Finite Group Databasebeta

← C2×#13079942 #15626566

Subgroups — C2×#13079942 #15626566

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13079942C2116yesmaximal, direct product factor
3C2×#10622634C211yesmaximal, characteristic, complemented
4C2×#10622679C212yesmaximal, complemented
5C2×#10622621C211yesmaximal, characteristic, complemented
6C2×#10622651C212yesmaximal, complemented
7C2×#10622661C212yesmaximal, complemented
8C2×#10622640C211yesmaximal, characteristic, complemented
9C2×#10622670C212yesmaximal, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C11×#529—24no—
15C11×#529C2218yescomplemented
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4325C2212yes—
28C22×#4323C2212yes—
29C2×#66983—21no—
30C2×#66983C2212yes—
31C23×C11⋊C8C2212yes—
32#10623008—24no—
33#10623008C2218yescomplemented
34C2×#66928—21no—
35C2×#66927C2211yescharacteristic
36C2×C4×D44—21no—
37C2×C4×D44C2212yes—
38C2×#66922C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622679C22116yescomplemented
42#10622670C22116yescomplemented
43#10622661C22116yescomplemented
44#10622651C22116yescomplemented
45#10622640C2218yescomplemented
46#10622634C2218yescomplemented
47#10622628C2218yescomplemented
48#10622621C2218yescomplemented
49C2×#66873C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2212yes—
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C2×#4339—28no—
66C2×#4339—48no—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2312yes—
70C22×C4×D11—22no—
71C22×Dic22—21no—
72C11×#126—28no—
73C11×#125—22no—
74C11×#125C2314yes—
75C11×#124—22no—
76C11×#124C2314yes—
77C11×#123—28no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2314yes—
80C11×#121—22no—
81C11×#121C2314yes—
82C4×Q8×C11—22no—
83C4×Q8×C11C2314yes—
84C4×D4×C11—28no—
85C4×D4×C11—22no—
86C4×D4×C11C2314yes—
87C11×#117—28no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11D411yescharacteristic
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D414yes—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2314yes—
106C2×#4325—44no—
107C2×#4325C2318yes—
108C2×#4323—44no—
109C2×#4323C2318yes—
110#66983—24no—
111#66983—28no—
112#66983C2318yes—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2312yes—
117C22×C11⋊C8—44no—
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2318yes—
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—
131#66873C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C4⋊(C11⋊C8)C2314yes—
136C4⋊(C11⋊C8)C2314yes—
137C4⋊(C11⋊C8)C2318yes—
138C2×#3247—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—22no—
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11C2412yes—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—44no—
151C2×D4×C11C2412yes—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—44no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—28no—
172C2×C22⋊D11—48no—
173C22×Dic11—22no—
174#4339—432no—
175C2×D44—22no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—24no—
179C2×D44—24no—
180C2×D44—44no—
181C2×D44—44no—
182C2×D44C2414yes—
183C2×C4×D11—28no—
184C2×C4×D11—48no—
185C2×Dic22—24no—
186C2×Dic22—44no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C2412yes—
194C11×C4⋊C4C2412yes—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C42×C11—24no—
201C42×C11C2×D412yes—
202C42×C11C2×D414yes—
203C42×C11C2×D412yes—
204C42×C11C2×D414yes—
205C42×C11C2412yes—
206C42×C11C2412yes—
207#4325—48no—
208#4323—48no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211C4⋊Dic11—22no—
212C4⋊Dic11—24no—
213C4⋊Dic11C2414yes—
214C2×C11⋊C8—24no—
215C2×C11⋊C8—24no—
216C2×C11⋊C8—48no—
217C2×C11⋊C8C2414yes—
218C2×C11⋊C8C2414yes—
219C2×#532—111no—
220C2×#529D1111yescharacteristic, complemented
221#3247—1116no—
222C2×#477—111no—
223C2×#478—112no—
224C2×#476—111no—
225C2×#466—112no—
226C2×#465—112no—
227C2×#460—111no—
228C2×#463—112no—
229C2×#459—111no—
230C22×C4⋊C8—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11AGL(1,ℤ/8)14yes—
238C23×C11C22×D412yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—24no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—44no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—42no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—48no—
250D4×C11—42no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—28no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—48no—
267C2×C4×C11#13514yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D412yes—
274C2×C4×C11H(5,𝔽2)12yes—
275C2×C4×C112−1+412yes—
276C2×C4×C11C2511yescharacteristic
277C22⋊D11—416no—
278C2×Dic11—24no—
279C2×Dic11—44no—
280D44—24no—
281D44—24no—
282D44—48no—
283D44—44no—
284D44—48no—
285C4×D11—416no—
286Dic22—48no—
287C11⋊C8—24no—
288C11⋊C8—24no—
289C22×#41—221no—
290C22×SD16—112no—
291C22×D8—112no—
292C23×C8—112no—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8—111no—
296C2×#127—111no—
297#529—24no—
298#529C2×D1118yescomplemented
299C2×#126—21no—
300C2×#125C2×D1111yescharacteristic
301C2×#124—221no—
302C2×#124C2×D1111yescharacteristic
303C2×#123—21no—
304C2×C22⋊Q8C2×D1111yescharacteristic
305C2×#121—112no—
306C2×#121—221no—
307C2×#121C2×D1111yescharacteristic
308C2×C4×Q8C2×D1111yescharacteristic
309C2×C4×D4—21no—
310C2×C4×D4—112no—
311C2×C4×D4—221no—
312C2×C4×D4C2×D1111yescharacteristic
313C2×#117—21no—
314C22×C42C2×D1111yescharacteristic
315#478—1116no—
316#477—118no—
317#476—118no—
318#466—1116no—
319#465—1116no—
320#463—1116no—
321#460—118no—
322#459—118no—
323C2×#107—112no—
324C2×#106—112no—
325C2×C4⋊C8—112no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8—111no—
328C2×C4⋊C8—118no—
329C2×#103—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102—112no—
333C22×C11—22no—
334C22×C11—28no—
335C22×C11—22no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—84no—
340C22×C11#53712yes—
341C22×C11C2×#13512yes—
342C22×C11C2×AGL(1,ℤ/8)14yes—
343C22×C11C2×AGL(1,ℤ/8)12yes—
344C22×C11C23×D411yescharacteristic
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—88no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11#53712yes—
357C4×C11C2×#13514yes—
358C4×C11C2×H(5,𝔽2)11yescharacteristic
359C4×C11C2×2−1+411yescharacteristic
360Dic11—44no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—221no—
364C22×Q8C22×D1111yescharacteristic
365C22×D4—21no—
366C22×D4—112no—
367C22×D4—222no—
368C22×D4—221no—
369C22×D4—221no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—222no—
373C23×C4C22⋊D1111yescharacteristic
374C23×C4C22⋊D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×SD16—118no—
377C2×SD16—444no—
378C2×D8—118no—
379C2×D8—444no—
380C22×C8—112no—
381C22×C8—112no—
382C22×C8—118no—
383C22×C8—444no—
384C4⋊Q8—114no—
385C4⋊Q8—222no—
386#127—114no—
387#127—222no—
388#126—28no—
389#125—22no—
390#125C22×D1114yes—
391#124—22no—
392#124—228no—
393#124C22×D1114yes—
394#123—28no—
395C22⋊Q8—22no—
396C22⋊Q8C22×D1114yes—
397#121—22no—
398#121—118no—
399#121—224no—
400#121—228no—
401#121C22×D1114yes—
402C4×Q8—22no—
403C4×Q8C22×D1114yes—
404C4×D4—28no—
405C4×D4—22no—
406C4×D4—118no—
407C4×D4—224no—
408C4×D4—228no—
409C4×D4C22×D1114yes—
410#117—28no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C42—21no—
427C2×C42C22⋊D1111yescharacteristic
428C2×C42C22⋊D1111yescharacteristic
429C2×C42C22⋊D1114yes—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1114yes—
433#107—118no—
434#106—118no—
435C4⋊C8—114no—
436C4⋊C8—114no—
437C4⋊C8—118no—
438#103—118no—
439#102—118no—
440#102—118no—
441#102—118no—
442C2×C11—24no—
443C2×C11—82no—
444C2×C11#324714yescomplemented
445C2×C11C2×#53711yescharacteristic
446C2×C11C22×#13511yescharacteristic
447C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
448D11—84no—
449C24—21no—
450C24—222no—
451C24C2×C22⋊D1111yescharacteristic
452#41—4432no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—224no—
457C2×Q8—444no—
458C2×Q8C23×D1112yes—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—44no—
464C2×D4—114no—
465C2×D4—228no—
466C2×D4—224no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—222no—
470C2×D4—224no—
471C2×D4—444no—
472C2×D4—448no—
473C2×D4—444no—
474C2×D4C23×D1112yes—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—44no—
484C22×C4—222no—
485C22×C4—228no—
486C22×C4—448no—
487C22×C4C2×C22⋊D1114yes—
488C22×C4C2×C22⋊D1114yes—
489C22×C4C2×C22⋊D1112yes—
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—448no—
498D8—448no—
499C2×C8—114no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8—224no—
503C2×C8—448no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—114no—
511C4⋊C4—222no—
512C4⋊C4—224no—
513C4⋊C4C23×D1112yes—
514C4⋊C4C23×D1112yes—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C42—24no—
523C42C2×C22⋊D1114yes—
524C42C2×C22⋊D1112yes—
525C42C2×C22⋊D1112yes—
526C42C2×C22⋊D1114yes—
527C42C23×D1112yes—
528C42C23×D1112yes—
529C11C2×#324711yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—224no—
537C23—444no—
538C23—444no—
539C23—444no—
540C23#6700214yes—
541C23C22×C22⋊D1112yes—
542C23C22×C22⋊D1111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—42no—
546Q8—448no—
547D4—22no—
548D4—22no—
549D4—48no—
550D4—42no—
551D4—224no—
552D4—224no—
553D4—448no—
554D4—4416no—
555D4—448no—
556D4—444no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—28no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—28no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—48no—
573C2×C4—224no—
574C2×C4—4416no—
575C2×C4—444no—
576C2×C4#6700314yes—
577C2×C4#6704212yes—
578C2×C4#6704312yes—
579C2×C4C22×C22⋊D1112yes—
580C2×C4C22×C22⋊D1112yes—
581C2×C4C22×C22⋊D1112yes—
582C2×C4C22×C22⋊D1112yes—
583C2×C4C22×C22⋊D1112yes—
584C2×C4C22×C22⋊D1111yescharacteristic
585C2×C4C24×D1111yescharacteristic
586C8—224no—
587C8—224no—
588C22—22no—
589C22—28no—
590C22—22no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—84no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—888no—
599C22C2×#6700214yes—
600C22C2×#6700212yes—
601C22C2×#6700312yes—
602C22#1062336412yes—
603C22C23×C22⋊D1111yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—444no—
612C4C2×#6700314yes—
613C4#1062336412yes—
614C4C2×#6704211yescharacteristic
615C4C2×#6704311yescharacteristic
616C2—24no—
617C2—82no—
618C2—884no—
619C2#1307994214yesdirect product factor
620C2C2×#1062336411yescharacteristic
621C2C22×#6700311yescharacteristic
622C2C22×#6700211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
hypercenterC2×#529D11
hypocenterC11C2×#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079942C2direct (N × H)
3. C2×#10622634C2semidirect
4. C2×#10622679C2semidirect
5. C2×#10622621C2semidirect
6. C2×#10622651C2semidirect
7. C2×#10622661C2semidirect
8. C2×#10622640C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622628C2semidirect
11. C22×C4⋊(C11⋊C8)C2semidirect
12. C2×C11×#529C2semidirect
15. C11×#529C22semidirect
33. #10623008C22semidirect
41. #10622679C22semidirect
42. #10622670C22semidirect
43. #10622661C22semidirect
44. #10622651C22semidirect
45. #10622640C22semidirect
46. #10622634C22semidirect
47. #10622628C22semidirect
48. #10622621C22semidirect
56. C2×C4⋊(C11⋊C8)C22semidirect
220. C2×#529D11semidirect
298. #529C2×D11semidirect
444. C2×C11#3247semidirect
529. C11C2×#3247semidirect
619. C2#13079942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130799422
C2×#106226342
C2×#106226792
C2×#106226212
C2×#106226512
C2×#106226612
C2×#106226402
C2×#106226702
C2×#106226282
C22×C4⋊(C11⋊C8)2
C2×C11×#5292
C2×#324711