Finite Group Databasebeta

← C2×#13081011 #15632238

Subgroups — C2×#13081011 #15632238

Order 2816.

1994 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623145C211yesmaximal, characteristic, complemented
2C2×#10623061C211yesmaximal, characteristic, complemented
3#13081011C2116yesmaximal, direct product factor
4C2×#10622471C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622350C211yesmaximal, characteristic, complemented
8C2×#10622504C211yesmaximal, characteristic, complemented
9C2×#10622379C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622651C211yesmaximal, characteristic, complemented
12C2×#10622369C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
14C2×#10622611C211yesmaximal, characteristic, complemented
15C2×D11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C2×C11×#121C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66991—21no—
20C2×#66991C2211yescharacteristic
21C2×#66988—21no—
22C2×D4×Dic11C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623145—24no—
30#10623145C2218yescomplemented
31#10623061—24no—
32#10623061C2218yescomplemented
33C2×#66948C2211yescharacteristic
34C2×#66946C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66937—21no—
40C2×#66936—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66932—21no—
43C2×#66929—21no—
44C2×C4×D44—21no—
45C11×#482C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622651C2218yescomplemented
60#10622611C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622504C2218yescomplemented
68D11×#107C2218yescomplemented
69#10622476C2218yescomplemented
70#10622471C2218yescomplemented
71#10622390C2218yescomplemented
72#10622388C2218yescomplemented
73#10622379C2218yescomplemented
74#10622369C2218yescomplemented
75#10622350C2218yescomplemented
76(C22⋊D11)⋊C8C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C23×Dic11—21no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#121—22no—
93C11×#121C2314yes—
94C11×#117—22no—
95C11×#117C2314yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11D411yescharacteristic
106#66991—28no—
107#66991—22no—
108#66991C2314yes—
109#66988—28no—
110D4×Dic11—22no—
111D4×Dic11C2314yes—
112C2×#4323—24no—
113C2×#4323C2314yes—
114#66983—22no—
115#66983C2314yes—
116C4×C22⋊D11D414yes—
117C4×C22⋊D11C2314yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122#66979—22no—
123#66979C2314yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4D411yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8—24no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2314yes—
139C22×C11⋊C8C2311yescharacteristic
140C2×C8×D11—24no—
141C2×C8×D11C2314yes—
142#66948—22no—
143#66948C2314yes—
144#66946—22no—
145#66946C2314yes—
146C4⋊C4×D11—22no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11C2314yes—
149C4⋊C4×D11C2314yes—
150#66943—22no—
151#66943—22no—
152#66943C2314yes—
153#66943C2314yes—
154#66937—28no—
155#66936—28no—
156(C22⋊D11)⋊C4—28no—
157#66932—28no—
158#66929—28no—
159C4×D44—28no—
160C11×#107C2314yes—
161C11×#106C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164C11×C22⋊C8C2314yes—
165#66896C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66882C2314yes—
170#66881C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3339—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C23×D11C2×D411yescharacteristic
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—82no—
189C2×D4×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—82no—
204C2×C22⋊D11C2×D414yes—
205C22×Dic11—24no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—82no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C2×D44—24no—
214C2×D44—21no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—44no—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—82no—
225C2×C4×D11—82no—
226C2×C4×D11—82no—
227C2×C4×D11C2×D412yes—
228C2×C4×D11C2412yes—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C42×C11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11C2×D414yes—
246#4323—28no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4C2×D414yes—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4C2×D414yes—
264C4×Dic11—24no—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C2×C11⋊C8—28no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8#4114yes—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C8×D11—28no—
273C2×#553—111no—
274C2×#553—111no—
275#3339—1116no—
276C2×#499—111no—
277C2×#481—111no—
278C2×#481—111no—
279C2×#482—111no—
280C2×#482D1111yescharacteristic, complemented
281C2×#478—111no—
282C2×#478—111no—
283C2×#466—111no—
284C2×#466—111no—
285C2×C4×D8—111no—
286C2×C8×D4—111no—
287C2×#427—111no—
288C22×#107—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11C22×D412yes—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11#13514yes—
305C22×D11C22×D412yes—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—42no—
309D4×C11—84no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4112yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—28no—
326C22⋊D11—48no—
327C22⋊D11—84no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—84no—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341D44—22no—
342D44—22no—
343D44—48no—
344D44—42no—
345C4×D11—24no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—84no—
349C4×D11—84no—
350C4×D11—84no—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8C2×#4114yes—
355C22×D8—111no—
356C23×C8—111no—
357C23×C8—111no—
358#553—118no—
359#553—118no—
360#553—224no—
361#553—224no—
362C2×#126—221no—
363C2×#126—221no—
364C2×#125—111no—
365C2×#125—111no—
366C2×#123—221no—
367C2×#123—221no—
368C2×#121—111no—
369C2×#121—111no—
370C2×#121—111no—
371C2×#121—221no—
372C2×#121—221no—
373C2×#121C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—221no—
378C2×C4×D4—221no—
379C2×#117—111no—
380C2×#117C2×D1111yescharacteristic
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383#499—118no—
384#482—118no—
385#482C2×D1118yescomplemented
386#481—118no—
387#481—118no—
388#478—118no—
389#478—118no—
390#466—118no—
391#466—118no—
392C4×D8—118no—
393C8×D4—118no—
394#427—118no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#107—118no—
400C2×#107C2×D1111yescharacteristic
401C2×#106—111no—
402C2×#106—111no—
403C2×#106—111no—
404C2×#106C2×D1111yescharacteristic
405C2×C4⋊C8—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102C2×D1111yescharacteristic
411C2×#102C2×D1111yescharacteristic
412C2×C22⋊C8—111no—
413C2×C22⋊C8C2×D1111yescharacteristic
414C2×C4×C8—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—44no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—84no—
423C22×C11#54712yes—
424C22×C11C2×#13512yes—
425C22×C11#57612yes—
426C22×C11C23×D411yescharacteristic
427C2×D11—28no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C2×D11C2×#13514yes—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11#54712yes—
440C4×C11C22×#4111yescharacteristic
441C4×C11C2×2−1+411yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×D4—21no—
449C22×D4—111no—
450C22×D4—111no—
451C22×D4—221no—
452C22×D4—221no—
453C22×D4—221no—
454C22×D4C22×D1111yescharacteristic
455C23×C4—111no—
456C23×C4—221no—
457C23×C4—221no—
458C23×C4—221no—
459C23×C4—221no—
460C23×C4C22×D1111yescharacteristic
461C2×D8—114no—
462C2×D8—224no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—114no—
466C22×C8—114no—
467C22×C8—224no—
468C22×C8—224no—
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471#126—228no—
472#126—228no—
473#125—114no—
474#125—114no—
475#125—222no—
476#125—222no—
477#123—228no—
478#123—228no—
479#121—22no—
480#121—114no—
481#121—114no—
482#121—114no—
483#121—228no—
484#121—222no—
485#121—222no—
486#121—228no—
487#121—222no—
488#121C22×D1114yes—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—114no—
492C4×D4—114no—
493C4×D4—228no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—228no—
497#117—22no—
498#117—114no—
499#117—222no—
500#117C22×D1114yes—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C42—21no—
529C2×C42—111no—
530C2×C42—221no—
531#107—114no—
532#107—114no—
533#107—114no—
534#107—114no—
535#107C22×D1114yes—
536#106—114no—
537#106—114no—
538#106—114no—
539#106C22×D1114yes—
540C4⋊C8—114no—
541#102—114no—
542#102—114no—
543#102—114no—
544#102—114no—
545#102C22×D1114yes—
546#102C22×D1114yes—
547C22⋊C8—114no—
548C22⋊C8C22×D1114yes—
549C4×C8—114no—
550C2×C11—42no—
551C2×C11—82no—
552C2×C11#333914yescomplemented
553C2×C11C2×#54711yescharacteristic
554C2×C11C22×#13511yescharacteristic
555C2×C11C2×#57611yescharacteristic
556D11—24no—
557D11—82no—
558C24—21no—
559C24—111no—
560C24—221no—
561C24D4×D1111yescharacteristic
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—114no—
568C2×D4—112no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—224no—
572C2×D4—224no—
573C2×D4—221no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—444no—
577C2×D4—444no—
578C2×D4—882no—
579C2×D4C23×D1112yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—882no—
600C22×C4—882no—
601C22×C4—882no—
602C22×C4—882no—
603C22×C4D4×D1112yes—
604C22×C4D4×D1111yescharacteristic
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607D8—228no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—114no—
611C2×C8—112no—
612C2×C8—112no—
613C2×C8—228no—
614C2×C8—228no—
615C2×C8—222no—
616C2×C8C23×D1112yes—
617C2×C8C23×D1112yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—114no—
622C4⋊C4—112no—
623C4⋊C4—112no—
624C4⋊C4—112no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4C23×D1112yes—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—114no—
640C22⋊C4—114no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C42—24no—
648C42—112no—
649C42—112no—
650C42—224no—
651C11C2×#333911yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—114no—
660C23—112no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23C2×D4×D1112yes—
668C23C2×D4×D1111yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673D4—228no—
674D4—222no—
675D4—222no—
676D4—448no—
677D4—448no—
678D4—442no—
679D4—884no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—112no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—884no—
706C2×C4—884no—
707C2×C4—884no—
708C2×C4—884no—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4#41×D1112yes—
712C2×C4#6704312yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—22no—
716C8—114no—
717C8—222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—114no—
727C22—228no—
728C22—222no—
729C22—222no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—884no—
734C22#1062318612yes—
735C22D11×#13512yes—
736C22#1062330512yes—
737C22C22×D4×D1111yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—222no—
743C4—222no—
744C4—222no—
745C4—442no—
746C4—442no—
747C4—442no—
748C4#1062318612yes—
749C4C2×#41×D1111yescharacteristic
750C4C2×#6704311yescharacteristic
751C2—42no—
752C2—82no—
753C2—224no—
754C2—882no—
755C2#1308101114yesdirect product factor
756C2C2×#1062318611yescharacteristic
757C2C2×D11×#13511yescharacteristic
758C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
hypercenterC2×#482D11
hypocenterC11C2×#3339
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623145C2semidirect
2. C2×#10623061C2semidirect
3. #13081011C2direct (N × H)
4. C2×#10622471C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622350C2semidirect
8. C2×#10622504C2semidirect
9. C2×#10622379C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622651C2semidirect
12. C2×#10622369C2semidirect
13. C2×(C22⋊D11)⋊C8C2semidirect
14. C2×#10622611C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#482C2semidirect
30. #10623145C22semidirect
32. #10623061C22semidirect
45. C11×#482C22semidirect
59. #10622651C22semidirect
60. #10622611C22semidirect
67. #10622504C22semidirect
68. D11×#107C22semidirect
69. #10622476C22semidirect
70. #10622471C22semidirect
71. #10622390C22semidirect
72. #10622388C22semidirect
73. #10622379C22semidirect
74. #10622369C22semidirect
75. #10622350C22semidirect
76. (C22⋊D11)⋊C8C22semidirect
280. C2×#482D11semidirect
385. #482C2×D11semidirect
552. C2×C11#3339semidirect
651. C11C2×#3339semidirect
755. C2#13081011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231452
C2×#106230612
#130810112
C2×#106224712
C2×#106224762
C2×#106223902
C2×#106223502
C2×#106225042
C2×#106223792
C2×#106223882
C2×#106226512
C2×#106223692
C2×(C22⋊D11)⋊C82
C2×#106226112
C2×D11×#1072
C2×C11×#4822
C2×#333911