Finite Group Databasebeta

← C2×#13080851 #15630607

Subgroups — C2×#13080851 #15630607

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×D4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080851C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622350C211yesmaximal, characteristic, complemented
6C2×#10622397C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622772C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic, complemented
12C2×D8×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622828C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11—21no—
19C22×D4×D11C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic, complemented
23C2×#67006—21no—
24C2×#66993C2211yescharacteristic
25C2×#66992—21no—
26C2×#66992—21no—
27D4×C22⋊D11—24no—
28D4×C22⋊D11C2218yescomplemented
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic, complemented
31C2×#66990—21no—
32C2×#66989—21no—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic, complemented
35C22×#4323C2211yescharacteristic, complemented
36C2×#66983C2211yescharacteristic
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×#66979C2211yescharacteristic, complemented
39C22×#4318C2211yescharacteristic, complemented
40C22×#4313C2211yescharacteristic, complemented
41#10623147—24no—
42#10623147C2218yescomplemented
43C2×#66945C2211yescharacteristic, complemented
44C2×#66941C2211yescharacteristic, complemented
45C2×#66938—21no—
46C2×#66930—21no—
47C11×#447C2218yescomplemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51#10622828C2218yescomplemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57#10622772C2218yescomplemented
58#10622769C2218yescomplemented
59#10622763C2218yescomplemented
60D8×Dic11C2218yescomplemented
61C2×#66885C2211yescharacteristic, complemented
62C2×#66885C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622652C2218yescomplemented
69C2×#66873C2211yescharacteristic, complemented
70C2×#66872C2211yescharacteristic, complemented
71#10622397C2218yescomplemented
72#10622383C2218yescomplemented
73#10622374C2218yescomplemented
74#10622373C2218yescomplemented
75#10622350C2218yescomplemented
76#10622342C2218yescomplemented
77C25×C11—21no—
78C24×D11—21no—
79C22×D4×C11—24no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—22no—
83C22×D4×C11—42no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2314yes—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—28no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—48no—
97C22×C22⋊D11D411yescharacteristic
98C23×Dic11—21no—
99C23×Dic11—21no—
100C2×D4×D11—24no—
101C2×D4×D11—22no—
102C2×D4×D11—42no—
103C2×D4×D11C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C2×C11×D8—24no—
108C2×C11×D8—42no—
109C2×C11×D8C2314yes—
110C2×C11×D8C2314yescomplemented
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×#121—22no—
114C11×#121C2314yescomplemented
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117#67006—28no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11D411yescharacteristic
124#66993—22no—
125#66993C2314yes—
126#66992—28no—
127#66992—28no—
128#66991—22no—
129#66991—22no—
130#66991C2314yes—
131#66991C2314yescomplemented
132#66990—28no—
133#66989—28no—
134D4×Dic11—22no—
135D4×Dic11—22no—
136D4×Dic11C2314yes—
137D4×Dic11C2314yescomplemented
138C2×#4323—42no—
139C2×#4323C2314yescomplemented
140#66983—22no—
141#66983C2314yes—
142C4×C22⋊D11D414yes—
143C4×C22⋊D11C2314yes—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4D411yescharacteristic
147#66979—22no—
148#66979C2314yescomplemented
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4D411yescharacteristic
154C2×C4×Dic11—21no—
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C2×#4318—42no—
158C2×#4318C2314yescomplemented
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C2×#4313—42no—
162C2×#4313C2314yescomplemented
163#66945—22no—
164#66945C2314yescomplemented
165#66941—22no—
166#66941C2314yescomplemented
167#66938—28no—
168#66930—28no—
169C11×#102C2314yes—
170C11×#102C2314yescomplemented
171C11×C22⋊C8C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yescomplemented
175#66896C2314yescomplemented
176#66896C2314yescomplemented
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yescomplemented
180#66882C2314yescomplemented
181#66881C2314yescomplemented
182Dic11⋊C8C2314yescomplemented
183C8×Dic11C2314yescomplemented
184#66873C2314yescomplemented
185#66872C2314yescomplemented
186C2×#3325—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—24no—
191C24×C11—44no—
192C24×C11—44no—
193C24×C11—82no—
194C24×C11C2×D411yescharacteristic
195C23×D11—21no—
196C23×D11—24no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—82no—
200C23×D11C2×D411yescharacteristic
201C2×D4×C11—28no—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—24no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—44no—
213C2×D4×C11—48no—
214C2×D4×C11—44no—
215C2×D4×C11—82no—
216C2×D4×C11#4114yes—
217C2×D4×C11C2412yes—
218C2×D4×C11C2412yes—
219C2×D4×C11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—21no—
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2411yescharacteristic
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—432no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—82no—
240C2×C22⋊D11—82no—
241C2×C22⋊D11C2×D414yes—
242C22×Dic11—24no—
243C22×Dic11—24no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—44no—
248C22×Dic11—44no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252D4×D11—28no—
253D4×D11—44no—
254D4×D11—48no—
255C2×D44—21no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44C2412yes—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—82no—
265C11×D8—28no—
266C11×D8—44no—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C22⋊C4—24no—
274C22⋊Dic11—24no—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11C2×D414yes—
280#4323—44no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4C2×D414yes—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11—21no—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2412yes—
290Dic11⋊C4—24no—
291Dic11⋊C4C2×D414yes—
292C4×Dic11—24no—
293C4×Dic11—24no—
294C4×Dic11C2×D412yes—
295C4×Dic11C2412yes—
296#4318—44no—
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×#469—111no—
311C2×#459—111no—
312C2×#447—111no—
313C2×#447D1111yescharacteristic, complemented
314C2×C4×D8—111no—
315C2×#436—111no—
316C2×#418—111no—
317C2×#418—111no—
318C23×C11—24no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—48no—
326C23×C11—48no—
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—816no—
337C23×C11C22×D412yes—
338C23×C11C22×D411yescharacteristic
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—48no—
344C22×D11—48no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351D4×C11—24no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—48no—
358D4×C11—42no—
359D4×C11—42no—
360D4×C11—84no—
361D4×C11C2×#4114yes—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4112yes—
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—28no—
374C22⋊D11—48no—
375C22⋊D11—48no—
376C22⋊D11—48no—
377C22⋊D11—48no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—48no—
389C2×Dic11—48no—
390C2×Dic11AGL(1,ℤ/8)14yes—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394D44—22no—
395D44—22no—
396D44—42no—
397C4×D11—24no—
398C4×D11—22no—
399C4×D11—22no—
400Dic22—84no—
401C8×C11—22no—
402C8×C11—22no—
403C11⋊C8—22no—
404C11⋊C8—22no—
405C23×D4—111no—
406C23×D4—221no—
407C23×D4C2×D1111yescharacteristic
408C22×D8—111no—
409C22×D8C2×D1111yescharacteristic
410C22×D8C2×D1111yescharacteristic, complemented
411C22×M16—111no—
412C22×M16—111no—
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—111no—
424C2×#121—221no—
425C2×#121—221no—
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#469—118no—
441#459—118no—
442#447—118no—
443#447C2×D1118yescomplemented
444C4×D8—118no—
445#436—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106—111no—
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
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8C2×D1111yescharacteristic, complemented
464C2×C4×C8—111no—
465C22×C11—22no—
466C22×C11—24no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—42no—
470C22×C11—48no—
471C22×C11—44no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—816no—
480C22×C11—84no—
481C22×C11—84no—
482C22×C11#54612yes—
483C22×C11C2×AGL(1,ℤ/8)12yes—
484C22×C11#57612yes—
485C22×C11C23×D411yescharacteristic
486C2×D11—22no—
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—44no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—816no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11#54612yes—
498C4×C11C22×#4111yescharacteristic
499C4×C11C2×H(5,𝔽2)11yescharacteristic
500Dic11—22no—
501Dic11—22no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505Dic11C2×AGL(1,ℤ/8)14yes—
506C25—21no—
507C25—221no—
508C22×Q8—221no—
509C22×D4—24no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—111no—
515C22×D4—114no—
516C22×D4—111no—
517C22×D4—222no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—228no—
522C22×D4—224no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—442no—
527C22×D4—448no—
528C22×D4C22×D1111yescharacteristic
529C22×D4C22×D1111yescharacteristic
530C22×D4C22×D1114yes—
531C22×D4C22×D1111yescharacteristic
532C23×C4—111no—
533C23×C4—221no—
534C23×C4—221no—
535C23×C4C22×D1111yescharacteristic
536C2×D8—24no—
537C2×D8—42no—
538C2×D8—114no—
539C2×D8—442no—
540C2×D8C22×D1114yes—
541C2×D8C22×D1114yescomplemented
542C2×M16—114no—
543C2×M16—114no—
544C2×M16—442no—
545C2×M16—442no—
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—114no—
558#121—114no—
559#121—114no—
560#121—228no—
561#121—222no—
562#121—222no—
563#121—228no—
564#121—222no—
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—111no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4C22×D1111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—111no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—221no—
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#106—114no—
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×D1114yes—
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8C22×D1114yescomplemented
614C4×C8—114no—
615C2×C11—44no—
616C2×C11—42no—
617C2×C11—82no—
618C2×C11—82no—
619C2×C11#332514yescomplemented
620C2×C11C2×#54611yescharacteristic
621C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
622C2×C11C2×#57611yescharacteristic
623D11—42no—
624D11—82no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—44no—
630C24—44no—
631C24—82no—
632C24—111no—
633C24—224no—
634C24—221no—
635C24—444no—
636C24—444no—
637C24—882no—
638C24D4×D1111yescharacteristic
639C2×Q8—224no—
640C2×Q8—882no—
641C2×D4—28no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—44no—
653C2×D4—48no—
654C2×D4—44no—
655C2×D4—82no—
656C2×D4—114no—
657C2×D4—112no—
658C2×D4—224no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—228no—
663C2×D4—224no—
664C2×D4—224no—
665C2×D4—224no—
666C2×D4—221no—
667C2×D4—222no—
668C2×D4—222no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—448no—
672C2×D4—444no—
673C2×D4—4432no—
674C2×D4—444no—
675C2×D4—444no—
676C2×D4—882no—
677C2×D4—882no—
678C2×D4#434114yes—
679C2×D4C23×D1112yes—
680C2×D4C23×D1112yes—
681C2×D4C23×D1112yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—111no—
686C22×C4—111no—
687C22×C4—111no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—224no—
691C22×C4—224no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—221no—
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—28no—
704D8—44no—
705D8—444no—
706M16—444no—
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—114no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4—221no—
725C4⋊C4C23×D1112yes—
726C22⋊C4—24no—
727C22⋊C4—114no—
728C22⋊C4—114no—
729C22⋊C4—224no—
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—24no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—48no—
749C23—48no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—84no—
759C23—816no—
760C23—112no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—448no—
766C23—448no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23—884no—
771C23—8816no—
772C23C2×D4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—884no—
775D4—24no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—42no—
783D4—42no—
784D4—84no—
785D4—228no—
786D4—222no—
787D4—222no—
788D4—448no—
789D4—448no—
790D4—448no—
791D4—448no—
792D4—442no—
793D4—884no—
794D4—884no—
795D4C2×#434114yes—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—114no—
803C2×C4—112no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—224no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—448no—
815C2×C4—448no—
816C2×C4—442no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4C2×#434112yes—
822C2×C4#6703712yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—44no—
833C22—48no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—84no—
844C22—84no—
845C22—222no—
846C22—222no—
847C22—222no—
848C22—444no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—884no—
854C22#1062312212yes—
855C22#1062328812yes—
856C22D11×AGL(1,ℤ/8)12yes—
857C22C22×D4×D1111yescharacteristic
858C4—22no—
859C4—42no—
860C4—114no—
861C4—222no—
862C4—222no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4#1062312212yes—
867C4C22×#434111yescharacteristic
868C4C2×#6703711yescharacteristic
869C2—42no—
870C2—44no—
871C2—82no—
872C2—82no—
873C2—442no—
874C2—882no—
875C2#1308085114yesdirect product factor
876C2C2×#1062312211yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623147C2semidirect
2. C2×D4×C22⋊D11C2semidirect
3. #13080851C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622350C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622772C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622769C2semidirect
12. C2×D8×Dic11C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622828C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#447C2semidirect
21. C22×C11×D8C22semidirect
22. C2×C11×#121C22semidirect
28. D4×C22⋊D11C22semidirect
30. C2×#66991C22semidirect
34. C2×D4×Dic11C22semidirect
35. C22×#4323C22semidirect
38. C2×#66979C22semidirect
39. C22×#4318C22semidirect
40. C22×#4313C22semidirect
42. #10623147C22semidirect
43. C2×#66945C22semidirect
44. C2×#66941C22semidirect
47. C11×#447C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. #10622828C22semidirect
54. C2×#66896C22semidirect
55. C2×#66896C22semidirect
56. C2×#66896C22semidirect
57. #10622772C22semidirect
58. #10622769C22semidirect
59. #10622763C22semidirect
60. D8×Dic11C22semidirect
61. C2×#66885C22semidirect
62. C2×#66885C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622652C22semidirect
69. C2×#66873C22semidirect
70. C2×#66872C22semidirect
71. #10622397C22semidirect
72. #10622383C22semidirect
73. #10622374C22semidirect
74. #10622373C22semidirect
75. #10622350C22semidirect
76. #10622342C22semidirect
110. C2×C11×D8C23semidirect
114. C11×#121C23semidirect
131. #66991C23semidirect
137. D4×Dic11C23semidirect
139. C2×#4323C23semidirect
148. #66979C23semidirect
158. C2×#4318C23semidirect
162. C2×#4313C23semidirect
164. #66945C23semidirect
166. #66941C23semidirect
170. C11×#102C23semidirect
171. C11×C22⋊C8C23semidirect
174. #66896C23semidirect
175. #66896C23semidirect
176. #66896C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. #66882C23semidirect
181. #66881C23semidirect
182. Dic11⋊C8C23semidirect
183. C8×Dic11C23semidirect
184. #66873C23semidirect
185. #66872C23semidirect
313. C2×#447D11semidirect
410. C22×D8C2×D11semidirect
426. C2×#121C2×D11semidirect
443. #447C2×D11semidirect
461. C2×#102C2×D11semidirect
463. C2×C22⋊C8C2×D11semidirect
541. C2×D8C22×D11semidirect
565. #121C22×D11semidirect
611. #102C22×D11semidirect
613. C22⋊C8C22×D11semidirect
619. C2×C11#3325semidirect
740. C11C2×#3325semidirect
875. C2#13080851direct (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×D4×C22⋊D112
#130808512
C2×#106223732
C2×#106223502
C2×#106223972
C2×#106223742
C2×#106226522
C2×#106227722
C2×#106227632
C2×#106227692
C2×D8×Dic112
C2×#106223422
C2×#106228282
C2×#106223832
C2×C11×#4472
C2×#332511