Finite Group Databasebeta

← C2×#13080762 #15630336

Subgroups — C2×#13080762 #15630336

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×#10623089C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic, complemented
3#13080762C2116yesmaximal, direct product factor
4C2×#10622326C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622479C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622388C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic, complemented
12C2×#10622769C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C23×D44—21no—
20C22×C11×D8C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C2×#66991C2211yescharacteristic, complemented
24C2×#66991C2211yescharacteristic, complemented
25C22×#4323C2211yescharacteristic, complemented
26C22×#4323C2211yescharacteristic, complemented
27C2×#66983—21no—
28C2×#66982—21no—
29C2×C4×C22⋊D11—21no—
30C22×#4313C2211yescharacteristic, complemented
31C22×C8×D11C2211yescharacteristic, complemented
32#10623089—24no—
33#10623089C2218yescomplemented
34D4×D44—24no—
35D4×D44C2218yescomplemented
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66945C2211yescharacteristic, complemented
39C2×C4⋊C4×D11C2211yescharacteristic, complemented
40C2×#66937—21no—
41C2×#66935—21no—
42C2×#66935—21no—
43C2×#66932—21no—
44C2×#66927C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66923C2211yescharacteristic, complemented
47C11×#442C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#97C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622769C2218yescomplemented
55#10622769C2218yescomplemented
56C2×#66885C2211yescharacteristic, complemented
57C2×#66885C2211yescharacteristic, complemented
58C2×#66885C2211yescharacteristic, complemented
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
61C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
62#10622628C2218yescomplemented
63#10622622C2218yescomplemented
64C2×#66873C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic, complemented
66C2×#66872C2211yescharacteristic, complemented
67C2×#66871C2211yescharacteristic, complemented
68C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
69#10622479C2218yescomplemented
70#10622476C2218yescomplemented
71#10622395C2218yescomplemented
72#10622388C2218yescomplemented
73#10622383C2218yescomplemented
74D11×#102C2218yescomplemented
75#10622326C2218yescomplemented
76#10622319C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C2×D4×D11—24no—
88C2×D4×D11—24no—
89C2×D4×D11—22no—
90C2×D4×D11—22no—
91C2×D4×D11—42no—
92C2×D4×D11—42no—
93C2×D4×D11C2314yes—
94C2×D4×D11C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—28no—
100C22×D44—48no—
101C22×D44D411yescharacteristic
102C22×D44C2311yescharacteristic
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C2×C11×D8—24no—
108C2×C11×D8C2314yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yescomplemented
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66991—22no—
123#66991—22no—
124#66991C2314yescomplemented
125#66991C2314yescomplemented
126C2×#4323—42no—
127C2×#4323—42no—
128C2×#4323C2314yescomplemented
129C2×#4323C2314yescomplemented
130#66983—28no—
131#66982—28no—
132C4×C22⋊D11—28no—
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×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×#4313—42no—
148C2×#4313C2314yescomplemented
149C2×C8×D11—42no—
150C2×C8×D11C2314yescomplemented
151#66948—22no—
152#66948—22no—
153#66948C2314yes—
154#66948C2314yes—
155#66945—22no—
156#66945C2314yescomplemented
157C4⋊C4×D11—22no—
158C4⋊C4×D11C2314yescomplemented
159#66937—28no—
160#66935—28no—
161#66935—28no—
162#66932—28no—
163#66927—22no—
164#66927C2314yes—
165C4×D44D414yes—
166C4×D44C2314yes—
167#66923—22no—
168#66923C2314yescomplemented
169C11×#106C2314yescomplemented
170C11×#102C2314yes—
171C11×#102C2314yescomplemented
172C11×#97C2314yescomplemented
173#66896C2314yes—
174#66896C2314yes—
175#66885C2314yescomplemented
176#66885C2314yescomplemented
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yescomplemented
180(C2×D11)⋊C8C2314yescomplemented
181#66873C2314yescomplemented
182#66873C2314yescomplemented
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—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11#4114yes—
207C2×D4×C11C2412yes—
208C2×D4×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—44no—
214C22×C4×C11—82no—
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—82no—
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—
236C2×D44—24no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44—24no—
242C2×D44—24no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44—432no—
250C2×D44—44no—
251C2×D44—82no—
252C2×D44C2×D414yes—
253C2×D44C2412yes—
254C2×D44C2412yes—
255C2×C4×D11—24no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—82no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2412yes—
264C2×C4×D11C2412yes—
265C11×D8—28no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11C2412yes—
269C2×C8×C11C2412yes—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C42×C11C2×D412yes—
277C42×C11C2412yes—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
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—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2×D414yes—
290C4⋊Dic11C2412yes—
291C4⋊Dic11C2412yes—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295C4×Dic11—24no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300#4313—44no—
301C8×D11—44no—
302C2×#553—111no—
303C2×D42—111no—
304#3318—1116no—
305C2×#490—111no—
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×#442D1111yescharacteristic, complemented
315C2×#435—111no—
316C2×#418—111no—
317C22×#102—111no—
318C23×C11—24no—
319C23×C11—22no—
320C23×C11—22no—
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—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—48no—
335C22×D11—48no—
336C22×D11—48no—
337C22×D11—42no—
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—24no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—42no—
356D4×C11C2×#4114yes—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—48no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—84no—
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—84no—
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—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—48no—
390D44—48no—
391D44—42no—
392D44—42no—
393D44—84no—
394C4×D11—24no—
395C4×D11—24no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—22no—
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×D8C2×D1111yescharacteristic
411C22×M16—111no—
412C23×C8—111no—
413#553—118no—
414#553—224no—
415D42—118no—
416D42—224no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#125—111no—
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—221no—
431C2×C4×D4C2×D1111yescharacteristic
432C2×C4×D4C2×D1111yescharacteristic, complemented
433C2×#117—111no—
434C22×C4⋊C4—111no—
435#490—118no—
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#442C2×D1118yescomplemented
445#435—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106C2×D1111yescharacteristic, complemented
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—111no—
458C2×#102—111no—
459C2×#102—118no—
460C2×#102C2×D1111yescharacteristic
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×#97C2×D1111yescharacteristic, complemented
465C22×C11—24no—
466C22×C11—48no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
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—22no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—44no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—816no—
491C2×D11—816no—
492C2×D11—84no—
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—114no—
509C22×D4—114no—
510C22×D4—111no—
511C22×D4—111no—
512C22×D4—111no—
513C22×D4—228no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—222no—
517C22×D4—222no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—448no—
527C22×D4—442no—
528C22×D4—442no—
529C22×D4C22×D1111yescharacteristic
530C22×D4C22×D1111yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—221no—
536C2×D8—24no—
537C2×D8—114no—
538C2×D8—114no—
539C2×D8—442no—
540C2×D8—442no—
541C2×D8C22×D1114yes—
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—114no—
551#127—222no—
552#126—228no—
553#125—114no—
554#125—222no—
555#123—228no—
556#121—114no—
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#121—222no—
566#120—228no—
567#120—228no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—228no—
573C4×D4C22×D1114yes—
574C4×D4C22×D1114yescomplemented
575#117—114no—
576#117—222no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4C22×D1111yescharacteristic
586C2×C4⋊C4C22×D1111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—111no—
590C2×C22⋊C4—111no—
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#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×D1114yes—
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8—114no—
614#97C22×D1114yescomplemented
615C2×C11—44no—
616C2×C11—82no—
617C2×C11#331814yescomplemented
618C2×C11C2×#54611yescharacteristic
619C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
620C2×C11C2×#57611yescharacteristic
621D11—24no—
622D11—42no—
623D11—82no—
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—22no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—114no—
645C2×D4—112no—
646C2×D4—112no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—224no—
659C2×D4—221no—
660C2×D4—221no—
661C2×D4—224no—
662C2×D4—222no—
663C2×D4—222no—
664C2×D4—444no—
665C2×D4—4432no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—448no—
671C2×D4—448no—
672C2×D4—444no—
673C2×D4—444no—
674C2×D4—444no—
675C2×D4—882no—
676C2×D4—882no—
677C2×D4#433914yes—
678C2×D4C23×D1112yes—
679C2×D4C23×D1112yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—44no—
685C22×C4—82no—
686C22×C4—111no—
687C22×C4—111no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—224no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—882no—
700C22×C4D4×D1111yescharacteristic
701C22×C4D4×D1111yescharacteristic
702C22×C4C23×D1111yescharacteristic
703D8—28no—
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—21no—
717C4⋊C4—21no—
718C4⋊C4—114no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4—224no—
725C4⋊C4—224no—
726C4⋊C4C23×D1112yes—
727C4⋊C4C23×D1112yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—114no—
731C22⋊C4—114no—
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—24no—
742C23—22no—
743C23—22no—
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—222no—
759C23—448no—
760C23—448no—
761C23—448no—
762C23—448no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—884no—
770C23—884no—
771C23—8816no—
772C23—8816no—
773C23C2×D4×D1111yescharacteristic
774D4—24no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—42no—
779D4—228no—
780D4—222no—
781D4—222no—
782D4—222no—
783D4—222no—
784D4—448no—
785D4—448no—
786D4—448no—
787D4—448no—
788D4—448no—
789D4—448no—
790D4—442no—
791D4—442no—
792D4—884no—
793D4—884no—
794D4C2×#433914yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—48no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—112no—
804C2×C4—112no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—224no—
808C2×C4—224no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—442no—
816C2×C4—442no—
817C2×C4—884no—
818C2×C4C2×#433912yes—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1112yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4#6704212yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—24no—
829C22—48no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—114no—
837C22—228no—
838C22—222no—
839C22—222no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—444no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—8816no—
852C22—884no—
853C22—884no—
854C22#1062308112yes—
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#1062308112yes—
867C4C22×#433911yescharacteristic
868C4C2×#6704211yescharacteristic
869C2—44no—
870C2—82no—
871C2—224no—
872C2—442no—
873C2—882no—
874C2—882no—
875C2#1308076214yesdirect product factor
876C2C2×#1062308111yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
hypercenterC2×#442D11
hypocenterC11C2×#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623089C2semidirect
2. C2×D4×D44C2semidirect
3. #13080762C2direct (N × H)
4. C2×#10622326C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622388C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622769C2semidirect
12. C2×#10622769C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622383C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#442C2semidirect
22. C2×C4×D4×C11C22semidirect
23. C2×#66991C22semidirect
24. C2×#66991C22semidirect
25. C22×#4323C22semidirect
26. C22×#4323C22semidirect
30. C22×#4313C22semidirect
31. C22×C8×D11C22semidirect
33. #10623089C22semidirect
35. D4×D44C22semidirect
38. C2×#66945C22semidirect
39. C2×C4⋊C4×D11C22semidirect
46. C2×#66923C22semidirect
47. C11×#442C22semidirect
48. C2×C11×#106C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#97C22semidirect
54. #10622769C22semidirect
55. #10622769C22semidirect
56. C2×#66885C22semidirect
57. C2×#66885C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
60. C2×(C2×D11)⋊C8C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. #10622628C22semidirect
63. #10622622C22semidirect
64. C2×#66873C22semidirect
65. C2×#66873C22semidirect
66. C2×#66872C22semidirect
67. C2×#66871C22semidirect
68. C2×C4⋊(C11⋊C8)C22semidirect
69. #10622479C22semidirect
70. #10622476C22semidirect
71. #10622395C22semidirect
72. #10622388C22semidirect
73. #10622383C22semidirect
74. D11×#102C22semidirect
75. #10622326C22semidirect
76. #10622319C22semidirect
114. C4×D4×C11C23semidirect
124. #66991C23semidirect
125. #66991C23semidirect
128. C2×#4323C23semidirect
129. C2×#4323C23semidirect
148. C2×#4313C23semidirect
150. C2×C8×D11C23semidirect
156. #66945C23semidirect
158. C4⋊C4×D11C23semidirect
168. #66923C23semidirect
169. C11×#106C23semidirect
171. C11×#102C23semidirect
172. C11×#97C23semidirect
175. #66885C23semidirect
176. #66885C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. #66873C23semidirect
182. #66873C23semidirect
183. #66872C23semidirect
184. #66871C23semidirect
185. C4⋊(C11⋊C8)C23semidirect
314. C2×#442D11semidirect
432. C2×C4×D4C2×D11semidirect
444. #442C2×D11semidirect
448. C2×#106C2×D11semidirect
461. C2×#102C2×D11semidirect
464. C2×#97C2×D11semidirect
574. C4×D4C22×D11semidirect
600. #106C22×D11semidirect
611. #102C22×D11semidirect
614. #97C22×D11semidirect
617. C2×C11#3318semidirect
740. C11C2×#3318semidirect
875. C2#13080762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230892
C2×D4×D442
#130807622
C2×#106223262
C2×#106224762
C2×#106224792
C2×#106226222
C2×#106223952
C2×#106223882
C2×#106226282
C2×#106227692
C2×#106223192
C2×#106223832
C2×D11×#1022
C2×C11×#4422
C2×#331811