Finite Group Databasebeta

← C2×#13078761 #15621893

Subgroups — C2×#13078761 #15621893

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×C4×#4339C211yesmaximal, characteristic, complemented
2#13078761C2116yesmaximal, direct product factor
3C2×#10622648C212yesmaximal, complemented
4C2×#10622707C211yesmaximal, characteristic, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622688C211yesmaximal, characteristic, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622650C212yesmaximal, complemented
9C2×#10622627C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C11×#532C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C22×#4339C2211yescharacteristic
15C11×#532—24no—
16C11×#532C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124—21no—
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2212yes—
24C22×C42×C11C2211yescharacteristic
25C22×#4324C2212yes—
26C22×#4323C2212yes—
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66979C2211yescharacteristic
30C4×#4339—24no—
31C4×#4339C2218yescomplemented
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66925—21no—
35C2×C42×D11—21no—
36C2×C4×Dic22C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622707C2218yescomplemented
42#10622700C2218yescomplemented
43#10622688C2218yescomplemented
44#10622685C2218yescomplemented
45#10622650C22116yescomplemented
46#10622648C22116yescomplemented
47#10622631C22116yescomplemented
48#10622627C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2212yes—
57C2×C11×#41—28no—
58C2×C11×#41—48no—
59C22×Q8×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C2×#4339—22no—
70C2×#4339—24no—
71C2×#4339—24no—
72C2×#4339C2314yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×Dic22C2311yescharacteristic
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8C2314yes—
80C11×#127—22no—
81C11×#127C2314yes—
82C11×#124—28no—
83C11×#121—28no—
84C11×#121—24no—
85C11×#121C2318yes—
86C4×D4×C11—28no—
87C4×D4×C11—24no—
88C4×D4×C11C2318yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D414yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2314yes—
99C2×C22⋊Dic11—21no—
100C2×#4324—28no—
101C2×#4324C2318yes—
102C2×#4323—28no—
103C2×#4323C2318yes—
104C4×C22⋊D11—28no—
105C4×C22⋊D11—28no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108#66979—22no—
109#66979C2314yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C22×C11⋊C8C2312yes—
118C22×C11⋊C8C2312yes—
119C4×D44—22no—
120C4×D44—22no—
121C4×D44C2314yes—
122C4×D44C2314yes—
123#66925—28no—
124C42×D11—28no—
125C4×Dic22—22no—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128C4×Dic22C2314yes—
129#66896C2318yes—
130#66896C2318yes—
131C22⋊(C11⋊C8)C2318yes—
132#66874C2318yes—
133#66873C2318yes—
134#66872C2318yes—
135#66871C2318yes—
136C4⋊(C11⋊C8)C2314yes—
137C4⋊(C11⋊C8)C2314yes—
138#66867C2318yes—
139C2×#3115—111nomaximal, Sylow
140C24×C11—22no—
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C11×#41—432no—
144C2×Q8×C11—24no—
145C2×Q8×C11—44no—
146C2×D4×C11—28no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—44no—
153C2×D4×C11—48no—
154C2×D4×C11—44no—
155C2×D4×C11C2414yes—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—28no—
161C22×C4×C11—42no—
162C22×C4×C11—48no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C2×C22⋊D11—28no—
174C2×C22⋊D11—24no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178#4339—216no—
179#4339—28no—
180#4339—28no—
181C2×D44—21no—
182C2×D44—22no—
183C2×D44#4114yescomplemented
184C2×D44C2412yes—
185C2×C4×D11—28no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—44no—
190C2×C4×D11—44no—
191C2×Dic22—21no—
192C2×Dic22—22no—
193C2×Dic22#4114yescomplemented
194C2×Dic22C2412yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4C2414yes—
198C11×C22⋊C4—28no—
199C11×C22⋊C4—28no—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202C42×C11C2×D414yes—
203C42×C11C2×D414yes—
204C42×C11C2412yes—
205C42×C11C2412yes—
206C22⋊Dic11—24no—
207#4324—216no—
208#4323—216no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11C2412yes—
214C4⋊Dic11C2412yes—
215Dic11⋊C4—24no—
216Dic11⋊C4—24no—
217C4×Dic11—24no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C2×C11⋊C8—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223C2×C11⋊C8C2414yes—
224C2×#532D1111yescharacteristic, complemented
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×#432—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—44no—
241C23×C11—44no—
242C23×C11—44no—
243C23×C11C22×D412yes—
244C23×C11C22×D411yescharacteristic
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—42no—
249Q8×C11—48no—
250D4×C11—24no—
251D4×C11—24no—
252D4×C11—48no—
253D4×C11—416no—
254D4×C11—44no—
255D4×C11—48no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—28no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—44no—
266C2×C4×C11—416no—
267C2×C4×C11—44no—
268C2×C4×C11AGL(1,ℤ/8)14yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D412yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2511yescharacteristic
278C22⋊D11—216no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285D44—24no—
286D44—22no—
287D44C2×#4114yescomplemented
288C4×D11—216no—
289C4×D11—48no—
290C4×D11—48no—
291Dic22—24no—
292Dic22—22no—
293Dic22C2×#4114yescomplemented
294C11⋊C8—24no—
295C11⋊C8—24no—
296C22×#41—21no—
297C22×#41—111no—
298C22×SD16—112no—
299C22×D8—112no—
300#532—24no—
301#532C2×D1118yescomplemented
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#127C2×D1111yescharacteristic
304C2×#124—21no—
305C2×#121—21no—
306C2×#121C2×D1112yes—
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—21no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C2×C4×D4—221no—
316C2×C4×D4C2×D1112yes—
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#432—118no—
330C2×#107—112no—
331C2×#106—112no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8—111no—
334C2×#103—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×#102—112no—
338C2×C22⋊C8—112no—
339C2×#97—112no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—88no—
348C22×C11#52512yes—
349C22×C11C2×AGL(1,ℤ/8)12yes—
350C22×C11#57512yes—
351C22×C11C23×D411yescharacteristic
352C2×D11—24no—
353C2×D11—48no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—44no—
361C4×C11#52512yes—
362C4×C11C2×AGL(1,ℤ/8)14yes—
363C4×C11C22×#4111yescharacteristic
364C4×C11C22×#4111yescharacteristic
365Dic11—24no—
366Dic11—42no—
367Dic11—42no—
368C2×#41—28no—
369C2×#41—48no—
370C2×#41—114no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41—222no—
374C22×Q8—21no—
375C22×Q8—111no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—111no—
380C22×D4—221no—
381C22×D4C22×D1112yes—
382C23×C4—22no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4C22⋊D1111yescharacteristic
387C23×C4C22⋊D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C2×SD16—118no—
390C2×SD16—228no—
391C2×D8—118no—
392C2×D8—228no—
393C22×C8—112no—
394C22×C8—112no—
395C4⋊Q8—22no—
396C4⋊Q8C22×D1114yes—
397#127—22no—
398#127C22×D1114yes—
399#124—28no—
400#121—28no—
401#121—24no—
402#121C22×D1118yes—
403C4×Q8—114no—
404C4×Q8—114no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×D4—28no—
408C4×D4—24no—
409C4×D4—114no—
410C4×D4—114no—
411C4×D4—228no—
412C4×D4—228no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4C22×D1118yes—
416#117—114no—
417#117—222no—
418#117—228no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1112yes—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—228no—
434C2×C42C22⋊D1111yescharacteristic
435C2×C42C22⋊D1114yes—
436C2×C42C22⋊D1111yescharacteristic
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439C2×C42C22×D1114yes—
440#107—118no—
441#106—118no—
442C4⋊C8—114no—
443C4⋊C8—114no—
444#103—118no—
445#102—118no—
446#102—118no—
447#102—118no—
448C22⋊C8—118no—
449#97—118no—
450C2×C11—42no—
451C2×C11—84no—
452C2×C11#311514yescomplemented
453C2×C11C2×#52511yescharacteristic
454C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
455C2×C11C2×#57511yescharacteristic
456D11—44no—
457C24—22no—
458C24—221no—
459C24C2×C22⋊D1111yescharacteristic
460#41—432no—
461#41—228no—
462#41—228no—
463#41—2216no—
464C2×Q8—24no—
465C2×Q8—44no—
466C2×Q8—114no—
467C2×Q8—112no—
468C2×Q8—222no—
469C2×Q8—221no—
470C2×D4—28no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—44no—
477C2×D4—48no—
478C2×D4—44no—
479C2×D4—114no—
480C2×D4—112no—
481C2×D4—228no—
482C2×D4—224no—
483C2×D4—222no—
484C2×D4—221no—
485C2×D4C23×D1114yes—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—42no—
492C22×C4—48no—
493C22×C4—228no—
494C22×C4—221no—
495C22×C4—224no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—444no—
501C22×C4—444no—
502C22×C4C2×C22⋊D1114yes—
503C22×C4C2×C22⋊D1112yes—
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1114yes—
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1112yes—
511C22×C4C23×D1111yescharacteristic
512SD16—2216no—
513D8—2216no—
514C2×C8—114no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8—224no—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4C23×D1114yes—
527C22⋊C4—28no—
528C22⋊C4—28no—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C42—224no—
533C42—224no—
534C42—224no—
535C42C2×C22⋊D1114yes—
536C42C2×C22⋊D1114yes—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C42C23×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—22no—
545C23—24no—
546C23—44no—
547C23—44no—
548C23—44no—
549C23—224no—
550C23—222no—
551C23—442no—
552C23—442no—
553C23C22×C22⋊D1112yes—
554C23C22×C22⋊D1111yescharacteristic
555Q8—48no—
556Q8—114no—
557Q8—224no—
558Q8—222no—
559D4—24no—
560D4—24no—
561D4—48no—
562D4—416no—
563D4—48no—
564D4—44no—
565D4—114no—
566D4—2216no—
567D4—224no—
568D4—222no—
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—24no—
578C2×C4—44no—
579C2×C4—416no—
580C2×C4—44no—
581C2×C4—2216no—
582C2×C4—224no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—448no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—448no—
590C2×C4#6698514yes—
591C2×C4#41×D1112yes—
592C2×C4#41×D1112yes—
593C2×C4C22×C22⋊D1112yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1112yes—
598C2×C4C22×C22⋊D1111yescharacteristic
599C2×C4C24×D1111yescharacteristic
600C8—224no—
601C8—224no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—88no—
610C22—224no—
611C22—442no—
612C22—442no—
613C22—448no—
614C22C2×#6698512yes—
615C22#1062335312yes—
616C22#1062335912yes—
617C22C23×C22⋊D1111yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—44no—
623C4—224no—
624C4—442no—
625C4—442no—
626C4C2×#6698514yes—
627C4#1062335912yes—
628C4C2×#41×D1111yescharacteristic
629C4C2×#41×D1111yescharacteristic
630C2—42no—
631C2—84no—
632C2—444no—
633C2#1307876114yesdirect product factor
634C2C2×#1062335911yescharacteristic
635C2C22×#6698511yescharacteristic
636C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4339C2semidirect
2. #13078761C2direct (N × H)
3. C2×#10622648C2semidirect
4. C2×#10622707C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622688C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622650C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622631C2semidirect
11. C2×#10622539C2semidirect
12. C2×C11×#532C2semidirect
16. C11×#532C22semidirect
31. C4×#4339C22semidirect
41. #10622707C22semidirect
42. #10622700C22semidirect
43. #10622688C22semidirect
44. #10622685C22semidirect
45. #10622650C22semidirect
46. #10622648C22semidirect
47. #10622631C22semidirect
48. #10622627C22semidirect
53. #10622539C22semidirect
183. C2×D44#41semidirect
193. C2×Dic22#41semidirect
224. C2×#532D11semidirect
287. D44C2×#41semidirect
293. Dic22C2×#41semidirect
301. #532C2×D11semidirect
452. C2×C11#3115semidirect
541. C11C2×#3115semidirect
633. C2#13078761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787612
C2×#106226482
C2×#106227072
C2×#106227002
C2×#106226882
C2×#106226852
C2×#106226502
C2×#106226272
C2×#106226312
C2×#106225392
C2×C11×#5322
C2×#311511