Finite Group Databasebeta

← C2×#13078158 #15620701

Subgroups — C2×#13078158 #15620701

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C22×#66972C211yesmaximal, characteristic, complemented
3C2×#10623205C211yesmaximal, characteristic, complemented
4C2×#10623105C211yesmaximal, characteristic, complemented
5#13078158C2116yesmaximal, direct product factor
6C2×#10622798C211yesmaximal, characteristic, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622776C211yesmaximal, characteristic, complemented
9C2×#10622432C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622456C211yesmaximal, characteristic, complemented
12C2×#10622399C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic, complemented
29C2×#66993C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66972—28no—
32C2×#66972C2218yescomplemented
33C2×#66967—28no—
34C2×#66967C2218yescomplemented
35C22×D88C2211yescharacteristic
36C22×D88C2211yescharacteristic, complemented
37C22×#4313C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623205—24no—
40#10623205C2218yescomplemented
41#10623105—24no—
42#10623105C2218yescomplemented
43C2×#66946—21no—
44C2×#66946C2211yescharacteristic, complemented
45C2×C4⋊C4×D11—21no—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66937—21no—
48C2×#66937—21no—
49C2×#66935—21no—
50C2×#66935—21no—
51C2×#66927C2211yescharacteristic
52C2×C4×D44—21no—
53C2×C4×D44C2211yescharacteristic, complemented
54C2×#66925—21no—
55C2×#66925C2211yescharacteristic
56C11×#464C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic
62#10622798C2218yescomplemented
63#10622776C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622670C2218yescomplemented
69#10622640C2218yescomplemented
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic, complemented
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622456C2218yescomplemented
74#10622452C2218yescomplemented
75#10622432C2218yescomplemented
76#10622416C2218yescomplemented
77#10622399C2218yescomplemented
78D11×#102C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×#4343—22no—
87C2×#4343—22no—
88C2×#4343—24no—
89C2×#4343—24no—
90C2×#4343—24no—
91C2×#4343D418yescomplemented
92C2×#4343C2314yes—
93C2×#4343C2314yes—
94C2×D4×D11—24no—
95C2×D4×D11—22no—
96C2×D4×D11—24no—
97C2×D4×D11C2314yes—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44C2311yescharacteristic
103C22×D44C2311yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11—21no—
110C22×C4×D11C2311yescharacteristic
111C2×C11×Q16—24no—
112C2×C11×Q16C2314yescomplemented
113C2×C11×SD16—24no—
114C2×C11×SD16C2314yes—
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×#124—22no—
118C11×#124C2314yes—
119C4×Q8×C11—22no—
120C4×Q8×C11C2314yescomplemented
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C42×C11—21no—
126C2×C42×C11C2311yescharacteristic
127#67000—22no—
128#67000C2314yes—
129Q8×Dic11—22no—
130Q8×Dic11C2314yescomplemented
131C2×#4325—24no—
132C2×#4325—24no—
133C2×#4325—24no—
134C2×#4325C2314yes—
135C2×#4325C2314yescomplemented
136C2×#4325C2314yescomplemented
137#66993—22no—
138#66993C2314yes—
139C2×#4323—24no—
140C2×#4323C2314yes—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4D411yescharacteristic
146C2×(C2×D11)⋊C4D411yescharacteristic
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4D411yescharacteristic
151C2×Dic11⋊C4D411yescharacteristic
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66972—232no—
157#66967—232no—
158C2×D88—24no—
159C2×D88—24no—
160C2×D88C2314yes—
161C2×D88C2314yescomplemented
162C2×#4313—24no—
163C2×#4313C2314yes—
164C2×C8×D11—24no—
165C2×C8×D11C2314yes—
166#66946—28no—
167#66946—22no—
168#66946C2314yescomplemented
169C4⋊C4×D11—22no—
170C4⋊C4×D11—28no—
171C4⋊C4×D11C2314yes—
172#66937—28no—
173#66937—28no—
174#66935—28no—
175#66935—28no—
176#66927—22no—
177#66927C2314yes—
178C4×D44—22no—
179C4×D44—28no—
180C4×D44C2314yescomplemented
181#66925—28no—
182#66925D414yes—
183#66925C2314yes—
184C11×C4⋊C8C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yes—
187#66899C2314yescomplemented
188#66896C2314yes—
189#66885C2314yes—
190#66885C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66873C2314yes—
194#66873C2314yescomplemented
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3045—111nomaximal, Sylow
197C24×C11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—24no—
202C23×D11—44no—
203C23×D11—82no—
204C23×D11—82no—
205C23×D11C2×D411yescharacteristic
206C2×Q8×C11—21no—
207C2×Q8×C11—21no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11C2×D414yes—
212C2×Q8×C11C2412yes—
213C2×Q8×C11C2412yes—
214C2×D4×C11—22no—
215C2×D4×C11—21no—
216C2×D4×C11—22no—
217C2×D4×C11C2412yes—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11—82no—
230C22×Dic11—21no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—216no—
235#4343—28no—
236#4343—28no—
237#4343—28no—
238#4343—48no—
239#4343C2×D4116yescomplemented
240D4×D11—28no—
241D4×D11—28no—
242D4×D11—48no—
243C2×D44—28no—
244C2×D44—24no—
245C2×D44—24no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44—21no—
249C2×D44—24no—
250C2×D44—24no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—44no—
257C2×D44—82no—
258C2×D44—82no—
259C2×D44C2×D414yes—
260C2×D44C2412yes—
261C2×D44C2412yes—
262C2×D44C2412yes—
263C2×C4×D11—28no—
264C2×C4×D11—24no—
265C2×C4×D11—24no—
266C2×C4×D11—24no—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×C4×D11—44no—
270C2×C4×D11—82no—
271C2×C4×D11—82no—
272C2×C4×D11—82no—
273C2×C4×D11C2×D414yes—
274C2×C4×D11C2×D412yes—
275C2×C4×D11#4114yes—
276C2×C4×D11C2412yes—
277C11×Q16—28no—
278C11×SD16—28no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—24no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C42×C11—24no—
289C42×C11C2×D412yes—
290C42×C11C2412yes—
291#4325—28no—
292#4325—28no—
293#4325—28no—
294#4323—28no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4C2×D414yes—
300(C2×D11)⋊C4C2×D414yes—
301C4⋊Dic11—24no—
302C4⋊Dic11—21no—
303C4⋊Dic11C2412yes—
304Dic11⋊C4—24no—
305Dic11⋊C4C2×D414yes—
306Dic11⋊C4C2×D414yes—
307C4×Dic11—24no—
308C4×Dic11C2×D412yes—
309C4×Dic11C2412yes—
310C2×C11⋊C8—22no—
311C2×C11⋊C8—22no—
312C2×C11⋊C8C2412yes—
313C2×C11⋊C8C2412yes—
314D88—28no—
315D88—28no—
316#4313—28no—
317C8×D11—28no—
318C22×AGL(1,ℤ/8)—111no—
319C22×#135—111no—
320C2×#535—111no—
321C2×#520—111no—
322#3045—1116no—
323C2×#464—111no—
324C2×#464D1111yescharacteristic, complemented
325C2×#460—111no—
326C2×#460—111no—
327C2×#463—111no—
328C2×#463—111no—
329C2×#459—111no—
330C2×#459—111no—
331C2×#424—111no—
332C2×#417—111no—
333C22×#102—111no—
334C23×C11—22no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11C22×D411yescharacteristic
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—24no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—48no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—816no—
357C22×D11#12114yes—
358C22×D11C22×D412yes—
359Q8×C11—24no—
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—42no—
364Q8×C11C22×D414yes—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—42no—
368C2×C4×C11—24no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D412yes—
380C2×C4×C11C2×#4112yes—
381C2×C4×C11C2511yescharacteristic
382C22⋊D11—48no—
383C22⋊D11—84no—
384C22⋊D11—84no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—42no—
389C2×Dic11#12114yes—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393D44—216no—
394D44—24no—
395D44—22no—
396D44—22no—
397D44—22no—
398D44—22no—
399D44—22no—
400D44—48no—
401D44—42no—
402D44—42no—
403D44—84no—
404D44—84no—
405D44C22×D414yes—
406C4×D11—216no—
407C4×D11—48no—
408C4×D11—84no—
409C4×D11—84no—
410C4×D11—84no—
411C4×D11#12118yes—
412C4×D11C22×D414yes—
413C4×D11C2×#4114yes—
414C8×C11—22no—
415C8×C11—22no—
416C11⋊C8—22no—
417C11⋊C8—22no—
418C22×#41—111no—
419C22×#41—111no—
420C23×D4—111no—
421C2×AGL(1,ℤ/8)—118no—
422C2×AGL(1,ℤ/8)—228no—
423C2×#135—118no—
424C2×#135—228no—
425C22×Q16C2×D1111yescharacteristic, complemented
426C22×SD16—111no—
427C22×SD16—111no—
428C22×SD16—111no—
429C22×SD16C2×D1111yescharacteristic
430C22×D8—111no—
431C22×D8—111no—
432C22×D8—111no—
433C22×M16—111no—
434C23×C8—111no—
435#535—118no—
436#535—224no—
437C2×#127—111no—
438C2×#127—111no—
439C2×#124—111no—
440C2×#124C2×D1111yescharacteristic
441C2×#121—221no—
442C2×#121—221no—
443C2×#120—221no—
444C2×#120—221no—
445#520—118no—
446#520—224no—
447C2×C4×Q8—111no—
448C2×C4×Q8C2×D1111yescharacteristic, complemented
449C2×C4×D4—111no—
450C2×C4×D4—111no—
451C2×C4×D4—221no—
452C2×C4×D4—221no—
453C2×#117—111no—
454C2×#117—221no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—221no—
457#464—118no—
458#464C2×D1118yescomplemented
459#463—118no—
460#463—118no—
461#460—118no—
462#460—118no—
463#459—118no—
464#459—118no—
465#424—118no—
466C2×C4⋊C8—111no—
467C2×C4⋊C8—111no—
468C2×C4⋊C8—111no—
469C2×C4⋊C8C2×D1111yescharacteristic, complemented
470#417—118no—
471C2×#103—111no—
472C2×#103C2×D1111yescharacteristic, complemented
473C2×#102—111no—
474C2×#102—111no—
475C2×#102—111no—
476C2×#102—111no—
477C2×#102—111no—
478C2×#102—118no—
479C2×#102C2×D1111yescharacteristic
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—84no—
484C22×C11C2×#12112yes—
485C22×C11#57612yes—
486C22×C11#57712yes—
487C22×C11C23×D411yescharacteristic
488C2×D11—28no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—24no—
492C2×D11—48no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—816no—
502C2×D11—84no—
503C2×D11—84no—
504C2×D11C2×#12114yes—
505C4×C11—24no—
506C4×C11—22no—
507C4×C11—22no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11C2×#12112yes—
511C4×C11C23×D411yescharacteristic
512C4×C11C22×#4111yescharacteristic
513Dic11—22no—
514Dic11—22no—
515Dic11—42no—
516Dic11C2×#12114yes—
517C25—221no—
518C2×#41—118no—
519C2×#41—114no—
520C2×#41—114no—
521C2×#41—222no—
522C2×#41—224no—
523C2×#41—222no—
524C2×#41—224no—
525C2×#41—224no—
526C22×Q8C22×D1111yescharacteristic
527C22×Q8C22×D1111yescharacteristic
528C22×D4—114no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—111no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—224no—
535C22×D4—224no—
536C22×D4—222no—
537C22×D4—221no—
538C22×D4—221no—
539C22×D4—221no—
540C22×D4—221no—
541C22×D4—221no—
542C22×D4C22×D1111yescharacteristic
543C23×C4—111no—
544C23×C4—221no—
545C23×C4—221no—
546C23×C4—221no—
547C23×C4—221no—
548C23×C4—221no—
549AGL(1,ℤ/8)—2232no—
550#135—2232no—
551C2×Q16—24no—
552C2×Q16C22×D1114yescomplemented
553C2×SD16—24no—
554C2×SD16—114no—
555C2×SD16—114no—
556C2×SD16—114no—
557C2×SD16—224no—
558C2×SD16—224no—
559C2×SD16—224no—
560C2×SD16C22×D1114yes—
561C2×D8—114no—
562C2×D8—114no—
563C2×D8—114no—
564C2×D8—224no—
565C2×D8—224no—
566C2×D8—224no—
567C2×M16—114no—
568C2×M16—224no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—114no—
572C22×C8—224no—
573C22×C8C22×D1111yescharacteristic
574C22×C8C22×D1111yescharacteristic
575#127—114no—
576#127—114no—
577#127—222no—
578#127—222no—
579#124—22no—
580#124—114no—
581#124—222no—
582#124C22×D1114yes—
583#121—228no—
584#121—228no—
585#120—228no—
586#120—228no—
587C4×Q8—22no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8C22×D1114yescomplemented
591C4×D4—114no—
592C4×D4—114no—
593C4×D4—228no—
594C4×D4—222no—
595C4×D4—228no—
596C4×D4—222no—
597#117—114no—
598#117—114no—
599#117—228no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—111no—
604C2×C4⋊C4—114no—
605C2×C4⋊C4—228no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—111no—
613C2×C22⋊C4—111no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C42—21no—
619C2×C42—111no—
620C2×C42—221no—
621C2×C42C22×D1111yescharacteristic
622C4⋊C8—114no—
623C4⋊C8—114no—
624C4⋊C8—114no—
625C4⋊C8C22×D1114yescomplemented
626#103—114no—
627#103C22×D1114yescomplemented
628#102—114no—
629#102—114no—
630#102—114no—
631#102—114no—
632#102—114no—
633#102C22×D1114yes—
634C2×C11—82no—
635C2×C11#304514yescomplemented
636C2×C11C22×#12111yescharacteristic
637C2×C11C2×#57611yescharacteristic
638C2×C11C2×#57711yescharacteristic
639D11—24no—
640D11—44no—
641D11—82no—
642D11—82no—
643C24—21no—
644C24—111no—
645C24—224no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—444no—
650C24—882no—
651C24—882no—
652#41—1116no—
653#41—2216no—
654#41—228no—
655#41—228no—
656#41—228no—
657#41—448no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8D4×D1114yes—
664C2×Q8C23×D1112yes—
665C2×Q8C23×D1112yes—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—114no—
670C2×D4—112no—
671C2×D4—112no—
672C2×D4—112no—
673C2×D4—224no—
674C2×D4—228no—
675C2×D4—224no—
676C2×D4—228no—
677C2×D4—228no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—221no—
682C2×D4—222no—
683C2×D4—222no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—444no—
692C2×D4—448no—
693C2×D4—444no—
694C2×D4—882no—
695C2×D4—882no—
696C2×D4—882no—
697C2×D4—882no—
698C2×D4C23×D1112yes—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—111no—
703C22×C4—112no—
704C22×C4—114no—
705C22×C4—114no—
706C22×C4—112no—
707C22×C4—111no—
708C22×C4—111no—
709C22×C4—224no—
710C22×C4—228no—
711C22×C4—224no—
712C22×C4—224no—
713C22×C4—224no—
714C22×C4—221no—
715C22×C4—224no—
716C22×C4—444no—
717C22×C4—882no—
718C22×C4—882no—
719C22×C4—882no—
720C22×C4D4×D1111yescharacteristic
721C22×C4D4×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723Q16—28no—
724SD16—28no—
725SD16—228no—
726SD16—228no—
727SD16—228no—
728D8—228no—
729D8—228no—
730D8—228no—
731M16—228no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—112no—
735C2×C8—112no—
736C2×C8—228no—
737C2×C8—222no—
738C2×C8—222no—
739C2×C8C23×D1112yes—
740C2×C8C23×D1112yes—
741C4⋊C4—24no—
742C4⋊C4—21no—
743C4⋊C4—114no—
744C4⋊C4—114no—
745C4⋊C4—112no—
746C4⋊C4—224no—
747C4⋊C4—224no—
748C4⋊C4—221no—
749C4⋊C4C23×D1112yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—114no—
753C22⋊C4—114no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C42—24no—
759C42—112no—
760C42—112no—
761C42—224no—
762C42D4×D1112yes—
763C42C23×D1112yes—
764C11C2×#304511yescharacteristic, complemented, Sylow
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—114no—
770C23—112no—
771C23—222no—
772C23—222no—
773C23—224no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—448no—
778C23—442no—
779C23—442no—
780C23—442no—
781C23—442no—
782C23—442no—
783C23—442no—
784C23—442no—
785C23—442no—
786C23—884no—
787C23—884no—
788C23—8816no—
789C23C2×D4×D1111yescharacteristic
790Q8—24no—
791Q8—22no—
792Q8—22no—
793Q8—22no—
794Q8—42no—
795Q8C2×D4×D1114yes—
796D4—22no—
797D4—22no—
798D4—42no—
799D4—114no—
800D4—2216no—
801D4—224no—
802D4—222no—
803D4—222no—
804D4—222no—
805D4—222no—
806D4—222no—
807D4—448no—
808D4—448no—
809D4—442no—
810D4—442no—
811D4—884no—
812D4—884no—
813D4—884no—
814D4—884no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—114no—
824C2×C4—112no—
825C2×C4—118no—
826C2×C4—114no—
827C2×C4—114no—
828C2×C4—112no—
829C2×C4—112no—
830C2×C4—2216no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—448no—
835C2×C4—442no—
836C2×C4—884no—
837C2×C4—884no—
838C2×C4—884no—
839C2×C4C2×D4×D1112yes—
840C2×C4C2×D4×D1112yes—
841C2×C4C2×D4×D1111yescharacteristic
842C2×C4C2×D4×D1112yes—
843C2×C4#41×D1112yes—
844C2×C4C24×D1111yescharacteristic
845C8—22no—
846C8—22no—
847C8—222no—
848C8—222no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—114no—
854C22—228no—
855C22—222no—
856C22—222no—
857C22—224no—
858C22—448no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—8816no—
868C22—884no—
869C22—884no—
870C22D11×#12112yes—
871C22#1062330012yes—
872C22#1062330912yes—
873C22C22×D4×D1111yescharacteristic
874C4—22no—
875C4—24no—
876C4—22no—
877C4—42no—
878C4—42no—
879C4—114no—
880C4—222no—
881C4—222no—
882C4—442no—
883C4D11×#12112yes—
884C4C22×D4×D1111yescharacteristic
885C4C2×#41×D1111yescharacteristic
886C2—82no—
887C2—224no—
888C2—444no—
889C2—882no—
890C2—882no—
891C2#1307815814yesdirect product factor
892C2C2×D11×#12111yescharacteristic
893C2C2×#1062330011yescharacteristic
894C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
hypercenterC2×#464D11
hypocenterC11C2×#3045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C22×#66972C2semidirect
3. C2×#10623205C2semidirect
4. C2×#10623105C2semidirect
5. #13078158C2direct (N × H)
6. C2×#10622798C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622776C2semidirect
9. C2×#10622432C2semidirect
10. C2×#10622670C2semidirect
11. C2×#10622456C2semidirect
12. C2×#10622399C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622416C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#464C2semidirect
20. C22×C11×Q16C22semidirect
23. C2×C4×Q8×C11C22semidirect
25. C2×Q8×Dic11C22semidirect
27. C22×#4325C22semidirect
28. C22×#4325C22semidirect
32. C2×#66972C22semidirect
34. C2×#66967C22semidirect
36. C22×D88C22semidirect
40. #10623205C22semidirect
42. #10623105C22semidirect
44. C2×#66946C22semidirect
53. C2×C4×D44C22semidirect
56. C11×#464C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. C2×C11×#103C22semidirect
60. C2×#66899C22semidirect
62. #10622798C22semidirect
63. #10622776C22semidirect
65. C2×#66885C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622670C22semidirect
69. #10622640C22semidirect
71. C2×#66873C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622456C22semidirect
74. #10622452C22semidirect
75. #10622432C22semidirect
76. #10622416C22semidirect
77. #10622399C22semidirect
78. D11×#102C22semidirect
91. C2×#4343D4semidirect
112. C2×C11×Q16C23semidirect
120. C4×Q8×C11C23semidirect
130. Q8×Dic11C23semidirect
135. C2×#4325C23semidirect
136. C2×#4325C23semidirect
161. C2×D88C23semidirect
168. #66946C23semidirect
180. C4×D44C23semidirect
184. C11×C4⋊C8C23semidirect
185. C11×#103C23semidirect
187. #66899C23semidirect
190. #66885C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
194. #66873C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
239. #4343C2×D4semidirect
324. C2×#464D11semidirect
425. C22×Q16C2×D11semidirect
448. C2×C4×Q8C2×D11semidirect
458. #464C2×D11semidirect
469. C2×C4⋊C8C2×D11semidirect
472. C2×#103C2×D11semidirect
552. C2×Q16C22×D11semidirect
590. C4×Q8C22×D11semidirect
625. C4⋊C8C22×D11semidirect
627. #103C22×D11semidirect
635. C2×C11#3045semidirect
764. C11C2×#3045semidirect
891. C2#13078158direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C22×#669722
C2×#106232052
C2×#106231052
#130781582
C2×#106227982
C2×#106226402
C2×#106227762
C2×#106224322
C2×#106226702
C2×#106224562
C2×#106223992
C2×#106224522
C2×#106224162
C2×D11×#1022
C2×C11×#4642
C2×#304511