Finite Group Databasebeta

← #15624351

Subgroups — #15624351

Order 2816.

2394 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C212yesmaximal, complemented
2#13079410C214yesmaximal, complemented
3#13079400C214yesmaximal, complemented
4#13079386C214yesmaximal, complemented
5#13079369C212yesmaximal, complemented
6#13079367C211yesmaximal, characteristic, complemented
7#13078532C214yesmaximal, complemented
8#13078199C214yesmaximal, complemented
9#13077839C214yesmaximal, complemented
10C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
11C11×#3189C211yesmaximal, characteristic, complemented
12C22×#4343C2212yescomplemented
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×#66999C2212yescomplemented
16C2×#66983C2212yes—
17C2×#66972C2214yescomplemented
18C22×C8×D11C2212yescomplemented
19#10623158—22no—
20#10623158—22no—
21#10623158—22no—
22#10623158—22no—
23#10623158C2214yes—
24#10623158C2214yes—
25#10623158C2214yescomplemented
26#10623158C2214yescomplemented
27C2×#66948C2212yescomplemented
28C2×#66947—22no—
29C2×#66946—22no—
30C2×#66945C2212yescomplemented
31C2×#66935—22no—
32C2×(C22⋊D11)⋊C4—22no—
33C11×#484C2214yescomplemented
34C11×#467C2214yescomplemented
35C11×#451C2214yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic
37#10622840C2214yescomplemented
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622801C2214yescomplemented
40#10622800C2218yescomplemented
41#10622728C2214yescomplemented
42C2×(C2×D11)⋊C8C2212yescomplemented
43#10622661C2218yescomplemented
44#10622659C2214yescomplemented
45#10622656C2214yescomplemented
46#10622581C2214yescomplemented
47#10622498C2218yescomplemented
48#10622496C2214yescomplemented
49#10622493C2214yescomplemented
50#10622427C2218yescomplemented
51#10622424C2218yescomplemented
52#10622420C2218yescomplemented
53#10622417C2218yescomplemented
54#10622349C2214yescomplemented
55#10622345C2214yescomplemented
56D11×C22⋊C8C2214yescomplemented
57D11×C22⋊C8C2214yescomplemented
58C24×D11D411yescharacteristic
59C22×Q8×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—22no—
62C23×Dic11D411yescharacteristic
63C2×#4343—22no—
64C2×#4343—22no—
65C2×#4343—48no—
66C2×#4343C2314yes—
67C2×#4343C2314yes—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44C2312yes—
71C22×C4×D11—22no—
72C22×C4×D11—44no—
73C22×C4×D11D412yes—
74C22×C4×D11D412yes—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2312yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2312yes—
81C2×C11×Q16C2314yescomplemented
82C22×C8×C11C2312yes—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8C2314yes—
86C11×C22⋊Q8C2314yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—22no—
90#66999—22no—
91#66999—22no—
92#66999C2314yes—
93#66999C2314yes—
94C2×#4325C2318yescomplemented
95#66983—22no—
96#66983—22no—
97#66983C2314yes—
98#66983C2314yes—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2312yes—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8C2312yes—
107#66972—48no—
108C2×D88C2314yescomplemented
109C2×C8×D11—44no—
110C2×C8×D11C2314yes—
111C2×C8×D11C2314yes—
112#66948—22no—
113#66948—22no—
114#66948C2314yes—
115#66948C2314yes—
116#66947—24no—
117#66947—24no—
118#66947—24no—
119#66947—24no—
120#66946—24no—
121#66946—24no—
122#66946—24no—
123#66946—24no—
124#66945—22no—
125#66945—22no—
126#66945C2314yes—
127#66945C2314yes—
128#66935—24no—
129#66935—24no—
130#66935—24no—
131#66935—24no—
132(C22⋊D11)⋊C4—24no—
133(C22⋊D11)⋊C4—24no—
134(C22⋊D11)⋊C4—24no—
135(C22⋊D11)⋊C4—24no—
136C11×#107C2314yescomplemented
137C11×#103C2318yescomplemented
138C11×C22⋊C8C2314yes—
139#66899C2318yescomplemented
140C22⋊(C11⋊C8)C2314yes—
141#66885C2318yescomplemented
142(C2×D11)⋊C8C2318yes—
143#66882C2314yescomplemented
144#66873C2318yescomplemented
145#66872C2318yescomplemented
146#60734—111nomaximal, Sylow
147C24×C11C2×D411yescharacteristic
148C23×D11—24no—
149C23×D11—22no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11C2×D411yescharacteristic
153C23×D11C2×D412yes—
154C23×D11C2×D412yes—
155C23×D11C2×D411yescharacteristic
156C2×Q8×C11—22no—
157C2×Q8×C11—44no—
158C2×Q8×C11C2414yes—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—48no—
169C22×Dic11—22no—
170C22×Dic11—42no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D412yes—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D412yes—
175#4343—216no—
176#4343—48no—
177#4343—48no—
178#4343—48no—
179C2×D44—24no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—24no—
183C2×D44—22no—
184C2×D44—44no—
185C2×D44—48no—
186C2×D44—48no—
187C2×D44C2414yes—
188C2×C4×D11—24no—
189C2×C4×D11—28no—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—42no—
193C2×C4×D11—44no—
194C2×C4×D11—42no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—42no—
198C2×C4×D11—48no—
199C2×C4×D11C2×D412yes—
200C2×C4×D11C2×D412yes—
201C2×C4×D11C2×D411yescharacteristic
202C2×C4×D11C2×D411yescharacteristic
203C2×C4×D11C2×D412yes—
204C2×C4×D11C2×D412yes—
205C2×C4×D11C2×D412yes—
206C2×C4×D11C2412yes—
207C2×C4×D11C2411yescharacteristic
208C2×C4×D11C2411yescharacteristic
209C11×Q16—44no—
210C2×C8×C11—42no—
211C2×C8×C11C2414yes—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4C2414yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218#4325—48no—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—24no—
227C4⋊Dic11—22no—
228C4⋊Dic11C2414yes—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231C4×Dic11—24no—
232C4×Dic11—24no—
233C2×C11⋊C8—42no—
234C2×C11⋊C8C2414yes—
235D88—44no—
236C8×D11—28no—
237C8×D11—44no—
238C2×#525—112no—
239#3191—114no—
240#3190—114no—
241#3189D1111yescharacteristic, complemented
242#3188—114no—
243#3187—112no—
244#3186—111no—
245#3091—114no—
246#3050—114no—
247#3002—114no—
248C22×C22⋊C8—111no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11#13514yescomplemented
252C23×C11C22×D411yescharacteristic
253C23×C11C22×D412yes—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—42no—
264C22×D11—41no—
265C22×D11—42no—
266C22×D11—41no—
267C22×D11—416no—
268C22×D11—44no—
269C22×D11—44no—
270C22×D11—44no—
271C22×D11C22×D412yes—
272C22×D11C22×D411yescharacteristic
273C22×D11C22×D411yescharacteristic
274Q8×C11—28no—
275Q8×C11—44no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—41no—
281C2×C4×C11—42no—
282C2×C4×C11—44no—
283C2×C4×C11—44no—
284C2×C4×C11C22×D412yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2511yescharacteristic
287C22⋊D11—48no—
288C22⋊D11—48no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—41no—
293C2×Dic11—42no—
294C2×Dic11—44no—
295C2×Dic11C22×D412yes—
296C2×Dic11C22×D411yescharacteristic
297C2×Dic11C22×D411yescharacteristic
298D44—28no—
299D44—44no—
300D44—48no—
301D44—48no—
302D44—48no—
303D44—48no—
304C4×D11—22no—
305C4×D11—24no—
306C4×D11—22no—
307C4×D11—24no—
308C4×D11—22no—
309C4×D11—24no—
310C4×D11—42no—
311C4×D11—42no—
312C4×D11—42no—
313C4×D11—48no—
314C4×D11—48no—
315C4×D11H(5,𝔽2)14yes—
316C8×C11—24no—
317C11⋊C8—24no—
318C22×#41—112no—
319C24×C4—111no—
320C2×#135—114no—
321C23×C8—112no—
322#525—114no—
323#525—114no—
324#525—114no—
325#525—114no—
326#525—222no—
327#525—222no—
328#525—222no—
329#525—222no—
330C2×#123—222no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8C2×D1112yes—
333C2×#121—112no—
334C2×#121—112no—
335C2×#120—222no—
336C2×C4×D4—222no—
337C2×C4×D4—222no—
338C2×#117—112no—
339#485—118no—
340#484C2×D1114yescomplemented
341#483—114no—
342#482—118no—
343#481—114no—
344#480—114no—
345#467—114no—
346#467C2×D1114yescomplemented
347#466—114no—
348#466—114no—
349#465—118no—
350#465—118no—
351#452—118no—
352#451C2×D1114yescomplemented
353#450—114no—
354#449—118no—
355#448—114no—
356#447—114no—
357#427—114no—
358#416—118no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—112no—
361C2×C22⋊C8—114no—
362C2×C22⋊C8—114no—
363C2×C22⋊C8C2×D1111yescharacteristic
364C22×C11—22no—
365C22×C11—21no—
366C22×C11—22no—
367C22×C11—21no—
368C22×C11—44no—
369C22×C11C2×#13514yes—
370C22×C11C2×#13512yes—
371C22×C11C23×D411yescharacteristic
372C2×D11—28no—
373C2×D11—21no—
374C2×D11—21no—
375C2×D11—21no—
376C2×D11—21no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—48no—
381C2×D11—48no—
382C2×D11—44no—
383C2×D11—44no—
384C2×D11—44no—
385C2×D11—44no—
386C2×D11—88no—
387C2×D11#53412yes—
388C2×D11#57512yes—
389C4×C11—22no—
390C4×C11—21no—
391C4×C11—44no—
392C4×C11—44no—
393C4×C11C2×H(5,𝔽2)12yes—
394Dic11—22no—
395Dic11—21no—
396Dic11—44no—
397Dic11#53412yes—
398C25—111no—
399C2×#41—114no—
400C2×#41—114no—
401C2×#41—222no—
402C2×#41—222no—
403C2×#41—448no—
404C22×Q8C22×D1112yes—
405C22×D4—112no—
406C22×D4—222no—
407C22×D4—222no—
408C22×D4—222no—
409C23×C4—111no—
410C23×C4—112no—
411C23×C4—111no—
412C23×C4—112no—
413C23×C4—112no—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—112no—
417C23×C4—111no—
418C23×C4—222no—
419C23×C4—444no—
420C23×C4C22×D1111yescharacteristic
421#135—448no—
422C2×Q16C22×D1114yescomplemented
423C2×SD16—118no—
424C2×D8—114no—
425C22×C8—112no—
426C22×C8—114no—
427C22×C8—114no—
428C22×C8—444no—
429C22×C8C22×D1112yes—
430#123—224no—
431#123—224no—
432#123—224no—
433#123—224no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—114no—
437C22⋊Q8—114no—
438C22⋊Q8—222no—
439C22⋊Q8—222no—
440C22⋊Q8C22×D1114yes—
441C22⋊Q8C22×D1114yes—
442#121—114no—
443#121—114no—
444#121—114no—
445#121—114no—
446#121—222no—
447#121—222no—
448#121—222no—
449#121—222no—
450#120—224no—
451#120—224no—
452#120—224no—
453#120—224no—
454C4×D4—224no—
455C4×D4—224no—
456C4×D4—224no—
457C4×D4—224no—
458C4×D4—224no—
459C4×D4—224no—
460C4×D4—224no—
461C4×D4—224no—
462#117—114no—
463#117—114no—
464#117—222no—
465#117—222no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4C22×D1112yes—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C42—222no—
476#107—114no—
477#107C22×D1114yescomplemented
478#106—118no—
479#103—118no—
480#103C22×D1118yescomplemented
481#102—118no—
482#102—118no—
483C22⋊C8—114no—
484C22⋊C8—118no—
485C22⋊C8C22×D1114yes—
486C2×C11—22no—
487C2×C11—24no—
488C2×C11C2×#53411yescharacteristic
489C2×C11C22×#13511yescharacteristic
490C2×C11C2×#57511yescharacteristic
491D11—22no—
492D11—22no—
493D11—42no—
494D11—84no—
495C24—111no—
496C24—112no—
497C24—112no—
498C24—111no—
499C24—224no—
500C24—222no—
501C24—442no—
502C24—442no—
503C24D4×D1111yescharacteristic
504#41—2216no—
505#41—448no—
506#41—448no—
507#41—448no—
508C2×Q8—22no—
509C2×Q8—44no—
510C2×Q8C23×D1114yes—
511C2×D4—114no—
512C2×D4—224no—
513C2×D4—224no—
514C2×D4—224no—
515C2×D4—224no—
516C2×D4—224no—
517C2×D4—224no—
518C2×D4—222no—
519C2×D4—444no—
520C2×D4—448no—
521C2×D4—448no—
522C2×D4—448no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—42no—
526C22×C4—111no—
527C22×C4—112no—
528C22×C4—111no—
529C22×C4—112no—
530C22×C4—111no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—111no—
534C22×C4—111no—
535C22×C4—112no—
536C22×C4—111no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—224no—
541C22×C4—228no—
542C22×C4—224no—
543C22×C4—224no—
544C22×C4—222no—
545C22×C4—442no—
546C22×C4—444no—
547C22×C4—442no—
548C22×C4—444no—
549C22×C4—442no—
550C22×C4—444no—
551C22×C4—448no—
552C22×C4—442no—
553C22×C4D4×D1112yes—
554C22×C4D4×D1111yescharacteristic
555C22×C4C23×D1112yes—
556C22×C4C23×D1111yescharacteristic
557Q16—44no—
558SD16—448no—
559D8—444no—
560C2×C8—42no—
561C2×C8—114no—
562C2×C8—228no—
563C2×C8—444no—
564C2×C8—442no—
565C2×C8C23×D1114yes—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—114no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—222no—
573C4⋊C4C23×D1114yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—224no—
579C22⋊C4—224no—
580C22⋊C4—224no—
581C22⋊C4—224no—
582C22⋊C4—224no—
583C22⋊C4—224no—
584C42—224no—
585C42—224no—
586C11#6073411yescharacteristic, complemented, Sylow
587C23—41no—
588C23—41no—
589C23—111no—
590C23—111no—
591C23—112no—
592C23—222no—
593C23—222no—
594C23—224no—
595C23—224no—
596C23—222no—
597C23—224no—
598C23—224no—
599C23—222no—
600C23—224no—
601C23—442no—
602C23—441no—
603C23—442no—
604C23—441no—
605C23—444no—
606C23—444no—
607C23—4416no—
608C23—444no—
609C23#6697214yescomplemented
610C23C2×D4×D1111yescharacteristic
611C23C2×D4×D1112yes—
612Q8—28no—
613Q8—44no—
614D4—228no—
615D4—444no—
616D4—448no—
617D4—448no—
618D4—448no—
619D4—448no—
620D4—448no—
621D4—448no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—111no—
631C2×C4—114no—
632C2×C4—112no—
633C2×C4—111no—
634C2×C4—224no—
635C2×C4—222no—
636C2×C4—224no—
637C2×C4—222no—
638C2×C4—224no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—224no—
642C2×C4—224no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—448no—
647C2×C4—448no—
648C2×C4—441no—
649C2×C4—442no—
650C2×C4—444no—
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4C2×D4×D1112yes—
653C2×C4C24×D1111yescharacteristic
654C8—24no—
655C8—224no—
656C22—22no—
657C22—21no—
658C22—22no—
659C22—21no—
660C22—44no—
661C22—112no—
662C22—112no—
663C22—228no—
664C22—221no—
665C22—221no—
666C22—221no—
667C22—221no—
668C22—222no—
669C22—222no—
670C22—222no—
671C22—448no—
672C22—448no—
673C22—444no—
674C22—444no—
675C22—444no—
676C22—444no—
677C22—888no—
678C22C2×#6697214yes—
679C22C2×#6697212yes—
680C22C22×D4×D1111yescharacteristic
681C4—22no—
682C4—21no—
683C4—44no—
684C4—44no—
685C4—112no—
686C4—222no—
687C4—221no—
688C4—444no—
689C4D11×H(5,𝔽2)12yes—
690C2—22no—
691C2—24no—
692C2—222no—
693C2—222no—
694C2—442no—
695C2—884no—
696C2D11×#53411yescharacteristic
697C2C22×#6697211yescharacteristic
698C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3189C2
socleC22×C11C23×D4
hypercenter#3189D11
hypocenterC11#60734
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. #13079410C2semidirect
3. #13079400C2semidirect
4. #13079386C2semidirect
5. #13079369C2semidirect
6. #13079367C2semidirect
7. #13078532C2semidirect
8. #13078199C2semidirect
9. #13077839C2semidirect
10. C2×D11×C22⋊C8C2semidirect
11. C11×#3189C2semidirect
12. C22×#4343C22semidirect
15. C2×#66999C22semidirect
17. C2×#66972C22semidirect
18. C22×C8×D11C22semidirect
25. #10623158C22semidirect
26. #10623158C22semidirect
27. C2×#66948C22semidirect
30. C2×#66945C22semidirect
33. C11×#484C22semidirect
34. C11×#467C22semidirect
35. C11×#451C22semidirect
37. #10622840C22semidirect
39. #10622801C22semidirect
40. #10622800C22semidirect
41. #10622728C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. #10622661C22semidirect
44. #10622659C22semidirect
45. #10622656C22semidirect
46. #10622581C22semidirect
47. #10622498C22semidirect
48. #10622496C22semidirect
49. #10622493C22semidirect
50. #10622427C22semidirect
51. #10622424C22semidirect
52. #10622420C22semidirect
53. #10622417C22semidirect
54. #10622349C22semidirect
55. #10622345C22semidirect
56. D11×C22⋊C8C22semidirect
57. D11×C22⋊C8C22semidirect
81. C2×C11×Q16C23semidirect
94. C2×#4325C23semidirect
108. C2×D88C23semidirect
136. C11×#107C23semidirect
137. C11×#103C23semidirect
139. #66899C23semidirect
141. #66885C23semidirect
143. #66882C23semidirect
144. #66873C23semidirect
145. #66872C23semidirect
241. #3189D11semidirect
251. C23×C11#135semidirect
340. #484C2×D11semidirect
346. #467C2×D11semidirect
352. #451C2×D11semidirect
422. C2×Q16C22×D11semidirect
477. #107C22×D11semidirect
480. #103C22×D11semidirect
586. C11#60734semidirect
609. C23#66972semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
#130794102
#130794002
#130793862
#130793692
#130793672
#130785322
#130781992
#130778392
C2×D11×C22⋊C82
C11×#31892
#6073411