Finite Group Databasebeta

← C2×#13079620 #15625030

Subgroups — C2×#13079620 #15625030

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic
3#13079620C2116yesmaximal, direct product factor
4C2×#10622673C211yesmaximal, characteristic, complemented
5C2×#10622328C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622411C212yesmaximal, complemented
8C2×#10622380C212yesmaximal, complemented
9C2×#10622421C212yesmaximal, complemented
10C2×#10622389C212yesmaximal
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2211yescharacteristic
14C22×D4×D11C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic, complemented
16C2×C11×#124C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#66999—21no—
19C2×Q8×Dic11—21no—
20C22×#4326C2212yescomplemented
21C2×#66989C2211yescharacteristic
22C22×#4324C2212yes—
23C22×Dic44C2212yescomplemented
24C22×#4314C2212yes—
25#10623259—24no—
26#10623259C2218yescomplemented
27D11×#124—24no—
28D11×#124C2218yes—
29C2×#66950C2212yes—
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66940C2212yescomplemented
33C2×#66938—21no—
34C2×#66938—21no—
35C2×C22⋊C4×D11—21no—
36C2×C22⋊C4×D11—21no—
37C2×#66928C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic, complemented
40C11×#489C2218yescomplemented
41C2×C11×#103C2212yescomplemented
42C2×C11×#102C2212yes—
43C2×C11×#97C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C8C2212yes—
45C2×Dic11⋊C8C2212yescomplemented
46#10622702C2218yescomplemented
47#10622673C2218yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic, complemented
51#10622421C22116yescomplemented
52#10622411C22116yescomplemented
53#10622389C22116yes—
54#10622380C22116yescomplemented
55#10622328C2218yescomplemented
56#10622318C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×Q8×D11—22no—
63C2×Q8×D11—44no—
64C2×Q8×D11C2314yes—
65C2×D4×D11—22no—
66C2×D4×D11—44no—
67C2×D4×D11C2314yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11D411yescharacteristic
71C22×C4×D11D411yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×Dic22—21no—
74C22×Dic22C2312yes—
75C22×Dic22C2311yescharacteristic
76C22×C8×C11C2312yes—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8C2314yescomplemented
79C11×#124—22no—
80C11×#124C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#67000—22no—
89#67000C2314yes—
90#66999—28no—
91Q8×Dic11—28no—
92C2×#4326—44no—
93C2×#4326C2318yescomplemented
94#66989—22no—
95#66989C2314yes—
96C2×#4324—44no—
97C2×#4324C2318yes—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—22no—
106C2×Dic11⋊C4—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112C2×Dic44—44no—
113C2×Dic44C2318yescomplemented
114C2×#4314—44no—
115C2×#4314C2318yes—
116#66950—24no—
117#66950C2318yes—
118#66945—28no—
119#66943—28no—
120#66940—24no—
121#66940C2318yescomplemented
122#66938—28no—
123#66938—28no—
124C22⋊C4×D11—28no—
125C22⋊C4×D11—28no—
126#66928—22no—
127#66928C2314yes—
128C42×D11D414yes—
129C42×D11C2314yes—
130#66922—22no—
131#66922C2314yescomplemented
132C11×#103C2318yescomplemented
133C11×#102C2318yes—
134C11×#97C2314yescomplemented
135(C2×D11)⋊C8C2318yes—
136Dic11⋊C8C2318yescomplemented
137#66874C2318yescomplemented
138#66873C2318yes—
139#66867C2314yescomplemented
140C2×#3215—111nomaximal, Sylow
141C24×C11—21no—
142C23×D11—21no—
143C23×D11—24no—
144C23×D11—44no—
145C23×D11—44no—
146C23×D11—44no—
147C23×D11C2×D411yescharacteristic
148C2×Q8×C11—24no—
149C2×Q8×C11—21no—
150C2×Q8×C11—24no—
151C2×Q8×C11—44no—
152C2×Q8×C11C2412yes—
153C2×D4×C11—21no—
154C2×D4×C11—24no—
155C2×D4×C11C2412yes—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—44no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168Q8×D11—48no—
169Q8×D11—48no—
170D4×D11—48no—
171D4×D11—48no—
172C2×D44—21no—
173C2×D44—24no—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—42no—
179C2×C4×D11—44no—
180C2×C4×D11C2×D412yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2412yes—
184C2×Dic22—24no—
185C2×Dic22—22no—
186C2×Dic22—21no—
187C2×Dic22—24no—
188C2×Dic22—24no—
189C2×Dic22—24no—
190C2×Dic22—44no—
191C2×Dic22C2412yes—
192C2×Dic22C2414yes—
193C2×C8×C11—24no—
194C2×C8×C11C2414yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4C2414yes—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C42×C11C2×D412yes—
201C42×C11C2412yes—
202C22⋊Dic11—24no—
203C22⋊Dic11—24no—
204#4326—48no—
205#4324—48no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211C4⋊Dic11—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—24no—
214Dic11⋊C4—28no—
215C4×Dic11—28no—
216C4×Dic11C2×D412yes—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2412yes—
220C2×C11⋊C8—24no—
221C2×C11⋊C8C2414yes—
222Dic44—48no—
223#4314—48no—
224C2×#533—111no—
225C22×#124—111no—
226#3215—1116no—
227C2×#497—111no—
228C2×#497—111no—
229C2×#489—111no—
230C2×#489D1111yescharacteristic, complemented
231C2×#464—112no—
232C2×#464—112no—
233C2×#451—112no—
234C2×#450—112no—
235C2×#432—111no—
236C23×C11—22no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—48no—
250C22×D11—816no—
251C22×D11#13714yes—
252C22×D11C22×D412yes—
253Q8×C11—24no—
254Q8×C11—48no—
255Q8×C11—42no—
256D4×C11—24no—
257D4×C11—42no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11H(5,𝔽2)14yes—
268C2×C4×C11C2511yescharacteristic
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—42no—
276C2×Dic11—44no—
277C2×Dic11C22×D412yes—
278C2×Dic11C22×D412yes—
279C2×Dic11C22×D412yes—
280D44—24no—
281D44—42no—
282C4×D11—28no—
283C4×D11—24no—
284C4×D11—24no—
285C4×D11—44no—
286C4×D11—48no—
287Dic22—24no—
288Dic22—24no—
289Dic22—24no—
290Dic22—48no—
291Dic22—44no—
292Dic22—42no—
293C8×C11—24no—
294C11⋊C8—24no—
295C23×Q8—111no—
296C23×D4—111no—
297C22×Q16—112no—
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301#533—118no—
302#533—224no—
303C2×C4⋊Q8—111no—
304C2×C4⋊Q8C2×D1111yescharacteristic, complemented
305C2×#125—221no—
306C2×#124—111no—
307C2×#124—111no—
308C2×#124—118no—
309C2×#124—111no—
310C2×#124—221no—
311C2×#124—221no—
312C2×#124—224no—
313C2×#124C2×D1111yescharacteristic
314C2×C22⋊Q8—112no—
315C2×C22⋊Q8—221no—
316C2×C4×Q8—112no—
317C2×C4×Q8—221no—
318C2×#117—221no—
319C22×C22⋊C4—221no—
320C22×C22⋊C4—221no—
321C22×C42—111no—
322#497—118no—
323#497—118no—
324#489—118no—
325#489C2×D1118yescomplemented
326#464—1116no—
327#464—1116no—
328#451—1116no—
329#450—1116no—
330#432—118no—
331C2×C4⋊C8—112no—
332C2×#103—112no—
333C2×#103C2×D1112yescomplemented
334C2×#102—112no—
335C2×#102C2×D1112yes—
336C2×C22⋊C8—112no—
337C2×#97—111no—
338C2×#97C2×D1111yescharacteristic, complemented
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—84no—
343C22×C11#53512yes—
344C22×C11C2×#13712yes—
345C22×C11#57512yes—
346C22×C11C23×D411yescharacteristic
347C2×D11—22no—
348C2×D11—28no—
349C2×D11—22no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—816no—
354C2×D11—84no—
355C2×D11C2×#13714yes—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—44no—
360C4×C11#53512yes—
361C4×C11C2×H(5,𝔽2)12yes—
362Dic11—22no—
363Dic11—22no—
364Dic11—22no—
365Dic11—42no—
366Dic11—44no—
367C25—221no—
368C22×Q8—21no—
369C22×Q8—114no—
370C22×Q8—112no—
371C22×Q8—111no—
372C22×Q8—221no—
373C22×Q8—222no—
374C22×Q8—444no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—114no—
377C22×D4—111no—
378C22×D4—222no—
379C22×D4—221no—
380C22×D4—444no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C2×Q16—118no—
387C2×Q16—118no—
388C2×Q16—444no—
389C2×Q16—444no—
390C2×SD16—118no—
391C2×SD16—118no—
392C2×SD16—444no—
393C2×SD16—444no—
394C22×C8—112no—
395C22×C8C22×D1112yes—
396C4⋊Q8—22no—
397C4⋊Q8—114no—
398C4⋊Q8—222no—
399C4⋊Q8C22×D1114yescomplemented
400#125—228no—
401#124—22no—
402#124—114no—
403#124—114no—
404#124—114no—
405#124—228no—
406#124—228no—
407#124—222no—
408#124—222no—
409#124—222no—
410#124C22×D1114yes—
411C22⋊Q8—118no—
412C22⋊Q8—224no—
413C22⋊Q8—228no—
414C4×Q8—118no—
415C4×Q8—224no—
416C4×Q8—228no—
417#117—228no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1112yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—228no—
427C2×C22⋊C4—228no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—114no—
439C2×C42—114no—
440C2×C42—222no—
441C2×C42C22×D1111yescharacteristic
442C4⋊C8—118no—
443#103—118no—
444#103C22×D1118yescomplemented
445#102—118no—
446#102C22×D1118yes—
447C22⋊C8—118no—
448#97—114no—
449#97C22×D1114yescomplemented
450C2×C11—82no—
451C2×C11#321514yescomplemented
452C2×C11C2×#53511yescharacteristic
453C2×C11C22×#13711yescharacteristic
454C2×C11C2×#57511yescharacteristic
455D11—24no—
456D11—82no—
457C24—21no—
458C24—111no—
459C24—224no—
460C24—221no—
461C24—444no—
462C24—444no—
463C24—444no—
464C2×Q8—24no—
465C2×Q8—21no—
466C2×Q8—24no—
467C2×Q8—44no—
468C2×Q8—112no—
469C2×Q8—114no—
470C2×Q8—224no—
471C2×Q8—222no—
472C2×Q8—221no—
473C2×Q8—224no—
474C2×Q8—224no—
475C2×Q8—224no—
476C2×Q8—444no—
477C2×Q8—448no—
478C2×Q8—448no—
479C2×Q8C23×D1112yes—
480C2×D4—21no—
481C2×D4—24no—
482C2×D4—112no—
483C2×D4—224no—
484C2×D4—221no—
485C2×D4—224no—
486C2×D4—448no—
487C2×D4—448no—
488C2×D4—444no—
489C2×D4C23×D1112yes—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—442no—
505C22×C4—444no—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509Q16—448no—
510Q16—448no—
511SD16—448no—
512SD16—448no—
513C2×C8—24no—
514C2×C8—114no—
515C2×C8—224no—
516C2×C8C23×D1114yes—
517C4⋊C4—24no—
518C4⋊C4—22no—
519C4⋊C4—228no—
520C4⋊C4—228no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4C23×D1114yes—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—224no—
527C22⋊C4—224no—
528C22⋊C4—228no—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C42—112no—
534C42—114no—
535C42—114no—
536C42—112no—
537C42—228no—
538C42D4×D1112yes—
539C42C23×D1112yes—
540C11C2×#321511yescharacteristic, complemented, Sylow
541C23—22no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—114no—
546C23—112no—
547C23—222no—
548C23—222no—
549C23—222no—
550C23—448no—
551C23—448no—
552C23—448no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—8816no—
557C23C2×D4×D1111yescharacteristic
558Q8—24no—
559Q8—48no—
560Q8—42no—
561Q8—224no—
562Q8—224no—
563Q8—224no—
564Q8—448no—
565Q8—442no—
566Q8—444no—
567D4—24no—
568D4—42no—
569D4—224no—
570D4—448no—
571D4—442no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—228no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—444no—
590C2×C4—448no—
591C2×C4—442no—
592C2×C4—444no—
593C2×C4C2×D4×D1112yes—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4#6704214yes—
597C2×C4C24×D1111yescharacteristic
598C8—24no—
599C8—224no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—84no—
604C22—114no—
605C22—228no—
606C22—222no—
607C22—222no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—8816no—
612C22—884no—
613C22#1062320512yes—
614C22#1062330412yes—
615C22D11×#13712yes—
616C22C22×D4×D1111yescharacteristic
617C4—22no—
618C4—22no—
619C4—42no—
620C4—44no—
621C4—222no—
622C4—222no—
623C4—222no—
624C4—442no—
625C4—444no—
626C4#1062320512yes—
627C4C2×#6704212yes—
628C2—82no—
629C2—224no—
630C2—882no—
631C2#1307962014yesdirect product factor
632C2C2×#1062320511yescharacteristic
633C2C2×D11×#13711yescharacteristic
634C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#489D11
hypocenterC11C2×#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079620C2direct (N × H)
4. C2×#10622673C2semidirect
5. C2×#10622328C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622421C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#489C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
20. C22×#4326C22semidirect
23. C22×Dic44C22semidirect
26. #10623259C22semidirect
32. C2×#66940C22semidirect
39. C2×#66922C22semidirect
40. C11×#489C22semidirect
41. C2×C11×#103C22semidirect
43. C2×C11×#97C22semidirect
45. C2×Dic11⋊C8C22semidirect
46. #10622702C22semidirect
47. #10622673C22semidirect
48. C2×#66874C22semidirect
50. C2×#66867C22semidirect
51. #10622421C22semidirect
52. #10622411C22semidirect
54. #10622380C22semidirect
55. #10622328C22semidirect
56. #10622318C22semidirect
78. C11×C4⋊Q8C23semidirect
93. C2×#4326C23semidirect
113. C2×Dic44C23semidirect
121. #66940C23semidirect
131. #66922C23semidirect
132. C11×#103C23semidirect
134. C11×#97C23semidirect
136. Dic11⋊C8C23semidirect
137. #66874C23semidirect
139. #66867C23semidirect
230. C2×#489D11semidirect
304. C2×C4⋊Q8C2×D11semidirect
325. #489C2×D11semidirect
333. C2×#103C2×D11semidirect
338. C2×#97C2×D11semidirect
399. C4⋊Q8C22×D11semidirect
444. #103C22×D11semidirect
449. #97C22×D11semidirect
451. C2×C11#3215semidirect
540. C11C2×#3215semidirect
631. C2#13079620direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×D11×#1242
#130796202
C2×#106226732
C2×#106223282
C2×#106227022
C2×#106224112
C2×#106223802
C2×#106224212
C2×#106223892
C2×#106223182
C2×C11×#4892
C2×#321511