Finite Group Databasebeta

← C4×#10623369 #15618016

Subgroups — C4×#10623369 #15618016

Order 2816.

2658 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623369C211yesmaximal, characteristic
2C4×#67043C211yesmaximal, characteristic, complemented
3#13077489C213yesmaximal, complemented
4#13077482C213yesmaximal, complemented
5#13077459C213yesmaximal, complemented
6#13077455C213yesmaximal, complemented
7C4×#66995C213yesmaximal, complemented
8C4×#67004C213yesmaximal, complemented
9C4×#67003C213yesmaximal, complemented
10C2×C4×#4326C213yesmaximal, complemented
11#13077214C211yesmaximal, characteristic, complemented
12#13077149C211yesmaximal, characteristic, complemented
13#13077146C211yesmaximal, characteristic, complemented
14C4×#67001C211yesmaximal, characteristic, complemented
15C4×C11×2−1+4C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×#67043C2211yescharacteristic
18C11×#520—23no—
19C11×#520C2213yes—
20C11×#520C2211yescharacteristic
21C11×#519—21no—
22C11×#519C2213yes—
23C4×C11×#41—23no—
24C4×C11×#41C2213yes—
25C4×C11×#41C2211yescharacteristic
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2213yes—
28#10623369C4116yesdirect product factor
29#10623358C2211yescharacteristic
30C2×#67004C2213yes—
31C2×#67003C2213yes—
32C2×#67001C2211yescharacteristic
33C2×#67001C2211yescharacteristic
34C22×#4326C2213yes—
35C2×#66995C2213yes—
36#10623103—21no—
37C4×Q8×D11—21no—
38#10623077—23no—
39C4×#4341—23no—
40#10623054C2213yes—
41#10623047C2213yes—
42C4×#4339C2213yes—
43C2×C4×Dic22C2213yes—
44#10622846C2213yes—
45#10622845C2213yes—
46#10622838C2213yes—
47C2×#66899C2213yes—
48#10622643C2216yes—
49#10622643C2216yes—
50C4×#4326C2213yes—
51C4×#4326C2216yes—
52C4×#4326C2216yes—
53C4×#4326C2216yes—
54C4×#4326C2213yes—
55#10622639C2216yes—
56C4×#4325C2213yes—
57C4×#4325C2213yes—
58#10622631C2216yes—
59C4×#4324C2213yes—
60C4×#4324C2213yes—
61C4×#4323C2211yescharacteristic
62C4×#4323C2213yes—
63#10622617C2213yes—
64#10622615C2213yes—
65#10622611C2213yes—
66#10622610C2213yes—
67#10622610C2213yes—
68#10622608C2213yes—
69C2×#66874C2213yes—
70#10622579C2213yes—
71#10622577C2213yes—
72C2×#66871C2213yes—
73C4×#4318C2213yes—
74C2×C4×C11⋊C8C2213yes—
75C11×2−1+4—24no—
76C11×2−1+4C2×C418yescomplemented
77C2×C11×#41—23no—
78C2×C11×#41C2313yes—
79C2×C11×#41C2311yescharacteristic
80C22×Q8×C11—21no—
81C22×Q8×C11C2313yes—
82#67043—24no—
83#67043C2×C418yescomplemented
84C2×Q8×D11—21no—
85C2×#4341—23no—
86C2×#4339C2313yes—
87C22×Dic22C2313yes—
88C4×Q8×C11—21no—
89C4×Q8×C11—23no—
90C4×Q8×C11—23no—
91C4×Q8×C11—23no—
92C4×Q8×C11—23no—
93C4×Q8×C11D411yescharacteristic
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11C2313yes—
96C4×Q8×C11C2316yes—
97C4×Q8×C11C2313yes—
98C4×D4×C11—23no—
99C4×D4×C11—23no—
100C4×D4×C11—23no—
101C4×D4×C11—26no—
102C4×D4×C11D413yes—
103C4×D4×C11D413yes—
104C4×D4×C11C2311yescharacteristic
105C4×D4×C11C2313yes—
106C11×#117—23no—
107C11×#117—26no—
108C11×#117—23no—
109C11×#117C2313yes—
110C11×#117C2313yes—
111C2×C11×C4⋊C4—23no—
112C2×C11×C4⋊C4—23no—
113C2×C11×C4⋊C4C2313yes—
114C2×C42×C11—23no—
115C2×C42×C11—23no—
116C2×C42×C11C2313yes—
117#67004C2×C4124yescomplemented
118#67003C2×C4124yescomplemented
119#67001—24no—
120#67001C2×C418yescomplemented
121Q8×Dic11—21no—
122C2×#4326C2×C4124yescomplemented
123C2×#4326C2316yes—
124C2×#4326C2313yes—
125#66995C2×C4124yescomplemented
126C2×#4325C2313yes—
127D4×Dic11—23no—
128C2×#4324C2313yes—
129C2×#4323C2311yescharacteristic
130C4×C22⋊D11—23no—
131C4×C22⋊D11—23no—
132#66979C2313yes—
133C2×C4⋊Dic11C2313yes—
134C2×Dic11⋊C4—23no—
135C2×C4×Dic11—23no—
136C2×#4318C2313yes—
137C2×#4318C2313yes—
138C22×C11⋊C8C2313yes—
139C22×C11⋊C8C2313yes—
140#66945—23no—
141C4⋊C4×D11—23no—
142#66940—23no—
143#66940—23no—
144(C22⋊D11)⋊C4—26no—
145#66930—26no—
146C4×D44C2311yescharacteristic
147C4×D44C2313yes—
148#66925—23no—
149C42×D11—23no—
150C4×Dic22—23no—
151C4×Dic22—23no—
152C4×Dic22C2313yes—
153C4×Dic22C2316yes—
154C4×Dic22C2313yes—
155#66899C2313yes—
156#66899C2316yes—
157#66899C2313yes—
158#66896C2313yes—
159#66896C2311yescharacteristic
160#66874C2316yes—
161#66874C2313yes—
162#66874C2313yes—
163#66873C2313yes—
164#66873C2311yescharacteristic
165#66872C2313yes—
166#66872C2313yes—
167#66871C2313yes—
168#66871C2316yes—
169#66871C2311yescharacteristic
170#66867C2316yes—
171C4×C11⋊C8C2311yescharacteristic
172C4×C11⋊C8C2313yes—
173C4×C11⋊C8C2313yes—
174C4×C11⋊C8C2313yes—
175C4×#578—111nomaximal, Sylow
176C11×#41—224no—
177C11×#41—26no—
178C11×#41C22×C4112yes—
179C11×#41C22×C414yes—
180C11×#41#4114yes—
181C2×Q8×C11—28no—
182C2×Q8×C11—23no—
183C2×Q8×C11—26no—
184C2×Q8×C11C22×C4112yes—
185C2×Q8×C11C2×D411yescharacteristic
186C2×Q8×C11C2413yes—
187C2×D4×C11—23no—
188C2×D4×C11C2×D413yes—
189C2×D4×C11C2411yescharacteristic
190C22×C4×C11—23no—
191C22×C4×C11—23no—
192C22×C4×C11—23no—
193C22×C4×C11—21no—
194C22×C4×C11—23no—
195C22×C4×C11C2×D413yes—
196C22×C4×C11C2×D413yes—
197C22×C4×C11C2413yes—
198C2×C22⋊D11—23no—
199C22×Dic11—23no—
200C22×Dic11—23no—
201Q8×D11—28no—
202#4341—224no—
203#4339—26no—
204#4339C22×C4112yes—
205C2×D44C2411yescharacteristic
206C2×C4×D11—23no—
207C2×C4×D11—21no—
208C2×C4×D11—23no—
209C2×Dic22—23no—
210C2×Dic22—26no—
211C2×Dic22C22×C4112yes—
212C2×Dic22C2413yes—
213C11×C4⋊C4—26no—
214C11×C4⋊C4—23no—
215C11×C4⋊C4—23no—
216C11×C4⋊C4—23no—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2×D413yes—
219C11×C4⋊C4C2413yes—
220C11×C4⋊C4C2411yescharacteristic
221C11×C22⋊C4—23no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—23no—
224C11×C22⋊C4C2×D416yes—
225C42×C11—23no—
226C42×C11—23no—
227C42×C11—26no—
228C42×C11—23no—
229C42×C11C2×D413yes—
230C42×C11C2×D413yes—
231C42×C11C2411yescharacteristic
232C42×C11C2413yes—
233C22⋊Dic11—23no—
234#4326C22×C4124yes—
235#4326C22×C4112yes—
236#4325C22×C4112yes—
237#4324C22×C4112yes—
238#4323C22×C414yes—
239(C2×D11)⋊C4—21no—
240(C2×D11)⋊C4—23no—
241C4⋊Dic11—23no—
242C4⋊Dic11C2413yes—
243C4⋊Dic11C2411yescharacteristic
244Dic11⋊C4—23no—
245Dic11⋊C4—26no—
246Dic11⋊C4—23no—
247C4×Dic11—23no—
248C4×Dic11—26no—
249C4×Dic11—23no—
250C4×Dic11—23no—
251#4318—26no—
252#4318C22×C4112yes—
253C2×C11⋊C8—26no—
254C2×C11⋊C8C22×C4112yes—
255C2×C11⋊C8C2411yescharacteristic
256C2×C11⋊C8C2413yes—
257C2×C11⋊C8C2411yescharacteristic
258C2×C11⋊C8C2413yes—
259C2×#578—111no—
260C4×2−1+4—111no—
261C4×2−1+4D1111yescharacteristic, complemented
262#2951—113no—
263#2950—113no—
264#2947—113no—
265#2947—113no—
266C4×#137—113no—
267C4×#137—113no—
268C4×#135—113no—
269C2×C4×Q16—113no—
270#2913—111no—
271#2898—111no—
272#2898—111no—
273C4×#131—111no—
274C23×C11—21no—
275C23×C11C22×D413yes—
276C22×D11—21no—
277Q8×C11—212no—
278Q8×C11—23no—
279Q8×C11C4×D414yes—
280Q8×C11C23×C416yes—
281D4×C11—212no—
282D4×C11—21no—
283D4×C11C4×D4112yes—
284D4×C11C23×C412yes—
285C2×C4×C11—212no—
286C2×C4×C11—23no—
287C2×C4×C11—212no—
288C2×C4×C11—26no—
289C2×C4×C11—21no—
290C2×C4×C11—23no—
291C2×C4×C11—43no—
292C2×C4×C11—42no—
293C2×C4×C11—83no—
294C2×C4×C11—83no—
295C2×C4×C11C23×C416yes—
296C2×C4×C11C22×D413yes—
297C2×C4×C11C22×D413yes—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D413yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4116yes—
302C2×C4×C11C2511yescharacteristic
303C22⋊D11—212no—
304C2×Dic11—212no—
305C2×Dic11—23no—
306C2×Dic11—21no—
307C2×Dic11—23no—
308C2×Dic11—83no—
309D44—21no—
310D44C23×C412yes—
311C4×D11—212no—
312C4×D11—42no—
313C4×D11—83no—
314Dic22—212no—
315Dic22—23no—
316Dic22C23×C416yes—
317C11⋊C8—21no—
318C11⋊C8—23no—
319C11⋊C8C23×C412yes—
320C11⋊C8C23×C416yes—
321C2×2−1+4—111no—
322C2×2−1+4C2×D1111yescharacteristic
323#578—1116no—
324C2×#137—113no—
325C2×#137—113no—
326C2×#135—113no—
327C22×Q16—113no—
328C2×#131—111no—
329C2×#131—111no—
330#520—23no—
331#520—111no—
332#520—113no—
333#520—223no—
334#520C2×D1113yes—
335#520C2×D1111yescharacteristic
336#519—21no—
337#519—113no—
338#519—221no—
339#519C2×D1113yes—
340C4×#41—23no—
341C4×#41—113no—
342C4×#41—223no—
343C4×#41C2×D1113yes—
344C4×#41C2×D1111yescharacteristic
345C2×C4×Q8—21no—
346C2×C4×Q8—113no—
347C2×C4×Q8—221no—
348C2×C4×Q8C2×D1113yes—
349#441—116no—
350#441—116no—
351#440—116no—
352#440—116no—
353C4×Q16—113no—
354C4×Q16—116no—
355C4×Q16—116no—
356C4×Q16—116no—
357C4×Q16—113no—
358C4×SD16—113no—
359C4×SD16—113no—
360C4×SD16—113no—
361C4×SD16—113no—
362C4×D8—111no—
363C4×D8—113no—
364#428—113no—
365#428—113no—
366#427—113no—
367C2×#107—113no—
368#419—113no—
369#419—113no—
370#417—113no—
371#417—113no—
372#416—113no—
373#416—113no—
374C2×#103—113no—
375C2×#103—113no—
376#405—113no—
377#405—113no—
378C4×M16—113no—
379C2×C4×C8—113no—
380C22×C11—23no—
381C22×C11—23no—
382C22×C11—22no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11C2×C4×D416yes—
386C22×C11C23×D411yescharacteristic
387C2×D11—22no—
388C2×D11—41no—
389C2×D11—41no—
390C4×C11—21no—
391C4×C11—23no—
392C4×C11—26no—
393C4×C11—23no—
394C4×C11—43no—
395C4×C11—41no—
396C4×C11C2×C4×D416yes—
397C4×C11#57812yescomplemented
398C4×C11C24×C411yescharacteristic
399C4×C11C22×#4111yescharacteristic
400Dic11—26no—
401Dic11—43no—
402Dic11—41no—
4032−1+4—24no—
4042−1+4—118no—
4052−1+4—224no—
4062−1+4C4×D1118yescomplemented
407C2×#41—23no—
408C2×#41—113no—
409C2×#41—223no—
410C2×#41C22×D1113yes—
411C2×#41C22×D1111yescharacteristic
412C22×Q8—21no—
413C22×Q8—113no—
414C22×Q8—221no—
415C22×Q8C22×D1113yes—
416#137—1124no—
417#137—1124no—
418#135—1124no—
419C2×Q16—1124no—
420C2×Q16—113no—
421C2×Q16—116no—
422C2×SD16—113no—
423C2×SD16—113no—
424C2×D8—111no—
425#131—118no—
426#131—224no—
427C2×M16—113no—
428C2×M16—113no—
429C22×C8—113no—
430C22×C8—113no—
431C4×Q8—21no—
432C4×Q8—23no—
433C4×Q8—23no—
434C4×Q8—23no—
435C4×Q8—23no—
436C4×Q8—113no—
437C4×Q8—116no—
438C4×Q8—113no—
439C4×Q8—221no—
440C4×Q8—223no—
441C4×Q8—223no—
442C4×Q8—223no—
443C4×Q8—223no—
444C4×Q8C22⋊D1111yescharacteristic
445C4×Q8C22⋊D1111yescharacteristic
446C4×Q8C22×D1113yes—
447C4×Q8C22×D1116yes—
448C4×Q8C22×D1113yes—
449C4×D4—23no—
450C4×D4—23no—
451C4×D4—23no—
452C4×D4—26no—
453C4×D4—111no—
454C4×D4—113no—
455C4×D4—223no—
456C4×D4—223no—
457C4×D4—223no—
458C4×D4—226no—
459C4×D4C22⋊D1113yes—
460C4×D4C22⋊D1113yes—
461C4×D4C22×D1111yescharacteristic
462C4×D4C22×D1113yes—
463#117—23no—
464#117—26no—
465#117—23no—
466#117—113no—
467#117—223no—
468#117—226no—
469#117—223no—
470#117C22×D1113yes—
471#117C22×D1113yes—
472C2×C4⋊C4—23no—
473C2×C4⋊C4—23no—
474C2×C4⋊C4—113no—
475C2×C4⋊C4—223no—
476C2×C4⋊C4—223no—
477C2×C4⋊C4C22×D1113yes—
478C2×C42—23no—
479C2×C42—23no—
480C2×C42—223no—
481C2×C42—223no—
482C2×C42C22×D1113yes—
483#107—113no—
484#107—116no—
485#107—111no—
486#106—113no—
487#106—113no—
488#103—113no—
489#103—116no—
490#103—113no—
491#103—113no—
492#103—116no—
493#103—113no—
494#102—111no—
495#102—113no—
496#102—111no—
497#102—113no—
498#97—116no—
499C4×C8—111no—
500C4×C8—113no—
501C4×C8—113no—
502C4×C8—113no—
503C2×C11—26no—
504C2×C11—42no—
505C2×C11C22×C4×D411yescharacteristic
506C2×C11C2×#57811yescharacteristic
507C2×C11#358411yescharacteristic
508D11—42no—
509#41—224no—
510#41—26no—
511#41—1112no—
512#41—2224no—
513#41—226no—
514#41C2×C4×D11112yes—
515#41C2×C4×D1114yes—
516#41#433914yes—
517C2×Q8—28no—
518C2×Q8—26no—
519C2×Q8—23no—
520C2×Q8—1112no—
521C2×Q8—113no—
522C2×Q8—228no—
523C2×Q8—226no—
524C2×Q8—223no—
525C2×Q8C2×C4×D11112yes—
526C2×Q8C2×C22⋊D1111yescharacteristic
527C2×Q8C23×D1113yes—
528C2×D4—23no—
529C2×D4—111no—
530C2×D4—223no—
531C2×D4C2×C22⋊D1113yes—
532C2×D4C23×D1111yescharacteristic
533C22×C4—23no—
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—21no—
537C22×C4—23no—
538C22×C4—223no—
539C22×C4—223no—
540C22×C4—223no—
541C22×C4—221no—
542C22×C4—223no—
543C22×C4C2×C22⋊D1113yes—
544C22×C4C2×C22⋊D1113yes—
545C22×C4C23×D1113yes—
546Q16—1112no—
547Q16—1124no—
548SD16—1112no—
549SD16—1112no—
550D8—114no—
551M16—1112no—
552M16—226no—
553C2×C8—1112no—
554C2×C8—111no—
555C2×C8—113no—
556C2×C8—111no—
557C2×C8—113no—
558C2×C8—226no—
559C4⋊C4—26no—
560C4⋊C4—23no—
561C4⋊C4—23no—
562C4⋊C4—23no—
563C4⋊C4—111no—
564C4⋊C4—113no—
565C4⋊C4—223no—
566C4⋊C4—226no—
567C4⋊C4—223no—
568C4⋊C4—223no—
569C4⋊C4C2×C22⋊D1113yes—
570C4⋊C4C2×C22⋊D1113yes—
571C4⋊C4C23×D1111yescharacteristic
572C4⋊C4C23×D1113yes—
573C22⋊C4—23no—
574C22⋊C4—21no—
575C22⋊C4—23no—
576C22⋊C4—223no—
577C22⋊C4—221no—
578C22⋊C4—223no—
579C22⋊C4C2×C22⋊D1116yes—
580C42—23no—
581C42—26no—
582C42—23no—
583C42—23no—
584C42—223no—
585C42—223no—
586C42—226no—
587C42—223no—
588C42C2×C22⋊D1113yes—
589C42C2×C22⋊D1113yes—
590C42C23×D1113yes—
591C42C23×D1111yescharacteristic
592C11C4×#57811yescharacteristic, complemented, Sylow
593C23—21no—
594C23—221no—
595C23C22×C22⋊D1113yes—
596Q8—212no—
597Q8—23no—
598Q8—116no—
599Q8—2212no—
600Q8—223no—
601Q8C4×C22⋊D1114yes—
602Q8C22×C4×D1116yes—
603D4—212no—
604D4—21no—
605D4—112no—
606D4—2212no—
607D4—221no—
608D4C4×C22⋊D11112yes—
609D4C22×C4×D1112yes—
610C2×C4—212no—
611C2×C4—23no—
612C2×C4—212no—
613C2×C4—26no—
614C2×C4—21no—
615C2×C4—23no—
616C2×C4—43no—
617C2×C4—42no—
618C2×C4—83no—
619C2×C4—83no—
620C2×C4—2212no—
621C2×C4—223no—
622C2×C4—2212no—
623C2×C4—221no—
624C2×C4—223no—
625C2×C4—442no—
626C2×C4—883no—
627C2×C4—883no—
628C2×C4C22×C4×D1116yes—
629C2×C4C2×#433916yes—
630C2×C4C22×C22⋊D1113yes—
631C2×C4C22×C22⋊D1113yes—
632C2×C4C22×C22⋊D1111yescharacteristic
633C2×C4C22×C22⋊D1113yes—
634C2×C4C22×C22⋊D1111yescharacteristic
635C2×C4C24×D1111yescharacteristic
636C8—112no—
637C8—116no—
638C8—221no—
639C8—223no—
640C22—23no—
641C22—23no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—222no—
646C22—441no—
647C22—441no—
648C22C2×C4×C22⋊D1116yes—
649C22C23×C22⋊D1111yescharacteristic
650C4—26no—
651C4—23no—
652C4—21no—
653C4—23no—
654C4—41no—
655C4—43no—
656C4—226no—
657C4—441no—
658C4—443no—
659C4C2×C4×C22⋊D1116yes—
660C4#1062336912yesdirect product factor
661C4C23×C4×D1111yescharacteristic
662C4C22×#433911yescharacteristic
663C2—26no—
664C2—42no—
665C2—442no—
666C2C22×C4×C22⋊D1111yescharacteristic
667C2C2×#1062336911yescharacteristic
668C2#1308338711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC4×C11×2−1+4C2
socleC22×C11C23×D4
prime radicalC2×#10623369C2
cosocleC2×C4×C11C25
hypercenterC4×2−1+4D11
hypocenterC11C4×#578
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#67043C2semidirect
3. #13077489C2semidirect
4. #13077482C2semidirect
5. #13077459C2semidirect
6. #13077455C2semidirect
7. C4×#66995C2semidirect
8. C4×#67004C2semidirect
9. C4×#67003C2semidirect
10. C2×C4×#4326C2semidirect
11. #13077214C2semidirect
12. #13077149C2semidirect
13. #13077146C2semidirect
14. C4×#67001C2semidirect
15. C4×C11×2−1+4C2semidirect
28. #10623369C4direct (N × H)
76. C11×2−1+4C2×C4semidirect
83. #67043C2×C4semidirect
117. #67004C2×C4semidirect
118. #67003C2×C4semidirect
120. #67001C2×C4semidirect
122. C2×#4326C2×C4semidirect
125. #66995C2×C4semidirect
261. C4×2−1+4D11semidirect
397. C4×C11#578semidirect
406. 2−1+4C4×D11semidirect
592. C11C4×#578semidirect
660. C4#10623369direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233692
C4×#670432
#130774892
#130774822
#130774592
#130774552
C4×#669952
C4×#670042
C4×#670032
C2×C4×#43262
#130772142
#130771492
#130771462
C4×#670012
C4×C11×2−1+42
C4×#57811