Finite Group Databasebeta

← C2×#13078117 #15620656

Subgroups — C2×#13078117 #15620656

Order 2816.

3074 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C22×D8×D11C211yesmaximal, characteristic, complemented
3C2×#10623205C211yesmaximal, characteristic, complemented
4C2×#10623076C211yesmaximal, characteristic, complemented
5#13078117C2116yesmaximal, direct product factor
6C2×#10622432C211yesmaximal, characteristic, complemented
7C2×#10622778C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622456C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622763C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×D8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic, complemented
23C2×C4×D4×C11C2211yescharacteristic, complemented
24C2×#67000C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic, complemented
26C2×#66993C2211yescharacteristic, complemented
27C2×D4×Dic11C2211yescharacteristic, complemented
28C22×#4323C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C22×#4323C2211yescharacteristic, complemented
31C2×C4×C22⋊D11—21no—
32C22×(C2×D11)⋊C4—21no—
33C2×#66967—28no—
34C2×#66967C2218yescomplemented
35C2×D8×D11—28no—
36C2×D8×D11C2218yescomplemented
37C22×D88C2211yescharacteristic
38C22×D88C2211yescharacteristic, complemented
39C22×#4313C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41#10623205—24no—
42#10623205C2218yescomplemented
43#10623076—24no—
44#10623076C2218yescomplemented
45C2×#66946C2211yescharacteristic, complemented
46C2×#66945C2211yescharacteristic
47C2×#66937—21no—
48C2×#66937—21no—
49C2×#66935—21no—
50C2×#66935—21no—
51C2×(C22⋊D11)⋊C4—21no—
52C2×C22⋊C4×D11—21no—
53C2×#66927C2211yescharacteristic, complemented
54C2×C4×D44C2211yescharacteristic, complemented
55C2×#66925C2211yescharacteristic
56C11×#463C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622778C2218yescomplemented
63#10622763C2218yescomplemented
64C2×#66885C2211yescharacteristic, complemented
65C2×#66885C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622670C2218yescomplemented
69#10622628C2218yescomplemented
70C2×#66873C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic, complemented
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622456C2218yescomplemented
74#10622452C2218yescomplemented
75#10622432C2218yescomplemented
76#10622417C2218yescomplemented
77#10622399C2218yescomplemented
78#10622383C2218yescomplemented
79C24×D11—21no—
80C24×D11—21no—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C23×Dic11—21no—
90C2×#4343—22no—
91C2×#4343—24no—
92C2×#4343—24no—
93C2×#4343C2314yes—
94C2×D4×D11—22no—
95C2×D4×D11—24no—
96C2×D4×D11—22no—
97C2×D4×D11—24no—
98C2×D4×D11—24no—
99C2×D4×D11D418yescomplemented
100C2×D4×D11C2314yes—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—21no—
105C22×D44C2311yescharacteristic
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11—21no—
110C22×C4×D11—21no—
111C22×C4×D11C2311yescharacteristic
112C2×C11×SD16—24no—
113C2×C11×SD16C2314yescomplemented
114C2×C11×D8—24no—
115C2×C11×D8C2314yes—
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2311yescharacteristic
118C11×#124—22no—
119C11×#124C2314yescomplemented
120C4×D4×C11—22no—
121C4×D4×C11C2314yescomplemented
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128#67000—22no—
129#67000C2314yescomplemented
130C2×#4325—24no—
131C2×#4325C2314yescomplemented
132#66993—22no—
133#66993C2314yescomplemented
134D4×Dic11—22no—
135D4×Dic11C2314yescomplemented
136C2×#4323—24no—
137C2×#4323—24no—
138C2×#4323—24no—
139C2×#4323C2314yes—
140C2×#4323C2314yes—
141C2×#4323C2314yescomplemented
142C4×C22⋊D11—28no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—28no—
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×(C2×D11)⋊C4D411yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4D411yescharacteristic
153C2×Dic11⋊C4D411yescharacteristic
154C2×C4×Dic11—21no—
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66967—232no—
159D8×D11—232no—
160C2×D88—24no—
161C2×D88—24no—
162C2×D88C2314yes—
163C2×D88C2314yescomplemented
164C2×#4313—24no—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11C2314yes—
168#66946—22no—
169#66946C2314yescomplemented
170#66945—22no—
171#66945C2314yes—
172#66937—28no—
173#66937—28no—
174#66935—28no—
175#66935—28no—
176(C22⋊D11)⋊C4—28no—
177C22⋊C4×D11—28no—
178#66927—22no—
179#66927C2314yescomplemented
180C4×D44—22no—
181C4×D44C2314yescomplemented
182#66925D414yes—
183#66925C2314yes—
184C11×C4⋊C8C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yescomplemented
187#66899C2314yescomplemented
188#66896C2314yescomplemented
189#66885C2314yescomplemented
190#66885C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66873C2314yescomplemented
194#66873C2314yescomplemented
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3041—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11—21no—
199C23×D11—21no—
200C23×D11—28no—
201C23×D11—24no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—24no—
205C23×D11—44no—
206C23×D11—82no—
207C23×D11—82no—
208C23×D11—82no—
209C23×D11—82no—
210C23×D11C2×D411yescharacteristic
211C2×Q8×C11—21no—
212C2×Q8×C11—22no—
213C2×Q8×C11—22no—
214C2×Q8×C11C2412yes—
215C2×D4×C11—21no—
216C2×D4×C11—22no—
217C2×D4×C11—21no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11C2×D414yes—
221C2×D4×C11C2412yes—
222C2×D4×C11C2412yes—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—24no—
226C22×C4×C11—82no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C2×C22⋊D11—28no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—24no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C22×Dic11—24no—
239C22×Dic11—21no—
240C22×Dic11—82no—
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243C22×Dic11C2×D411yescharacteristic
244#4343—28no—
245#4343—28no—
246#4343—48no—
247D4×D11—216no—
248D4×D11—28no—
249D4×D11—28no—
250D4×D11—28no—
251D4×D11—48no—
252D4×D11C2×D4116yescomplemented
253C2×D44—24no—
254C2×D44—21no—
255C2×D44—21no—
256C2×D44—21no—
257C2×D44—24no—
258C2×D44—24no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—44no—
265C2×D44—82no—
266C2×D44—82no—
267C2×D44C2×D414yes—
268C2×D44C2412yes—
269C2×D44C2412yes—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—44no—
275C2×C4×D11—82no—
276C2×C4×D11—82no—
277C2×C4×D11C2×D414yes—
278C2×C4×D11C2×D412yes—
279C2×C4×D11#4114yes—
280C2×C4×D11C2412yes—
281C11×SD16—28no—
282C11×D8—28no—
283C2×C8×C11—22no—
284C2×C8×C11—22no—
285C2×C8×C11C2412yes—
286C2×C8×C11C2412yes—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C42×C11C2×D412yes—
293C42×C11C2412yes—
294C22⋊Dic11—24no—
295#4325—28no—
296#4323—28no—
297#4323—28no—
298#4323—28no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4C2×D414yes—
305(C2×D11)⋊C4C2×D414yes—
306C4⋊Dic11—21no—
307C4⋊Dic11C2412yes—
308Dic11⋊C4C2×D414yes—
309Dic11⋊C4C2×D414yes—
310C4×Dic11—24no—
311C4×Dic11C2×D412yes—
312C4×Dic11C2412yes—
313C2×C11⋊C8—22no—
314C2×C11⋊C8—22no—
315C2×C11⋊C8C2412yes—
316C2×C11⋊C8C2412yes—
317D88—28no—
318D88—28no—
319#4313—28no—
320C8×D11—28no—
321C22×AGL(1,ℤ/8)—111no—
322C23×D8—111no—
323C2×#535—111no—
324C2×#518—111no—
325#3041—1116no—
326C2×#463—111no—
327C2×#463—111no—
328C2×#463—111no—
329C2×#463D1111yescharacteristic, complemented
330C2×#459—111no—
331C2×#459—111no—
332C2×#459—111no—
333C2×#459—111no—
334C2×#424—111no—
335C2×#418—111no—
336C2×#416—111no—
337C23×C11—24no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11C22×D411yescharacteristic
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—24no—
349C22×D11—22no—
350C22×D11—216no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—48no—
362C22×D11—816no—
363C22×D11—84no—
364C22×D11—84no—
365C22×D11—84no—
366C22×D11—84no—
367C22×D11—816no—
368C22×D11#12114yes—
369C22×D11C22×D412yes—
370Q8×C11—22no—
371Q8×C11—22no—
372Q8×C11—42no—
373D4×C11—24no—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—22no—
377D4×C11—42no—
378D4×C11C22×D414yes—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11—84no—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D412yes—
390C2×C4×C11C2×#4112yes—
391C2×C4×C11C2511yescharacteristic
392C22⋊D11—216no—
393C22⋊D11—48no—
394C22⋊D11—84no—
395C22⋊D11—84no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—42no—
400C2×Dic11—84no—
401C2×Dic11#12114yes—
402C2×Dic11C22×D412yes—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405D44—24no—
406D44—22no—
407D44—22no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44—48no—
412D44—42no—
413D44—42no—
414D44—84no—
415D44—84no—
416D44C22×D414yes—
417C4×D11—48no—
418C4×D11—84no—
419C4×D11—84no—
420C4×D11#12118yes—
421C4×D11C22×D414yes—
422C4×D11C2×#4114yes—
423C8×C11—22no—
424C8×C11—22no—
425C11⋊C8—22no—
426C11⋊C8—22no—
427C22×#41—111no—
428C23×D4—111no—
429C23×D4—111no—
430C2×AGL(1,ℤ/8)—118no—
431C2×AGL(1,ℤ/8)—228no—
432C22×SD16—111no—
433C22×SD16C2×D1111yescharacteristic, complemented
434C22×D8—111no—
435C22×D8—111no—
436C22×D8—111no—
437C22×D8—118no—
438C22×D8—111no—
439C22×D8—111no—
440C22×D8—228no—
441C22×D8C2×D1111yescharacteristic
442C22×M16—111no—
443C23×C8—111no—
444#535—118no—
445#535—224no—
446C2×#127—111no—
447C2×#127—111no—
448C2×#124—111no—
449C2×#124C2×D1111yescharacteristic, complemented
450C2×#121—221no—
451C2×#121—221no—
452C2×#120—221no—
453C2×#120—221no—
454#518—118no—
455#518—224no—
456C2×C4×D4—111no—
457C2×C4×D4—111no—
458C2×C4×D4—111no—
459C2×C4×D4—221no—
460C2×C4×D4—221no—
461C2×C4×D4C2×D1111yescharacteristic, complemented
462C2×#117—111no—
463C2×#117—111no—
464C22×C22⋊C4—221no—
465C22×C22⋊C4—221no—
466#463—118no—
467#463—118no—
468#463—118no—
469#463C2×D1118yescomplemented
470#459—118no—
471#459—118no—
472#459—118no—
473#459—118no—
474#424—118no—
475C2×C4⋊C8—111no—
476C2×C4⋊C8—111no—
477C2×C4⋊C8—111no—
478C2×C4⋊C8C2×D1111yescharacteristic, complemented
479#418—118no—
480#416—118no—
481C2×#103—111no—
482C2×#103C2×D1111yescharacteristic, complemented
483C2×#102—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×#102—111no—
487C2×#102—111no—
488C2×#102C2×D1111yescharacteristic, complemented
489C22×C11—24no—
490C22×C11—48no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—84no—
497C22×C11C2×#12112yes—
498C22×C11#57612yes—
499C22×C11#57612yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—28no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—24no—
505C2×D11—48no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—816no—
515C2×D11—816no—
516C2×D11—84no—
517C2×D11—84no—
518C2×D11C2×#12114yes—
519C4×C11—22no—
520C4×C11—22no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11C2×#12112yes—
524C4×C11C23×D411yescharacteristic
525C4×C11C22×#4111yescharacteristic
526Dic11—22no—
527Dic11—22no—
528Dic11—42no—
529Dic11C2×#12114yes—
530C25—221no—
531C25—221no—
532C2×#41—114no—
533C2×#41—222no—
534C2×#41—224no—
535C2×#41—224no—
536C22×Q8C22×D1111yescharacteristic
537C22×D4—118no—
538C22×D4—114no—
539C22×D4—114no—
540C22×D4—111no—
541C22×D4—111no—
542C22×D4—111no—
543C22×D4—221no—
544C22×D4—222no—
545C22×D4—224no—
546C22×D4—224no—
547C22×D4—224no—
548C22×D4—222no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4C22×D1111yescharacteristic
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4—221no—
563AGL(1,ℤ/8)—2232no—
564C2×SD16—24no—
565C2×SD16—114no—
566C2×SD16—224no—
567C2×SD16C22×D1114yescomplemented
568C2×D8—24no—
569C2×D8—114no—
570C2×D8—114no—
571C2×D8—114no—
572C2×D8—114no—
573C2×D8—114no—
574C2×D8—224no—
575C2×D8—224no—
576C2×D8—2232no—
577C2×D8—224no—
578C2×D8—224no—
579C2×D8—224no—
580C2×D8C22×D1114yes—
581C2×M16—114no—
582C2×M16—224no—
583C22×C8—111no—
584C22×C8—111no—
585C22×C8—114no—
586C22×C8—224no—
587C22×C8C22×D1111yescharacteristic
588C22×C8C22×D1111yescharacteristic
589#127—114no—
590#127—114no—
591#127—222no—
592#127—222no—
593#124—22no—
594#124—114no—
595#124—222no—
596#124C22×D1114yescomplemented
597#121—228no—
598#121—228no—
599#120—228no—
600#120—228no—
601C4×D4—22no—
602C4×D4—114no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—228no—
608C4×D4—228no—
609C4×D4—222no—
610C4×D4C22×D1114yescomplemented
611#117—114no—
612#117—114no—
613#117—114no—
614#117—222no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4C22×D1111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—228no—
625C2×C22⋊C4—228no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C42—111no—
633C2×C42—221no—
634C2×C42C22×D1111yescharacteristic
635C4⋊C8—114no—
636C4⋊C8—114no—
637C4⋊C8—114no—
638C4⋊C8C22×D1114yescomplemented
639#103—114no—
640#103C22×D1114yescomplemented
641#102—114no—
642#102—114no—
643#102—114no—
644#102—114no—
645#102—114no—
646#102C22×D1114yescomplemented
647C2×C11—44no—
648C2×C11—82no—
649C2×C11#304114yescomplemented
650C2×C11C22×#12111yescharacteristic
651C2×C11C2×#57611yescharacteristic
652C2×C11C2×#57611yescharacteristic
653D11—24no—
654D11—44no—
655D11—82no—
656D11—82no—
657C24—21no—
658C24—21no—
659C24—111no—
660C24—224no—
661C24—228no—
662C24—224no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—444no—
667C24—882no—
668C24—882no—
669C24—882no—
670C24—882no—
671#41—228no—
672#41—228no—
673#41—448no—
674C2×Q8—21no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8C23×D1112yes—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—1116no—
684C2×D4—114no—
685C2×D4—112no—
686C2×D4—112no—
687C2×D4—112no—
688C2×D4—224no—
689C2×D4—2216no—
690C2×D4—228no—
691C2×D4—228no—
692C2×D4—228no—
693C2×D4—224no—
694C2×D4—228no—
695C2×D4—224no—
696C2×D4—224no—
697C2×D4—224no—
698C2×D4—221no—
699C2×D4—222no—
700C2×D4—222no—
701C2×D4—221no—
702C2×D4—221no—
703C2×D4—224no—
704C2×D4—224no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—222no—
708C2×D4—444no—
709C2×D4—448no—
710C2×D4—444no—
711C2×D4—882no—
712C2×D4—882no—
713C2×D4—882no—
714C2×D4—882no—
715C2×D4D4×D1114yes—
716C2×D4C23×D1112yes—
717C2×D4C23×D1112yes—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—82no—
722C22×C4—111no—
723C22×C4—112no—
724C22×C4—114no—
725C22×C4—114no—
726C22×C4—112no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—224no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—221no—
733C22×C4—224no—
734C22×C4—444no—
735C22×C4—882no—
736C22×C4—882no—
737C22×C4—882no—
738C22×C4D4×D1111yescharacteristic
739C22×C4D4×D1111yescharacteristic
740C22×C4C23×D1111yescharacteristic
741SD16—28no—
742SD16—228no—
743D8—28no—
744D8—228no—
745D8—228no—
746D8—228no—
747D8—228no—
748D8—228no—
749M16—228no—
750C2×C8—22no—
751C2×C8—22no—
752C2×C8—112no—
753C2×C8—112no—
754C2×C8—228no—
755C2×C8—222no—
756C2×C8—222no—
757C2×C8C23×D1112yes—
758C2×C8C23×D1112yes—
759C4⋊C4—21no—
760C4⋊C4—114no—
761C4⋊C4—114no—
762C4⋊C4—112no—
763C4⋊C4—221no—
764C4⋊C4C23×D1112yes—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—114no—
769C22⋊C4—114no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C42—112no—
777C42—112no—
778C42—224no—
779C42D4×D1112yes—
780C42C23×D1112yes—
781C11C2×#304111yescharacteristic, complemented, Sylow
782C23—24no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—114no—
791C23—112no—
792C23—2216no—
793C23—222no—
794C23—222no—
795C23—224no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—448no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—442no—
805C23—442no—
806C23—442no—
807C23—442no—
808C23—8816no—
809C23—884no—
810C23—884no—
811C23—884no—
812C23—884no—
813C23—8816no—
814C23C2×D4×D1111yescharacteristic
815Q8—22no—
816Q8—22no—
817Q8—42no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—42no—
823D4—114no—
824D4—2216no—
825D4—224no—
826D4—222no—
827D4—222no—
828D4—222no—
829D4—222no—
830D4—222no—
831D4—448no—
832D4—448no—
833D4—442no—
834D4—442no—
835D4—884no—
836D4—884no—
837D4—884no—
838D4—884no—
839D4C2×D4×D1114yes—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—84no—
847C2×C4—114no—
848C2×C4—112no—
849C2×C4—118no—
850C2×C4—114no—
851C2×C4—114no—
852C2×C4—112no—
853C2×C4—112no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—448no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4—884no—
861C2×C4—884no—
862C2×C4C2×D4×D1112yes—
863C2×C4C2×D4×D1112yes—
864C2×C4C2×D4×D1111yescharacteristic
865C2×C4C2×D4×D1112yes—
866C2×C4#41×D1112yes—
867C2×C4C24×D1111yescharacteristic
868C8—22no—
869C8—22no—
870C8—222no—
871C8—222no—
872C22—24no—
873C22—48no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—84no—
880C22—114no—
881C22—228no—
882C22—222no—
883C22—222no—
884C22—224no—
885C22—448no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22—8816no—
895C22—8816no—
896C22—884no—
897C22—884no—
898C22D11×#12112yes—
899C22#1062330012yes—
900C22#1062330512yes—
901C22C22×D4×D1111yescharacteristic
902C4—22no—
903C4—22no—
904C4—42no—
905C4—42no—
906C4—114no—
907C4—222no—
908C4—222no—
909C4—442no—
910C4D11×#12112yes—
911C4C22×D4×D1111yescharacteristic
912C4C2×#41×D1111yescharacteristic
913C2—44no—
914C2—82no—
915C2—224no—
916C2—444no—
917C2—882no—
918C2—882no—
919C2#1307811714yesdirect product factor
920C2C2×D11×#12111yescharacteristic
921C2C2×#1062330011yescharacteristic
922C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
hypercenterC2×#463D11
hypocenterC11C2×#3041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C22×D8×D11C2semidirect
3. C2×#10623205C2semidirect
4. C2×#10623076C2semidirect
5. #13078117C2direct (N × H)
6. C2×#10622432C2semidirect
7. C2×#10622778C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622456C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622763C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622383C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#463C2semidirect
20. C22×C11×SD16C22semidirect
22. C2×C11×#124C22semidirect
23. C2×C4×D4×C11C22semidirect
24. C2×#67000C22semidirect
25. C22×#4325C22semidirect
26. C2×#66993C22semidirect
27. C2×D4×Dic11C22semidirect
30. C22×#4323C22semidirect
34. C2×#66967C22semidirect
36. C2×D8×D11C22semidirect
38. C22×D88C22semidirect
42. #10623205C22semidirect
44. #10623076C22semidirect
45. C2×#66946C22semidirect
53. C2×#66927C22semidirect
54. C2×C4×D44C22semidirect
56. C11×#463C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
60. C2×#66899C22semidirect
61. C2×#66896C22semidirect
62. #10622778C22semidirect
63. #10622763C22semidirect
64. C2×#66885C22semidirect
65. C2×#66885C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622670C22semidirect
69. #10622628C22semidirect
70. C2×#66873C22semidirect
71. C2×#66873C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622456C22semidirect
74. #10622452C22semidirect
75. #10622432C22semidirect
76. #10622417C22semidirect
77. #10622399C22semidirect
78. #10622383C22semidirect
99. C2×D4×D11D4semidirect
113. C2×C11×SD16C23semidirect
119. C11×#124C23semidirect
121. C4×D4×C11C23semidirect
129. #67000C23semidirect
131. C2×#4325C23semidirect
133. #66993C23semidirect
135. D4×Dic11C23semidirect
141. C2×#4323C23semidirect
163. C2×D88C23semidirect
169. #66946C23semidirect
179. #66927C23semidirect
181. C4×D44C23semidirect
184. C11×C4⋊C8C23semidirect
185. C11×#103C23semidirect
186. C11×#102C23semidirect
187. #66899C23semidirect
188. #66896C23semidirect
189. #66885C23semidirect
190. #66885C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
193. #66873C23semidirect
194. #66873C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
252. D4×D11C2×D4semidirect
329. C2×#463D11semidirect
433. C22×SD16C2×D11semidirect
449. C2×#124C2×D11semidirect
461. C2×C4×D4C2×D11semidirect
469. #463C2×D11semidirect
478. C2×C4⋊C8C2×D11semidirect
482. C2×#103C2×D11semidirect
488. C2×#102C2×D11semidirect
567. C2×SD16C22×D11semidirect
596. #124C22×D11semidirect
610. C4×D4C22×D11semidirect
638. C4⋊C8C22×D11semidirect
640. #103C22×D11semidirect
646. #102C22×D11semidirect
649. C2×C11#3041semidirect
781. C11C2×#3041semidirect
919. C2#13078117direct (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×D8×D112
C2×#106232052
C2×#106230762
#130781172
C2×#106224322
C2×#106227782
C2×#106226702
C2×#106224562
C2×#106226282
C2×#106223992
C2×#106227632
C2×#106224522
C2×#106223832
C2×#106224172
C2×C11×#4632
C2×#304111