Finite Group Databasebeta

← C2×#13080111 #15628738

Subgroups — C2×#13080111 #15628738

Order 2816.

3226 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C2×#10623348C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13080111C2116yesmaximal, direct product factor
5C2×#10622789C211yesmaximal, characteristic, complemented
6C2×#10622787C211yesmaximal, characteristic, complemented
7C2×#10622728C211yesmaximal, characteristic, complemented
8C2×#10622776C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622785C211yesmaximal, characteristic, complemented
11C2×#10622840C211yesmaximal, characteristic, complemented
12C2×#10622782C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×#10622724C211yesmaximal, characteristic, complemented
16C23×C11×SD16C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11—21no—
20C22×#4343C2211yescharacteristic, complemented
21C22×D4×D11C2211yescharacteristic
22C22×C11×SD16—28no—
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic, complemented
26C22×C11×SD16C2211yescharacteristic, complemented
27C22×C11×SD16C2218yescomplemented
28C23×C8×C11C2211yescharacteristic, complemented
29C2×#67006—21no—
30#10623348—24no—
31#10623348C2218yescomplemented
32C2×#67000—21no—
33C2×#67000C2211yescharacteristic, complemented
34C2×#66999—21no—
35C2×#66999C2211yescharacteristic, complemented
36C2×Q8×Dic11C2211yescharacteristic, complemented
37C22×#4325C2211yescharacteristic, complemented
38C22×#4325C2211yescharacteristic, complemented
39C2×#66993C2211yescharacteristic
40C2×#66992—21no—
41D4×C22⋊D11—24no—
42D4×C22⋊D11C2218yescomplemented
43C2×#66991C2211yescharacteristic
44C2×#66990—21no—
45C2×D4×Dic11C2211yescharacteristic
46C22×#4323C2211yescharacteristic
47C22×#4323C2211yescharacteristic, complemented
48C2×#66983—21no—
49C2×#66983C2211yescharacteristic
50C2×#66983C2211yescharacteristic, complemented
51C2×C4×C22⋊D11—21no—
52C2×C4×C22⋊D11C2211yescharacteristic
53C2×#66967—28no—
54C2×#66967C2218yescomplemented
55C22×D88C2211yescharacteristic, complemented
56C22×#4313C2211yescharacteristic, complemented
57#10622840C2218yescomplemented
58C2×#66899C2211yescharacteristic, complemented
59C2×#66899C2211yescharacteristic, complemented
60#10622830C2218yescomplemented
61C2×#66896C2211yescharacteristic
62C2×#66896C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622789C2218yescomplemented
65#10622787C2218yescomplemented
66#10622785C2218yescomplemented
67#10622782C2218yescomplemented
68#10622778C2218yescomplemented
69#10622777C2218yescomplemented
70#10622776C2218yescomplemented
71#10622728C2218yescomplemented
72C2×#66885C2211yescharacteristic, complemented
73C2×#66885C2211yescharacteristic, complemented
74#10622724C2218yescomplemented
75C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
76C2×#66882C2211yescharacteristic, complemented
77C2×#66879C2211yescharacteristic, complemented
78C2×Dic11⋊C8C2211yescharacteristic, complemented
79C25×C11—21no—
80C24×D11—21no—
81C22×Q8×C11—21no—
82C22×Q8×C11—22no—
83C22×Q8×C11—24no—
84C22×Q8×C11—42no—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×Q8×C11C2314yescomplemented
88C22×D4×C11—24no—
89C22×D4×C11—21no—
90C22×D4×C11—22no—
91C22×D4×C11—42no—
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2314yes—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—28no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—21no—
103C22×C22⋊D11—21no—
104C22×C22⋊D11—48no—
105C22×C22⋊D11D411yescharacteristic
106C23×Dic11—21no—
107C2×#4343—22no—
108C2×#4343—24no—
109C2×#4343—42no—
110C2×#4343C2314yescomplemented
111C2×D4×D11—24no—
112C2×D4×D11—22no—
113C2×D4×D11—42no—
114C2×D4×D11C2314yes—
115C22×D44—21no—
116C22×D44C2311yescharacteristic
117C22×D44C2311yescharacteristic
118C22×C4×D11—21no—
119C22×C4×D11C2311yescharacteristic
120C2×C11×SD16—24no—
121C2×C11×SD16—24no—
122C2×C11×SD16—232no—
123C2×C11×SD16—24no—
124C2×C11×SD16D418yescomplemented
125C2×C11×SD16C2314yes—
126C2×C11×SD16C2314yes—
127C2×C11×SD16C2314yescomplemented
128C2×C11×SD16C2314yescomplemented
129C22×C8×C11—24no—
130C22×C8×C11C2311yescharacteristic
131C22×C8×C11C2311yescharacteristic
132C22×C8×C11C2314yescomplemented
133#67006—28no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11D411yescharacteristic
137#67000—28no—
138#67000—22no—
139#67000C2314yescomplemented
140#66999—22no—
141#66999—28no—
142#66999C2314yescomplemented
143Q8×Dic11—22no—
144Q8×Dic11C2314yescomplemented
145C2×#4325—24no—
146C2×#4325—42no—
147C2×#4325C2314yescomplemented
148C2×#4325C2314yescomplemented
149#66993—22no—
150#66993C2314yes—
151#66992—28no—
152#66991—22no—
153#66991C2314yes—
154#66990—28no—
155D4×Dic11—22no—
156D4×Dic11C2314yes—
157C2×#4323—24no—
158C2×#4323—42no—
159C2×#4323C2314yes—
160C2×#4323C2314yescomplemented
161#66983—22no—
162#66983—22no—
163#66983—28no—
164#66983C2314yes—
165#66983C2314yescomplemented
166C4×C22⋊D11—28no—
167C4×C22⋊D11D414yes—
168C4×C22⋊D11C2314yes—
169C2×(C2×D11)⋊C4—21no—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×(C2×D11)⋊C4—21no—
174C2×(C2×D11)⋊C4D411yescharacteristic
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×Dic11⋊C4—21no—
179C2×Dic11⋊C4D411yescharacteristic
180C2×C4×Dic11—21no—
181C2×C4×Dic11C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183C22×C11⋊C8C2311yescharacteristic
184#66967—232no—
185C2×D88—24no—
186C2×D88C2314yescomplemented
187C2×#4313—24no—
188C2×#4313C2314yescomplemented
189#66899C2314yescomplemented
190#66899C2314yescomplemented
191#66896C2314yes—
192#66896C2314yescomplemented
193C22⋊(C11⋊C8)C2314yescomplemented
194#66885C2314yescomplemented
195#66885C2314yescomplemented
196(C2×D11)⋊C8C2314yescomplemented
197#66882C2314yescomplemented
198#66879C2314yescomplemented
199Dic11⋊C8C2314yescomplemented
200C2×#3265—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—24no—
204C24×C11—44no—
205C24×C11—44no—
206C24×C11—82no—
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—24no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—82no—
214C23×D11C2×D411yescharacteristic
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—24no—
218C2×Q8×C11—22no—
219C2×Q8×C11—28no—
220C2×Q8×C11—22no—
221C2×Q8×C11—22no—
222C2×Q8×C11—44no—
223C2×Q8×C11—44no—
224C2×Q8×C11—48no—
225C2×Q8×C11C2×D414yescomplemented
226C2×Q8×C11C2412yes—
227C2×Q8×C11C2412yes—
228C2×D4×C11—28no—
229C2×D4×C11—21no—
230C2×D4×C11—22no—
231C2×D4×C11—24no—
232C2×D4×C11—21no—
233C2×D4×C11—22no—
234C2×D4×C11—22no—
235C2×D4×C11—44no—
236C2×D4×C11—48no—
237C2×D4×C11—44no—
238C2×D4×C11C2×D414yes—
239C2×D4×C11C2412yes—
240C2×D4×C11C2412yes—
241C22×C4×C11—21no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—21no—
245C22×C4×C11—24no—
246C22×C4×C11—44no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—432no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—82no—
265C2×C22⋊D11C2×D414yes—
266C22×Dic11—24no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—44no—
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272C22×Dic11C2×D411yescharacteristic
273#4343—28no—
274#4343—44no—
275#4343—48no—
276D4×D11—28no—
277D4×D11—44no—
278D4×D11—48no—
279C2×D44—24no—
280C2×D44—21no—
281C2×D44—21no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44—44no—
287C2×D44C2412yes—
288C2×D44C2412yes—
289C2×C4×D11—24no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—44no—
293C2×C4×D11C2×D412yes—
294C2×C4×D11C2412yes—
295C11×SD16—28no—
296C11×SD16—28no—
297C11×SD16—28no—
298C11×SD16C2×D4116yescomplemented
299C2×C8×C11—28no—
300C2×C8×C11—22no—
301C2×C8×C11C2×D414yescomplemented
302C2×C8×C11C2412yes—
303C2×C8×C11C2412yes—
304C22⋊Dic11—24no—
305C22⋊Dic11—24no—
306C22⋊Dic11C2×D414yes—
307#4325—28no—
308#4325—44no—
309#4323—28no—
310#4323—44no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4C2×D414yes—
317C4⋊Dic11—24no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11C2412yes—
321C4⋊Dic11C2412yes—
322Dic11⋊C4—24no—
323Dic11⋊C4C2×D414yes—
324C4×Dic11—24no—
325C4×Dic11C2×D412yes—
326C4×Dic11C2412yes—
327C2×C11⋊C8—22no—
328C2×C11⋊C8—22no—
329C2×C11⋊C8C2412yes—
330C2×C11⋊C8C2412yes—
331D88—28no—
332#4313—28no—
333C22×AGL(1,ℤ/8)—111no—
334C23×SD16D1111yescharacteristic, complemented
335C2×#548—111no—
336C2×D42—111no—
337#3265—1116no—
338C2×#496—111no—
339C2×#468—111no—
340C2×#466—111no—
341C2×#460—111no—
342C2×#463—111no—
343C2×#449—111no—
344C2×#448—111no—
345C2×#450—111no—
346C2×#447—111no—
347C2×#440—111no—
348C2×#435—111no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—24no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—48no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—48no—
360C23×C11—42no—
361C23×C11—84no—
362C23×C11—816no—
363C23×C11AGL(1,ℤ/8)14yescomplemented
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—48no—
372C22×D11—48no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—84no—
380C22×D11—816no—
381C22×D11C22×D412yes—
382Q8×C11—24no—
383Q8×C11—22no—
384Q8×C11—22no—
385Q8×C11—22no—
386Q8×C11—48no—
387Q8×C11—42no—
388Q8×C11C22×D414yescomplemented
389D4×C11—24no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—48no—
394D4×C11—42no—
395D4×C11C22×D414yes—
396C2×C4×C11—24no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—24no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—48no—
404C2×C4×C11—42no—
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D412yes—
408C2×C4×C11H(5,𝔽2)12yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—28no—
411C22⋊D11—48no—
412C22⋊D11—48no—
413C22⋊D11—48no—
414C22⋊D11—48no—
415C22⋊D11—48no—
416C22⋊D11—84no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—48no—
423C2×Dic11—42no—
424C2×Dic11—42no—
425C2×Dic11C22×D412yes—
426C2×Dic11C22×D412yes—
427C2×Dic11C22×D412yes—
428D44—22no—
429D44—22no—
430D44—22no—
431D44—22no—
432D44—48no—
433D44—42no—
434D44—42no—
435C4×D11—24no—
436C4×D11—22no—
437C4×D11—22no—
438C4×D11—48no—
439C8×C11—22no—
440C8×C11C22×D414yescomplemented
441C11⋊C8—22no—
442C11⋊C8—22no—
443C22×#41—111no—
444C23×Q8C2×D1111yescharacteristic, complemented
445C23×D4—111no—
446C23×D4—221no—
447C23×D4C2×D1111yescharacteristic
448C2×AGL(1,ℤ/8)—118no—
449C2×AGL(1,ℤ/8)—228no—
450C22×SD16—28no—
451C22×SD16—111no—
452C22×SD16—111no—
453C22×SD16C2×D1111yescharacteristic
454C22×SD16C2×D1111yescharacteristic
455C22×SD16C2×D1111yescharacteristic, complemented
456C22×SD16C2×D1111yescharacteristic, complemented
457C22×SD16C2×D1118yescomplemented
458C22×D8—111no—
459C22×D8—111no—
460C22×D8—111no—
461C22×M16—111no—
462C23×C8C2×D1111yescharacteristic, complemented
463#548—118no—
464#548—224no—
465D42—118no—
466D42—224no—
467C2×#127—111no—
468C2×#124—111no—
469C2×#124—221no—
470C2×C22⋊Q8—111no—
471C2×C22⋊Q8—221no—
472C2×#121—111no—
473C2×#121—111no—
474C2×#121—111no—
475C2×#121—221no—
476C2×#121—221no—
477C2×#120—221no—
478C2×#120—221no—
479C2×C4×Q8—111no—
480C2×C4×D4—111no—
481C2×C4×D4—111no—
482C2×C4×D4—221no—
483#496—118no—
484#468—118no—
485#466—118no—
486#463—118no—
487#460—118no—
488#450—118no—
489#449—118no—
490#448—118no—
491#447—118no—
492#440—118no—
493#435—118no—
494C2×#107—111no—
495C2×C4⋊C8—111no—
496C2×#103—111no—
497C2×#103—111no—
498C2×#102—111no—
499C2×#102—111no—
500C2×#102—111no—
501C2×#102—111no—
502C2×C22⋊C8—111no—
503C2×C22⋊C8—111no—
504C2×#97—111no—
505C22×C11—22no—
506C22×C11—28no—
507C22×C11—22no—
508C22×C11—24no—
509C22×C11—48no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—816no—
516C22×C11—84no—
517C22×C11D4212yes—
518C22×C11C2×AGL(1,ℤ/8)12yes—
519C22×C11C2×AGL(1,ℤ/8)14yescomplemented
520C22×C11#57712yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—22no—
525C2×D11—44no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—816no—
533C2×D11—84no—
534C2×D11—84no—
535C4×C11—22no—
536C4×C11—24no—
537C4×C11—42no—
538C4×C11D4212yes—
539C4×C11C23×D411yescharacteristic
540C4×C11C2×H(5,𝔽2)11yescharacteristic
541Dic11—22no—
542Dic11—22no—
543Dic11—22no—
544Dic11—42no—
545Dic11—42no—
546C25—21no—
547C25—221no—
548C2×#41—114no—
549C2×#41—222no—
550C2×#41—224no—
551C2×#41—442no—
552C22×Q8—21no—
553C22×Q8—22no—
554C22×Q8—24no—
555C22×Q8—42no—
556C22×Q8C22×D1111yescharacteristic
557C22×Q8C22×D1111yescharacteristic
558C22×Q8C22×D1114yescomplemented
559C22×D4—24no—
560C22×D4—21no—
561C22×D4—22no—
562C22×D4—42no—
563C22×D4—111no—
564C22×D4—114no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—221no—
568C22×D4—222no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4—228no—
573C22×D4—224no—
574C22×D4—221no—
575C22×D4—221no—
576C22×D4—221no—
577C22×D4—442no—
578C22×D4—448no—
579C22×D4C22×D1111yescharacteristic
580C22×D4C22×D1114yes—
581C22×D4C22×D1111yescharacteristic
582C23×C4—21no—
583C23×C4—111no—
584C23×C4—221no—
585C23×C4—221no—
586C23×C4C22×D1111yescharacteristic
587AGL(1,ℤ/8)—2232no—
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—232no—
591C2×SD16—24no—
592C2×SD16—114no—
593C2×SD16—114no—
594C2×SD16—224no—
595C2×SD16—442no—
596C2×SD16C22⋊D1118yescomplemented
597C2×SD16C22×D1114yes—
598C2×SD16C22×D1114yes—
599C2×SD16C22×D1114yescomplemented
600C2×SD16C22×D1114yescomplemented
601C2×D8—114no—
602C2×D8—114no—
603C2×D8—114no—
604C2×D8—224no—
605C2×D8—224no—
606C2×D8—442no—
607C2×M16—114no—
608C2×M16—224no—
609C22×C8—24no—
610C22×C8—111no—
611C22×C8—111no—
612C22×C8C22×D1111yescharacteristic
613C22×C8C22×D1111yescharacteristic
614C22×C8C22×D1114yescomplemented
615#127—114no—
616#127—222no—
617#124—114no—
618#124—222no—
619#124—228no—
620C22⋊Q8—114no—
621C22⋊Q8—228no—
622C22⋊Q8—222no—
623#121—114no—
624#121—114no—
625#121—114no—
626#121—228no—
627#121—228no—
628#121—222no—
629#121—222no—
630#121—222no—
631#120—228no—
632#120—228no—
633C4×Q8—114no—
634C4×Q8—222no—
635C4×D4—114no—
636C4×D4—114no—
637C4×D4—114no—
638C4×D4—222no—
639C4×D4—228no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—221no—
644C2×C4⋊C4—221no—
645C2×C22⋊C4—111no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C42—111no—
655C2×C42—221no—
656#107—114no—
657C4⋊C8—114no—
658#103—114no—
659#103—114no—
660#102—114no—
661#102—114no—
662#102—114no—
663#102—114no—
664C22⋊C8—114no—
665C22⋊C8—114no—
666#97—114no—
667C2×C11—24no—
668C2×C11—44no—
669C2×C11—82no—
670C2×C11#326514yescomplemented
671C2×C11C2×D4211yescharacteristic
672C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
673C2×C11C2×#57711yescharacteristic
674D11—42no—
675D11—82no—
676D11—82no—
677C24—21no—
678C24—21no—
679C24—24no—
680C24—44no—
681C24—44no—
682C24—82no—
683C24—111no—
684C24—224no—
685C24—221no—
686C24—221no—
687C24—444no—
688C24—444no—
689C24—882no—
690C24D4×D1111yescharacteristic
691#41—228no—
692#41—444no—
693#41—448no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—24no—
697C2×Q8—22no—
698C2×Q8—28no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—48no—
704C2×Q8C2×C22⋊D1114yescomplemented
705C2×Q8C23×D1112yes—
706C2×Q8C23×D1112yes—
707C2×D4—28no—
708C2×D4—21no—
709C2×D4—24no—
710C2×D4—21no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—114no—
718C2×D4—112no—
719C2×D4—112no—
720C2×D4—224no—
721C2×D4—224no—
722C2×D4—224no—
723C2×D4—224no—
724C2×D4—224no—
725C2×D4—228no—
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—221no—
730C2×D4—221no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—222no—
734C2×D4—222no—
735C2×D4—444no—
736C2×D4—444no—
737C2×D4—448no—
738C2×D4—444no—
739C2×D4—444no—
740C2×D4—4432no—
741C2×D4—444no—
742C2×D4—444no—
743C2×D4—444no—
744C2×D4—882no—
745C2×D4C2×C22⋊D1114yes—
746C2×D4C23×D1112yes—
747C2×D4C23×D1112yes—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—24no—
752C22×C4—21no—
753C22×C4—44no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—111no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—224no—
760C22×C4—224no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4D4×D1112yes—
768C22×C4D4×D1111yescharacteristic
769C22×C4C23×D1112yes—
770C22×C4C23×D1111yescharacteristic
771SD16—28no—
772SD16—28no—
773SD16—28no—
774SD16—228no—
775SD16—444no—
776SD16C2×C22⋊D11116yescomplemented
777D8—228no—
778D8—228no—
779D8—444no—
780M16—228no—
781C2×C8—22no—
782C2×C8—28no—
783C2×C8—112no—
784C2×C8—112no—
785C2×C8—222no—
786C2×C8—222no—
787C2×C8C2×C22⋊D1114yescomplemented
788C2×C8C23×D1112yes—
789C2×C8C23×D1112yes—
790C4⋊C4—114no—
791C4⋊C4—112no—
792C4⋊C4—112no—
793C4⋊C4—224no—
794C4⋊C4—224no—
795C4⋊C4—221no—
796C4⋊C4—221no—
797C22⋊C4—114no—
798C22⋊C4—114no—
799C22⋊C4—224no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—224no—
803C22⋊C4—224no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C42—112no—
807C42—112no—
808C42—224no—
809C11C2×#326511yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—24no—
813C23—22no—
814C23—22no—
815C23—48no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—48no—
820C23—42no—
821C23—42no—
822C23—84no—
823C23—816no—
824C23—112no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—448no—
831C23—448no—
832C23—442no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23—442no—
837C23—442no—
838C23—884no—
839C23—8816no—
840C23#6696714yescomplemented
841C23C2×D4×D1112yes—
842C23C2×D4×D1111yescharacteristic
843Q8—24no—
844Q8—22no—
845Q8—22no—
846Q8—22no—
847Q8—48no—
848Q8—42no—
849Q8C22×C22⋊D1114yescomplemented
850D4—24no—
851D4—22no—
852D4—22no—
853D4—22no—
854D4—48no—
855D4—42no—
856D4—228no—
857D4—222no—
858D4—222no—
859D4—222no—
860D4—222no—
861D4—448no—
862D4—448no—
863D4—448no—
864D4—448no—
865D4—448no—
866D4—448no—
867D4—442no—
868D4—442no—
869D4—884no—
870D4C22×C22⋊D1114yes—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—48no—
879C2×C4—42no—
880C2×C4—112no—
881C2×C4—112no—
882C2×C4—112no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—448no—
892C2×C4—448no—
893C2×C4—442no—
894C2×C4—442no—
895C2×C4C2×D4×D1112yes—
896C2×C4C2×D4×D1111yescharacteristic
897C2×C4#6703712yes—
898C2×C4C22×C22⋊D1112yes—
899C2×C4C24×D1111yescharacteristic
900C8—22no—
901C8—222no—
902C8—222no—
903C8C22×C22⋊D1114yescomplemented
904C22—28no—
905C22—22no—
906C22—22no—
907C22—24no—
908C22—48no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—84no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—444no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—8816no—
927C22—884no—
928C22—884no—
929C22C2×#6696712yes—
930C22C2×#6696714yescomplemented
931C22#1062329312yes—
932C22D4×C22⋊D1112yes—
933C22C22×D4×D1111yescharacteristic
934C4—22no—
935C4—24no—
936C4—42no—
937C4—222no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—442no—
942C4D4×C22⋊D1112yes—
943C4C2×#6703711yescharacteristic
944C4C23×C22⋊D1111yescharacteristic
945C2—24no—
946C2—44no—
947C2—82no—
948C2—442no—
949C2—882no—
950C2—882no—
951C2#1308011114yesdirect product factor
952C2C2×D4×C22⋊D1111yescharacteristic
953C2C22×#6696711yescharacteristic
954C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC23×C11×SD16C2
socleC23×C11C22×D4
hypercenterC23×SD16D11
hypocenterC11C2×#3265
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C2×#10623348C2semidirect
3. C2×D4×C22⋊D11C2semidirect
4. #13080111C2direct (N × H)
5. C2×#10622789C2semidirect
6. C2×#10622787C2semidirect
7. C2×#10622728C2semidirect
8. C2×#10622776C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622785C2semidirect
11. C2×#10622840C2semidirect
12. C2×#10622782C2semidirect
13. C2×#10622830C2semidirect
14. C2×#10622777C2semidirect
15. C2×#10622724C2semidirect
16. C23×C11×SD16C2semidirect
17. C23×Q8×C11C22semidirect
20. C22×#4343C22semidirect
25. C22×C11×SD16C22semidirect
26. C22×C11×SD16C22semidirect
27. C22×C11×SD16C22semidirect
28. C23×C8×C11C22semidirect
31. #10623348C22semidirect
33. C2×#67000C22semidirect
35. C2×#66999C22semidirect
36. C2×Q8×Dic11C22semidirect
37. C22×#4325C22semidirect
38. C22×#4325C22semidirect
42. D4×C22⋊D11C22semidirect
47. C22×#4323C22semidirect
50. C2×#66983C22semidirect
54. C2×#66967C22semidirect
55. C22×D88C22semidirect
56. C22×#4313C22semidirect
57. #10622840C22semidirect
58. C2×#66899C22semidirect
59. C2×#66899C22semidirect
60. #10622830C22semidirect
62. C2×#66896C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622789C22semidirect
65. #10622787C22semidirect
66. #10622785C22semidirect
67. #10622782C22semidirect
68. #10622778C22semidirect
69. #10622777C22semidirect
70. #10622776C22semidirect
71. #10622728C22semidirect
72. C2×#66885C22semidirect
73. C2×#66885C22semidirect
74. #10622724C22semidirect
75. C2×(C2×D11)⋊C8C22semidirect
76. C2×#66882C22semidirect
77. C2×#66879C22semidirect
78. C2×Dic11⋊C8C22semidirect
87. C22×Q8×C11C23semidirect
110. C2×#4343C23semidirect
124. C2×C11×SD16D4semidirect
127. C2×C11×SD16C23semidirect
128. C2×C11×SD16C23semidirect
132. C22×C8×C11C23semidirect
139. #67000C23semidirect
142. #66999C23semidirect
144. Q8×Dic11C23semidirect
147. C2×#4325C23semidirect
148. C2×#4325C23semidirect
160. C2×#4323C23semidirect
165. #66983C23semidirect
186. C2×D88C23semidirect
188. C2×#4313C23semidirect
189. #66899C23semidirect
190. #66899C23semidirect
192. #66896C23semidirect
193. C22⋊(C11⋊C8)C23semidirect
194. #66885C23semidirect
195. #66885C23semidirect
196. (C2×D11)⋊C8C23semidirect
197. #66882C23semidirect
198. #66879C23semidirect
199. Dic11⋊C8C23semidirect
225. C2×Q8×C11C2×D4semidirect
298. C11×SD16C2×D4semidirect
301. C2×C8×C11C2×D4semidirect
334. C23×SD16D11semidirect
363. C23×C11AGL(1,ℤ/8)semidirect
388. Q8×C11C22×D4semidirect
440. C8×C11C22×D4semidirect
444. C23×Q8C2×D11semidirect
455. C22×SD16C2×D11semidirect
456. C22×SD16C2×D11semidirect
457. C22×SD16C2×D11semidirect
462. C23×C8C2×D11semidirect
519. C22×C11C2×AGL(1,ℤ/8)semidirect
558. C22×Q8C22×D11semidirect
596. C2×SD16C22⋊D11semidirect
599. C2×SD16C22×D11semidirect
600. C2×SD16C22×D11semidirect
614. C22×C8C22×D11semidirect
670. C2×C11#3265semidirect
704. C2×Q8C2×C22⋊D11semidirect
776. SD16C2×C22⋊D11semidirect
787. C2×C8C2×C22⋊D11semidirect
809. C11C2×#3265semidirect
840. C23#66967semidirect
849. Q8C22×C22⋊D11semidirect
903. C8C22×C22⋊D11semidirect
930. C22C2×#66967semidirect
951. C2#13080111direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C2×#106233482
C2×D4×C22⋊D112
#130801112
C2×#106227892
C2×#106227872
C2×#106227282
C2×#106227762
C2×#106227782
C2×#106227852
C2×#106228402
C2×#106227822
C2×#106228302
C2×#106227772
C2×#106227242
C23×C11×SD162
C2×#326511