Finite Group Databasebeta

← C2×#13079980 #15626619

Subgroups — C2×#13079980 #15626619

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×#10623256C211yesmaximal, characteristic, complemented
2C2×#10623088C211yesmaximal, characteristic, complemented
3#13079980C2116yesmaximal, direct product factor
4C2×#10622707C211yesmaximal, characteristic, complemented
5C2×#10622504C212yesmaximal, complemented
6C2×#10622395C212yesmaximal, complemented
7C2×#10622499C212yesmaximal, complemented
8C2×#10622461C211yesmaximal, characteristic, complemented
9C2×#10622400C212yesmaximal, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622450C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000—21no—
17C2×#66991C2211yescharacteristic
18C2×#66989C2211yescharacteristic
19C22×#4323C2212yes—
20C2×C4×C22⋊D11—21no—
21C2×#66979—21no—
22C22×#4314C2212yes—
23C22×#4313C2212yes—
24#10623256—24no—
25#10623256C2218yescomplemented
26#10623088—24no—
27#10623088C2218yescomplemented
28C2×#66950C2211yescharacteristic
29C2×#66948—21no—
30C2×#66948C2212yes—
31C2×#66946—21no—
32C2×#66946C2212yes—
33C2×#66943C2211yescharacteristic
34C2×#66936—21no—
35C2×#66932—21no—
36C2×#66927C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#474C2218yescomplemented
40C2×C11×#107C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#102C2212yes—
43C2×#66885C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622707C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622504C22116yescomplemented
52#10622499C22116yescomplemented
53#10622461C2218yescomplemented
54#10622450C2218yescomplemented
55#10622400C22116yescomplemented
56#10622395C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C2×#4343—28no—
62C2×#4343—48no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×C4×D11—22no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2312yes—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C4×D4×C11—22no—
76C4×D4×C11C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85#67000—28no—
86#66991—22no—
87#66991C2314yes—
88#66989—22no—
89#66989C2314yes—
90C2×#4323—44no—
91C2×#4323C2318yes—
92C4×C22⋊D11—28no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96#66979—28no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C2×#4314—44no—
108C2×#4314C2318yes—
109C2×#4313—44no—
110C2×#4313C2318yes—
111#66950—22no—
112#66950C2314yes—
113#66948—24no—
114#66948—28no—
115#66948C2318yes—
116#66946—24no—
117#66946—28no—
118#66946C2318yes—
119#66943—22no—
120#66943C2314yes—
121#66936—28no—
122#66932—28no—
123#66927—22no—
124#66927C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129C11×#107C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#102C2318yes—
132#66885C2318yes—
133Dic11⋊C8C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66872C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3251—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—44no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11C2412yes—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162#4343—432no—
163C2×D44—28no—
164C2×D44—22no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—44no—
170C2×D44—48no—
171C2×D44—44no—
172C2×D44C2414yes—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—42no—
178C2×C4×D11—48no—
179C2×C4×D11C2×D412yes—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2412yes—
183C2×Dic22—21no—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22C2412yes—
187C2×C8×C11—24no—
188C2×C8×C11C2414yes—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2414yes—
193C11×C4⋊C4C2412yes—
194C11×C22⋊C4—24no—
195C42×C11C2×D412yes—
196C42×C11C2412yes—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200#4323—48no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210C4×Dic11—24no—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2412yes—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217#4314—48no—
218#4313—48no—
219C2×#532—111no—
220C2×#529—111no—
221#3251—1116no—
222C2×#475—111no—
223C2×#478—112no—
224C2×#474D1111yescharacteristic, complemented
225C2×#469—112no—
226C2×#468—112no—
227C2×#460—111no—
228C2×#463—112no—
229C2×#459—111no—
230C2×#423—111no—
231C23×C11—22no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11C22×D412yes—
244Q8×C11—48no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—48no—
254C2×C4×C11AGL(1,ℤ/8)14yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11H(5,𝔽2)12yes—
259C2×C4×C112−1+412yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—48no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272D44—24no—
273D44—24no—
274D44—48no—
275D44—416no—
276D44—44no—
277D44—48no—
278C4×D11—24no—
279C4×D11—28no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—44no—
283C4×D11—416no—
284Dic22—22no—
285Dic22—22no—
286Dic22—42no—
287C8×C11—24no—
288C11⋊C8—24no—
289C22×#41—221no—
290C22×SD16—112no—
291C22×D8—112no—
292C22×M16—112no—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8C2×D1111yescharacteristic
296C2×#127—111no—
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#474C2×D1118yescomplemented
318#469—1116no—
319#468—1116no—
320#463—1116no—
321#460—118no—
322#459—118no—
323C2×#107C2×D1112yes—
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—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—84no—
337C22×C11#53712yes—
338C22×C11C2×AGL(1,ℤ/8)12yes—
339C22×C11#57512yes—
340C22×C11C23×D411yescharacteristic
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—88no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—44no—
352C4×C11#53712yes—
353C4×C11C2×AGL(1,ℤ/8)14yes—
354C4×C11C2×H(5,𝔽2)11yescharacteristic
355C4×C11C2×2−1+411yescharacteristic
356Dic11—22no—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360Dic11—42no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—21no—
364C22×Q8—111no—
365C22×D4—112no—
366C22×D4—222no—
367C22×D4—221no—
368C22×D4—221no—
369C22×D4—221no—
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—118no—
379C2×D8—444no—
380C2×M16—118no—
381C2×M16—444no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384C4⋊Q8—22no—
385C4⋊Q8C22×D1114yes—
386#127—114no—
387#127—222no—
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—224no—
400#121—228no—
401#121—222no—
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—21no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1112yes—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
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#107C22×D1118yes—
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#325114yescomplemented
444C2×C11C2×#53711yescharacteristic
445C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C2×#57511yescharacteristic
447D11—42no—
448D11—84no—
449C24—21no—
450C24—111no—
451C24—222no—
452#41—4432no—
453C2×Q8—24no—
454C2×Q8—44no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—222no—
458C2×Q8—222no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—114no—
463C2×D4—228no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—222no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—444no—
471C2×D4—448no—
472C2×D4—444no—
473C2×D4—444no—
474C2×D4C23×D1112yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—44no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—114no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—228no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—448no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497SD16—448no—
498D8—448no—
499M16—448no—
500C2×C8—24no—
501C2×C8—114no—
502C2×C8—224no—
503C2×C8C23×D1114yes—
504C4⋊C4—24no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—112no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—221no—
512C4⋊C4—224no—
513C4⋊C4C23×D1112yes—
514C4⋊C4C23×D1114yes—
515C22⋊C4—24no—
516C22⋊C4—228no—
517C22⋊C4—228no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C22⋊C4—224no—
522C42—114no—
523C42—112no—
524C42—114no—
525C42—112no—
526C42—224no—
527C42D4×D1112yes—
528C42C23×D1112yes—
529C11C2×#325111yescharacteristic, complemented, Sylow
530C23—22no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—112no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—224no—
539C23—444no—
540C23—444no—
541C23—444no—
542C23C2×D4×D1111yescharacteristic
543Q8—48no—
544Q8—222no—
545Q8—222no—
546Q8—442no—
547D4—22no—
548D4—22no—
549D4—42no—
550D4—224no—
551D4—224no—
552D4—448no—
553D4—4416no—
554D4—448no—
555D4—448no—
556D4—444no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—228no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—444no—
576C2×C4—4416no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4#6696414yes—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1112yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#6704012yes—
584C2×C4#6704212yes—
585C2×C4C24×D1111yescharacteristic
586C8—24no—
587C8—224no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—84no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—888no—
600C22#1062316012yes—
601C22C2×#6696412yes—
602C22#1062330812yes—
603C22C22×D4×D1111yescharacteristic
604C4—22no—
605C4—42no—
606C4—44no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—442no—
611C4—442no—
612C4#1062316012yes—
613C4C2×#6696414yes—
614C4C2×#6704011yescharacteristic
615C4C2×#6704211yescharacteristic
616C2—82no—
617C2—442no—
618C2—884no—
619C2#1307998014yesdirect product factor
620C2C2×#1062316011yescharacteristic
621C2C22×#6696411yescharacteristic
622C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11C2×#3251
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×#10623088C2semidirect
3. #13079980C2direct (N × H)
4. C2×#10622707C2semidirect
5. C2×#10622504C2semidirect
6. C2×#10622395C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622461C2semidirect
9. C2×#10622400C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622450C2semidirect
12. C2×C11×#474C2semidirect
25. #10623256C22semidirect
27. #10623088C22semidirect
39. C11×#474C22semidirect
45. #10622707C22semidirect
46. #10622628C22semidirect
51. #10622504C22semidirect
52. #10622499C22semidirect
53. #10622461C22semidirect
54. #10622450C22semidirect
55. #10622400C22semidirect
56. #10622395C22semidirect
224. C2×#474D11semidirect
317. #474C2×D11semidirect
443. C2×C11#3251semidirect
529. C11C2×#3251semidirect
619. C2#13079980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106230882
#130799802
C2×#106227072
C2×#106225042
C2×#106223952
C2×#106224992
C2×#106224612
C2×#106224002
C2×#106226282
C2×#106224502
C2×C11×#4742
C2×#325111