Finite Group Databasebeta

← C2×#13078768 #15621900

Subgroups — C2×#13078768 #15621900

Order 2816.

2430 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×#10623008C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3#13078768C2116yesmaximal, direct product factor
4C2×#10622350C212yesmaximal, complemented
5C2×#10622464C211yesmaximal, characteristic, complemented
6C2×#10622459C211yesmaximal, characteristic, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622456C211yesmaximal, characteristic, complemented
9C2×#10622347C212yesmaximal, complemented
10C2×#10622324C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C2×C11×#432C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×#4339C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#66983—21no—
17C2×#66983C2212yes—
18C2×C4×C22⋊D11—21no—
19C2×C4×C22⋊D11—21no—
20C2×#66979C2211yescharacteristic
21C22×D88C2212yes—
22C22×#4314C2212yes—
23#10623008—24no—
24#10623008C2218yescomplemented
25C2×#66928—21no—
26C2×#66927C2211yescharacteristic
27C4×#4339—24no—
28C4×#4339C2218yescomplemented
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×C42×D11—21no—
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C11×#432C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2212yes—
42C2×C11×#97C2212yes—
43C2×#66885C2212yes—
44C2×#66885C2212yes—
45C2×#66885C2212yes—
46C2×#66882C2212yes—
47C2×#66881C2212yes—
48C2×#66880C2212yes—
49#10622464C2218yescomplemented
50#10622461C2218yescomplemented
51#10622459C2218yescomplemented
52#10622456C2218yescomplemented
53#10622350C22116yescomplemented
54#10622347C22116yescomplemented
55#10622324C22116yescomplemented
56#10622323C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—22no—
62C2×#4339—22no—
63C2×#4339—28no—
64C2×#4339—24no—
65C2×#4339—24no—
66C2×#4339—48no—
67C2×#4339C2314yes—
68C22×D44—21no—
69C22×D44—21no—
70C22×D44C2312yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×Dic22—21no—
77C22×Dic22C2311yescharacteristic
78C22×C8×C11C2312yes—
79C22×C8×C11C2312yes—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D414yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2314yes—
86C2×C22⋊Dic11—21no—
87#66983—24no—
88#66983—28no—
89#66983C2318yes—
90C4×C22⋊D11—28no—
91C4×C22⋊D11—28no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96#66979—22no—
97#66979C2314yes—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2312yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×D88—28no—
108C2×D88C2318yes—
109C2×#4314—28no—
110C2×#4314C2318yes—
111#66928—28no—
112#66927—22no—
113#66927C2314yes—
114C4×D44—28no—
115C4×D44—22no—
116C4×D44—22no—
117C4×D44—24no—
118C4×D44C2314yes—
119C4×D44C2314yes—
120C4×D44C2318yes—
121#66925—28no—
122C42×D11—28no—
123#66922—22no—
124#66922C2314yes—
125C4×Dic22—22no—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128C4×Dic22C2314yes—
129C11×C4⋊C8C2314yes—
130C11×C4⋊C8C2314yes—
131C11×C22⋊C8C2318yes—
132C11×#97C2318yes—
133#66885C2318yes—
134#66885C2318yes—
135#66885C2318yes—
136#66882C2318yes—
137#66881C2318yes—
138#66880C2318yes—
139C2×#3115—111nomaximal, Sylow
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—28no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—48no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165#4339—216no—
166#4339—28no—
167#4339—28no—
168#4339—432no—
169C2×D44—21no—
170C2×D44—22no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—22no—
174C2×D44—24no—
175C2×D44—24no—
176C2×D44—44no—
177C2×D44—44no—
178C2×D44#4114yescomplemented
179C2×D44C2414yes—
180C2×D44C2412yes—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—28no—
186C2×C4×D11—44no—
187C2×C4×D11—48no—
188C2×C4×D11—44no—
189C2×Dic22—21no—
190C2×Dic22—24no—
191C2×Dic22—22no—
192C2×Dic22—44no—
193C2×Dic22#4114yescomplemented
194C2×Dic22C2412yes—
195C2×C8×C11—24no—
196C2×C8×C11—24no—
197C2×C8×C11C2414yes—
198C2×C8×C11C2414yes—
199C42×C11C2×D412yes—
200C42×C11C2×D412yes—
201C42×C11C2×D414yes—
202C42×C11C2×D414yes—
203C42×C11C2412yes—
204C42×C11C2412yes—
205C22⋊Dic11—24no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—22no—
213C4⋊Dic11—24no—
214C4⋊Dic11C2414yes—
215C4⋊Dic11C2412yes—
216C4⋊Dic11C2412yes—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219C4×Dic11—24no—
220C4×Dic11—24no—
221C4×Dic11—24no—
222D88—216no—
223#4314—216no—
224C2×#532—111no—
225C2×C4×#41—111no—
226#3115—1116no—
227C2×#482—112no—
228C2×#475—111no—
229C2×#474—111no—
230C2×#460—111no—
231C2×#459—111no—
232C2×#449—112no—
233C2×#442—112no—
234C2×#440—112no—
235C2×#432D1111yescharacteristic, complemented
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11C22×D412yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—44no—
258C2×C4×C11AGL(1,ℤ/8)14yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D412yes—
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4112yes—
267C2×C4×C11C2511yescharacteristic
268C22⋊D11—216no—
269C22⋊D11—416no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278D44—24no—
279D44—22no—
280D44—24no—
281D44—24no—
282D44—48no—
283D44—44no—
284D44—48no—
285D44C2×#4114yescomplemented
286C4×D11—216no—
287C4×D11—48no—
288C4×D11—416no—
289C4×D11—48no—
290Dic22—24no—
291Dic22—22no—
292Dic22—48no—
293Dic22C2×#4114yescomplemented
294C8×C11—24no—
295C8×C11—24no—
296C22×#41—111no—
297C22×#41—221no—
298C22×SD16—112no—
299C22×D8—112no—
300#532—118no—
301#532—224no—
302C2×C4⋊Q8—111no—
303C2×#127—111no—
304C2×#124—221no—
305C2×#121—112no—
306C2×#121—221no—
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4—112no—
314C2×C4×D4—221no—
315C2×C4×D4—221no—
316C2×C4×D4—221no—
317C2×#117—111no—
318C2×#117—221no—
319C22×C42—221no—
320C22×C42C2×D1111yescharacteristic
321#482—1116no—
322#475—118no—
323#474—118no—
324#460—118no—
325#459—118no—
326#449—1116no—
327#442—1116no—
328#440—1116no—
329#432C2×D1118yescomplemented
330C2×#107—112no—
331C2×#106—112no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×#103—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×#102—112no—
338C2×C22⋊C8C2×D1112yes—
339C2×#97C2×D1112yes—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—44no—
344C22×C11#52512yes—
345C22×C11C2×AGL(1,ℤ/8)12yes—
346C22×C11#57512yes—
347C22×C11C23×D411yescharacteristic
348C2×D11—24no—
349C2×D11—48no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—88no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11#52512yes—
361C4×C11C2×AGL(1,ℤ/8)14yes—
362C4×C11C22×#4111yescharacteristic
363C4×C11C22×#4111yescharacteristic
364Dic11—24no—
365Dic11—44no—
366Dic11—42no—
367Dic11—42no—
368C2×#41—114no—
369C2×#41—224no—
370C2×#41—224no—
371C2×#41—222no—
372C2×#41—228no—
373C2×#41—448no—
374C22×Q8—111no—
375C22×Q8—221no—
376C22×D4—111no—
377C22×D4—112no—
378C22×D4—221no—
379C22×D4—222no—
380C22×D4—221no—
381C22×D4—221no—
382C23×C4—221no—
383C23×C4—222no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4D4411yescharacteristic
387C23×C4D4411yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C2×SD16—118no—
390C2×SD16—228no—
391C2×D8—118no—
392C2×D8—228no—
393C22×C8C22×D1112yes—
394C22×C8C22×D1112yes—
395C4⋊Q8—114no—
396C4⋊Q8—222no—
397#127—114no—
398#127—222no—
399#124—228no—
400#121—118no—
401#121—224no—
402#121—228no—
403C4×Q8—114no—
404C4×Q8—114no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×D4—114no—
408C4×D4—114no—
409C4×D4—118no—
410C4×D4—228no—
411C4×D4—228no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—224no—
415C4×D4—228no—
416#117—114no—
417#117—222no—
418#117—228no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—228no—
434C2×C42D4411yescharacteristic
435C2×C42D4414yes—
436C2×C42D4411yescharacteristic
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439C2×C42C22×D1114yes—
440#107—118no—
441#106—118no—
442C4⋊C8C22×D1114yes—
443C4⋊C8C22×D1114yes—
444#103—118no—
445#102—118no—
446#102—118no—
447#102—118no—
448C22⋊C8C22×D1118yes—
449#97C22×D1118yes—
450C2×C11—42no—
451C2×C11#311514yescomplemented
452C2×C11C2×#52511yescharacteristic
453C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
454C2×C11C2×#57511yescharacteristic
455D11—44no—
456D11—84no—
457C24—221no—
458C24—222no—
459C24C2×D4411yescharacteristic
460#41—228no—
461#41—228no—
462#41—2216no—
463#41—4432no—
464C2×Q8—114no—
465C2×Q8—112no—
466C2×Q8—221no—
467C2×Q8—224no—
468C2×Q8—222no—
469C2×Q8—444no—
470C2×D4—114no—
471C2×D4—112no—
472C2×D4—114no—
473C2×D4—228no—
474C2×D4—224no—
475C2×D4—228no—
476C2×D4—221no—
477C2×D4—224no—
478C2×D4—222no—
479C2×D4—224no—
480C2×D4—222no—
481C2×D4—224no—
482C2×D4—224no—
483C2×D4—444no—
484C2×D4—448no—
485C2×D4—444no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—228no—
491C22×C4—221no—
492C22×C4—224no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—228no—
499C22×C4—448no—
500C22×C4—444no—
501C22×C4—444no—
502C22×C4C2×D4414yes—
503C22×C4C2×D4412yes—
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4414yes—
509C22×C4C2×D4411yescharacteristic
510C22×C4C23×D1112yes—
511C22×C4C23×D1111yescharacteristic
512SD16—2216no—
513D8—2216no—
514C2×C8—24no—
515C2×C8—24no—
516C2×C8C23×D1114yes—
517C2×C8C23×D1114yes—
518C4⋊C4—112no—
519C4⋊C4—112no—
520C4⋊C4—114no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—224no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C42—224no—
533C42—224no—
534C42—224no—
535C42C2×D4414yes—
536C42C2×D4414yes—
537C42C2×D4412yes—
538C42C2×D4412yes—
539C42C23×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—22no—
545C23—224no—
546C23—222no—
547C23—224no—
548C23—442no—
549C23—442no—
550C23—444no—
551C23—444no—
552C23—444no—
553C23C22×D4412yes—
554C23C22×D4411yescharacteristic
555Q8—114no—
556Q8—224no—
557Q8—222no—
558Q8—448no—
559D4—114no—
560D4—2216no—
561D4—224no—
562D4—222no—
563D4—224no—
564D4—224no—
565D4—448no—
566D4—4416no—
567D4—448no—
568D4—444no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—28no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—44no—
578C2×C4—2216no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—4416no—
585C2×C4—448no—
586C2×C4—444no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—448no—
590C2×C4#6696114yes—
591C2×C4C22×D4412yes—
592C2×C4C22×D4412yes—
593C2×C4C22×D4412yes—
594C2×C4C22×D4412yes—
595C2×C4C22×D4412yes—
596C2×C4C22×D4411yescharacteristic
597C2×C4#41×D1112yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—24no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—44no—
606C22—224no—
607C22—442no—
608C22—442no—
609C22—448no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—888no—
614C22#1062305512yes—
615C22C2×#6696112yes—
616C22#1062327912yes—
617C22C23×D4411yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—224no—
623C4—444no—
624C4—442no—
625C4—442no—
626C4#1062305512yes—
627C4C2×#6696114yes—
628C4C2×#41×D1111yescharacteristic
629C4C2×#41×D1111yescharacteristic
630C2—42no—
631C2—444no—
632C2—884no—
633C2#1307876814yesdirect product factor
634C2C2×#1062305511yescharacteristic
635C2C22×#6696111yescharacteristic
636C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
hypercenterC2×#432D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×C4×#4339C2semidirect
3. #13078768C2direct (N × H)
4. C2×#10622350C2semidirect
5. C2×#10622464C2semidirect
6. C2×#10622459C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622456C2semidirect
9. C2×#10622347C2semidirect
10. C2×#10622324C2semidirect
11. C2×#10622323C2semidirect
12. C2×C11×#432C2semidirect
24. #10623008C22semidirect
28. C4×#4339C22semidirect
38. C11×#432C22semidirect
49. #10622464C22semidirect
50. #10622461C22semidirect
51. #10622459C22semidirect
52. #10622456C22semidirect
53. #10622350C22semidirect
54. #10622347C22semidirect
55. #10622324C22semidirect
56. #10622323C22semidirect
178. C2×D44#41semidirect
193. C2×Dic22#41semidirect
235. C2×#432D11semidirect
285. D44C2×#41semidirect
293. Dic22C2×#41semidirect
329. #432C2×D11semidirect
451. C2×C11#3115semidirect
541. C11C2×#3115semidirect
633. C2#13078768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×C4×#43392
#130787682
C2×#106223502
C2×#106224642
C2×#106224592
C2×#106224612
C2×#106224562
C2×#106223472
C2×#106223242
C2×#106223232
C2×C11×#4322
C2×#311511