Finite Group Databasebeta

← C2×#13080112 #15628739

Subgroups — C2×#13080112 #15628739

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×#67002C211yesmaximal, characteristic, complemented
2C23×#4325C211yesmaximal, characteristic, complemented
3C2×D4×D44C211yesmaximal, characteristic, complemented
4#13080112C2116yesmaximal, direct product factor
5C2×#10622671C211yesmaximal, characteristic, complemented
6C2×#10622662C211yesmaximal, characteristic, complemented
7C2×#10622651C211yesmaximal, characteristic, complemented
8C2×#10622640C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622840C211yesmaximal, characteristic, complemented
12C2×#10622659C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622624C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×Q8×C11C2211yescharacteristic, complemented
19C22×D4×D11—21no—
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C11×#548—24no—
23C11×#548C2218yescomplemented
24C2×C11×#124—21no—
25C2×C11×#124C2211yescharacteristic, complemented
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C4×Q8×C11C2211yescharacteristic, complemented
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67002—28no—
34C2×#67002C2218yescomplemented
35C22×#4325—28no—
36C22×#4325C2211yescharacteristic
37C22×#4325C2211yescharacteristic
38C22×#4325C2211yescharacteristic, complemented
39C22×#4325C2211yescharacteristic, complemented
40C22×#4325C2211yescharacteristic, complemented
41C22×#4325C2211yescharacteristic, complemented
42C22×#4325C2218yescomplemented
43C22×#4323C2211yescharacteristic
44C22×#4323C2211yescharacteristic, complemented
45C22×#4323C2211yescharacteristic, complemented
46C2×#66983C2211yescharacteristic
47C2×#66983C2211yescharacteristic
48C22×#4318C2211yescharacteristic, complemented
49C23×C11⋊C8C2211yescharacteristic, complemented
50D4×D44—24no—
51D4×D44C2218yescomplemented
52C2×#66948—21no—
53C2×#66935—21no—
54C2×#66935—21no—
55C2×#66927C2211yescharacteristic
56C2×C4×D44C2211yescharacteristic
57#10622851C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622671C2218yescomplemented
65#10622670C2218yescomplemented
66#10622662C2218yescomplemented
67#10622659C2218yescomplemented
68#10622651C2218yescomplemented
69#10622649C2218yescomplemented
70#10622640C2218yescomplemented
71#10622639C2218yescomplemented
72#10622624C2218yescomplemented
73C2×#66873C2211yescharacteristic
74C2×#66873C2211yescharacteristic, complemented
75C2×#66873C2211yescharacteristic, complemented
76C2×#66871C2211yescharacteristic, complemented
77C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
78C2×#66867C2211yescharacteristic, complemented
79C24×D11—21no—
80C24×D11—21no—
81C2×C11×#41—22no—
82C2×C11×#41—24no—
83C2×C11×#41—42no—
84C2×C11×#41C2314yescomplemented
85C22×Q8×C11—21no—
86C22×Q8×C11—22no—
87C22×Q8×C11—24no—
88C22×Q8×C11—42no—
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2314yescomplemented
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C2×D4×D11—28no—
103C2×D4×D11—48no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44—22no—
110C22×D44—22no—
111C22×D44—21no—
112C22×D44—42no—
113C22×D44—42no—
114C22×D44C2311yescharacteristic
115C22×D44C2311yescharacteristic
116C22×D44C2314yes—
117C22×D44C2314yes—
118C22×D44C2311yescharacteristic
119C22×C4×D11—21no—
120C11×#124—28no—
121C11×#124—22no—
122C11×#124C2314yescomplemented
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—28no—
125C11×C22⋊Q8C2314yescomplemented
126C11×#121—28no—
127C11×#121—22no—
128C11×#121C2314yescomplemented
129C4×Q8×C11—22no—
130C4×Q8×C11C2314yescomplemented
131C4×D4×C11—28no—
132C4×D4×C11D414yes—
133C4×D4×C11C2314yes—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C42×C11—21no—
145C2×C42×C11C2311yescharacteristic
146#67002—232no—
147C2×#4325—24no—
148C2×#4325—24no—
149C2×#4325—24no—
150C2×#4325—232no—
151C2×#4325—24no—
152C2×#4325—42no—
153C2×#4325D418yescomplemented
154C2×#4325C2314yes—
155C2×#4325C2314yes—
156C2×#4325C2314yescomplemented
157C2×#4325C2314yescomplemented
158C2×#4325C2314yescomplemented
159C2×#4325C2314yescomplemented
160C2×#4323—24no—
161C2×#4323—24no—
162C2×#4323—42no—
163C2×#4323C2314yes—
164C2×#4323C2314yescomplemented
165C2×#4323C2314yescomplemented
166#66983—22no—
167#66983—22no—
168#66983C2314yes—
169#66983C2314yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×#4318—24no—
175C2×#4318C2314yescomplemented
176C22×C11⋊C8—24no—
177C22×C11⋊C8C2311yescharacteristic
178C22×C11⋊C8C2311yescharacteristic
179C22×C11⋊C8C2311yescharacteristic
180C22×C11⋊C8C2311yescharacteristic
181C22×C11⋊C8C2314yescomplemented
182#66948—28no—
183#66935—28no—
184#66935—28no—
185#66927—22no—
186#66927C2314yes—
187C4×D44—22no—
188C4×D44C2314yes—
189#66899C2314yescomplemented
190#66899C2314yescomplemented
191#66896C2314yescomplemented
192C22⋊(C11⋊C8)C2314yescomplemented
193C22⋊(C11⋊C8)C2314yescomplemented
194#66873C2314yes—
195#66873C2314yescomplemented
196#66873C2314yescomplemented
197#66871C2314yescomplemented
198C4⋊(C11⋊C8)C2314yescomplemented
199#66867C2314yescomplemented
200C2×#3265—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11C2×D411yescharacteristic
203C24×C11C2×D411yescharacteristic
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—24no—
208C23×D11—24no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—82no—
214C23×D11—82no—
215C11×#41—28no—
216C11×#41—44no—
217C11×#41—48no—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—24no—
221C2×Q8×C11—22no—
222C2×Q8×C11—28no—
223C2×Q8×C11—22no—
224C2×Q8×C11—22no—
225C2×Q8×C11—44no—
226C2×Q8×C11—44no—
227C2×Q8×C11—48no—
228C2×Q8×C11C2×D414yescomplemented
229C2×Q8×C11C2412yes—
230C2×Q8×C11C2412yes—
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—24no—
234C2×D4×C11—22no—
235C2×D4×C11—21no—
236C2×D4×C11—22no—
237C2×D4×C11—44no—
238C2×D4×C11—44no—
239C2×D4×C11C2×D414yes—
240C2×D4×C11C2412yes—
241C22×C4×C11—21no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—44no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C22×Dic11—21no—
266D4×D11—432no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—21no—
270C2×D44—21no—
271C2×D44—21no—
272C2×D44—24no—
273C2×D44—24no—
274C2×D44—24no—
275C2×D44—24no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—44no—
282C2×D44—44no—
283C2×D44—44no—
284C2×D44—44no—
285C2×D44—48no—
286C2×D44—48no—
287C2×D44—44no—
288C2×D44—82no—
289C2×D44C2×D414yes—
290C2×D44C2412yes—
291C2×D44C2412yes—
292C2×D44C2412yes—
293C2×C4×D11—24no—
294C2×C4×D11—44no—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4C2×D414yes—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4C2×D414yes—
305C11×C22⋊C4C2×D414yes—
306C42×C11—24no—
307C42×C11C2×D412yes—
308C42×C11C2412yes—
309#4325—28no—
310#4325—28no—
311#4325—28no—
312#4325—28no—
313#4325—44no—
314#4325C2×D4116yescomplemented
315#4323—28no—
316#4323—28no—
317#4323—44no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321C4⋊Dic11—21no—
322C4⋊Dic11C2412yes—
323#4318—28no—
324C2×C11⋊C8—28no—
325C2×C11⋊C8—22no—
326C2×C11⋊C8—22no—
327C2×C11⋊C8—22no—
328C2×C11⋊C8C2×D414yescomplemented
329C2×C11⋊C8C2412yes—
330C2×C11⋊C8C2412yes—
331C2×C11⋊C8C2412yes—
332C2×C11⋊C8C2412yes—
333C22×AGL(1,ℤ/8)—111no—
334C23×SD16—111no—
335C2×#548D1111yescharacteristic, complemented
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—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11AGL(1,ℤ/8)14yescomplemented
359C23×C11C22×D412yes—
360C23×C11C22×D412yes—
361C23×C11C22×D411yescharacteristic
362C22×D11—24no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—48no—
367C22×D11—48no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—48no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—84no—
379C22×D11—84no—
380C22×D11—816no—
381C22×D11—816no—
382Q8×C11—24no—
383Q8×C11—22no—
384Q8×C11—22no—
385Q8×C11—22no—
386Q8×C11—48no—
387Q8×C11—42no—
388Q8×C11C22×D414yescomplemented
389D4×C11—28no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—48no—
393D4×C11—48no—
394D4×C11—42no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—24no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—24no—
402C2×C4×C11—24no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—48no—
410C2×C4×C11—48no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11C22×D412yes—
414C2×C4×C11C22×D412yes—
415C2×C4×C11C22×D412yes—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11H(5,𝔽2)12yes—
420C2×C4×C11C2511yescharacteristic
421C22⋊D11—48no—
422C22⋊D11—48no—
423C2×Dic11—22no—
424C2×Dic11—42no—
425D44—24no—
426D44—22no—
427D44—22no—
428D44—22no—
429D44—22no—
430D44—22no—
431D44—48no—
432D44—48no—
433D44—48no—
434D44—42no—
435D44—42no—
436D44—84no—
437D44C22×D414yes—
438C4×D11—48no—
439C11⋊C8—22no—
440C11⋊C8—22no—
441C11⋊C8—22no—
442C11⋊C8C22×D414yescomplemented
443C22×#41C2×D1111yescharacteristic, complemented
444C23×Q8C2×D1111yescharacteristic, complemented
445C23×D4—111no—
446C23×D4—111no—
447C23×D4—221no—
448C2×AGL(1,ℤ/8)—118no—
449C2×AGL(1,ℤ/8)—228no—
450C22×SD16—111no—
451C22×SD16—111no—
452C22×SD16—111no—
453C22×SD16—111no—
454C22×SD16—111no—
455C22×SD16—118no—
456C22×SD16—111no—
457C22×SD16—228no—
458C22×D8—111no—
459C22×D8—111no—
460C22×D8—111no—
461C22×M16—111no—
462C23×C8—111no—
463#548—24no—
464#548C2×D1118yescomplemented
465D42—118no—
466D42—224no—
467C2×#127—111no—
468C2×#124—21no—
469C2×#124C2×D1111yescharacteristic, complemented
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8C2×D1111yescharacteristic, complemented
472C2×#121—21no—
473C2×#121—111no—
474C2×#121—111no—
475C2×#121—221no—
476C2×#121C2×D1111yescharacteristic, complemented
477C2×#120—221no—
478C2×#120—221no—
479C2×C4×Q8C2×D1111yescharacteristic, complemented
480C2×C4×D4—21no—
481C2×C4×D4—111no—
482C2×C4×D4C2×D1111yescharacteristic
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—22no—
509C22×C11—22no—
510C22×C11—22no—
511C22×C11—44no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—84no—
516C22×C11D4212yes—
517C22×C11C2×AGL(1,ℤ/8)12yes—
518C22×C11C2×AGL(1,ℤ/8)14yescomplemented
519C22×C11#57712yes—
520C22×C11C23×D411yescharacteristic
521C2×D11—24no—
522C2×D11—48no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—816no—
532C2×D11—816no—
533C2×D11—84no—
534C2×D11—84no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—24no—
538C4×C11—22no—
539C4×C11—22no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11D4212yes—
543C4×C11C23×D411yescharacteristic
544C4×C11C2×H(5,𝔽2)11yescharacteristic
545Dic11—42no—
546C25—221no—
547C25—221no—
548C2×#41—22no—
549C2×#41—24no—
550C2×#41—42no—
551C2×#41C22×D1114yescomplemented
552C22×Q8—21no—
553C22×Q8—22no—
554C22×Q8—24no—
555C22×Q8—42no—
556C22×Q8C22×D1111yescharacteristic
557C22×Q8C22×D1111yescharacteristic
558C22×Q8C22×D1114yescomplemented
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4—111no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—228no—
571C22×D4—221no—
572C22×D4—221no—
573C22×D4—221no—
574C22×D4—222no—
575C22×D4—222no—
576C22×D4—221no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4—448no—
580C22×D4C22⋊D1111yescharacteristic
581C22×D4C22×D1111yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—221no—
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1111yescharacteristic
587AGL(1,ℤ/8)—2232no—
588C2×SD16—118no—
589C2×SD16—114no—
590C2×SD16—114no—
591C2×SD16—114no—
592C2×SD16—114no—
593C2×SD16—114no—
594C2×SD16—114no—
595C2×SD16—224no—
596C2×SD16—2232no—
597C2×SD16—224no—
598C2×SD16—224no—
599C2×SD16—224no—
600C2×SD16—442no—
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—111no—
610C22×C8—111no—
611C22×C8—114no—
612C22×C8—111no—
613C22×C8—111no—
614C22×C8—224no—
615#127—114no—
616#127—222no—
617#124—28no—
618#124—22no—
619#124C22×D1114yescomplemented
620C22⋊Q8—22no—
621C22⋊Q8—28no—
622C22⋊Q8C22×D1114yescomplemented
623#121—28no—
624#121—22no—
625#121—114no—
626#121—114no—
627#121—222no—
628#121—222no—
629#121—228no—
630#121C22×D1114yescomplemented
631#120—228no—
632#120—228no—
633C4×Q8—22no—
634C4×Q8C22×D1114yescomplemented
635C4×D4—28no—
636C4×D4—114no—
637C4×D4—222no—
638C4×D4C22⋊D1114yes—
639C4×D4C22×D1114yes—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4C22⋊D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4C22⋊D1111yescharacteristic
653C2×C22⋊C4C22⋊D1111yescharacteristic
654C2×C42—21no—
655C2×C42C22×D1111yescharacteristic
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—42no—
669C2×C11—82no—
670C2×C11#326514yescomplemented
671C2×C11C2×D4211yescharacteristic
672C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
673C2×C11C2×#57711yescharacteristic
674D11—44no—
675D11—82no—
676D11—82no—
677C24—21no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—224no—
682C24—224no—
683C24—444no—
684C24—444no—
685C24—444no—
686C24—444no—
687C24—882no—
688C24—882no—
689C24C2×C22⋊D1111yescharacteristic
690C24C2×C22⋊D1111yescharacteristic
691#41—28no—
692#41—44no—
693#41—48no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—24no—
698C2×Q8—28no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—48no—
704C2×Q8D4×D1114yescomplemented
705C2×Q8C23×D1112yes—
706C2×Q8C23×D1112yes—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—114no—
716C2×D4—112no—
717C2×D4—112no—
718C2×D4—112no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—224no—
722C2×D4—224no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4—221no—
729C2×D4—224no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—221no—
733C2×D4—221no—
734C2×D4—224no—
735C2×D4—444no—
736C2×D4—444no—
737C2×D4—448no—
738C2×D4—448no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—4432no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—882no—
746C2×D4C2×C22⋊D1114yes—
747C2×D4C23×D1112yes—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—24no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—24no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—221no—
760C22×C4—224no—
761C22×C4—444no—
762C22×C4C2×C22⋊D1112yes—
763C22×C4C2×C22⋊D1112yes—
764C22×C4C2×C22⋊D1111yescharacteristic
765C22×C4C2×C22⋊D1111yescharacteristic
766C22×C4C2×C22⋊D1111yescharacteristic
767C22×C4C2×C22⋊D1111yescharacteristic
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C22×C4C23×D1111yescharacteristic
771SD16—1116no—
772SD16—228no—
773SD16—228no—
774SD16—228no—
775SD16—228no—
776SD16—444no—
777D8—228no—
778D8—228no—
779D8—444no—
780M16—228no—
781C2×C8—114no—
782C2×C8—112no—
783C2×C8—112no—
784C2×C8—112no—
785C2×C8—112no—
786C2×C8—228no—
787C2×C8—222no—
788C2×C8—222no—
789C2×C8—222no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—21no—
793C4⋊C4—112no—
794C4⋊C4—221no—
795C4⋊C4C2×C22⋊D1114yes—
796C4⋊C4C23×D1112yes—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—224no—
802C22⋊C4—224no—
803C22⋊C4—224no—
804C22⋊C4C2×C22⋊D1114yes—
805C22⋊C4C2×C22⋊D1114yes—
806C42—24no—
807C42C2×C22⋊D1112yes—
808C42C23×D1112yes—
809C11C2×#326511yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—224no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—448no—
824C23—448no—
825C23—448no—
826C23—442no—
827C23—442no—
828C23—442no—
829C23—442no—
830C23—442no—
831C23—442no—
832C23—448no—
833C23—442no—
834C23—442no—
835C23—884no—
836C23—884no—
837C23—8816no—
838C23—8816no—
839C23#6700214yescomplemented
840C23C22×C22⋊D1112yes—
841C23C22×C22⋊D1112yes—
842C23C22×C22⋊D1111yescharacteristic
843Q8—24no—
844Q8—22no—
845Q8—22no—
846Q8—22no—
847Q8—48no—
848Q8—42no—
849Q8C2×D4×D1114yescomplemented
850D4—28no—
851D4—22no—
852D4—22no—
853D4—48no—
854D4—48no—
855D4—42no—
856D4—114no—
857D4—224no—
858D4—222no—
859D4—222no—
860D4—222no—
861D4—222no—
862D4—222no—
863D4—448no—
864D4—448no—
865D4—448no—
866D4—448no—
867D4—448no—
868D4—442no—
869D4—442no—
870D4—884no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—48no—
886C2×C4—48no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—222no—
890C2×C4—448no—
891C2×C4—442no—
892C2×C4C2×D4×D1112yes—
893C2×C4#6703712yes—
894C2×C4C22×C22⋊D1112yes—
895C2×C4C22×C22⋊D1112yes—
896C2×C4C22×C22⋊D1112yes—
897C2×C4C22×C22⋊D1112yes—
898C2×C4C22×C22⋊D1111yescharacteristic
899C2×C4C24×D1111yescharacteristic
900C8—114no—
901C8—222no—
902C8—222no—
903C8—222no—
904C22—28no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—44no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—84no—
915C22—224no—
916C22—448no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—8816no—
926C22—8816no—
927C22—884no—
928C22—884no—
929C22D4×C22⋊D1112yes—
930C22C2×#6700212yes—
931C22C2×#6700214yescomplemented
932C22#1062336812yes—
933C22C23×C22⋊D1111yescharacteristic
934C4—22no—
935C4—22no—
936C4—24no—
937C4—22no—
938C4—22no—
939C4—42no—
940C4—42no—
941C4—442no—
942C4D4×C22⋊D1112yes—
943C4C22×D4×D1111yescharacteristic
944C4C2×#6703711yescharacteristic
945C2—24no—
946C2—42no—
947C2—82no—
948C2—444no—
949C2—882no—
950C2—882no—
951C2#1308011214yesdirect product factor
952C2C2×D4×C22⋊D1111yescharacteristic
953C2C22×#6700211yescharacteristic
954C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11C2×#3265
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C23×#4325C2semidirect
3. C2×D4×D44C2semidirect
4. #13080112C2direct (N × H)
5. C2×#10622671C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622640C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622840C2semidirect
12. C2×#10622659C2semidirect
13. C2×#10622649C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622624C2semidirect
16. C2×C11×#548C2semidirect
17. C22×C11×#41C22semidirect
18. C23×Q8×C11C22semidirect
23. C11×#548C22semidirect
25. C2×C11×#124C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×#121C22semidirect
30. C2×C4×Q8×C11C22semidirect
34. C2×#67002C22semidirect
38. C22×#4325C22semidirect
39. C22×#4325C22semidirect
40. C22×#4325C22semidirect
41. C22×#4325C22semidirect
42. C22×#4325C22semidirect
44. C22×#4323C22semidirect
45. C22×#4323C22semidirect
48. C22×#4318C22semidirect
49. C23×C11⋊C8C22semidirect
51. D4×D44C22semidirect
57. #10622851C22semidirect
58. #10622840C22semidirect
59. C2×#66899C22semidirect
60. C2×#66899C22semidirect
61. C2×#66896C22semidirect
62. C2×C22⋊(C11⋊C8)C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622671C22semidirect
65. #10622670C22semidirect
66. #10622662C22semidirect
67. #10622659C22semidirect
68. #10622651C22semidirect
69. #10622649C22semidirect
70. #10622640C22semidirect
71. #10622639C22semidirect
72. #10622624C22semidirect
74. C2×#66873C22semidirect
75. C2×#66873C22semidirect
76. C2×#66871C22semidirect
77. C2×C4⋊(C11⋊C8)C22semidirect
78. C2×#66867C22semidirect
84. C2×C11×#41C23semidirect
91. C22×Q8×C11C23semidirect
122. C11×#124C23semidirect
125. C11×C22⋊Q8C23semidirect
128. C11×#121C23semidirect
130. C4×Q8×C11C23semidirect
153. C2×#4325D4semidirect
156. C2×#4325C23semidirect
157. C2×#4325C23semidirect
158. C2×#4325C23semidirect
159. C2×#4325C23semidirect
164. C2×#4323C23semidirect
165. C2×#4323C23semidirect
175. C2×#4318C23semidirect
181. C22×C11⋊C8C23semidirect
189. #66899C23semidirect
190. #66899C23semidirect
191. #66896C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
193. C22⋊(C11⋊C8)C23semidirect
195. #66873C23semidirect
196. #66873C23semidirect
197. #66871C23semidirect
198. C4⋊(C11⋊C8)C23semidirect
199. #66867C23semidirect
228. C2×Q8×C11C2×D4semidirect
314. #4325C2×D4semidirect
328. C2×C11⋊C8C2×D4semidirect
335. C2×#548D11semidirect
358. C23×C11AGL(1,ℤ/8)semidirect
388. Q8×C11C22×D4semidirect
442. C11⋊C8C22×D4semidirect
443. C22×#41C2×D11semidirect
444. C23×Q8C2×D11semidirect
464. #548C2×D11semidirect
469. C2×#124C2×D11semidirect
471. C2×C22⋊Q8C2×D11semidirect
476. C2×#121C2×D11semidirect
479. C2×C4×Q8C2×D11semidirect
518. C22×C11C2×AGL(1,ℤ/8)semidirect
551. C2×#41C22×D11semidirect
558. C22×Q8C22×D11semidirect
619. #124C22×D11semidirect
622. C22⋊Q8C22×D11semidirect
630. #121C22×D11semidirect
634. C4×Q8C22×D11semidirect
670. C2×C11#3265semidirect
704. C2×Q8D4×D11semidirect
809. C11C2×#3265semidirect
839. C23#67002semidirect
849. Q8C2×D4×D11semidirect
931. C22C2×#67002semidirect
951. C2#13080112direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C23×#43252
C2×D4×D442
#130801122
C2×#106226712
C2×#106226622
C2×#106226512
C2×#106226402
C2×#106226702
C2×#106228512
C2×#106228402
C2×#106226592
C2×#106226492
C2×#106226392
C2×#106226242
C2×C11×#5482
C2×#326511