Finite Group Databasebeta

← C2×#13079614 #15625024

Subgroups — C2×#13079614 #15625024

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#13079614C2116yesmaximal, direct product factor
4C2×#10622699C211yesmaximal, characteristic, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622798C212yesmaximal, complemented
8C2×#10622779C212yesmaximal, complemented
9C2×#10622799C212yesmaximal, complemented
10C2×#10622782C212yesmaximal
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#497C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2211yescharacteristic
14C22×D4×D11C2211yescharacteristic
15C22×C11×Q16C2212yescomplemented
16C22×C11×SD16C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#124C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999C2212yes—
21C2×Q8×Dic11C2212yescomplemented
22C22×#4326C2212yescomplemented
23C22×#4325C2212yes—
24C2×#66989C2211yescharacteristic
25#10623259—24no—
26#10623259C2218yescomplemented
27D11×#124—24no—
28D11×#124C2218yes—
29C2×#66950—21no—
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66940—21no—
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×#497C2218yescomplemented
41C2×C11×#97C2211yescharacteristic, complemented
42C2×#66899C2212yescomplemented
43C2×#66896C2212yes—
44#10622799C22116yescomplemented
45#10622798C22116yescomplemented
46#10622782C22116yes—
47#10622779C22116yescomplemented
48C2×#66885C2212yes—
49C2×(C2×D11)⋊C8C2212yes—
50C2×#66880C2212yescomplemented
51C2×Dic11⋊C8C2212yescomplemented
52#10622699C2218yescomplemented
53#10622668C2218yescomplemented
54C2×#66867C2211yescharacteristic, complemented
55#10622327C2218yescomplemented
56#10622318C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11C2312yes—
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×Dic22—21no—
75C22×Dic22C2311yescharacteristic
76C2×C11×Q16—44no—
77C2×C11×Q16C2318yescomplemented
78C2×C11×SD16—44no—
79C2×C11×SD16C2318yes—
80C22×C8×C11C2312yes—
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8C2314yescomplemented
83C11×#124—22no—
84C11×#124C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#67000—22no—
93#67000C2314yes—
94#66999—24no—
95#66999C2318yes—
96Q8×Dic11—24no—
97Q8×Dic11C2318yescomplemented
98C2×#4326—44no—
99C2×#4326C2318yescomplemented
100C2×#4325—44no—
101C2×#4325C2318yes—
102#66989—22no—
103#66989C2314yes—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11C2312yes—
112C2×Dic11⋊C4—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11D411yescharacteristic
115C2×C4×Dic11D411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C22×C11⋊C8C2312yes—
118#66950—28no—
119#66945—28no—
120#66943—28no—
121#66940—28no—
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×#97C2314yescomplemented
133#66899C2318yescomplemented
134#66896C2318yes—
135#66885C2318yes—
136(C2×D11)⋊C8C2318yes—
137#66880C2318yescomplemented
138Dic11⋊C8C2318yescomplemented
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—22no—
149C2×Q8×C11—21no—
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11C2412yes—
154C2×Q8×C11C2414yes—
155C2×D4×C11—21no—
156C2×D4×C11—24no—
157C2×D4×C11C2412yes—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—44no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170Q8×D11—48no—
171Q8×D11—48no—
172D4×D11—48no—
173D4×D11—48no—
174C2×D44—21no—
175C2×D44—24no—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—42no—
181C2×C4×D11—44no—
182C2×C4×D11C2×D412yes—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2×D414yes—
185C2×C4×D11C2412yes—
186C2×Dic22—24no—
187C2×Dic22—24no—
188C2×Dic22—21no—
189C2×Dic22—24no—
190C2×Dic22—44no—
191C2×Dic22—44no—
192C2×Dic22C2412yes—
193C11×Q16—48no—
194C11×SD16—48no—
195C2×C8×C11—24no—
196C2×C8×C11C2414yes—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C42×C11C2×D412yes—
202C42×C11C2412yes—
203C22⋊Dic11—24no—
204C22⋊Dic11—24no—
205#4326—48no—
206#4325—48no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—28no—
213C4⋊Dic11—22no—
214C4⋊Dic11—24no—
215C4⋊Dic11C2414yes—
216Dic11⋊C4—28no—
217C4×Dic11—28no—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C4×Dic11C2412yes—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224C2×#533—111no—
225C22×#124—111no—
226#3215—1116no—
227C2×#497—111no—
228C2×#497D1111yescharacteristic, complemented
229C2×#489—111no—
230C2×#489—111no—
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—24no—
255Q8×C11—24no—
256Q8×C11—42no—
257Q8×C11—44no—
258D4×C11—24no—
259D4×C11—42no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11H(5,𝔽2)14yes—
270C2×C4×C11C2511yescharacteristic
271C22⋊D11—48no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—42no—
278C2×Dic11—44no—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282D44—24no—
283D44—42no—
284C4×D11—28no—
285C4×D11—24no—
286C4×D11—24no—
287C4×D11—44no—
288C4×D11—48no—
289Dic22—24no—
290Dic22—48no—
291Dic22—48no—
292Dic22—42no—
293C8×C11—24no—
294C11⋊C8—24no—
295C23×Q8—111no—
296C23×D4—111no—
297C22×Q16—112no—
298C22×Q16C2×D1112yescomplemented
299C22×SD16—112no—
300C22×SD16C2×D1112yes—
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#497C2×D1118yescomplemented
324#489—118no—
325#489—118no—
326#464—1116no—
327#464—1116no—
328#451—1116no—
329#450—1116no—
330#432—118no—
331C2×C4⋊C8—112no—
332C2×#103—112no—
333C2×#103—112no—
334C2×#102—112no—
335C2×#102—112no—
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—44no—
359C4×C11—42no—
360C4×C11#53512yes—
361C4×C11C2×H(5,𝔽2)12yes—
362Dic11—22no—
363Dic11—22no—
364Dic11—22no—
365Dic11—42no—
366Dic11—44no—
367C25—221no—
368C22×Q8—114no—
369C22×Q8—111no—
370C22×Q8—221no—
371C22×Q8—222no—
372C22×Q8—221no—
373C22×Q8—444no—
374C22×Q8C22×D1112yes—
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—44no—
387C2×Q16—118no—
388C2×Q16—444no—
389C2×Q16C22×D1118yescomplemented
390C2×SD16—44no—
391C2×SD16—118no—
392C2×SD16—444no—
393C2×SD16C22×D1118yes—
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—228no—
413C22⋊Q8—224no—
414C4×Q8—118no—
415C4×Q8—228no—
416C4×Q8—224no—
417#117—228no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
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#103—118no—
445#102—118no—
446#102—118no—
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—22no—
465C2×Q8—21no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—112no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—221no—
473C2×Q8—224no—
474C2×Q8—444no—
475C2×Q8—444no—
476C2×Q8—448no—
477C2×Q8—448no—
478C2×Q8C23×D1112yes—
479C2×Q8C23×D1114yes—
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—48no—
510Q16—448no—
511SD16—48no—
512SD16—448no—
513C2×C8—24no—
514C2×C8—114no—
515C2×C8—224no—
516C2×C8C23×D1114yes—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—114no—
520C4⋊C4—228no—
521C4⋊C4—228no—
522C4⋊C4—222no—
523C4⋊C4—224no—
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—24no—
560Q8—24no—
561Q8—44no—
562Q8—42no—
563Q8—224no—
564Q8—448no—
565Q8—448no—
566Q8—442no—
567D4—24no—
568D4—42no—
569D4—224no—
570D4—448no—
571D4—442no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—44no—
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#6703714yes—
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#1062324612yes—
614C22D11×#13712yes—
615C22#1062330812yes—
616C22C22×D4×D1111yescharacteristic
617C4—22no—
618C4—22no—
619C4—42no—
620C4—44no—
621C4—222no—
622C4—222no—
623C4—222no—
624C4—442no—
625C4—444no—
626C4#1062324612yes—
627C4C2×#6703712yes—
628C2—82no—
629C2—224no—
630C2—882no—
631C2#1307961414yesdirect product factor
632C2C2×#1062324611yescharacteristic
633C2C2×D11×#13711yescharacteristic
634C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#497D11
hypocenterC11C2×#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079614C2direct (N × H)
4. C2×#10622699C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622799C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#497C2semidirect
15. C22×C11×Q16C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
21. C2×Q8×Dic11C22semidirect
22. C22×#4326C22semidirect
26. #10623259C22semidirect
39. C2×#66922C22semidirect
40. C11×#497C22semidirect
41. C2×C11×#97C22semidirect
42. C2×#66899C22semidirect
44. #10622799C22semidirect
45. #10622798C22semidirect
47. #10622779C22semidirect
50. C2×#66880C22semidirect
51. C2×Dic11⋊C8C22semidirect
52. #10622699C22semidirect
53. #10622668C22semidirect
54. C2×#66867C22semidirect
55. #10622327C22semidirect
56. #10622318C22semidirect
77. C2×C11×Q16C23semidirect
82. C11×C4⋊Q8C23semidirect
97. Q8×Dic11C23semidirect
99. C2×#4326C23semidirect
131. #66922C23semidirect
132. C11×#97C23semidirect
133. #66899C23semidirect
137. #66880C23semidirect
138. Dic11⋊C8C23semidirect
139. #66867C23semidirect
228. C2×#497D11semidirect
298. C22×Q16C2×D11semidirect
304. C2×C4⋊Q8C2×D11semidirect
323. #497C2×D11semidirect
338. C2×#97C2×D11semidirect
389. C2×Q16C22×D11semidirect
399. C4⋊Q8C22×D11semidirect
449. #97C22×D11semidirect
451. C2×C11#3215semidirect
540. C11C2×#3215semidirect
631. C2#13079614direct (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
#130796142
C2×#106226992
C2×#106223272
C2×#106226682
C2×#106227982
C2×#106227792
C2×#106227992
C2×#106227822
C2×#106223182
C2×C11×#4972
C2×#321511