Finite Group Databasebeta

← C2×#13079974 #15626613

Subgroups — C2×#13079974 #15626613

Order 2816.

2178 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×#10623247C211yesmaximal, characteristic, complemented
2C2×#10623088C211yesmaximal, characteristic, complemented
3#13079974C2116yesmaximal, direct product factor
4C2×#10622464C211yesmaximal, characteristic, complemented
5C2×#10622376C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622772C212yesmaximal, complemented
8C2×#10622393C212yesmaximal, complemented
9C2×#10622688C211yesmaximal, characteristic, complemented
10C2×#10622766C212yesmaximal, complemented
11C2×#10622450C211yesmaximal, characteristic, complemented
12C2×C11×#459C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×C11×D8C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991—21no—
18C2×#66991C2211yescharacteristic
19C2×#66991C2212yes—
20C2×#66989—21no—
21C2×#66989C2211yescharacteristic
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2212yes—
24C22×#4324C2212yes—
25C2×C4×C22⋊D11—21no—
26C2×#66979—21no—
27C22×#4313C2212yes—
28#10623247—24no—
29#10623247C2218yescomplemented
30#10623088—24no—
31#10623088C2218yescomplemented
32C2×#66950C2211yescharacteristic
33C2×#66943C2211yescharacteristic
34C2×#66936—21no—
35C2×#66932—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#459C2218yescomplemented
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#102C2212yes—
42C2×#66896C2212yes—
43C2×#66896C2212yes—
44#10622772C22116yescomplemented
45#10622766C22116yescomplemented
46C2×#66881C2212yes—
47C2×#66880C2212yes—
48C2×Dic11⋊C8C2212yes—
49#10622688C2218yescomplemented
50#10622620C2218yescomplemented
51C2×#66871C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622464C2218yescomplemented
54#10622450C2218yescomplemented
55#10622393C22116yescomplemented
56#10622376C22116yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C22⋊D11—21no—
63C22×C22⋊D11—22no—
64C23×Dic11—22no—
65C2×#4341—28no—
66C2×#4341—48no—
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C2×C11×D8—44no—
73C2×C11×D8C2318yes—
74C22×C8×C11C2312yes—
75C11×#127—22no—
76C11×#127C2314yes—
77C4×D4×C11—22no—
78C4×D4×C11C2314yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87#66991—24no—
88#66991—28no—
89#66991—22no—
90#66991C2318yes—
91#66991C2314yes—
92#66989—28no—
93#66989—22no—
94#66989C2314yes—
95D4×Dic11—24no—
96D4×Dic11—28no—
97D4×Dic11C2318yes—
98C2×#4324—44no—
99C2×#4324C2318yes—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4—21no—
102#66979—28no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2312yes—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115C2×#4313—44no—
116C2×#4313C2318yes—
117#66950—22no—
118#66950C2314yes—
119#66943—22no—
120#66943C2314yes—
121#66936—28no—
122#66932—28no—
123C42×D11D414yes—
124C42×D11C2314yes—
125#66922—22no—
126#66922C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#102C2318yes—
131#66896C2318yes—
132#66896C2318yes—
133#66881C2318yes—
134#66880C2318yes—
135Dic11⋊C8C2318yes—
136#66871C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3251—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—22no—
141C23×D11C2×D411yescharacteristic
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—22no—
150C2×D4×C11—44no—
151C2×D4×C11—44no—
152C2×D4×C11C2412yes—
153C2×D4×C11C2414yes—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—44no—
164C22×Dic11—28no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—48no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4341—432no—
173C2×C4×D11—24no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—42no—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D414yes—
179C2×C4×D11C2×D414yes—
180C2×C4×D11C2412yes—
181C2×Dic22—21no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—44no—
186C2×Dic22C2412yes—
187C11×D8—48no—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C2412yes—
192C11×C22⋊C4—24no—
193C42×C11C2×D412yes—
194C42×C11C2412yes—
195C22⋊Dic11—24no—
196C22⋊Dic11—24no—
197C22⋊Dic11—24no—
198C22⋊Dic11—28no—
199C22⋊Dic11—28no—
200#4324—48no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—22no—
206C4⋊Dic11—24no—
207C4⋊Dic11C2414yes—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211C4×Dic11—24no—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218#4313—48no—
219C2×#532—111no—
220C2×#529—111no—
221#3251—1116no—
222C2×#475—111no—
223C2×#478—112no—
224C2×#474—111no—
225C2×#469—112no—
226C2×#468—112no—
227C2×#460—111no—
228C2×#463—112no—
229C2×#459D1111yescharacteristic, complemented
230C2×#423—111no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—44no—
234C23×C11—42no—
235C23×C11—44no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—44no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11C22×D412yes—
244D4×C11—24no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—24no—
248D4×C11—48no—
249D4×C11—44no—
250D4×C11—42no—
251D4×C11—48no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—42no—
255C2×C4×C11—48no—
256C2×C4×C11AGL(1,ℤ/8)14yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D412yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C112−1+412yes—
262C2×C4×C11C2511yescharacteristic
263C22⋊D11—416no—
264C22⋊D11—48no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—416no—
272C2×Dic11—42no—
273C2×Dic11—44no—
274C2×Dic11—42no—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278C4×D11—24no—
279C4×D11—28no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—44no—
283Dic22—22no—
284Dic22—22no—
285Dic22—42no—
286Dic22—48no—
287C8×C11—24no—
288C11⋊C8—24no—
289C22×#41—221no—
290C22×SD16—112no—
291C22×D8C2×D1112yes—
292C22×M16—112no—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8—111no—
296C2×#127C2×D1111yescharacteristic
297#529—118no—
298#529—224no—
299C2×#126—221no—
300C2×#125—111no—
301C2×#124—111no—
302C2×#124—221no—
303C2×#123—221no—
304C2×C22⋊Q8—111no—
305C2×#121—111no—
306C2×#121—112no—
307C2×#121—221no—
308C2×C4×Q8—111no—
309C2×C4×D4—112no—
310C2×C4×D4—221no—
311C2×C4×D4—221no—
312C2×C4×D4C2×D1111yescharacteristic
313C2×#117—221no—
314C22×C42—111no—
315#478—1116no—
316#475—118no—
317#474—118no—
318#469—1116no—
319#468—1116no—
320#463—1116no—
321#460—118no—
322#459C2×D1118yescomplemented
323C2×#107—112no—
324C2×#106—112no—
325#423—118no—
326C2×C4⋊C8—112no—
327C2×C4⋊C8—111no—
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×#103—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102C2×D1112yes—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—42no—
339C22×C11—88no—
340C22×C11—84no—
341C22×C11#53712yes—
342C22×C11C2×AGL(1,ℤ/8)12yes—
343C22×C11#57512yes—
344C22×C11C23×D411yescharacteristic
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—44no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11#53712yes—
352C4×C11C2×AGL(1,ℤ/8)14yes—
353C4×C11C2×H(5,𝔽2)11yescharacteristic
354C4×C11C2×2−1+411yescharacteristic
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—44no—
360Dic11—42no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—111no—
364C22×Q8—221no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—221no—
368C22×D4—222no—
369C22×D4C22×D1112yes—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—222no—
376C2×SD16—118no—
377C2×SD16—444no—
378C2×D8—44no—
379C2×D8C22×D1118yes—
380C2×M16—118no—
381C2×M16—444no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384C4⋊Q8—114no—
385C4⋊Q8—222no—
386#127—22no—
387#127C22×D1114yes—
388#126—228no—
389#125—114no—
390#125—222no—
391#124—114no—
392#124—222no—
393#124—228no—
394#123—228no—
395C22⋊Q8—114no—
396C22⋊Q8—222no—
397#121—114no—
398#121—118no—
399#121—222no—
400#121—224no—
401#121—228no—
402C4×Q8—114no—
403C4×Q8—222no—
404C4×D4—22no—
405C4×D4—118no—
406C4×D4—224no—
407C4×D4—228no—
408C4×D4—228no—
409C4×D4C22×D1114yes—
410#117—228no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42—221no—
432C2×C42C22×D1111yescharacteristic
433#107—118no—
434#106—118no—
435C4⋊C8—118no—
436C4⋊C8—114no—
437C4⋊C8C22×D1114yes—
438#103—118no—
439#102—118no—
440#102—118no—
441#102C22×D1118yes—
442C2×C11—82no—
443C2×C11—84no—
444C2×C11#325114yescomplemented
445C2×C11C2×#53711yescharacteristic
446C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
447C2×C11C2×#57511yescharacteristic
448D11—42no—
449C24—21no—
450C24—22no—
451C24—111no—
452#41—4432no—
453C2×Q8—112no—
454C2×Q8—221no—
455C2×Q8—224no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—444no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—22no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—224no—
470C2×D4—228no—
471C2×D4—448no—
472C2×D4—444no—
473C2×D4C23×D1112yes—
474C2×D4C23×D1114yes—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—44no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—114no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—228no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—442no—
493C22×C4—448no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497SD16—448no—
498D8—48no—
499M16—448no—
500C2×C8—24no—
501C2×C8—114no—
502C2×C8—224no—
503C2×C8C23×D1114yes—
504C4⋊C4—21no—
505C4⋊C4—112no—
506C4⋊C4—114no—
507C4⋊C4—224no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—222no—
511C4⋊C4—221no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C4⋊C4C23×D1112yes—
515C22⋊C4—24no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—224no—
522C42—114no—
523C42—112no—
524C42—114no—
525C42—112no—
526C42—224no—
527C42D4×D1112yes—
528C42C23×D1112yes—
529C11C2×#325111yescharacteristic, complemented, Sylow
530C23—22no—
531C23—24no—
532C23—42no—
533C23—44no—
534C23—44no—
535C23—42no—
536C23—42no—
537C23—44no—
538C23—112no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23C2×D4×D1111yescharacteristic
543Q8—222no—
544Q8—222no—
545Q8—448no—
546Q8—442no—
547D4—22no—
548D4—24no—
549D4—22no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—42no—
554D4—44no—
555D4—4416no—
556D4—448no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—48no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—228no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—444no—
575C2×C4—4416no—
576C2×C4—444no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4#6696414yes—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1112yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#6703712yes—
584C2×C4#6704312yes—
585C2×C4C24×D1111yescharacteristic
586C8—24no—
587C8—224no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—44no—
592C22—44no—
593C22—42no—
594C22—84no—
595C22—88no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—444no—
600C22#1062313912yes—
601C22C2×#6696412yes—
602C22#1062330412yes—
603C22C22×D4×D1111yescharacteristic
604C4—22no—
605C4—42no—
606C4—222no—
607C4—222no—
608C4—222no—
609C4—442no—
610C4—444no—
611C4—442no—
612C4#1062313912yes—
613C4C2×#6696414yes—
614C4C2×#6703711yescharacteristic
615C4C2×#6704311yescharacteristic
616C2—82no—
617C2—84no—
618C2—442no—
619C2#1307997414yesdirect product factor
620C2C2×#1062313911yescharacteristic
621C2C22×#6696411yescharacteristic
622C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3251
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×#10623088C2semidirect
3. #13079974C2direct (N × H)
4. C2×#10622464C2semidirect
5. C2×#10622376C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622688C2semidirect
10. C2×#10622766C2semidirect
11. C2×#10622450C2semidirect
12. C2×C11×#459C2semidirect
29. #10623247C22semidirect
31. #10623088C22semidirect
39. C11×#459C22semidirect
44. #10622772C22semidirect
45. #10622766C22semidirect
49. #10622688C22semidirect
50. #10622620C22semidirect
53. #10622464C22semidirect
54. #10622450C22semidirect
55. #10622393C22semidirect
56. #10622376C22semidirect
229. C2×#459D11semidirect
322. #459C2×D11semidirect
444. C2×C11#3251semidirect
529. C11C2×#3251semidirect
619. C2#13079974direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×#106230882
#130799742
C2×#106224642
C2×#106223762
C2×#106226202
C2×#106227722
C2×#106223932
C2×#106226882
C2×#106227662
C2×#106224502
C2×C11×#4592
C2×#325111