Finite Group Databasebeta

← #14677266

Subgroups — #14677266

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic
3C2×#10622843C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic
5#13066864C214yesmaximal, complemented
6#13066845C211yesmaximal, characteristic, complemented
7(C2×D11)⋊#95C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#391C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C23×C4×D11C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#67000—24no—
16C2×#67000—24no—
17C2×#67000C418yescomplemented
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2214yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×C4×D44—24no—
25C2×C4×D44—24no—
26C2×C4×D44—24no—
27C11×#391—24no—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30#10622843—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2214yes—
34C2×C11⋊#95C2214yes—
35#10622601—24no—
36C24×D11C2312yes—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11C2×C414yescomplemented
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44C2×C414yes—
57C22×D44D414yes—
58C22×D44D414yes—
59C22×C4×D11—24no—
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11—28no—
63C22×C4×D11—44no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11D414yes—
70#67000—232no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4C2×C4116yescomplemented
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11D414yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11C2×C414yescomplemented
89C4×D44—232no—
90C11×#95—24no—
91C11×#95—24no—
92C11⋊#95—24no—
93C11⋊#95—28no—
94C11⋊#95—24no—
95C11⋊#95—44no—
96#14027—111nomaximal, Sylow
97C24×C11C2411yescharacteristic
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—24no—
101C23×D11—24no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11C22×C414yes—
107C23×D11C2×D414yes—
108C23×D11C2×D414yes—
109C2×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—44no—
113C2×Q8×C11—44no—
114C2×Q8×C11—44no—
115C2×Q8×C11—44no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
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×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4114yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11C22×C414yes—
162C22×Dic11C2×D414yes—
163C22×Dic11#4114yes—
164C2×D44—28no—
165C2×D44—28no—
166C2×D44—28no—
167C2×D44—28no—
168C2×D44—28no—
169C2×D44—28no—
170C2×D44C22⋊C4116yes—
171C2×C4×D11—216no—
172C2×C4×D11—416no—
173C2×C4×D11—416no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C11×C4⋊C4—44no—
177C42×C11—28no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—232no—
180(C2×D11)⋊C4—416no—
181C4⋊Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11—44no—
184C22×#124—111no—
185C22×C4×D4—111no—
186C2×#391—111no—
187C2×#391D1111yescharacteristic, complemented
188C2×#390—111no—
189#1440—114no—
190C4⋊#95—111no—
191C22⋊#95—114no—
192C4×#95—111no—
193C23×C11C23×C411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×D411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C112−1+412yes—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—28no—
207C22×D11—28no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—42no—
217C22×D11—44no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11C2×C22⋊C418yes—
227Q8×C11—416no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11C2×C22⋊C414yes—
250C2×C4×C11C4×D414yes—
251C2×C4×C11C4×D414yes—
252C2×C4×C11#12014yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12314yes—
256C2×C4×C11#12414yescomplemented
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276D44—232no—
277C4×D11—432no—
278C23×Q8C2×D1111yescharacteristic
279C23×D4—111no—
280C24×C4—112no—
281C2×#124—118no—
282C2×#124—224no—
283C2×#124—224no—
284C2×C4×D4—224no—
285C2×C4×D4—224no—
286C2×C4×D4—224no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C22⋊C4—114no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—114no—
292C22×C42—111no—
293C22×C42—111no—
294C22×C42C2×D1111yescharacteristic
295#391—24no—
296#391—224no—
297#390—224no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—114no—
301C2×#95—114no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11C2×C4×D411yescharacteristic
306C22×C11C2×C4×D411yescharacteristic
307C22×C11C4×#4112yes—
308C22×C11#52012yes—
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×#12111yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×#12311yescharacteristic
313C22×C11C2×#12411yescharacteristic
314C22×C11#52912yes—
315C22×C11#53211yescharacteristic
316C22×C11#53511yescharacteristic
317C22×C11#53611yescharacteristic
318C22×C11#54212yes—
319C22×C11#54612yes—
320C22×C11#54612yes—
321C22×C11#54612yes—
322C22×C11#54712yes—
323C22×C11#54712yes—
324C22×C11#54812yes—
325C22×C11#55612yes—
326C22×C11#55912yes—
327C2×D11—216no—
328C2×D11—28no—
329C2×D11—44no—
330C2×D11—48no—
331C2×D11—48no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—48no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C4×C11—24no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—82no—
342C4×C11#38618yes—
343Dic11—44no—
344Dic11—44no—
345Dic11—44no—
346C25—112no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8C4×D1114yescomplemented
354C22×D4—114no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—222no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—222no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—224no—
365C23×C4—224no—
366C23×C4—224no—
367C23×C4—228no—
368C23×C4—444no—
369C23×C4C22×D1112yes—
370C23×C4C22×D1112yes—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374#124—2232no—
375C4×D4—2232no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C22⋊C4—1116no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—444no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—114no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42C22⋊D1114yes—
400#95—24no—
401#95—24no—
402#95—224no—
403#95—228no—
404#95—224no—
405#95—444no—
406C2×C11C2×#38611yescharacteristic
407C2×C11C4×#12411yescharacteristic
408C2×C11#232611yescharacteristic
409C2×C11#233912yes—
410C2×C11#236712yes—
411C2×C11#242712yes—
412C2×C11#243211yescharacteristic
413C2×C11#243511yescharacteristic
414C2×C11#244712yes—
415C2×C11#254411yescharacteristic
416C2×C11#254711yescharacteristic
417D11—48no—
418C24—114no—
419C24—114no—
420C24—114no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—224no—
425C24—224no—
426C24—224no—
427C24—224no—
428C24—222no—
429C24C23×D1111yescharacteristic
430C2×Q8—28no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×D4—1116no—
438C2×D4—228no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—228no—
443C2×D4—228no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—2216no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—4416no—
483C22×C4—4416no—
484C22×C4—448no—
485C22×C4—448no—
486C22×C4C2×C4×D1114yes—
487C22×C4C2×C4×D1112yes—
488C22×C4#433912yes—
489C22×C4D4×D1112yes—
490C22×C4D4×D1112yes—
491C22×C4D4×D1112yes—
492C22×C4#434112yes—
493C22×C4#434314yes—
494C22×C4C2×C22⋊D1112yes—
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1112yes—
497C4⋊C4—44no—
498C4⋊C4—228no—
499C22⋊C4—2232no—
500C22⋊C4—2216no—
501C22⋊C4—4416no—
502C42—28no—
503C42—228no—
504C42—444no—
505C11#1402711yescharacteristic, complemented, Sylow
506C23—118no—
507C23—228no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—228no—
515C23—228no—
516C23—228no—
517C23—228no—
518C23—228no—
519C23—444no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—444no—
525C23—444no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23C22×C4×D1111yescharacteristic
530C23C2×#433911yescharacteristic
531C23C2×D4×D1111yescharacteristic
532C23C2×D4×D1111yescharacteristic
533C23C2×D4×D1111yescharacteristic
534C23C2×#434111yescharacteristic
535C23C2×#434312yes—
536C23#6704012yes—
537C23#41×D1112yes—
538C23#6704212yes—
539C23C22×C22⋊D1111yescharacteristic
540Q8—416no—
541D4—2232no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—228no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4432no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—444no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4C22⋊C4×D1114yes—
584C2×C4(C22⋊D11)⋊C414yes—
585C2×C4#6693614yes—
586C2×C4#6693714yes—
587C2×C4C4×C22⋊D1114yes—
588C2×C4#6699014yes—
589C2×C4#6699114yes—
590C2×C4#6700014yescomplemented
591C22—2216no—
592C22—228no—
593C22—448no—
594C22—444no—
595C22—448no—
596C22—448no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22C2×C22⋊C4×D1111yescharacteristic
603C22C2×(C22⋊D11)⋊C411yescharacteristic
604C22C2×#6693611yescharacteristic
605C22C2×#6693711yescharacteristic
606C22C4×#434312yes—
607C22#1062310512yes—
608C22#1062311112yes—
609C22#1062311312yes—
610C22#1062316112yes—
611C22#1062316112yes—
612C22#1062316212yes—
613C22#1062316412yes—
614C22#1062320712yes—
615C22#1062321212yes—
616C22#1062325712yes—
617C22#1062326312yes—
618C22C2×C4×C22⋊D1111yescharacteristic
619C22C2×#6699011yescharacteristic
620C22C2×#6699111yescharacteristic
621C22C2×#6700011yescharacteristic
622C22#1062334711yescharacteristic
623C22#1062336111yescharacteristic
624C22#1062336311yescharacteristic
625C4—24no—
626C4—42no—
627C4—44no—
628C4—82no—
629C4—444no—
630C4—444no—
631C4—444no—
632C4#1062256918yes—
633C2—448no—
634C2C2×#1062256911yescharacteristic
635C2C4×#6700011yescharacteristic
636C2#1307132311yescharacteristic
637C2#1307144512yes—
638C2#1307169212yes—
639C2#1307219412yes—
640C2#1307224511yescharacteristic
641C2#1307226811yescharacteristic
642C2#1307240412yes—
643C2#1307358811yescharacteristic
644C2#1307361211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#391D11
hypocenterC11#14027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. C2×#10622843C2semidirect
5. #13066864C2semidirect
6. #13066845C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. C4×C11⋊#95C2semidirect
9. C2×C11×#391C2semidirect
17. C2×#67000C4semidirect
43. C22×Q8×C11C2×C4semidirect
79. C2×(C2×D11)⋊C4C2×C4semidirect
88. C2×C4×Dic11C2×C4semidirect
187. C2×#391D11semidirect
256. C2×C4×C11#124semidirect
353. C22×Q8C4×D11semidirect
505. C11#14027semidirect
590. C2×C4#67000semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
C22×C4×D442
C2×#106228432
C2×#106226012
#130668642
#130668452
(C2×D11)⋊#952
C4×C11⋊#952
C2×C11×#3912
#1402711