Finite Group Databasebeta

← C2×#13079703 #15625121

Subgroups — C2×#13079703 #15625121

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×#10623213C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic, complemented
3#13079703C2116yesmaximal, direct product factor
4C2×#10622671C211yesmaximal, characteristic, complemented
5C2×#10622668C211yesmaximal, characteristic, complemented
6C2×#10622307C211yesmaximal, characteristic, complemented
7C2×#10622798C211yesmaximal, characteristic, complemented
8C2×#10622776C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622800C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622303C211yesmaximal, characteristic, complemented
16C2×C11×#495C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×D8C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic, complemented
25C2×#67000C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic
29C22×#4325C2211yescharacteristic, complemented
30C2×#66993C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic, complemented
33C22×#4323C2211yescharacteristic
34C22×#4323C2211yescharacteristic, complemented
35#10623213—24no—
36#10623213C2218yescomplemented
37#10623205—24no—
38#10623205C2218yescomplemented
39C2×#66939—21no—
40C2×#66938—21no—
41C2×#66937—21no—
42C2×#66937—21no—
43C2×#66935—21no—
44C2×#66935—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66927C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×#66922C2211yescharacteristic, complemented
50C11×#495C2218yescomplemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622800C2218yescomplemented
57#10622798C2218yescomplemented
58#10622785C2218yescomplemented
59#10622782C2218yescomplemented
60#10622778C2218yescomplemented
61#10622776C2218yescomplemented
62#10622769C2218yescomplemented
63#10622763C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic, complemented
67C2×#66885C2211yescharacteristic, complemented
68C2×(C2×D11)⋊C8C2211yescharacteristic
69C2×(C2×D11)⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic, complemented
71C2×Dic11⋊C8C2211yescharacteristic, complemented
72#10622671C2218yescomplemented
73#10622668C2218yescomplemented
74C2×#66867C2211yescharacteristic, complemented
75#10622307C2218yescomplemented
76#10622303C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C2×#4343—22no—
88C2×#4343—42no—
89C2×#4343—42no—
90C2×#4343C2314yes—
91C2×D4×D11—22no—
92C2×D4×D11—42no—
93C2×D4×D11—42no—
94C2×D4×D11C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44—21no—
98C22×D44C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22—21no—
103C2×C11×Q16—42no—
104C2×C11×Q16C2314yescomplemented
105C2×C11×SD16—42no—
106C2×C11×SD16—42no—
107C2×C11×SD16C2314yes—
108C2×C11×SD16C2314yescomplemented
109C2×C11×D8—42no—
110C2×C11×D8C2314yes—
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×#124—22no—
114C11×#124—22no—
115C11×#124C2314yes—
116C11×#124C2314yescomplemented
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124#67000—22no—
125#67000C2314yes—
126#66999—22no—
127#66999C2314yes—
128Q8×Dic11—22no—
129Q8×Dic11C2314yescomplemented
130C2×#4325—42no—
131C2×#4325—42no—
132C2×#4325C2314yes—
133C2×#4325C2314yescomplemented
134#66993—22no—
135#66993C2314yes—
136#66991—22no—
137#66991C2314yes—
138D4×Dic11—22no—
139D4×Dic11C2314yescomplemented
140C2×#4323—42no—
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×#4323C2314yescomplemented
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4D411yescharacteristic
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×C4⋊Dic11—21no—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4D411yescharacteristic
155C2×Dic11⋊C4D411yescharacteristic
156C2×C4×Dic11—21no—
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160#66939—28no—
161#66938—28no—
162#66937—28no—
163#66937—28no—
164#66935—28no—
165#66935—28no—
166#66932—28no—
167#66931—28no—
168#66927—22no—
169#66927C2314yes—
170#66925D414yes—
171#66925C2314yes—
172#66922—22no—
173#66922C2314yescomplemented
174C4×C8×C11C2314yescomplemented
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yes—
178#66896C2314yes—
179#66885C2314yes—
180#66885C2314yes—
181#66885C2314yescomplemented
182#66885C2314yescomplemented
183(C2×D11)⋊C8C2314yes—
184(C2×D11)⋊C8C2314yes—
185Dic11⋊C8C2314yescomplemented
186Dic11⋊C8C2314yescomplemented
187#66867C2314yescomplemented
188C2×#3224—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C2×Q8×C11—21no—
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11C2412yes—
205C2×Q8×C11C2412yes—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11C2412yes—
213C2×D4×C11C2412yes—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—82no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C22×Dic11—24no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—82no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—44no—
235#4343—44no—
236#4343—48no—
237D4×D11—44no—
238D4×D11—44no—
239D4×D11—48no—
240C2×D44—24no—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—24no—
244C2×D44—24no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—44no—
250C2×D44—82no—
251C2×D44—82no—
252C2×D44C2412yes—
253C2×D44C2412yes—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—44no—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2412yes—
260C2×Dic22—24no—
261C2×Dic22—82no—
262C11×Q16—44no—
263C11×SD16—44no—
264C11×SD16—44no—
265C11×D8—44no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11C2412yes—
269C2×C8×C11C2412yes—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C42×C11C2×D412yes—
275C42×C11C2412yes—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278#4325—44no—
279#4325—44no—
280#4323—44no—
281#4323—44no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4C2×D414yes—
286(C2×D11)⋊C4C2×D414yes—
287C4⋊Dic11—24no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—24no—
291C4⋊Dic11C2412yes—
292C4⋊Dic11C2412yes—
293Dic11⋊C4—24no—
294Dic11⋊C4C2×D414yes—
295Dic11⋊C4C2×D414yes—
296C4×Dic11—24no—
297C4×Dic11C2×D412yes—
298C4×Dic11C2412yes—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303C2×#542—111no—
304C2×#535—111no—
305#3224—1116no—
306C2×#496—111no—
307C2×#495D1111yescharacteristic, complemented
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—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—48no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—84no—
341C22×D11—84no—
342C22×D11—816no—
343C22×D11C22×D412yes—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349Q8×C11—42no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—42no—
355D4×C11—42no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11H(5,𝔽2)12yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C22⋊D11—48no—
369C22⋊D11—84no—
370C22⋊D11—84no—
371C22⋊D11—84no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—84no—
380C2×Dic11C22×D412yes—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—48no—
388D44—42no—
389D44—42no—
390D44—84no—
391D44—84no—
392C4×D11—24no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—48no—
396Dic22—84no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41—111no—
402C23×D4—111no—
403C22×Q16C2×D1111yescharacteristic, complemented
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16C2×D1111yescharacteristic
407C22×SD16C2×D1111yescharacteristic, complemented
408C22×D8—111no—
409C22×D8—111no—
410C22×D8C2×D1111yescharacteristic
411#542—118no—
412#542—224no—
413#535—118no—
414#535—224no—
415C2×C4⋊Q8—111no—
416C2×#127—111no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—221no—
421C2×#124C2×D1111yescharacteristic
422C2×#124C2×D1111yescharacteristic, complemented
423C2×#123—221no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—221no—
426C2×#121—111no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#120—221no—
430C2×#120—221no—
431C2×C4×Q8—111no—
432C2×C4×D4—111no—
433C2×#117—111no—
434#496—118no—
435#495C2×D1118yescomplemented
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×C8C2×D1111yescharacteristic, complemented
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—84no—
468C22×C11—84no—
469C22×C11#53512yes—
470C22×C11#57612yes—
471C22×C11#57712yes—
472C22×C11C23×D411yescharacteristic
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—44no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—816no—
484C2×D11—84no—
485C2×D11—84no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11#53512yes—
491C4×C11C2×H(5,𝔽2)11yescharacteristic
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—442no—
502C2×#41—442no—
503C22×Q8—221no—
504C22×Q8C22×D1111yescharacteristic
505C22×Q8C22×D1111yescharacteristic
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—442no—
518C22×D4—442no—
519C22×D4C22×D1111yescharacteristic
520C22×D4C22×D1111yescharacteristic
521C23×C4—111no—
522C23×C4—221no—
523C23×C4—221no—
524C2×Q16—42no—
525C2×Q16C22×D1114yescomplemented
526C2×SD16—42no—
527C2×SD16—42no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×SD16C22×D1114yes—
533C2×SD16C22×D1114yescomplemented
534C2×D8—42no—
535C2×D8—114no—
536C2×D8—114no—
537C2×D8—442no—
538C2×D8—442no—
539C2×D8C22×D1114yes—
540C22×C8—111no—
541C22×C8—111no—
542C22×C8C22×D1111yescharacteristic
543C22×C8C22×D1111yescharacteristic
544C4⋊Q8—114no—
545C4⋊Q8—222no—
546#127—114no—
547#127—114no—
548#127—222no—
549#127—222no—
550#126—228no—
551#124—22no—
552#124—22no—
553#124—114no—
554#124—222no—
555#124—228no—
556#124C22×D1114yes—
557#124C22×D1114yescomplemented
558#123—228no—
559C22⋊Q8—114no—
560C22⋊Q8—228no—
561C22⋊Q8—222no—
562#121—114no—
563#121—228no—
564#121—228no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×Q8—114no—
569C4×Q8—222no—
570C4×D4—114no—
571C4×D4—222no—
572#117—114no—
573#117—114no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—111no—
586C2×C22⋊C4—111no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C42—111no—
593C2×C42—221no—
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×C8C22×D1114yescomplemented
609C2×C11—82no—
610C2×C11—82no—
611C2×C11#322414yescomplemented
612C2×C11C2×#53511yescharacteristic
613C2×C11C2×#57611yescharacteristic
614C2×C11C2×#57711yescharacteristic
615D11—42no—
616D11—82no—
617D11—82no—
618C24—21no—
619C24—21no—
620C24—111no—
621C24—224no—
622C24—221no—
623C24—221no—
624C24—444no—
625C24—882no—
626C24—882no—
627#41—444no—
628#41—444no—
629#41—448no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—224no—
637C2×Q8—882no—
638C2×Q8C23×D1112yes—
639C2×Q8C23×D1112yes—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—112no—
647C2×D4—112no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—221no—
654C2×D4—221no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—448no—
665C2×D4—444no—
666C2×D4—882no—
667C2×D4—882no—
668C2×D4—882no—
669C2×D4—882no—
670C2×D4—882no—
671C2×D4C23×D1112yes—
672C2×D4C23×D1112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—111no—
676C22×C4—111no—
677C22×C4—111no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—224no—
681C22×C4—224no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—444no—
687C22×C4—882no—
688C22×C4D4×D1111yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4C23×D1111yescharacteristic
691Q16—44no—
692SD16—44no—
693SD16—44no—
694SD16—444no—
695SD16—444no—
696D8—44no—
697D8—444no—
698D8—444no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—112no—
702C2×C8—112no—
703C2×C8—222no—
704C2×C8—222no—
705C2×C8C23×D1112yes—
706C2×C8C23×D1112yes—
707C4⋊C4—114no—
708C4⋊C4—114no—
709C4⋊C4—112no—
710C4⋊C4—112no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—224no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—114no—
721C22⋊C4—114no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C42—112no—
728C42—112no—
729C42—224no—
730C42D4×D1112yes—
731C42C23×D1112yes—
732C11C2×#322411yescharacteristic, complemented, Sylow
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—112no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—448no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23—884no—
755C23—884no—
756C23—8816no—
757C23C2×D4×D1111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—42no—
763Q8—42no—
764Q8—884no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777D4—442no—
778D4—442no—
779D4—884no—
780D4—884no—
781D4—884no—
782D4—884no—
783D4—884no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—112no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—224no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—448no—
802C2×C4—442no—
803C2×C4—442no—
804C2×C4—884no—
805C2×C4C2×D4×D1112yes—
806C2×C4C2×D4×D1112yes—
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4#6703712yes—
809C2×C4#6703712yes—
810C2×C4C24×D1111yescharacteristic
811C8—22no—
812C8—22no—
813C8—222no—
814C8—222no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—84no—
822C22—84no—
823C22—222no—
824C22—222no—
825C22—222no—
826C22—444no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—8816no—
834C22—884no—
835C22—884no—
836C22#1062324612yes—
837C22#1062330012yes—
838C22#1062330112yes—
839C22C22×D4×D1111yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—222no—
845C4—222no—
846C4—222no—
847C4—442no—
848C4—442no—
849C4#1062324612yes—
850C4C2×#6703711yescharacteristic
851C4C2×#6703711yescharacteristic
852C2—82no—
853C2—82no—
854C2—442no—
855C2—882no—
856C2—882no—
857C2#1307970314yesdirect product factor
858C2C2×#1062324611yescharacteristic
859C2C2×#1062330011yescharacteristic
860C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#495C2
socleC23×C11C22×D4
hypercenterC2×#495D11
hypocenterC11C2×#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10623213C2semidirect
2. C2×#10623205C2semidirect
3. #13079703C2direct (N × H)
4. C2×#10622671C2semidirect
5. C2×#10622668C2semidirect
6. C2×#10622307C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622776C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622800C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622303C2semidirect
16. C2×C11×#495C2semidirect
19. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
24. C2×C11×#124C22semidirect
27. C2×Q8×Dic11C22semidirect
29. C22×#4325C22semidirect
32. C2×D4×Dic11C22semidirect
34. C22×#4323C22semidirect
36. #10623213C22semidirect
38. #10623205C22semidirect
49. C2×#66922C22semidirect
50. C11×#495C22semidirect
51. C2×C4×C8×C11C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
56. #10622800C22semidirect
57. #10622798C22semidirect
58. #10622785C22semidirect
59. #10622782C22semidirect
60. #10622778C22semidirect
61. #10622776C22semidirect
62. #10622769C22semidirect
63. #10622763C22semidirect
66. C2×#66885C22semidirect
67. C2×#66885C22semidirect
70. C2×Dic11⋊C8C22semidirect
71. C2×Dic11⋊C8C22semidirect
72. #10622671C22semidirect
73. #10622668C22semidirect
74. C2×#66867C22semidirect
75. #10622307C22semidirect
76. #10622303C22semidirect
104. C2×C11×Q16C23semidirect
108. C2×C11×SD16C23semidirect
116. C11×#124C23semidirect
129. Q8×Dic11C23semidirect
133. C2×#4325C23semidirect
139. D4×Dic11C23semidirect
143. C2×#4323C23semidirect
173. #66922C23semidirect
174. C4×C8×C11C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
181. #66885C23semidirect
182. #66885C23semidirect
185. Dic11⋊C8C23semidirect
186. Dic11⋊C8C23semidirect
187. #66867C23semidirect
307. C2×#495D11semidirect
403. C22×Q16C2×D11semidirect
407. C22×SD16C2×D11semidirect
422. C2×#124C2×D11semidirect
435. #495C2×D11semidirect
460. C2×C4×C8C2×D11semidirect
525. C2×Q16C22×D11semidirect
533. C2×SD16C22×D11semidirect
557. #124C22×D11semidirect
608. C4×C8C22×D11semidirect
611. C2×C11#3224semidirect
732. C11C2×#3224semidirect
857. C2#13079703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232132
C2×#106232052
#130797032
C2×#106226712
C2×#106226682
C2×#106223072
C2×#106227982
C2×#106227762
C2×#106227782
C2×#106227632
C2×#106228002
C2×#106227852
C2×#106227822
C2×#106227692
C2×#106223032
C2×C11×#4952
C2×#322411