Finite Group Databasebeta

← C2×#13080247 #15628903

Subgroups — C2×#13080247 #15628903

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic, complemented
2C2×#10623362C211yesmaximal, characteristic, complemented
3C2×#10623337C211yesmaximal, characteristic, complemented
4#13080247C2116yesmaximal, direct product factor
5C2×#10622768C211yesmaximal, characteristic, complemented
6C2×#10622750C211yesmaximal, characteristic, complemented
7C2×#10622772C211yesmaximal, characteristic, complemented
8C2×#10622779C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic, complemented
20C22×#4341C2211yescharacteristic
21C2×C11×AGL(1,ℤ/8)—28no—
22C2×C11×AGL(1,ℤ/8)C2218yescomplemented
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×D8C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×#67006—21no—
29C22×C22⋊Dic11—21no—
30#10623362—24no—
31#10623362C2218yescomplemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C22×#4326C2211yescharacteristic, complemented
34#10623337—24no—
35#10623337C2218yescomplemented
36C2×#66992—21no—
37C2×#66991—21no—
38C2×#66991C2211yescharacteristic
39C2×#66991C2211yescharacteristic, complemented
40C2×#66989—21no—
41C2×#66989C2211yescharacteristic
42C2×#66989C2211yescharacteristic, complemented
43C2×#66988—21no—
44C2×D4×Dic11C2211yescharacteristic
45C22×#4324C2211yescharacteristic
46C22×#4324C2211yescharacteristic
47C22×#4324C2211yescharacteristic, complemented
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11C2211yescharacteristic
50C2×#66977—21no—
51C2×#66977C2211yescharacteristic
52C2×#66977C2211yescharacteristic
53C2×#66968—28no—
54C2×#66968C2218yescomplemented
55C22×Dic44C2211yescharacteristic, complemented
56C22×#4313C2211yescharacteristic, complemented
57#10622852C2218yescomplemented
58C2×#66899C2211yescharacteristic, complemented
59#10622831C2218yescomplemented
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×#66896C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622783C2218yescomplemented
65#10622779C2218yescomplemented
66SD16×Dic11C2218yescomplemented
67#10622772C2218yescomplemented
68#10622771C2218yescomplemented
69#10622768C2218yescomplemented
70#10622766C2218yescomplemented
71#10622750C2218yescomplemented
72#10622741C2218yescomplemented
73C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
74C2×#66881C2211yescharacteristic, complemented
75C2×#66880C2211yescharacteristic, complemented
76C2×#66880C2211yescharacteristic, complemented
77C2×Dic11⋊C8C2211yescharacteristic, complemented
78C2×C8×Dic11C2211yescharacteristic, complemented
79C25×C11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—24no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—22no—
89C22×D4×C11—42no—
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2314yes—
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11D411yescharacteristic
100C23×Dic11—21no—
101C23×Dic11—21no—
102C2×Q8×D11—22no—
103C2×Q8×D11—24no—
104C2×Q8×D11—42no—
105C2×Q8×D11C2314yescomplemented
106C2×#4341—24no—
107C2×#4341—22no—
108C2×#4341—42no—
109C2×#4341C2314yes—
110C22×C4×D11—21no—
111C22×C4×D11C2311yescharacteristic
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2311yescharacteristic
115C11×AGL(1,ℤ/8)—232no—
116C2×C11×SD16—24no—
117C2×C11×SD16D418yescomplemented
118C2×C11×SD16C2314yes—
119C2×C11×SD16C2314yes—
120C2×C11×D8—24no—
121C2×C11×D8—24no—
122C2×C11×D8C2314yes—
123C2×C11×D8C2314yes—
124C2×C11×M16—24no—
125C2×C11×M16C2314yes—
126C22×C8×C11C2311yescharacteristic
127C22×C8×C11C2311yescharacteristic
128#67006—28no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11—21no—
137C2×C22⋊Dic11—21no—
138C2×C22⋊Dic11—28no—
139C2×C22⋊Dic11D411yescharacteristic
140Q8×Dic11—22no—
141Q8×Dic11C2314yescomplemented
142C2×#4326—24no—
143C2×#4326C2314yescomplemented
144#66992—28no—
145#66991—28no—
146#66991—22no—
147#66991—22no—
148#66991C2314yes—
149#66991C2314yescomplemented
150#66989—28no—
151#66989—22no—
152#66989—22no—
153#66989C2314yes—
154#66989C2314yescomplemented
155#66988—28no—
156D4×Dic11—22no—
157D4×Dic11C2314yes—
158C2×#4324—24no—
159C2×#4324—42no—
160C2×#4324—42no—
161C2×#4324C2314yes—
162C2×#4324C2314yes—
163C2×#4324C2314yescomplemented
164C4×C22⋊D11—28no—
165C4×C22⋊D11D414yes—
166C4×C22⋊D11C2314yes—
167C2×(C2×D11)⋊C4D411yescharacteristic
168C2×C4⋊Dic11—21no—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171#66977—22no—
172#66977—22no—
173#66977—28no—
174#66977C2314yes—
175#66977C2314yes—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—21no—
178C2×Dic11⋊C4D411yescharacteristic
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66968—232no—
184C2×Dic44—24no—
185C2×Dic44C2314yescomplemented
186C2×#4313—24no—
187C2×#4313C2314yescomplemented
188#66899C2314yescomplemented
189#66896C2314yes—
190#66896C2314yes—
191#66896C2314yescomplemented
192C22⋊(C11⋊C8)C2314yes—
193(C2×D11)⋊C8C2314yescomplemented
194#66881C2314yescomplemented
195#66880C2314yescomplemented
196#66880C2314yescomplemented
197Dic11⋊C8C2314yescomplemented
198C8×Dic11C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—24no—
204C24×C11—44no—
205C24×C11—44no—
206C24×C11—82no—
207C24×C11C2×D411yescharacteristic
208C23×D11C2×D411yescharacteristic
209C11×#41—28no—
210C11×#41—44no—
211C11×#41—48no—
212C2×Q8×C11—21no—
213C2×Q8×C11—22no—
214C2×Q8×C11C2×D414yes—
215C2×Q8×C11C2412yes—
216C2×D4×C11—28no—
217C2×D4×C11—24no—
218C2×D4×C11—21no—
219C2×D4×C11—22no—
220C2×D4×C11—22no—
221C2×D4×C11—24no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—44no—
228C2×D4×C11—48no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
231C2×D4×C11C2×D414yes—
232C2×D4×C11C2412yes—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—24no—
239C22×C4×C11—44no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2411yescharacteristic
244C2×C22⋊D11—24no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—24no—
247C2×C22⋊D11—42no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—82no—
251C2×C22⋊D11C2×D414yes—
252C22×Dic11—24no—
253C22×Dic11—24no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—44no—
259C22×Dic11—82no—
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262C22×Dic11C2×D411yescharacteristic
263Q8×D11—28no—
264Q8×D11—44no—
265Q8×D11—48no—
266#4341—28no—
267#4341—44no—
268#4341—48no—
269C2×C4×D11—24no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×C4×D11—44no—
273C2×C4×D11C2×D412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—24no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—21no—
279C2×Dic22—21no—
280C2×Dic22—22no—
281C2×Dic22—22no—
282C2×Dic22—44no—
283C2×Dic22C2412yes—
284C2×Dic22C2412yes—
285C11×SD16—28no—
286C11×SD16C2×D4116yescomplemented
287C11×D8—28no—
288C11×D8—28no—
289C11×M16—28no—
290C2×C8×C11—22no—
291C2×C8×C11C2×D414yes—
292C2×C8×C11C2412yes—
293C2×C8×C11C2412yes—
294C22⋊Dic11—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11—24no—
297C22⋊Dic11—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11—24no—
303C22⋊Dic11C2×D414yes—
304#4326—28no—
305#4324—28no—
306#4324—44no—
307#4324—44no—
308(C2×D11)⋊C4C2×D414yes—
309C4⋊Dic11—24no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313C4⋊Dic11C2412yes—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4C2×D414yes—
317C4×Dic11—24no—
318C4×Dic11C2×D412yes—
319C4×Dic11C2412yes—
320C2×C11⋊C8—22no—
321C2×C11⋊C8—22no—
322C2×C11⋊C8C2412yes—
323C2×C11⋊C8C2412yes—
324Dic44—28no—
325#4313—28no—
326C22×#137—111no—
327C22×AGL(1,ℤ/8)D1111yescharacteristic, complemented
328C2×#548—111no—
329C2×#546—111no—
330#3275—1116no—
331C2×#495—111no—
332C2×#470—111no—
333C2×#469—111no—
334C2×#464—111no—
335C2×#463—111no—
336C2×#452—111no—
337C2×#449—111no—
338C2×#448—111no—
339C2×#450—111no—
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—48no—
350C23×C11—48no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—84no—
360C23×C11—816no—
361C23×C11C22×D412yes—
362C23×C11C22×D411yescharacteristic
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11C22×D412yes—
367Q8×C11—24no—
368Q8×C11—22no—
369Q8×C11C22×D414yes—
370D4×C11—24no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—48no—
377D4×C11—48no—
378D4×C11—42no—
379D4×C11—42no—
380D4×C11C22×D414yes—
381C2×C4×C11—24no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—24no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—48no—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11H(5,𝔽2)12yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—44no—
394C22⋊D11—48no—
395C22⋊D11—48no—
396C22⋊D11—84no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—48no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11—84no—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412C2×Dic11C22×D412yes—
413C4×D11—24no—
414C4×D11—22no—
415C4×D11—22no—
416C4×D11—48no—
417Dic22—22no—
418Dic22—22no—
419Dic22—22no—
420Dic22—22no—
421Dic22—48no—
422Dic22—42no—
423Dic22—42no—
424C8×C11—22no—
425C8×C11C22×D414yes—
426C11⋊C8—22no—
427C11⋊C8—22no—
428C22×#41—111no—
429C22×#41C2×D1111yescharacteristic
430C23×Q8—111no—
431C23×D4C2×D1111yescharacteristic
432C2×#137—118no—
433C2×#137—228no—
434C2×AGL(1,ℤ/8)—28no—
435C2×AGL(1,ℤ/8)C2×D1118yescomplemented
436C22×Q16—111no—
437C22×Q16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16C2×D1111yescharacteristic
442C22×SD16C2×D1111yescharacteristic
443C22×D8C2×D1111yescharacteristic
444C22×D8C2×D1111yescharacteristic
445C22×M16—111no—
446C22×M16C2×D1111yescharacteristic
447#548—118no—
448#548—224no—
449#546—118no—
450#546—224no—
451C2×#124—111no—
452C2×#124—111no—
453C2×#124—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—221no—
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461C2×#121—221no—
462C2×#120—221no—
463C2×C4×Q8—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—221no—
467C22×C22⋊C4—221no—
468#495—118no—
469#470—118no—
470#469—118no—
471#464—118no—
472#463—118no—
473#452—118no—
474#450—118no—
475#449—118no—
476#448—118no—
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×#102—111no—
487C2×C22⋊C8—111no—
488C2×C22⋊C8—111no—
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—24no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—44no—
495C22×C11—48no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—816no—
505C22×C11—84no—
506C22×C11—84no—
507C22×C11D4212yes—
508C22×C11#57512yes—
509C22×C11#57712yes—
510C22×C11C23×D411yescharacteristic
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—44no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11D4212yes—
518C4×C11C23×D411yescharacteristic
519C4×C11C2×H(5,𝔽2)11yescharacteristic
520Dic11—22no—
521Dic11—22no—
522Dic11—22no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527C25—21no—
528C2×#41—22no—
529C2×#41—24no—
530C2×#41—42no—
531C2×#41—114no—
532C2×#41—222no—
533C2×#41—224no—
534C2×#41—442no—
535C2×#41C22×D1114yes—
536C22×Q8—114no—
537C22×Q8—111no—
538C22×Q8—111no—
539C22×Q8—221no—
540C22×Q8—222no—
541C22×Q8—224no—
542C22×Q8—442no—
543C22×Q8C22×D1111yescharacteristic
544C22×D4—24no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—22no—
548C22×D4—42no—
549C22×D4—111no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4C22×D1111yescharacteristic
554C22×D4C22×D1111yescharacteristic
555C22×D4C22×D1114yes—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#137—2232no—
564AGL(1,ℤ/8)—232no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16—224no—
569C2×SD16—24no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—224no—
574C2×SD16—442no—
575C2×SD16—442no—
576C2×SD16C22⋊D1118yescomplemented
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
579C2×D8—24no—
580C2×D8—24no—
581C2×D8C22×D1114yes—
582C2×D8C22×D1114yes—
583C2×M16—24no—
584C2×M16—114no—
585C2×M16—224no—
586C2×M16C22×D1114yes—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#124—114no—
592#124—114no—
593#124—222no—
594#124—222no—
595#124—228no—
596#123—228no—
597C22⋊Q8—114no—
598C22⋊Q8—114no—
599C22⋊Q8—228no—
600C22⋊Q8—222no—
601C22⋊Q8—222no—
602#121—114no—
603#121—114no—
604#121—228no—
605#121—222no—
606#121—222no—
607#121—228no—
608#120—228no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—228no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C42—111no—
635C2×C42—221no—
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103—114no—
641#102—114no—
642#102—114no—
643#102—114no—
644C22⋊C8—114no—
645C22⋊C8—114no—
646C4×C8—114no—
647C2×C11—42no—
648C2×C11—44no—
649C2×C11—82no—
650C2×C11—82no—
651C2×C11#327514yescomplemented
652C2×C11C2×D4211yescharacteristic
653C2×C11C2×#57511yescharacteristic
654C2×C11C2×#57711yescharacteristic
655D11—42no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—24no—
660C24—44no—
661C24—44no—
662C24—82no—
663C24—111no—
664C24D4×D1111yescharacteristic
665#41—28no—
666#41—44no—
667#41—48no—
668#41—228no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—112no—
674C2×Q8—112no—
675C2×Q8—224no—
676C2×Q8—221no—
677C2×Q8—221no—
678C2×Q8—228no—
679C2×Q8—222no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—222no—
683C2×Q8—444no—
684C2×Q8—444no—
685C2×Q8—448no—
686C2×Q8C2×C22⋊D1114yes—
687C2×Q8C23×D1112yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—21no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—44no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—114no—
704C2×D4—224no—
705C2×D4—224no—
706C2×D4—224no—
707C2×D4—442no—
708C2×D4—444no—
709C2×D4—444no—
710C2×D4—882no—
711C2×D4C2×C22⋊D1114yes—
712C2×D4C23×D1112yes—
713C2×D4C23×D1112yes—
714C2×D4C23×D1112yes—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—44no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—224no—
726C22×C4—224no—
727C22×C4—224no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—228no—
743SD16—28no—
744SD16—228no—
745SD16—444no—
746SD16—444no—
747SD16C2×C22⋊D11116yescomplemented
748D8—28no—
749D8—28no—
750M16—28no—
751M16—228no—
752C2×C8—22no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—222no—
756C2×C8—222no—
757C2×C8C2×C22⋊D1114yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—114no—
761C4⋊C4—112no—
762C4⋊C4—112no—
763C4⋊C4—224no—
764C4⋊C4—221no—
765C4⋊C4—221no—
766C4⋊C4—224no—
767C4⋊C4—224no—
768C22⋊C4—114no—
769C22⋊C4—114no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C42—112no—
780C42—112no—
781C42—224no—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—48no—
791C23—48no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—84no—
801C23—816no—
802C23—112no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—222no—
811Q8—222no—
812Q8—222no—
813Q8—222no—
814Q8—448no—
815Q8—442no—
816Q8—442no—
817Q8C22×C22⋊D1114yes—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—22no—
824D4—48no—
825D4—48no—
826D4—42no—
827D4—42no—
828D4—444no—
829D4—448no—
830D4—448no—
831D4—884no—
832D4C22×C22⋊D1114yes—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—48no—
840C2×C4—112no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—224no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—448no—
854C2×C4—448no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4#6703712yes—
863C2×C4C22×C22⋊D1112yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—222no—
867C8—222no—
868C8C22×C22⋊D1114yes—
869C22—22no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—44no—
874C22—48no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—816no—
884C22—84no—
885C22—84no—
886C22—222no—
887C22—222no—
888C22—222no—
889C22—444no—
890C22#1062330412yes—
891C22#1062330612yes—
892C22D4×C22⋊D1112yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—24no—
896C4—222no—
897C4—222no—
898C4—222no—
899C4—442no—
900C4—442no—
901C4—442no—
902C4—442no—
903C4D4×C22⋊D1112yes—
904C4C2×#6703711yescharacteristic
905C4C23×C22⋊D1111yescharacteristic
906C2—42no—
907C2—44no—
908C2—82no—
909C2—82no—
910C2—442no—
911C2#1308024714yesdirect product factor
912C2C2×D4×C22⋊D1111yescharacteristic
913C2C2×#1062330411yescharacteristic
914C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C2×#10623362C2semidirect
3. C2×#10623337C2semidirect
4. #13080247C2direct (N × H)
5. C2×#10622768C2semidirect
6. C2×#10622750C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622771C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622831C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622741C2semidirect
16. C22×C11×AGL(1,ℤ/8)C2semidirect
19. C22×Q8×D11C22semidirect
22. C2×C11×AGL(1,ℤ/8)C22semidirect
31. #10623362C22semidirect
32. C2×Q8×Dic11C22semidirect
33. C22×#4326C22semidirect
35. #10623337C22semidirect
39. C2×#66991C22semidirect
42. C2×#66989C22semidirect
47. C22×#4324C22semidirect
54. C2×#66968C22semidirect
55. C22×Dic44C22semidirect
56. C22×#4313C22semidirect
57. #10622852C22semidirect
58. C2×#66899C22semidirect
59. #10622831C22semidirect
62. C2×#66896C22semidirect
64. #10622783C22semidirect
65. #10622779C22semidirect
66. SD16×Dic11C22semidirect
67. #10622772C22semidirect
68. #10622771C22semidirect
69. #10622768C22semidirect
70. #10622766C22semidirect
71. #10622750C22semidirect
72. #10622741C22semidirect
73. C2×(C2×D11)⋊C8C22semidirect
74. C2×#66881C22semidirect
75. C2×#66880C22semidirect
76. C2×#66880C22semidirect
77. C2×Dic11⋊C8C22semidirect
78. C2×C8×Dic11C22semidirect
105. C2×Q8×D11C23semidirect
117. C2×C11×SD16D4semidirect
141. Q8×Dic11C23semidirect
143. C2×#4326C23semidirect
149. #66991C23semidirect
154. #66989C23semidirect
163. C2×#4324C23semidirect
185. C2×Dic44C23semidirect
187. C2×#4313C23semidirect
188. #66899C23semidirect
191. #66896C23semidirect
193. (C2×D11)⋊C8C23semidirect
194. #66881C23semidirect
195. #66880C23semidirect
196. #66880C23semidirect
197. Dic11⋊C8C23semidirect
198. C8×Dic11C23semidirect
286. C11×SD16C2×D4semidirect
327. C22×AGL(1,ℤ/8)D11semidirect
435. C2×AGL(1,ℤ/8)C2×D11semidirect
576. C2×SD16C22⋊D11semidirect
651. C2×C11#3275semidirect
747. SD16C2×C22⋊D11semidirect
782. C11C2×#3275semidirect
911. C2#13080247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C2×#106233622
C2×#106233372
#130802472
C2×#106227682
C2×#106227502
C2×#106227722
C2×#106227792
C2×#106227662
C2×#106228522
C2×#106227712
C2×#106227832
C2×#106228312
C2×SD16×Dic112
C2×#106227412
C22×C11×AGL(1,ℤ/8)2
C2×#327511