Finite Group Databasebeta

← C2×#13080756 #15630330

Subgroups — C2×#13080756 #15630330

Order 2816.

2642 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×#10623226C211yesmaximal, characteristic, complemented
2C2×#10623248C211yesmaximal, characteristic, complemented
3#13080756C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622685C211yesmaximal, characteristic, complemented
10C2×#10622386C211yesmaximal, characteristic, complemented
11C2×#10622386C211yesmaximal, characteristic, complemented
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#490C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic, complemented
22C2×#66991—21no—
23C2×#66991C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66990—21no—
26C2×#66990—21no—
27C22×#4323C2211yescharacteristic, complemented
28C22×#4323C2211yescharacteristic, complemented
29C22×D88C2211yescharacteristic
30C22×#4313C2211yescharacteristic, complemented
31C22×C8×D11C2211yescharacteristic, complemented
32#10623248—24no—
33#10623248C2218yescomplemented
34#10623226—24no—
35#10623226C2218yescomplemented
36C2×#66951—21no—
37C2×#66948—21no—
38C2×#66948C2211yescharacteristic, complemented
39C2×#66948C2211yescharacteristic, complemented
40C2×#66947—21no—
41C2×#66946—21no—
42C2×#66945C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic, complemented
47C11×#490C2218yescomplemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#97C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic, complemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic, complemented
57C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59C2×#66881C2211yescharacteristic, complemented
60#10622685C2218yescomplemented
61#10622679C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622395C2218yescomplemented
68#10622392C2218yescomplemented
69#10622390C2218yescomplemented
70#10622388C2218yescomplemented
71#10622386C2218yescomplemented
72#10622386C2218yescomplemented
73#10622383C2218yescomplemented
74D11×#102C2218yescomplemented
75#10622324C2218yescomplemented
76#10622319C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C2×D4×D11—28no—
88C2×D4×D11—24no—
89C2×D4×D11—24no—
90C2×D4×D11—22no—
91C2×D4×D11—22no—
92C2×D4×D11—42no—
93C2×D4×D11—42no—
94C2×D4×D11—48no—
95C2×D4×D11C2314yes—
96C2×D4×D11C2314yes—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44D411yescharacteristic
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#127—22no—
110C11×#127C2314yes—
111C11×#125—22no—
112C11×#125C2314yescomplemented
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120#66991—22no—
121#66991—22no—
122#66991—28no—
123#66991C2314yes—
124#66991C2314yes—
125#66990—28no—
126#66990—28no—
127C2×#4323—42no—
128C2×#4323—42no—
129C2×#4323C2314yescomplemented
130C2×#4323C2314yescomplemented
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4D411yescharacteristic
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×D88—24no—
146C2×D88C2314yes—
147C2×#4313—42no—
148C2×#4313C2314yescomplemented
149C2×C8×D11—42no—
150C2×C8×D11C2314yescomplemented
151#66951—28no—
152#66948—28no—
153#66948—22no—
154#66948—22no—
155#66948C2314yescomplemented
156#66948C2314yescomplemented
157#66947—28no—
158#66946—28no—
159#66945—22no—
160#66945C2314yescomplemented
161C4⋊C4×D11—22no—
162C4⋊C4×D11C2314yescomplemented
163C4×D44—22no—
164C4×D44—22no—
165C4×D44D414yes—
166C4×D44C2314yes—
167C4×D44C2314yes—
168C4×D44C2314yescomplemented
169C11×#102C2314yescomplemented
170C11×#102C2314yescomplemented
171C11×#102C2314yescomplemented
172C11×#102C2314yescomplemented
173C11×#97C2314yescomplemented
174#66896C2314yescomplemented
175#66896C2314yescomplemented
176#66885C2314yes—
177#66885C2314yescomplemented
178(C2×D11)⋊C8C2314yescomplemented
179(C2×D11)⋊C8C2314yescomplemented
180#66881C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yescomplemented
184#66871C2314yescomplemented
185C4⋊(C11⋊C8)C2314yescomplemented
186C2×#3318—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—82no—
198C23×D11—82no—
199C23×D11C2×D411yescharacteristic
200C23×D11C2×D411yescharacteristic
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
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—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230D4×D11—28no—
231D4×D11—28no—
232D4×D11—44no—
233D4×D11—44no—
234D4×D11—48no—
235D4×D11—48no—
236D4×D11—432no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—24no—
240C2×D44—21no—
241C2×D44—21no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44C2×D414yes—
248C2×D44#4114yes—
249C2×D44C2412yes—
250C2×D44C2412yes—
251C2×C4×D11—24no—
252C2×C4×D11—24no—
253C2×C4×D11—24no—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—44no—
259C2×C4×D11—82no—
260C2×C4×D11—82no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2412yes—
264C2×C4×D11C2412yes—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4C2412yes—
274C11×C4⋊C4C2412yes—
275C42×C11C2×D412yes—
276C42×C11C2412yes—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279#4323—44no—
280#4323—44no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4C2×D414yes—
287(C2×D11)⋊C4C2×D414yes—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11C2×D414yes—
291C4⋊Dic11C2412yes—
292C4⋊Dic11C2412yes—
293Dic11⋊C4—24no—
294C4×Dic11—24no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299D88—28no—
300#4313—44no—
301C8×D11—44no—
302C2×#553—111no—
303C2×D42—111no—
304#3318—1116no—
305C2×#490D1111yescharacteristic, complemented
306C2×#481—111no—
307C2×#482—111no—
308C2×#478—111no—
309C2×#469—111no—
310C2×#466—111no—
311C2×#459—111no—
312C2×#447—111no—
313C2×#447—111no—
314C2×#442—111no—
315C2×#435—111no—
316C2×#418—111no—
317C22×#102—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11C22×D411yescharacteristic
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—24no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—48no—
336C22×D11—48no—
337C22×D11—48no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—48no—
344C22×D11—84no—
345C22×D11—84no—
346C22×D11—816no—
347C22×D11—816no—
348C22×D11AGL(1,ℤ/8)14yes—
349C22×D11C22×D412yes—
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—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4112yes—
369C2×C4×C11H(5,𝔽2)12yes—
370C2×C4×C11C2511yescharacteristic
371C22⋊D11—48no—
372C22⋊D11—48no—
373C22⋊D11—48no—
374C22⋊D11—48no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—28no—
384D44—24no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—42no—
390D44—84no—
391D44C2×#4114yes—
392C4×D11—24no—
393C4×D11—24no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—48no—
399C4×D11—84no—
400C4×D11—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×D8—111no—
411C22×M16—111no—
412C23×C8—111no—
413#553—118no—
414#553—224no—
415D42—118no—
416D42—224no—
417C2×#127C2×D1111yescharacteristic
418C2×#126—221no—
419C2×#125C2×D1111yescharacteristic, complemented
420C2×#123—221no—
421C2×#121—111no—
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—221no—
426C2×#121—221no—
427C2×#120—221no—
428C2×#120—221no—
429C2×C4×D4—111no—
430C2×C4×D4—111no—
431C2×C4×D4—111no—
432C2×C4×D4—221no—
433C2×#117—111no—
434C22×C4⋊C4—111no—
435#490C2×D1118yescomplemented
436#482—118no—
437#481—118no—
438#478—118no—
439#469—118no—
440#466—118no—
441#459—118no—
442#447—118no—
443#447—118no—
444#442—118no—
445#435—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106—111no—
449C2×C4⋊C8—111no—
450#418—118no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—118no—
458C2×#102C2×D1111yescharacteristic, complemented
459C2×#102C2×D1111yescharacteristic, complemented
460C2×#102C2×D1111yescharacteristic, complemented
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×#97C2×D1111yescharacteristic, complemented
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—84no—
472C22×C11—84no—
473C22×C11#54612yes—
474C22×C11C2×AGL(1,ℤ/8)12yes—
475C22×C11#57612yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—22no—
478C2×D11—28no—
479C2×D11—22no—
480C2×D11—24no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—44no—
485C2×D11—48no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—816no—
492C2×D11—816no—
493C2×D11—84no—
494C2×D11C2×AGL(1,ℤ/8)14yes—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11#54612yes—
500C4×C11C22×#4111yescharacteristic
501C4×C11C2×H(5,𝔽2)11yescharacteristic
502Dic11—22no—
503Dic11—22no—
504Dic11—42no—
505Dic11—42no—
506C25—221no—
507C25—221no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—114no—
511C22×D4—114no—
512C22×D4—111no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—222no—
518C22×D4—222no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—228no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—442no—
527C22×D4—442no—
528C22×D4—448no—
529C22×D4C22×D1111yescharacteristic
530C22×D4C22×D1111yescharacteristic
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—221no—
534C23×C4—221no—
535C23×C4—221no—
536C2×D8—114no—
537C2×D8—114no—
538C2×D8—114no—
539C2×D8—224no—
540C2×D8—442no—
541C2×D8—442no—
542C2×M16—114no—
543C2×M16—442no—
544C22×C8—111no—
545C22×C8—111no—
546C22×C8—114no—
547C22×C8—442no—
548C22×C8C22×D1111yescharacteristic
549C22×C8C22×D1111yescharacteristic
550#127—22no—
551#127C22×D1114yes—
552#126—228no—
553#125—22no—
554#125C22×D1114yescomplemented
555#123—228no—
556#121—114no—
557#121—114no—
558#121—114no—
559#121—114no—
560#121—222no—
561#121—222no—
562#121—228no—
563#121—228no—
564#121—222no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—228no—
573C4×D4—222no—
574C4×D4—222no—
575#117—114no—
576#117—222no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4C22×D1111yescharacteristic
586C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
596C2×C42—221no—
597C2×C42C22×D1111yescharacteristic
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#102C22×D1114yescomplemented
609#102C22×D1114yescomplemented
610#102C22×D1114yescomplemented
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8—114no—
614#97C22×D1114yescomplemented
615C2×C11—82no—
616C2×C11—82no—
617C2×C11#331814yescomplemented
618C2×C11C2×#54611yescharacteristic
619C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
620C2×C11C2×#57611yescharacteristic
621D11—24no—
622D11—42no—
623D11—44no—
624D11—82no—
625C24—21no—
626C24—21no—
627C24—111no—
628C24—111no—
629C24—224no—
630C24—224no—
631C24—221no—
632C24—221no—
633C24—444no—
634C24—444no—
635C24—444no—
636C24—444no—
637C24—882no—
638C24—882no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—44no—
648C2×D4—82no—
649C2×D4—114no—
650C2×D4—114no—
651C2×D4—112no—
652C2×D4—112no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—224no—
658C2×D4—228no—
659C2×D4—228no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—221no—
663C2×D4—221no—
664C2×D4—222no—
665C2×D4—222no—
666C2×D4—222no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—448no—
671C2×D4—448no—
672C2×D4—444no—
673C2×D4—444no—
674C2×D4—4432no—
675C2×D4—444no—
676C2×D4—444no—
677C2×D4—882no—
678C2×D4C23×D1112yes—
679C2×D4C23×D1112yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—111no—
683C22×C4—111no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—224no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—224no—
696C22×C4—224no—
697C22×C4—444no—
698C22×C4—882no—
699C22×C4—882no—
700C22×C4D4×D1111yescharacteristic
701C22×C4D4×D1111yescharacteristic
702C22×C4C23×D1111yescharacteristic
703D8—228no—
704D8—444no—
705D8—444no—
706M16—444no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—112no—
710C2×C8—112no—
711C2×C8—222no—
712C2×C8—222no—
713C2×C8—444no—
714C2×C8C23×D1112yes—
715C2×C8C23×D1112yes—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—114no—
721C4⋊C4—112no—
722C4⋊C4—112no—
723C4⋊C4—224no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4C23×D1112yes—
727C4⋊C4C23×D1112yes—
728C22⋊C4—114no—
729C22⋊C4—114no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4—224no—
736C22⋊C4—224no—
737C42—224no—
738C42D4×D1112yes—
739C42C23×D1112yes—
740C11C2×#331811yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—114no—
750C23—112no—
751C23—112no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—224no—
759C23—222no—
760C23—448no—
761C23—448no—
762C23—448no—
763C23—448no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—884no—
770C23—884no—
771C23—8816no—
772C23—8816no—
773C23C2×D4×D1111yescharacteristic
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—114no—
783D4—228no—
784D4—222no—
785D4—222no—
786D4—222no—
787D4—224no—
788D4—448no—
789D4—448no—
790D4—448no—
791D4—448no—
792D4—448no—
793D4—442no—
794D4—884no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—112no—
802C2×C4—112no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—224no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—448no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—884no—
817C2×C4—884no—
818C2×C4C2×D4×D1112yes—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4#41×D1112yes—
822C2×C4#6704212yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—84no—
835C22—84no—
836C22—114no—
837C22—228no—
838C22—222no—
839C22—222no—
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#1062320712yes—
855C22D11×AGL(1,ℤ/8)12yes—
856C22#1062330512yes—
857C22C22×D4×D1111yescharacteristic
858C4—22no—
859C4—22no—
860C4—42no—
861C4—42no—
862C4—222no—
863C4—222no—
864C4—442no—
865C4—442no—
866C4#1062320712yes—
867C4C2×#41×D1111yescharacteristic
868C4C2×#6704211yescharacteristic
869C2—82no—
870C2—82no—
871C2—224no—
872C2—442no—
873C2—444no—
874C2—882no—
875C2#1308075614yesdirect product factor
876C2C2×#1062320711yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
hypercenterC2×#490D11
hypocenterC11C2×#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623248C2semidirect
3. #13080756C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622685C2semidirect
10. C2×#10622386C2semidirect
11. C2×#10622386C2semidirect
12. C2×#10622324C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622383C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#490C2semidirect
21. C2×C11×#125C22semidirect
27. C22×#4323C22semidirect
28. C22×#4323C22semidirect
30. C22×#4313C22semidirect
31. C22×C8×D11C22semidirect
33. #10623248C22semidirect
35. #10623226C22semidirect
38. C2×#66948C22semidirect
39. C2×#66948C22semidirect
42. C2×#66945C22semidirect
43. C2×C4⋊C4×D11C22semidirect
46. C2×C4×D44C22semidirect
47. C11×#490C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#97C22semidirect
53. C2×#66896C22semidirect
54. C2×#66896C22semidirect
56. C2×#66885C22semidirect
57. C2×(C2×D11)⋊C8C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. C2×#66881C22semidirect
60. #10622685C22semidirect
61. #10622679C22semidirect
64. C2×#66872C22semidirect
65. C2×#66871C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622395C22semidirect
68. #10622392C22semidirect
69. #10622390C22semidirect
70. #10622388C22semidirect
71. #10622386C22semidirect
72. #10622386C22semidirect
73. #10622383C22semidirect
74. D11×#102C22semidirect
75. #10622324C22semidirect
76. #10622319C22semidirect
112. C11×#125C23semidirect
129. C2×#4323C23semidirect
130. C2×#4323C23semidirect
148. C2×#4313C23semidirect
150. C2×C8×D11C23semidirect
155. #66948C23semidirect
156. #66948C23semidirect
160. #66945C23semidirect
162. C4⋊C4×D11C23semidirect
168. C4×D44C23semidirect
169. C11×#102C23semidirect
170. C11×#102C23semidirect
171. C11×#102C23semidirect
172. C11×#102C23semidirect
173. C11×#97C23semidirect
174. #66896C23semidirect
175. #66896C23semidirect
177. #66885C23semidirect
178. (C2×D11)⋊C8C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. #66881C23semidirect
183. #66872C23semidirect
184. #66871C23semidirect
185. C4⋊(C11⋊C8)C23semidirect
305. C2×#490D11semidirect
419. C2×#125C2×D11semidirect
435. #490C2×D11semidirect
458. C2×#102C2×D11semidirect
459. C2×#102C2×D11semidirect
460. C2×#102C2×D11semidirect
461. C2×#102C2×D11semidirect
464. C2×#97C2×D11semidirect
554. #125C22×D11semidirect
608. #102C22×D11semidirect
609. #102C22×D11semidirect
610. #102C22×D11semidirect
611. #102C22×D11semidirect
614. #97C22×D11semidirect
617. C2×C11#3318semidirect
740. C11C2×#3318semidirect
875. C2#13080756direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232262
C2×#106232482
#130807562
C2×#106223902
C2×#106223922
C2×#106226792
C2×#106223952
C2×#106223882
C2×#106226852
C2×#106223862
C2×#106223242
C2×#106223192
C2×#106223832
C2×D11×#1022
C2×C11×#4902
C2×#331811