Finite Group Databasebeta

← C2×#13079578 #15624942

Subgroups — C2×#13079578 #15624942

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic, complemented
2C22×#66989C211yesmaximal, characteristic, complemented
3#13079578C2116yesmaximal, direct product factor
4C2×#10622768C212yesmaximal, complemented
5C2×#10622381C212yesmaximal, complemented
6C2×#10622380C212yesmaximal, complemented
7C2×#10622766C212yesmaximal, complemented
8C2×#10622352C211yesmaximal, characteristic, complemented
9C2×#10622653C211yesmaximal, characteristic, complemented
10C2×#10622831C211yesmaximal, characteristic, complemented
11C2×#10622331C211yesmaximal, characteristic, complemented
12C2×C11×#447C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×D8C2212yes—
16C2×C11×#121C2211yescharacteristic
17C22×C22⋊Dic11—21no—
18C22×C22⋊Dic11—21no—
19C2×#66989—21no—
20C2×#66989—21no—
21C2×#66989—24no—
22C2×#66989C2212yes—
23C2×#66989C2212yes—
24C2×#66989C2218yescomplemented
25C2×#66989C2211yescharacteristic, complemented
26C2×#66988—21no—
27C2×D4×Dic11—21no—
28C2×D4×Dic11C2211yescharacteristic, complemented
29C22×#4324C2212yes—
30C22×#4324C2212yescomplemented
31C2×#66977C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×Dic44C2212yescomplemented
34#10623131—24no—
35#10623131C2218yescomplemented
36C2×#66943C2211yescharacteristic, complemented
37C2×#66940C2211yescharacteristic, complemented
38C2×#66932—21no—
39C2×#66930—21no—
40C11×#447C2218yes—
41C2×C11×#102C2212yes—
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622831C2218yescomplemented
44C2×#66896C2212yes—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622768C22116yescomplemented
47#10622766C22116yescomplemented
48C2×#66880C2212yescomplemented
49C2×Dic11⋊C8C2212yescomplemented
50C2×C8×Dic11C2212yescomplemented
51#10622653C2218yescomplemented
52C2×#66874C2212yescomplemented
53#10622381C22116yescomplemented
54#10622380C22116yescomplemented
55#10622352C2218yescomplemented
56#10622331C2218yescomplemented
57C25×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—44no—
62C22×D4×C11C2312yes—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2314yes—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C23×Dic11—21no—
68C23×Dic11D411yescharacteristic
69C23×Dic11D411yescharacteristic
70C22×Dic22—21no—
71C22×Dic22—22no—
72C22×Dic22—44no—
73C22×Dic22C2311yescharacteristic
74C22×Dic22C2312yes—
75C22×Dic22C2314yes—
76C2×C11×D8—44no—
77C2×C11×D8C2318yes—
78C22×C8×C11C2312yes—
79C11×#121—22no—
80C11×#121C2314yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—28no—
92C2×C22⋊Dic11—28no—
93#66989—24no—
94#66989—24no—
95#66989—28no—
96#66989—28no—
97#66989—22no—
98#66989C2318yes—
99#66989C2318yes—
100#66989C2314yescomplemented
101#66988—28no—
102D4×Dic11—28no—
103D4×Dic11—22no—
104D4×Dic11C2314yescomplemented
105C2×#4324—44no—
106C2×#4324—44no—
107C2×#4324C2318yes—
108C2×#4324C2318yescomplemented
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977C2314yes—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11D411yescharacteristic
118C2×C4×Dic11D411yescharacteristic
119C2×C4×Dic11D414yes—
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2314yes—
123C22×C11⋊C8C2312yes—
124C2×Dic44—44no—
125C2×Dic44C2318yescomplemented
126#66943—22no—
127#66943C2314yescomplemented
128#66940—22no—
129#66940C2314yescomplemented
130#66932—28no—
131#66930—28no—
132C11×#102C2318yes—
133C11×C22⋊C8C2314yes—
134#66896C2318yes—
135C22⋊(C11⋊C8)C2314yes—
136#66880C2318yescomplemented
137Dic11⋊C8C2318yescomplemented
138C8×Dic11C2318yescomplemented
139#66874C2318yescomplemented
140C2×#3211—111nomaximal, Sylow
141C24×C11—24no—
142C24×C11—22no—
143C24×C11—21no—
144C24×C11—44no—
145C24×C11—44no—
146C24×C11—44no—
147C24×C11C2×D411yescharacteristic
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—48no—
156C2×D4×C11—44no—
157C2×D4×C11—48no—
158C2×D4×C11—44no—
159C2×D4×C11C2414yes—
160C2×D4×C11C2412yes—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11—42no—
174C22×Dic11—44no—
175C22×Dic11—44no—
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D414yes—
181C22×Dic11C2×D414yes—
182C2×Dic22—21no—
183C2×Dic22—24no—
184C2×Dic22—22no—
185C2×Dic22—24no—
186C2×Dic22—24no—
187C2×Dic22—24no—
188C2×Dic22—48no—
189C2×Dic22—44no—
190C2×Dic22—48no—
191C2×Dic22C2414yes—
192C2×Dic22C2412yes—
193C11×D8—48no—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2412yes—
198C11×C22⋊C4—24no—
199C22⋊Dic11—24no—
200C22⋊Dic11—24no—
201C22⋊Dic11—24no—
202C22⋊Dic11—28no—
203C22⋊Dic11—28no—
204C22⋊Dic11—28no—
205C22⋊Dic11—28no—
206C22⋊Dic11—24no—
207#4324—48no—
208#4324—48no—
209C4⋊Dic11—24no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215C4×Dic11—24no—
216C4×Dic11C2×D414yes—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2412yes—
221C4×Dic11C2412yes—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224Dic44—48no—
225C2×#529—111no—
226C22×#124—111no—
227#3211—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#464—112no—
231C2×#463—112no—
232C2×#451—111no—
233C2×#448—111no—
234C2×#450—111no—
235C2×#447D1111yescharacteristic
236C2×#431—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11—48no—
242C23×C11—48no—
243C23×C11—44no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—48no—
247C23×C11—44no—
248C23×C11—42no—
249C23×C11—44no—
250C23×C11—816no—
251C23×C11#13514yes—
252C23×C11C22×D412yes—
253C23×C11C22×D411yescharacteristic
254D4×C11—24no—
255D4×C11—24no—
256D4×C11—24no—
257D4×C11—48no—
258D4×C11—48no—
259D4×C11—42no—
260D4×C11—44no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—42no—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11H(5,𝔽2)14yes—
269C2×C4×C11C2511yescharacteristic
270C2×Dic11—28no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—44no—
279C2×Dic11—48no—
280C2×Dic11—48no—
281C2×Dic11—44no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11C22×D412yes—
285C2×Dic11C22×D412yes—
286C2×Dic11C22×D412yes—
287C2×Dic11C22×D412yes—
288Dic22—24no—
289Dic22—24no—
290Dic22—24no—
291Dic22—48no—
292Dic22—42no—
293Dic22—44no—
294C8×C11—24no—
295C11⋊C8—24no—
296C23×Q8—111no—
297C23×D4C2×D1111yescharacteristic
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8C2×D1112yes—
302#529—118no—
303#529—224no—
304C2×#126—221no—
305C2×#125—111no—
306C2×#124—112no—
307C2×#124—111no—
308C2×#124—112no—
309C2×#124—118no—
310C2×#124—221no—
311C2×#124—221no—
312C2×#124—224no—
313C2×#123—221no—
314C2×C22⋊Q8—111no—
315C2×#121C2×D1111yescharacteristic
316C2×C4×Q8—111no—
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C2×#117—221no—
320C22×C22⋊C4—221no—
321C22×C22⋊C4—221no—
322C22×C42—111no—
323#495—1116no—
324#488—1116no—
325#464—1116no—
326#463—1116no—
327#451—118no—
328#450—118no—
329#448—118no—
330#447C2×D1118yes—
331#431—118no—
332C2×C4⋊C8—112no—
333C2×#103—112no—
334C2×#103—112no—
335C2×#102—112no—
336C2×#102C2×D1112yes—
337C2×C22⋊C8—111no—
338C2×C22⋊C8C2×D1111yescharacteristic
339C2×C4×C8—112no—
340C22×C11—22no—
341C22×C11—28no—
342C22×C11—22no—
343C22×C11—44no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11—42no—
349C22×C11—816no—
350C22×C11—84no—
351C22×C11—88no—
352C22×C11#53512yes—
353C22×C11C2×#13514yes—
354C22×C11C2×#13512yes—
355C22×C11#57512yes—
356C22×C11C23×D411yescharacteristic
357C4×C11—22no—
358C4×C11—42no—
359C4×C11#53512yes—
360C4×C11C2×H(5,𝔽2)12yes—
361Dic11—22no—
362Dic11—22no—
363Dic11—22no—
364Dic11—22no—
365Dic11—44no—
366Dic11—42no—
367Dic11—42no—
368C25—21no—
369C22×Q8—111no—
370C22×Q8—112no—
371C22×Q8—114no—
372C22×Q8—222no—
373C22×Q8—221no—
374C22×Q8—444no—
375C22×D4—21no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—44no—
379C22×D4C22×D1111yescharacteristic
380C22×D4C22×D1112yes—
381C22×D4C22×D1114yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4C22×D1111yescharacteristic
387C2×Q16—118no—
388C2×Q16—444no—
389C2×SD16—118no—
390C2×SD16—118no—
391C2×SD16—444no—
392C2×SD16—444no—
393C2×D8—44no—
394C2×D8C22×D1118yes—
395C22×C8—112no—
396C22×C8C22×D1112yes—
397#126—228no—
398#125—114no—
399#125—222no—
400#124—118no—
401#124—118no—
402#124—114no—
403#124—228no—
404#124—224no—
405#124—224no—
406#124—228no—
407#124—222no—
408#123—228no—
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411#121—22no—
412#121C22×D1114yes—
413C4×Q8—114no—
414C4×Q8—222no—
415C4×D4—114no—
416C4×D4—222no—
417C4×D4—228no—
418#117—228no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—228no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—228no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—114no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—114no—
442C2×C42—221no—
443C4⋊C8—118no—
444#103—118no—
445#103—118no—
446#102—118no—
447#102C22×D1118yes—
448C22⋊C8—114no—
449C22⋊C8C22×D1114yes—
450C4×C8—118no—
451C2×C11—24no—
452C2×C11—82no—
453C2×C11—84no—
454C2×C11#321114yescomplemented
455C2×C11C2×#53511yescharacteristic
456C2×C11C22×#13511yescharacteristic
457C2×C11C2×#57511yescharacteristic
458C24—24no—
459C24—21no—
460C24—22no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24D4×D1111yescharacteristic
465C2×Q8—114no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—224no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—448no—
474C2×Q8—444no—
475C2×Q8—448no—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—48no—
486C2×D4—44no—
487C2×D4C23×D1114yes—
488C2×D4C23×D1112yes—
489C22×C4—24no—
490C22×C4—21no—
491C22×C4—114no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—114no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—442no—
504C22×C4—444no—
505C22×C4—444no—
506C22×C4D4×D1112yes—
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1112yes—
509C22×C4C23×D1111yescharacteristic
510Q16—448no—
511SD16—448no—
512SD16—448no—
513D8—48no—
514C2×C8—24no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8C23×D1114yes—
518C4⋊C4—21no—
519C4⋊C4—112no—
520C4⋊C4—224no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—224no—
525C4⋊C4C23×D1112yes—
526C22⋊C4—24no—
527C22⋊C4—228no—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C42—114no—
536C42—112no—
537C42—112no—
538C42—114no—
539C42—112no—
540C42—112no—
541C42—224no—
542C11C2×#321111yescharacteristic, complemented, Sylow
543C23—22no—
544C23—22no—
545C23—22no—
546C23—24no—
547C23—48no—
548C23—48no—
549C23—42no—
550C23—48no—
551C23—44no—
552C23—42no—
553C23—44no—
554C23—44no—
555C23—42no—
556C23—816no—
557C23#6696514yes—
558C23C2×D4×D1112yes—
559C23C2×D4×D1111yescharacteristic
560Q8—224no—
561Q8—224no—
562Q8—224no—
563Q8—448no—
564Q8—444no—
565Q8—442no—
566D4—24no—
567D4—24no—
568D4—24no—
569D4—48no—
570D4—48no—
571D4—42no—
572D4—44no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—228no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—444no—
591C2×C4—448no—
592C2×C4—448no—
593C2×C4—442no—
594C2×C4—444no—
595C2×C4—442no—
596C2×C4C2×D4×D1112yes—
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4#6703714yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—28no—
603C22—22no—
604C22—22no—
605C22—44no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—42no—
610C22—44no—
611C22—816no—
612C22—88no—
613C22—84no—
614C22#1062312312yes—
615C22C2×#6696514yes—
616C22C2×#6696512yes—
617C22#1062330412yes—
618C22C22×D4×D1111yescharacteristic
619C4—22no—
620C4—42no—
621C4—222no—
622C4—222no—
623C4—222no—
624C4—222no—
625C4—444no—
626C4—442no—
627C4—442no—
628C4#1062312312yes—
629C4C2×#6703712yes—
630C2—24no—
631C2—84no—
632C2—82no—
633C2#1307957814yesdirect product factor
634C2C2×#1062312311yescharacteristic
635C2C22×#6696511yescharacteristic
636C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623131C2semidirect
2. C22×#66989C2semidirect
3. #13079578C2direct (N × H)
4. C2×#10622768C2semidirect
5. C2×#10622381C2semidirect
6. C2×#10622380C2semidirect
7. C2×#10622766C2semidirect
8. C2×#10622352C2semidirect
9. C2×#10622653C2semidirect
10. C2×#10622831C2semidirect
11. C2×#10622331C2semidirect
24. C2×#66989C22semidirect
25. C2×#66989C22semidirect
28. C2×D4×Dic11C22semidirect
30. C22×#4324C22semidirect
33. C22×Dic44C22semidirect
35. #10623131C22semidirect
36. C2×#66943C22semidirect
37. C2×#66940C22semidirect
43. #10622831C22semidirect
46. #10622768C22semidirect
47. #10622766C22semidirect
48. C2×#66880C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. C2×C8×Dic11C22semidirect
51. #10622653C22semidirect
52. C2×#66874C22semidirect
53. #10622381C22semidirect
54. #10622380C22semidirect
55. #10622352C22semidirect
56. #10622331C22semidirect
100. #66989C23semidirect
104. D4×Dic11C23semidirect
108. C2×#4324C23semidirect
125. C2×Dic44C23semidirect
127. #66943C23semidirect
129. #66940C23semidirect
136. #66880C23semidirect
137. Dic11⋊C8C23semidirect
138. C8×Dic11C23semidirect
139. #66874C23semidirect
454. C2×C11#3211semidirect
542. C11C2×#3211semidirect
633. C2#13079578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231312
C22×#669892
#130795782
C2×#106227682
C2×#106223812
C2×#106223802
C2×#106227662
C2×#106223522
C2×#106226532
C2×#106228312
C2×#106223312
C2×C11×#4472
C2×#321111