11C22⋊C4116yescomplemented
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D414yes—
175C22×Dic11C2×D414yes—
176C22×Dic11#4118yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—44no—
179C22⋊Dic11—44no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—216no—
184C4×Dic11—232no—
185C22×#123—111no—
186C23×C42—111no—
187C2×#386—111no—
188C2×#386—111no—
189C2×#381—111no—
190#1437—114no—
191#1436—114no—
192C22⋊#95—111no—
193C22⋊#95D1111yescharacteristic, complemented
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×C11C2×C22⋊C414yes—
205C23×C11C4×D414yes—
206C23×C11C4×D414yes—
207C23×C11#12014yes—
208C23×C11#12114yes—
209C23×C11#12114yes—
210C23×C11#12314yes—
211C23×C11C23×C411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D411yescharacteristic
214C23×C11C22×D411yescharacteristic
215C23×C11C22×D411yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4114yes—
218C23×C11C2×#4111yescharacteristic
219C23×C11C2×#4114yes—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—28no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—41no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—44no—
237C2×C4×C11—232no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11#12318yescomplemented
253C22⋊D11—416no—
254C2×Dic11—232no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—232no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278C2×Dic11C2×C22⋊C418yes—
279C2×Dic11#12318yescomplemented
280C23×D4—111no—
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—112no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4C2×D1111yescharacteristic
294C22×C42—114no—
295C22×C42—224no—
296C22×C42—224no—
297C22×C42—224no—
298#386—224no—
299#386—224no—
300#381—224no—
301C2×#95—114no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—114no—
305C2×#95C2×D1114yes—
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#38618yes—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11C2×C4×D411yescharacteristic
318C22×C11C4×#4114yes—
319C22×C11C2×#12011yescharacteristic
320C22×C11C2×#12111yescharacteristic
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12312yes—
323C22×C11C2×#12311yescharacteristic
324C22×C11C2×#12312yes—
325C22×C11#52512yes—
326C22×C11#52512yes—
327C22×C11#52512yes—
328C22×C11#52512yes—
329C22×C11#52914yes—
330C22×C11#52914yes—
331C22×C11#53214yes—
332C2×D11—42no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C4×C11—28no—
342C4×C11—44no—
343C4×C11—82no—
344Dic11—28no—
345Dic11—28no—
346Dic11—42no—
347Dic11—82no—
348C25—111no—
349C25C22×D1111yescharacteristic
350C22×D4—114no—
351C22×D4—222no—
352C22×D4—222no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—222no—
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—111no—
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×C4D4414yes—
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
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—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4C4×D1114yes—
399C2×C42—228no—
400C2×C42—228no—
401C2×C42—2232no—
402C2×C42—228no—
403#95—28no—
404#95—228no—
405#95—228no—
406#95—224no—
407#95—224no—
408C2×C11—28no—
409C2×C11C2×#38611yescharacteristic
410C2×C11#229712yes—
411C2×C11C4×#12312yes—
412C2×C11C4×#12312yes—
413C2×C11#284911yescharacteristic
414C2×C11#284911yescharacteristic
415C2×C11#285312yes—
416C2×C11#285412yes—
417C2×C11#285412yes—
418D11—82no—
419C24—24no—
420C24—24no—
421C24—112no—
422C24—221no—
423C24—221no—
424C24—221no—
425C24—221no—
426C24—221no—
427C24—224no—
428C24—221no—
429C24—224no—
430C24C2×C4×D1112yes—
431C24C2×D4412yes—
432C24#433912yes—
433C24D4×D1112yes—
434C24D4×D1112yes—
435C24D4×D1112yes—
436C24#434312yes—
437C24C23×D1111yescharacteristic
438C2×D4—228no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—444no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—444no—
445C22×C4—216no—
446C22×C4—216no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—216no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—1116no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—118no—
467C22×C4—112no—
468C22×C4—2216no—
469C22×C4—2216no—
470C22×C4—2216no—
471C22×C4—228no—
472C22×C4—228no—
473C22×C4—228no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—222no—
495C22×C4—224no—
496C22×C4C2×C4×D1114yes—
497C22×C4C2×D4414yes—
498C22×C4#434118yes—
499C4⋊C4—2216no—
500C22⋊C4—28no—
501C22⋊C4—44no—
502C22⋊C4—2216no—
503C22⋊C4—448no—
504C22⋊C4—444no—
505C22⋊C4—448no—
506C42—2232no—
507C11#1470611yescharacteristic, complemented, Sylow
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—24no—
513C23—24no—
514C23—28no—
515C23—28no—
516C23—24no—
517C23—24no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—228no—
522C23—441no—
523C23—441no—
524C23—442no—
525C23—441no—
526C23—441no—
527C23—442no—
528C23—444no—
529C23—442no—
530C23—442no—
531C23—444no—
532C23—444no—
533C23—442no—
534C23—442no—
535C23C4×D4414yes—
536C23C22⋊C4×D1114yes—
537C23#6693514yes—
538C23#6693714yes—
539C23#6694614yes—
540C23#6694714yes—
541C23#6694814yes—
542C23C22×C4×D1111yescharacteristic
543C23C22×D4411yescharacteristic
544C23C2×#433911yescharacteristic
545C23C2×D4×D1111yescharacteristic
546C23C2×D4×D1111yescharacteristic
547C23C2×D4×D1111yescharacteristic
548C23C2×#434114yes—
549C23C2×#434311yescharacteristic
550C23#41×D1114yes—
551D4—4416no—
552C2×C4—232no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—118no—
568C2×C4—118no—
569C2×C4—2232no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—2232no—
578C2×C4—228no—
579C2×C4—224no—
580C2×C4—228no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—444no—
592C2×C4—444no—
593C2×C4#6693918yescomplemented
594C22—28no—
595C22—28no—
596C22—24no—
597C22—24no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—444no—
603C22—444no—
604C22—442no—
605C22—444no—
606C22—881no—
607C22—881no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22#1062227818yes—
612C22C2×C4×D4411yescharacteristic
613C22C2×C22⋊C4×D1111yescharacteristic
614C22C2×#6693511yescharacteristic
615C22C2×#6693711yescharacteristic
616C22C2×#6693912yes—
617C22C2×#6694611yescharacteristic
618C22C2×#6694711yescharacteristic
619C22C2×#6694811yescharacteristic
620C22#1062305512yes—
621C22C4×#434114yes—
622C22#1062306914yes—
623C22#1062311712yes—
624C22#1062311712yes—
625C22#1062312714yes—
626C22#1062315514yes—
627C22D11×#12312yes—
628C22#1062318712yes—
629C4—28no—
630C4—44no—
631C4—82no—
632C4—228no—
633C4—228no—
634C4—442no—
635C4—882no—
636C2—28no—
637C2—882no—
638C2C2×#1062227811yescharacteristic
639C2#1307110112yes—
640C2#1307113512yes—
641C2C4×#6693912yes—
642C2#1307690911yescharacteristic
643C2#1307691011yescharacteristic
644C2#1307694112yes—
645C2#1307694412yes—
646C2#1307694812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic11C2semidirect
5. C2×#10622556C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. #13066838C2semidirect
9. C11×C22⋊#95C2semidirect
27. C2×#66939C4semidirect
82. C2×(C2×D11)⋊C4C2×C4semidirect
85. C2×C4⋊Dic11C2×C4semidirect
170. C22×Dic11C22⋊C4semidirect
193. C22⋊#95D11semidirect
252. C2×C4×C11#123semidirect
279. C2×Dic11#123semidirect
507. C11#14706semidirect
593. C2×C4#66939semidirect

Maximal subgroups

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

subgroupindex
C22×#669392
C23×C4×Dic112
C2×#106228262
C2×#106225712
C2×#106225562
#130668522
#130668502
#130668382
C11×C22⋊#952
#1470611