Finite Group Databasebeta

← C2×#13078767 #15621899

Subgroups — C2×#13078767 #15621899

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
2#13078767C2116yesmaximal, direct product factor
3C2×#10622616C212yesmaximal, complemented
4C2×#10622633C211yesmaximal, characteristic, complemented
5C2×#10622620C211yesmaximal, characteristic, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622628C211yesmaximal, characteristic, complemented
8C2×#10622851C212yesmaximal, complemented
9C2×#10622627C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339—21no—
15C4×C11×#41—24no—
16C4×C11×#41C2218yescomplemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C2×C11×#117C2211yescharacteristic
25C22×C42×C11—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4325C2212yes—
28C22×#4323C2212yes—
29C2×#66983—21no—
30C2×#66983C2212yes—
31#10623008—24no—
32#10623008C2218yescomplemented
33C2×#66928—21no—
34C2×#66927C2211yescharacteristic
35C2×C4×D44—21no—
36C2×C4×D44C2212yes—
37C2×#66922C2211yescharacteristic
38#10622851C22116yescomplemented
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41C2×C22⋊(C11⋊C8)C2212yes—
42#10622640C2218yescomplemented
43#10622639C22116yescomplemented
44#10622633C2218yescomplemented
45#10622628C2218yescomplemented
46#10622627C22116yescomplemented
47#10622620C2218yescomplemented
48#10622616C22116yescomplemented
49C2×#66873C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2212yes—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41—22no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—22no—
71C2×#4339—28no—
72C2×#4339—48no—
73C22×D44—21no—
74C22×D44—21no—
75C22×D44C2312yes—
76C22×C4×D11—22no—
77C22×Dic22—21no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C4×Q8×C11C2314yes—
82C4×D4×C11—28no—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11C2314yes—
87C4×D4×C11C2314yes—
88C11×#117—22no—
89C11×#117—28no—
90C11×#117C2314yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11—28no—
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D414yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2314yes—
108C2×#4325—28no—
109C2×#4325C2318yes—
110C2×#4323—28no—
111C2×#4323C2318yes—
112#66983—24no—
113#66983—28no—
114#66983C2318yes—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11C2312yes—
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2312yes—
121#66928—28no—
122#66927—22no—
123#66927C2314yes—
124C4×D44—28no—
125C4×D44—24no—
126C4×D44C2318yes—
127#66922—22no—
128#66922C2314yes—
129#66899C2318yes—
130#66896C2318yes—
131C22⋊(C11⋊C8)C2318yes—
132#66873C2318yes—
133#66873C2318yes—
134#66872C2318yes—
135#66871C2318yes—
136C4⋊(C11⋊C8)C2314yes—
137C4⋊(C11⋊C8)C2314yes—
138#66867C2318yes—
139C2×#3115—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C23×D11—22no—
143C11×#41—216no—
144C11×#41—28no—
145C11×#41—28no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11#4114yescomplemented
149C2×Q8×C11C2412yes—
150C2×D4×C11—28no—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11#4114yescomplemented
155C2×D4×C11C2412yes—
156C22×C4×C11—28no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—42no—
167C22×C4×C11—44no—
168C22×C4×C11—44no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D414yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2412yes—
178C22×C4×C11C2411yescharacteristic
179C2×C22⋊D11—28no—
180C2×C22⋊D11—48no—
181C22×Dic11—22no—
182#4339—432no—
183C2×D44—22no—
184C2×D44—24no—
185C2×D44—24no—
186C2×D44—24no—
187C2×D44—24no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44C2414yes—
191C2×C4×D11—28no—
192C2×C4×D11—48no—
193C2×Dic22—24no—
194C2×Dic22—44no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C2412yes—
200C11×C4⋊C4C2412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C42×C11—24no—
205C42×C11—24no—
206C42×C11—24no—
207C42×C11C2×D412yes—
208C42×C11C2×D414yes—
209C42×C11C2×D412yes—
210C42×C11C2×D414yes—
211C42×C11C2412yes—
212C42×C11C2412yes—
213#4325—216no—
214#4323—216no—
215(C2×D11)⋊C4—28no—
216(C2×D11)⋊C4—28no—
217C4⋊Dic11—22no—
218C4⋊Dic11—24no—
219C4⋊Dic11C2414yes—
220C2×C11⋊C8—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223C2×C11⋊C8C2414yes—
224C2×#532—111no—
225C2×C4×#41D1111yescharacteristic, complemented
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—24no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11C22×D412yes—
244C23×C11C22×D411yescharacteristic
245C22×D11—24no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249Q8×C11—24no—
250Q8×C11—22no—
251Q8×C11C2×#4114yescomplemented
252D4×C11—216no—
253D4×C11—24no—
254D4×C11—22no—
255D4×C11C2×#4114yescomplemented
256C2×C4×C11—216no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—28no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—48no—
274C2×C4×C11AGL(1,ℤ/8)14yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D412yes—
281C2×C4×C11C2×#4112yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2511yescharacteristic
284C22⋊D11—416no—
285C2×Dic11—24no—
286C2×Dic11—44no—
287D44—24no—
288D44—24no—
289D44—48no—
290D44—44no—
291D44—48no—
292C4×D11—416no—
293Dic22—48no—
294C11⋊C8—24no—
295C11⋊C8—24no—
296C22×#41—221no—
297C22×#41C2×D1111yescharacteristic
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—24no—
308C4×#41C2×D1118yescomplemented
309C2×C4×Q8C2×D1111yescharacteristic
310C2×C4×Q8C2×D1111yescharacteristic
311C2×C4×D4—21no—
312C2×C4×D4—21no—
313C2×C4×D4—112no—
314C2×C4×D4—221no—
315C2×C4×D4C2×D1111yescharacteristic
316C2×C4×D4C2×D1111yescharacteristic
317C2×#117—21no—
318C2×#117C2×D1111yescharacteristic
319C22×C42—21no—
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—24no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—44no—
345C22×C11—48no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11#52512yes—
349C22×C11C2×AGL(1,ℤ/8)12yes—
350C22×C11#57512yes—
351C22×C11C23×D411yescharacteristic
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—88no—
356C4×C11—22no—
357C4×C11—24no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11#52512yes—
364C4×C11C2×AGL(1,ℤ/8)14yes—
365C4×C11C22×#4111yescharacteristic
366C4×C11C22×#4111yescharacteristic
367Dic11—44no—
368C2×#41—24no—
369C2×#41—24no—
370C2×#41—22no—
371C2×#41—228no—
372C2×#41—448no—
373C2×#41C22×D1114yes—
374C22×Q8—221no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—21no—
377C22×D4—112no—
378C22×D4—222no—
379C22×D4—221no—
380C22×D4—221no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—222no—
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—114no—
396C4⋊Q8—222no—
397#127—114no—
398#127—222no—
399#124—228no—
400#121—118no—
401#121—224no—
402#121—228no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8C22×D1114yes—
406C4×Q8C22×D1114yes—
407C4×D4—28no—
408C4×D4—28no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—118no—
412C4×D4—224no—
413C4×D4—228no—
414C4×D4C22×D1114yes—
415C4×D4C22×D1114yes—
416#117—22no—
417#117—28no—
418#117C22×D1114yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—28no—
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—44no—
452C2×C11#311514yescomplemented
453C2×C11C2×#52511yescharacteristic
454C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
455C2×C11C2×#57511yescharacteristic
456D11—84no—
457C24—21no—
458C24—222no—
459C24C2×C22⋊D1111yescharacteristic
460#41—216no—
461#41—28no—
462#41—28no—
463#41—4432no—
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8—224no—
467C2×Q8—444no—
468C2×Q8#433914yescomplemented
469C2×Q8C23×D1112yes—
470C2×D4—28no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—114no—
475C2×D4—228no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—224no—
479C2×D4—222no—
480C2×D4—224no—
481C2×D4—444no—
482C2×D4—448no—
483C2×D4—444no—
484C2×D4#433914yescomplemented
485C2×D4C23×D1112yes—
486C22×C4—28no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—42no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—222no—
500C22×C4—228no—
501C22×C4—448no—
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—24no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—114no—
523C4⋊C4—222no—
524C4⋊C4—224no—
525C4⋊C4C23×D1112yes—
526C4⋊C4C23×D1112yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C42—24no—
533C42—24no—
534C42—24no—
535C42C2×C22⋊D1114yes—
536C42C2×C22⋊D1114yes—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C42C23×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—22no—
543C23—24no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—42no—
548C23—42no—
549C23—224no—
550C23—444no—
551C23—444no—
552C23—444no—
553C23C22×C22⋊D1112yes—
554C23C22×C22⋊D1111yescharacteristic
555Q8—24no—
556Q8—22no—
557Q8—448no—
558Q8C2×#433914yescomplemented
559D4—216no—
560D4—24no—
561D4—22no—
562D4—224no—
563D4—224no—
564D4—448no—
565D4—4416no—
566D4—444no—
567D4—448no—
568D4C2×#433914yescomplemented
569C2×C4—216no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—28no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—44no—
583C2×C4—48no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—48no—
587C2×C4—224no—
588C2×C4—4416no—
589C2×C4—444no—
590C2×C4#6700214yes—
591C2×C4C2×#433912yes—
592C2×C4C2×#433912yes—
593C2×C4C22×C22⋊D1112yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1111yescharacteristic
598C2×C4C22×C22⋊D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—224no—
601C8—224no—
602C22—22no—
603C22—24no—
604C22—22no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—48no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—888no—
614C22#1062332212yes—
615C22C2×#6700212yes—
616C22#1062335312yes—
617C22C23×C22⋊D1111yescharacteristic
618C4—22no—
619C4—24no—
620C4—22no—
621C4—22no—
622C4—22no—
623C4—42no—
624C4—42no—
625C4—444no—
626C4#1062332212yes—
627C4C2×#6700214yes—
628C4C22×#433911yescharacteristic
629C4C22×#433911yescharacteristic
630C2—42no—
631C2—44no—
632C2—884no—
633C2#1307876714yesdirect product factor
634C2C2×#1062332211yescharacteristic
635C2C22×#6700211yescharacteristic
636C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC23×C11C22×D4
hypercenterC2×C4×#41D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13078767C2direct (N × H)
3. C2×#10622616C2semidirect
4. C2×#10622633C2semidirect
5. C2×#10622620C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622628C2semidirect
8. C2×#10622851C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622639C2semidirect
11. C2×#10622539C2semidirect
12. C2×C4×C11×#41C2semidirect
16. C4×C11×#41C22semidirect
32. #10623008C22semidirect
38. #10622851C22semidirect
42. #10622640C22semidirect
43. #10622639C22semidirect
44. #10622633C22semidirect
45. #10622628C22semidirect
46. #10622627C22semidirect
47. #10622620C22semidirect
48. #10622616C22semidirect
53. #10622539C22semidirect
148. C2×Q8×C11#41semidirect
154. C2×D4×C11#41semidirect
225. C2×C4×#41D11semidirect
251. Q8×C11C2×#41semidirect
255. D4×C11C2×#41semidirect
308. C4×#41C2×D11semidirect
452. C2×C11#3115semidirect
468. C2×Q8#4339semidirect
484. C2×D4#4339semidirect
541. C11C2×#3115semidirect
558. Q8C2×#4339semidirect
568. D4C2×#4339semidirect
633. C2#13078767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130787672
C2×#106226162
C2×#106226332
C2×#106226202
C2×#106226402
C2×#106226282
C2×#106228512
C2×#106226272
C2×#106226392
C2×#106225392
C2×C4×C11×#412
C2×#311511