Finite Group Databasebeta

← C2×#13079710 #15625128

Subgroups — C2×#13079710 #15625128

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13079710C2116yesmaximal, direct product factor
3C2×#10622687C211yesmaximal, characteristic, complemented
4C2×#10622672C211yesmaximal, characteristic, complemented
5C2×#10622668C211yesmaximal, characteristic, complemented
6C2×#10622683C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622688C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622685C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14C2×#10622830C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#535C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C11×#535—24no—
20C11×#535C2218yescomplemented
21C2×C11×#127C2211yescharacteristic
22C2×C11×#127C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121—21no—
27C2×C11×#120—21no—
28C2×C11×#120—21no—
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic, complemented
31C22×#4325C2211yescharacteristic, complemented
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4324C2211yescharacteristic, complemented
35C22×#4323C2211yescharacteristic
36C22×#4323C2211yescharacteristic
37C22×#4323C2211yescharacteristic, complemented
38C2×#66983C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40#10623065—24no—
41#10623065C2218yescomplemented
42C2×#66951—21no—
43C2×#66949—21no—
44C2×#66938—21no—
45C2×#66936—21no—
46C2×#66928C2211yescharacteristic, complemented
47C2×C4×D44C2211yescharacteristic, complemented
48C2×#66922C2211yescharacteristic, complemented
49C2×C4×Dic22C2211yescharacteristic, complemented
50#10622852C2218yescomplemented
51#10622851C2218yescomplemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54#10622831C2218yescomplemented
55#10622830C2218yescomplemented
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×#66896C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622688C2218yescomplemented
65#10622687C2218yescomplemented
66#10622685C2218yescomplemented
67#10622683C2218yescomplemented
68#10622672C2218yescomplemented
69#10622670C2218yescomplemented
70#10622668C2218yescomplemented
71#10622667C2218yescomplemented
72#10622613C2218yescomplemented
73C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
74C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
75C2×#66867C2211yescharacteristic, complemented
76C2×C4×C11⋊C8C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11—22no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—42no—
91C22×D4×C11—42no—
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2314yes—
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×Dic22—21no—
102C22×Dic22C2311yescharacteristic
103C11×#127—22no—
104C11×#127—22no—
105C11×#127C2314yes—
106C11×#127C2314yes—
107C11×#124—22no—
108C11×#124—22no—
109C11×#124C2314yes—
110C11×#124C2314yes—
111C11×#121—28no—
112C11×#121—28no—
113C11×#120—28no—
114C11×#120—28no—
115C11×#117D414yes—
116C11×#117C2314yes—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×#4326—42no—
129C2×#4326C2314yescomplemented
130C2×#4325—42no—
131C2×#4325C2314yescomplemented
132C2×#4324—42no—
133C2×#4324—42no—
134C2×#4324—42no—
135C2×#4324C2314yes—
136C2×#4324C2314yes—
137C2×#4324C2314yescomplemented
138C2×#4323—42no—
139C2×#4323—42no—
140C2×#4323—42no—
141C2×#4323C2314yes—
142C2×#4323C2314yes—
143C2×#4323C2314yescomplemented
144#66983—22no—
145#66983C2314yes—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153#66977—22no—
154#66977C2314yes—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66951—28no—
163#66949—28no—
164#66938—28no—
165#66936—28no—
166#66928—22no—
167#66928C2314yescomplemented
168C4×D44—22no—
169C4×D44C2314yescomplemented
170#66922—22no—
171#66922C2314yescomplemented
172C4×Dic22—22no—
173C4×Dic22C2314yescomplemented
174#66899C2314yescomplemented
175#66899C2314yescomplemented
176#66896C2314yes—
177#66896C2314yes—
178#66896C2314yes—
179#66896C2314yes—
180#66896C2314yescomplemented
181#66896C2314yescomplemented
182C22⋊(C11⋊C8)C2314yes—
183C22⋊(C11⋊C8)C2314yes—
184C4⋊(C11⋊C8)C2314yescomplemented
185C4⋊(C11⋊C8)C2314yescomplemented
186#66867C2314yescomplemented
187C4×C11⋊C8C2314yescomplemented
188C2×#3224—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—24no—
193C24×C11—44no—
194C24×C11—82no—
195C24×C11—82no—
196C24×C11C2×D411yescharacteristic
197C23×D11—21no—
198C11×#41—44no—
199C11×#41—44no—
200C11×#41—48no—
201C2×Q8×C11—21no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11C2412yes—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—24no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—48no—
224C2×D4×C11—44no—
225C2×D4×C11—82no—
226C2×D4×C11—82no—
227C2×D4×C11—82no—
228C2×D4×C11—82no—
229C2×D4×C11C2412yes—
230C2×D4×C11C2412yes—
231C2×D4×C11C2412yes—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—21no—
235C22×C4×C11—24no—
236C22×C4×C11—44no—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—82no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C2×D44—21no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44C2412yes—
254C2×C4×D11—24no—
255C2×C4×D11—82no—
256C2×Dic22—21no—
257C2×Dic22—24no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—82no—
261C2×Dic22C2412yes—
262C11×C4⋊C4C2×D414yes—
263C11×C4⋊C4C2×D414yes—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4C2×D414yes—
269C11×C22⋊C4C2×D414yes—
270C42×C11C2×D412yes—
271C42×C11C2×D412yes—
272C42×C11C2412yes—
273C42×C11C2412yes—
274C22⋊Dic11—24no—
275#4326—44no—
276#4325—44no—
277#4324—44no—
278#4324—44no—
279#4324—44no—
280#4323—44no—
281#4323—44no—
282#4323—44no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—24no—
290C4⋊Dic11C2412yes—
291C4⋊Dic11C2412yes—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294C4×Dic11—24no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303C2×#542—111no—
304C2×#535D1111yescharacteristic, complemented
305#3224—1116no—
306C2×#496—111no—
307C2×#495—111no—
308C2×#489—111no—
309C2×#486—111no—
310C2×#464—111no—
311C2×#460—111no—
312C2×#463—111no—
313C2×#459—111no—
314C2×#452—111no—
315C2×#449—111no—
316C2×#450—111no—
317C2×#447—111no—
318C2×#433—111no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—48no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—84no—
336C23×C11—84no—
337C23×C11—816no—
338C23×C11C22×D412yes—
339C23×C11C22×D411yescharacteristic
340C22×D11—22no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—42no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—48no—
354D4×C11—48no—
355D4×C11—42no—
356D4×C11—42no—
357D4×C11—42no—
358D4×C11—84no—
359D4×C11—84no—
360D4×C11—84no—
361D4×C11—84no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—24no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—48no—
372C2×C4×C11—42no—
373C2×C4×C11C22×D412yes—
374C2×C4×C11C22×D412yes—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11H(5,𝔽2)12yes—
380C2×C4×C11H(5,𝔽2)12yes—
381C2×C4×C11C2511yescharacteristic
382C22⋊D11—84no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389D44—22no—
390D44—22no—
391D44—42no—
392C4×D11—84no—
393Dic22—22no—
394Dic22—22no—
395Dic22—42no—
396Dic22—84no—
397C11⋊C8—22no—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41C2×D1111yescharacteristic
402C23×D4C2×D1111yescharacteristic
403C22×Q16—111no—
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16—111no—
407C22×SD16—111no—
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411#542—118no—
412#542—224no—
413#535—24no—
414#535C2×D1118yescomplemented
415C2×C4⋊Q8—111no—
416C2×#127C2×D1111yescharacteristic
417C2×#127C2×D1111yescharacteristic
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—221no—
421C2×#124C2×D1111yescharacteristic
422C2×#124C2×D1111yescharacteristic
423C2×#123—221no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—221no—
426C2×#121—21no—
427C2×#121—21no—
428C2×#121—111no—
429C2×#120—21no—
430C2×#120—21no—
431C2×C4×Q8—111no—
432C2×C4×D4—111no—
433C2×#117C2×D1111yescharacteristic
434#496—118no—
435#495—118no—
436#489—118no—
437#486—118no—
438#464—118no—
439#463—118no—
440#460—118no—
441#459—118no—
442#452—118no—
443#450—118no—
444#449—118no—
445#447—118no—
446#433—118no—
447C2×C4⋊C8—111no—
448C2×C4⋊C8—111no—
449C2×#103—111no—
450C2×#103—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×#97—111no—
460C2×C4×C8—111no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—44no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—816no—
475C22×C11—84no—
476C22×C11—84no—
477C22×C11—84no—
478C22×C11#53512yes—
479C22×C11#57612yes—
480C22×C11#57712yes—
481C22×C11C23×D411yescharacteristic
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—84no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—22no—
489C4×C11—22no—
490C4×C11—22no—
491C4×C11—42no—
492C4×C11#53512yes—
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494C4×C11C2×H(5,𝔽2)11yescharacteristic
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498C25—21no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41C22×D1114yes—
503C22×Q8—111no—
504C22×Q8—221no—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4—111no—
516C22×D4—221no—
517C22×D4C22×D1111yescharacteristic
518C22×D4C22×D1111yescharacteristic
519C22×D4C22×D1111yescharacteristic
520C22×D4C22×D1114yes—
521C23×C4—21no—
522C23×C4—221no—
523C23×C4C22×D1111yescharacteristic
524C2×Q16—114no—
525C2×Q16—442no—
526C2×SD16—114no—
527C2×SD16—114no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×SD16—442no—
533C2×SD16—442no—
534C2×D8—114no—
535C2×D8—114no—
536C2×D8—114no—
537C2×D8—442no—
538C2×D8—442no—
539C2×D8—442no—
540C22×C8—111no—
541C22×C8—111no—
542C22×C8—111no—
543C22×C8—111no—
544C4⋊Q8—114no—
545C4⋊Q8—222no—
546#127—22no—
547#127—22no—
548#127C22×D1114yes—
549#127C22×D1114yes—
550#126—228no—
551#124—22no—
552#124—22no—
553#124—114no—
554#124—228no—
555#124—222no—
556#124C22×D1114yes—
557#124C22×D1114yes—
558#123—228no—
559C22⋊Q8—114no—
560C22⋊Q8—222no—
561C22⋊Q8—228no—
562#121—28no—
563#121—28no—
564#121—114no—
565#121—222no—
566#120—28no—
567#120—28no—
568C4×Q8—114no—
569C4×Q8—222no—
570C4×D4—114no—
571C4×D4—222no—
572#117C22⋊D1114yes—
573#117C22×D1114yes—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—221no—
577C2×C4⋊C4—221no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4C22⋊D1111yescharacteristic
580C2×C4⋊C4C22⋊D1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4C22⋊D1111yescharacteristic
591C2×C22⋊C4C22⋊D1111yescharacteristic
592C2×C42—221no—
593C2×C42C22×D1111yescharacteristic
594C2×C42C22×D1111yescharacteristic
595C4⋊C8—114no—
596C4⋊C8—114no—
597#103—114no—
598#103—114no—
599#102—114no—
600#102—114no—
601#102—114no—
602#102—114no—
603#102—114no—
604#102—114no—
605C22⋊C8—114no—
606C22⋊C8—114no—
607#97—114no—
608C4×C8—114no—
609C2×C11—42no—
610C2×C11—82no—
611C2×C11—82no—
612C2×C11—82no—
613C2×C11#322414yescomplemented
614C2×C11C2×#53511yescharacteristic
615C2×C11C2×#57611yescharacteristic
616C2×C11C2×#57711yescharacteristic
617D11—82no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—24no—
622C24—44no—
623C24—82no—
624C24—82no—
625C24—221no—
626C24C2×C22⋊D1111yescharacteristic
627#41—44no—
628#41—44no—
629#41—48no—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—112no—
634C2×Q8—221no—
635C2×Q8—224no—
636C2×Q8—222no—
637C2×Q8—222no—
638C2×Q8—882no—
639C2×Q8C23×D1112yes—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C2×D4—44no—
660C2×D4—82no—
661C2×D4—82no—
662C2×D4—82no—
663C2×D4—82no—
664C2×D4—112no—
665C2×D4—224no—
666C2×D4—222no—
667C2×D4—222no—
668C2×D4—221no—
669C2×D4—882no—
670C2×D4C23×D1112yes—
671C2×D4C23×D1112yes—
672C2×D4C23×D1112yes—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—44no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—224no—
682C22×C4—882no—
683C22×C4C2×C22⋊D1112yes—
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C2×C22⋊D1111yescharacteristic
688C22×C4C2×C22⋊D1111yescharacteristic
689C22×C4C23×D1112yes—
690C22×C4C23×D1111yescharacteristic
691Q16—444no—
692SD16—444no—
693SD16—444no—
694SD16—444no—
695SD16—444no—
696D8—444no—
697D8—444no—
698D8—444no—
699C2×C8—112no—
700C2×C8—112no—
701C2×C8—112no—
702C2×C8—112no—
703C2×C8—222no—
704C2×C8—222no—
705C2×C8—222no—
706C2×C8—222no—
707C4⋊C4—112no—
708C4⋊C4—112no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4C2×C22⋊D1114yes—
715C4⋊C4C2×C22⋊D1114yes—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—224no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4C2×C22⋊D1114yes—
726C22⋊C4C2×C22⋊D1114yes—
727C42—224no—
728C42C2×C22⋊D1112yes—
729C42C2×C22⋊D1112yes—
730C42C23×D1112yes—
731C42C23×D1112yes—
732C11C2×#322411yescharacteristic, complemented, Sylow
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—48no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—84no—
750C23—84no—
751C23—816no—
752C23—222no—
753C23—442no—
754C23—442no—
755C23—442no—
756C23C22×C22⋊D1112yes—
757C23C22×C22⋊D1111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—222no—
762Q8—222no—
763Q8—442no—
764Q8—884no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—84no—
777D4—84no—
778D4—84no—
779D4—84no—
780D4—222no—
781D4—222no—
782D4—442no—
783D4—884no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4—442no—
801C2×C4—884no—
802C2×C4#6703712yes—
803C2×C4#6703712yes—
804C2×C4C22×C22⋊D1112yes—
805C2×C4C22×C22⋊D1112yes—
806C2×C4C22×C22⋊D1112yes—
807C2×C4C22×C22⋊D1112yes—
808C2×C4C22×C22⋊D1112yes—
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C24×D1111yescharacteristic
811C8—222no—
812C8—222no—
813C8—222no—
814C8—222no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—816no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—884no—
836C22#1062333612yes—
837C22#1062336612yes—
838C22#1062336712yes—
839C22C23×C22⋊D1111yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—442no—
847C4—442no—
848C4—442no—
849C4#1062333612yes—
850C4C2×#6703711yescharacteristic
851C4C2×#6703711yescharacteristic
852C2—42no—
853C2—82no—
854C2—82no—
855C2—82no—
856C2—882no—
857C2#1307971014yesdirect product factor
858C2C2×#1062333611yescharacteristic
859C2C2×#1062336611yescharacteristic
860C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11C2×#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13079710C2direct (N × H)
3. C2×#10622687C2semidirect
4. C2×#10622672C2semidirect
5. C2×#10622668C2semidirect
6. C2×#10622683C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622688C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622685C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622831C2semidirect
14. C2×#10622830C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#535C2semidirect
20. C11×#535C22semidirect
30. C22×#4326C22semidirect
31. C22×#4325C22semidirect
34. C22×#4324C22semidirect
37. C22×#4323C22semidirect
41. #10623065C22semidirect
46. C2×#66928C22semidirect
47. C2×C4×D44C22semidirect
48. C2×#66922C22semidirect
49. C2×C4×Dic22C22semidirect
50. #10622852C22semidirect
51. #10622851C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
54. #10622831C22semidirect
55. #10622830C22semidirect
60. C2×#66896C22semidirect
61. C2×#66896C22semidirect
64. #10622688C22semidirect
65. #10622687C22semidirect
66. #10622685C22semidirect
67. #10622683C22semidirect
68. #10622672C22semidirect
69. #10622670C22semidirect
70. #10622668C22semidirect
71. #10622667C22semidirect
72. #10622613C22semidirect
73. C2×C4⋊(C11⋊C8)C22semidirect
74. C2×C4⋊(C11⋊C8)C22semidirect
75. C2×#66867C22semidirect
76. C2×C4×C11⋊C8C22semidirect
129. C2×#4326C23semidirect
131. C2×#4325C23semidirect
137. C2×#4324C23semidirect
143. C2×#4323C23semidirect
167. #66928C23semidirect
169. C4×D44C23semidirect
171. #66922C23semidirect
173. C4×Dic22C23semidirect
174. #66899C23semidirect
175. #66899C23semidirect
180. #66896C23semidirect
181. #66896C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
185. C4⋊(C11⋊C8)C23semidirect
186. #66867C23semidirect
187. C4×C11⋊C8C23semidirect
304. C2×#535D11semidirect
414. #535C2×D11semidirect
613. C2×C11#3224semidirect
732. C11C2×#3224semidirect
857. C2#13079710direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130797102
C2×#106226872
C2×#106226722
C2×#106226682
C2×#106226832
C2×#106226672
C2×#106226882
C2×#106226702
C2×#106226852
C2×#106228522
C2×#106228512
C2×#106228312
C2×#106228302
C2×#106226132
C2×C11×#5352
C2×#322411