Finite Group Databasebeta

← C2×#13080853 #15630609

Subgroups — C2×#13080853 #15630609

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623147C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic, complemented
3#13080853C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622648C211yesmaximal, characteristic, complemented
7C2×#10622483C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622649C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic, complemented
12C2×#10622369C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622744C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#469C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24C2×#66993C2211yescharacteristic
25C2×#66992—21no—
26C2×#66991C2211yescharacteristic, complemented
27C2×#66990—21no—
28C2×#66989—21no—
29C2×D4×Dic11C2211yescharacteristic, complemented
30C22×#4323C2211yescharacteristic
31C22×#4323C2211yescharacteristic, complemented
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66979C2211yescharacteristic, complemented
34C22×#4313C2211yescharacteristic, complemented
35#10623147—24no—
36#10623147C2218yescomplemented
37#10623140—24no—
38#10623140C2218yescomplemented
39C2×#66948C2211yescharacteristic
40C2×#66946C2211yescharacteristic
41C2×#66945C2211yescharacteristic, complemented
42C2×#66941C2211yescharacteristic, complemented
43C2×#66938—21no—
44C2×#66937—21no—
45C2×#66935—21no—
46C2×#66930—21no—
47C11×#469C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic, complemented
53C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
54#10622769C2218yescomplemented
55#10622763C2218yescomplemented
56#10622744C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic, complemented
61C2×#66885C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65#10622649C2218yescomplemented
66#10622648C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622483C2218yescomplemented
72#10622479C2218yescomplemented
73#10622395C2218yescomplemented
74#10622383C2218yescomplemented
75#10622373C2218yescomplemented
76#10622369C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11D411yescharacteristic
89C23×Dic11—21no—
90C2×D4×D11—28no—
91C2×D4×D11—24no—
92C2×D4×D11—22no—
93C2×D4×D11—42no—
94C2×D4×D11—48no—
95C2×D4×D11C2314yes—
96C22×D44—24no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—22no—
100C22×D44—42no—
101C22×D44C2311yescharacteristic
102C22×D44C2314yes—
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C2×C11×D8—42no—
108C2×C11×D8C2314yescomplemented
109C2×C11×M16—42no—
110C2×C11×M16C2314yescomplemented
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×#121—22no—
114C11×#121—22no—
115C11×#121C2314yes—
116C11×#121C2314yescomplemented
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11D411yescharacteristic
125#66993—22no—
126#66993C2314yes—
127#66992—28no—
128#66991—22no—
129#66991C2314yescomplemented
130#66990—28no—
131#66989—28no—
132D4×Dic11—22no—
133D4×Dic11C2314yescomplemented
134C2×#4323—24no—
135C2×#4323—42no—
136C2×#4323C2314yes—
137C2×#4323C2314yescomplemented
138C4×C22⋊D11D414yes—
139C4×C22⋊D11C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4D411yescharacteristic
144#66979—22no—
145#66979C2314yescomplemented
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×#4313—42no—
156C2×#4313C2314yescomplemented
157#66948—22no—
158#66948C2314yes—
159#66946—22no—
160#66946C2314yes—
161#66945—22no—
162#66945C2314yescomplemented
163#66941—22no—
164#66941C2314yescomplemented
165#66938—28no—
166#66937—28no—
167#66935—28no—
168#66930—28no—
169C11×#106C2314yescomplemented
170C11×#102C2314yescomplemented
171C11×#102C2314yescomplemented
172#66896C2314yescomplemented
173#66896C2314yescomplemented
174C22⋊(C11⋊C8)C2314yescomplemented
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181C8×Dic11C2314yescomplemented
182#66873C2314yes—
183#66873C2314yescomplemented
184#66872C2314yescomplemented
185#66871C2314yescomplemented
186C2×#3325—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—82no—
199C23×D11—82no—
200C23×D11C2×D411yescharacteristic
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—44no—
210C2×D4×C11—82no—
211C2×D4×C11C2412yes—
212C2×D4×C11C2412yes—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11—82no—
230C2×C22⋊D11C2×D414yes—
231C22×Dic11—24no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—44no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238D4×D11—28no—
239D4×D11—44no—
240D4×D11—48no—
241D4×D11—432no—
242C2×D44—24no—
243C2×D44—28no—
244C2×D44—21no—
245C2×D44—24no—
246C2×D44—21no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—44no—
251C2×D44—44no—
252C2×D44—48no—
253C2×D44—44no—
254C2×D44#4114yes—
255C2×D44C2412yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—82no—
265C11×D8—44no—
266C11×M16—44no—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4C2412yes—
274C11×C4⋊C4C2412yes—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
280C22⋊Dic11C2×D414yes—
281#4323—28no—
282#4323—44no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4C2×D414yes—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—24no—
292Dic11⋊C4C2×D414yes—
293C4×Dic11—24no—
294C4×Dic11—24no—
295C4×Dic11C2×D412yes—
296C4×Dic11C2412yes—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301#4313—44no—
302C2×#555—111no—
303C2×D42—111no—
304#3325—1116no—
305C2×#486—111no—
306C2×#482—111no—
307C2×#482—111no—
308C2×#476—111no—
309C2×#469—111no—
310C2×#469D1111yescharacteristic, complemented
311C2×#459—111no—
312C2×#447—111no—
313C2×#447—111no—
314C2×C4×D8—111no—
315C2×#436—111no—
316C2×#418—111no—
317C2×#418—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11C22×D412yes—
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C22×D11—24no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—48no—
338C22×D11—48no—
339C22×D11—48no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—48no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—84no—
347C22×D11—84no—
348C22×D11—816no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—48no—
356D4×C11—42no—
357D4×C11—42no—
358D4×C11—84no—
359C2×C4×C11—22no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C2×#4112yes—
370C2×C4×C11H(5,𝔽2)12yes—
371C2×C4×C11C2511yescharacteristic
372C22⋊D11—28no—
373C22⋊D11—48no—
374C22⋊D11—48no—
375C22⋊D11—84no—
376C22⋊D11—84no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—48no—
384C2×Dic11AGL(1,ℤ/8)14yes—
385C2×Dic11C22×D412yes—
386C2×Dic11C22×D412yes—
387C2×Dic11C22×D412yes—
388D44—24no—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—48no—
393D44—48no—
394D44—42no—
395D44C2×#4114yes—
396C4×D11—24no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400Dic22—84no—
401C8×C11—22no—
402C8×C11—22no—
403C11⋊C8—22no—
404C11⋊C8—22no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4—221no—
408C22×D8—111no—
409C22×D8—111no—
410C22×D8C2×D1111yescharacteristic, complemented
411C22×M16—111no—
412C22×M16C2×D1111yescharacteristic, complemented
413#555—118no—
414#555—224no—
415D42—118no—
416D42—224no—
417C2×C4⋊Q8—111no—
418C2×#127—111no—
419C2×#124—221no—
420C2×#124—221no—
421C2×#121—111no—
422C2×#121—111no—
423C2×#121—221no—
424C2×#121—221no—
425C2×#121C2×D1111yescharacteristic
426C2×#121C2×D1111yescharacteristic, complemented
427C2×#120—221no—
428C2×#120—221no—
429C2×C4×D4—111no—
430C2×C4×D4—111no—
431C2×C4×D4—111no—
432C2×#117—111no—
433C2×#117—111no—
434C2×#117—221no—
435#486—118no—
436#482—118no—
437#482—118no—
438#476—118no—
439#469—118no—
440#469C2×D1118yescomplemented
441#459—118no—
442#447—118no—
443#447—118no—
444C4×D8—118no—
445#436—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106C2×D1111yescharacteristic, complemented
449C2×C4⋊C8—111no—
450#418—118no—
451#418—118no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102C2×D1111yescharacteristic, complemented
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×C4×C8—111no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—44no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—84no—
476C22×C11—84no—
477C22×C11#54612yes—
478C22×C11C2×AGL(1,ℤ/8)12yes—
479C22×C11#57612yes—
480C22×C11C23×D411yescharacteristic
481C2×D11—24no—
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—22no—
485C2×D11—42no—
486C2×D11—44no—
487C2×D11—48no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—816no—
493C2×D11—816no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11#54612yes—
499C4×C11C22×#4111yescharacteristic
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501Dic11—22no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11C2×AGL(1,ℤ/8)14yes—
506C25—221no—
507C25—221no—
508C22×Q8—221no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—111no—
512C22×D4—114no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—114no—
516C22×D4—224no—
517C22×D4—221no—
518C22×D4—222no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—224no—
523C22×D4—228no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—222no—
527C22×D4—442no—
528C22×D4—442no—
529C22×D4—448no—
530C22×D4C22×D1111yescharacteristic
531C22×D4C22×D1111yescharacteristic
532C23×C4—111no—
533C23×C4—221no—
534C23×C4—221no—
535C23×C4C22×D1111yescharacteristic
536C2×D8—42no—
537C2×D8—114no—
538C2×D8—114no—
539C2×D8—224no—
540C2×D8—442no—
541C2×D8C22×D1114yescomplemented
542C2×M16—42no—
543C2×M16—114no—
544C2×M16—442no—
545C2×M16C22×D1114yescomplemented
546C22×C8—111no—
547C22×C8—111no—
548C22×C8C22×D1111yescharacteristic
549C22×C8C22×D1111yescharacteristic
550C4⋊Q8—114no—
551C4⋊Q8—222no—
552#127—114no—
553#127—222no—
554#124—228no—
555#124—228no—
556#121—22no—
557#121—22no—
558#121—114no—
559#121—114no—
560#121—228no—
561#121—222no—
562#121—222no—
563#121—228no—
564#121C22×D1114yes—
565#121C22×D1114yescomplemented
566#120—228no—
567#120—228no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—222no—
573C4×D4—222no—
574#117—114no—
575#117—114no—
576#117—228no—
577#117—222no—
578#117—222no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C4⋊C4C22×D1111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—111no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C22⋊C4—221no—
595C2×C42—111no—
596C2×C42—221no—
597C2×C42—221no—
598#107—114no—
599#106—114no—
600#106C22×D1114yescomplemented
601C4⋊C8—114no—
602#102—114no—
603#102—114no—
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608#102—114no—
609#102—114no—
610#102C22×D1114yescomplemented
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8—114no—
614C4×C8—114no—
615C2×C11—42no—
616C2×C11—82no—
617C2×C11—82no—
618C2×C11#332514yescomplemented
619C2×C11C2×#54611yescharacteristic
620C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
621C2×C11C2×#57611yescharacteristic
622D11—42no—
623D11—44no—
624D11—82no—
625C24—21no—
626C24—21no—
627C24—111no—
628C24—224no—
629C24—221no—
630C24—221no—
631C24—224no—
632C24—444no—
633C24—444no—
634C24—444no—
635C24—444no—
636C24—882no—
637C24—882no—
638C24D4×D1111yescharacteristic
639C2×Q8—224no—
640C2×Q8—882no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—82no—
651C2×D4—114no—
652C2×D4—114no—
653C2×D4—112no—
654C2×D4—112no—
655C2×D4—228no—
656C2×D4—224no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—228no—
662C2×D4—224no—
663C2×D4—221no—
664C2×D4—224no—
665C2×D4—221no—
666C2×D4—222no—
667C2×D4—222no—
668C2×D4—222no—
669C2×D4—444no—
670C2×D4—448no—
671C2×D4—444no—
672C2×D4—444no—
673C2×D4—444no—
674C2×D4—444no—
675C2×D4—448no—
676C2×D4—444no—
677C2×D4—4432no—
678C2×D4—882no—
679C2×D4—882no—
680C2×D4C23×D1112yes—
681C2×D4C23×D1112yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—111no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—444no—
698C22×C4—444no—
699C22×C4D4×D1112yes—
700C22×C4D4×D1111yescharacteristic
701C22×C4C23×D1112yes—
702C22×C4C23×D1111yescharacteristic
703D8—44no—
704D8—228no—
705D8—444no—
706M16—44no—
707M16—444no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—112no—
711C2×C8—112no—
712C2×C8—222no—
713C2×C8—222no—
714C2×C8C23×D1112yes—
715C2×C8C23×D1112yes—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—114no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4C23×D1112yes—
725C4⋊C4C23×D1112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—114no—
729C22⋊C4—114no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4—224no—
736C42—112no—
737C42—112no—
738C42—224no—
739C42—224no—
740C11C2×#332511yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—112no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—224no—
757C23—222no—
758C23—222no—
759C23—448no—
760C23—448no—
761C23—448no—
762C23—448no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—884no—
769C23—884no—
770C23—8816no—
771C23—8816no—
772C23C2×D4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—884no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—48no—
780D4—42no—
781D4—42no—
782D4—84no—
783D4—114no—
784D4—228no—
785D4—224no—
786D4—222no—
787D4—222no—
788D4—222no—
789D4—448no—
790D4—448no—
791D4—448no—
792D4—448no—
793D4—442no—
794D4—884no—
795D4—884no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—448no—
816C2×C4—448no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4#6703712yes—
822C2×C4#41×D1112yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22—84no—
840C22—222no—
841C22—224no—
842C22—222no—
843C22—222no—
844C22—444no—
845C22—448no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—8816no—
852C22—8816no—
853C22—884no—
854C22#1062314112yes—
855C22D11×AGL(1,ℤ/8)12yes—
856C22#1062330512yes—
857C22C22×D4×D1111yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—114no—
862C4—222no—
863C4—222no—
864C4—442no—
865C4—442no—
866C4#1062314112yes—
867C4C2×#6703711yescharacteristic
868C4C2×#41×D1111yescharacteristic
869C2—42no—
870C2—82no—
871C2—82no—
872C2—442no—
873C2—444no—
874C2—882no—
875C2#1308085314yesdirect product factor
876C2C2×#1062314111yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#469C2
socleC23×C11C22×D4
hypercenterC2×#469D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#10623147C2semidirect
2. C2×#10623140C2semidirect
3. #13080853C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622648C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622649C2semidirect
11. C2×#10622769C2semidirect
12. C2×#10622369C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622744C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#469C2semidirect
20. C22×C11×D8C22semidirect
21. C22×C11×M16C22semidirect
23. C2×C11×#121C22semidirect
26. C2×#66991C22semidirect
29. C2×D4×Dic11C22semidirect
31. C22×#4323C22semidirect
33. C2×#66979C22semidirect
34. C22×#4313C22semidirect
36. #10623147C22semidirect
38. #10623140C22semidirect
41. C2×#66945C22semidirect
42. C2×#66941C22semidirect
47. C11×#469C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#102C22semidirect
51. C2×#66896C22semidirect
52. C2×#66896C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622769C22semidirect
55. #10622763C22semidirect
56. #10622744C22semidirect
57. #10622741C22semidirect
60. C2×#66885C22semidirect
61. C2×#66885C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. C2×C8×Dic11C22semidirect
65. #10622649C22semidirect
66. #10622648C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622483C22semidirect
72. #10622479C22semidirect
73. #10622395C22semidirect
74. #10622383C22semidirect
75. #10622373C22semidirect
76. #10622369C22semidirect
108. C2×C11×D8C23semidirect
110. C2×C11×M16C23semidirect
116. C11×#121C23semidirect
129. #66991C23semidirect
133. D4×Dic11C23semidirect
137. C2×#4323C23semidirect
145. #66979C23semidirect
156. C2×#4313C23semidirect
162. #66945C23semidirect
164. #66941C23semidirect
169. C11×#106C23semidirect
170. C11×#102C23semidirect
171. C11×#102C23semidirect
172. #66896C23semidirect
173. #66896C23semidirect
174. C22⋊(C11⋊C8)C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. Dic11⋊C8C23semidirect
181. C8×Dic11C23semidirect
183. #66873C23semidirect
184. #66872C23semidirect
185. #66871C23semidirect
310. C2×#469D11semidirect
410. C22×D8C2×D11semidirect
412. C22×M16C2×D11semidirect
426. C2×#121C2×D11semidirect
440. #469C2×D11semidirect
448. C2×#106C2×D11semidirect
460. C2×#102C2×D11semidirect
461. C2×#102C2×D11semidirect
541. C2×D8C22×D11semidirect
545. C2×M16C22×D11semidirect
565. #121C22×D11semidirect
600. #106C22×D11semidirect
610. #102C22×D11semidirect
611. #102C22×D11semidirect
618. C2×C11#3325semidirect
740. C11C2×#3325semidirect
875. C2#13080853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231472
C2×#106231402
#130808532
C2×#106223732
C2×#106224792
C2×#106226482
C2×#106224832
C2×#106223952
C2×#106227632
C2×#106226492
C2×#106227692
C2×#106223692
C2×#106227412
C2×#106227442
C2×#106223832
C2×C11×#4692
C2×#332511