Finite Group Databasebeta

← C2×#13079742 #15625812

Subgroups — C2×#13079742 #15625812

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C22×#66941C211yesmaximal, characteristic, complemented
3#13079742C2116yesmaximal, direct product factor
4C2×#10622468C212yesmaximal, complemented
5C2×#10622373C212yesmaximal, complemented
6C2×#10622348C211yesmaximal, characteristic, complemented
7C2×#10622581C211yesmaximal, characteristic, complemented
8C2×#10622647C211yesmaximal, characteristic, complemented
9C2×#10622483C212yesmaximal, complemented
10C2×#10622374C212yesmaximal, complemented
11C2×#10622331C211yesmaximal, characteristic, complemented
12C2×C11×#481C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C23×Dic22—21no—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×#66992—21no—
19C2×D4×Dic11C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4—21no—
23C22×C4×Dic11C2211yescharacteristic
24#10623127—24no—
25#10623127C2218yes—
26C2×#66946C2211yescharacteristic
27C2×#66941—24no—
28C2×#66941—21no—
29C2×#66941—21no—
30C2×#66941C2212yes—
31C2×#66941C2212yes—
32C2×#66941C2211yescharacteristic
33C2×#66941C2218yescomplemented
34C2×#66938—21no—
35C2×(C22⋊D11)⋊C4—21no—
36C11×#481C2218yescomplemented
37C2×C11×#106C2212yes—
38C2×C11×#102C2212yes—
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×#66896C2212yes—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×#66885C2212yes—
43C2×#66881C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622647C2218yescomplemented
47#10622581C2218yescomplemented
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51#10622483C22116yescomplemented
52#10622468C22116yescomplemented
53#10622374C22116yescomplemented
54#10622373C22116yescomplemented
55#10622348C2218yescomplemented
56#10622331C2218yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C23×Dic11D411yescharacteristic
67C23×Dic11D411yescharacteristic
68C2×#4341—28no—
69C2×#4341—48no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22—21no—
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—28no—
76C22×Dic22—48no—
77C22×C8×C11C2312yes—
78C11×#121—22no—
79C11×#121C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87#66993—22no—
88#66993C2314yes—
89#66992—28no—
90D4×Dic11—22no—
91D4×Dic11C2314yes—
92#66983—22no—
93#66983C2314yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—28no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D414yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2314yes—
111C22×C11⋊C8C2312yes—
112#66946—22no—
113#66946C2314yes—
114#66941—24no—
115#66941—24no—
116#66941—28no—
117#66941—28no—
118#66941—22no—
119#66941C2314yes—
120#66941C2318yes—
121#66941C2318yes—
122#66938—28no—
123(C22⋊D11)⋊C4—28no—
124C11×#106C2318yes—
125C11×#102C2318yes—
126C11×C22⋊C8C2314yes—
127#66896C2318yes—
128C22⋊(C11⋊C8)C2314yes—
129#66885C2318yes—
130#66881C2318yes—
131Dic11⋊C8C2318yes—
132C8×Dic11C2318yes—
133#66873C2318yes—
134#66872C2318yes—
135#66872C2318yes—
136C2×#3227—111nomaximal, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—44no—
144C2×D4×C11C2412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—44no—
166C22×Dic11—44no—
167C22×Dic11SD1618yes—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D414yes—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D411yescharacteristic
174#4341—432no—
175C2×D44—21no—
176C2×D44—24no—
177C2×D44C2412yes—
178C2×C4×D11—24no—
179C2×C4×D11—44no—
180C2×Dic22—24no—
181C2×Dic22—28no—
182C2×Dic22—28no—
183C2×Dic22—432no—
184C2×Dic22—48no—
185C2×Dic22—44no—
186C2×Dic22—48no—
187C2×C8×C11—24no—
188C2×C8×C11C2414yes—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2412yes—
193C11×C4⋊C4C2414yes—
194C11×C22⋊C4—24no—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198C4⋊Dic11—24no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2412yes—
202C4⋊Dic11C2414yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—28no—
205Dic11⋊C4—28no—
206C4×Dic11C2×D414yes—
207C4×Dic11C2×D414yes—
208C4×Dic11C2×D412yes—
209C4×Dic11C2×D412yes—
210C4×Dic11C2412yes—
211C4×Dic11C2412yes—
212C2×C11⋊C8—24no—
213C2×C11⋊C8C2414yes—
214C2×#532—111no—
215C22×C4⋊Q8—111no—
216#3227—1116no—
217C2×#498—112no—
218C2×#486—112no—
219C2×#481—111no—
220C2×#481—111no—
221C2×#481—111no—
222C2×#481D1111yescharacteristic, complemented
223C2×#476—112no—
224C2×#476—112no—
225C2×#431—111no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C2×SD1614yes—
233C23×C11C22×D412yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239D4×C11—24no—
240D4×C11—48no—
241D4×C11—42no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—48no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C112−1+414yes—
253C2×C4×C11C2511yescharacteristic
254C22⋊D11—48no—
255C22⋊D11—48no—
256C22⋊D11—48no—
257C2×Dic11—22no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—48no—
262C2×Dic11—42no—
263C2×Dic11—44no—
264C2×Dic11—48no—
265C2×Dic11C2×SD1614yes—
266C2×Dic11C2×SD1614yes—
267C2×Dic11C2×SD16116yes—
268C2×Dic11AGL(1,ℤ/8)14yes—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272C2×Dic11C22×D412yes—
273D44—24no—
274D44—42no—
275C4×D11—48no—
276Dic22—416no—
277Dic22—48no—
278Dic22—416no—
279C8×C11—24no—
280C11⋊C8—24no—
281C22×#41—221no—
282C23×Q8—221no—
283#532—118no—
284#532—224no—
285C2×C4⋊Q8—112no—
286C2×C4⋊Q8—111no—
287C2×C4⋊Q8—112no—
288C2×C4⋊Q8—118no—
289C2×C4⋊Q8—221no—
290C2×C4⋊Q8—221no—
291C2×C4⋊Q8—224no—
292C2×#127—111no—
293C2×#124—221no—
294C2×#121—111no—
295C2×#121—221no—
296C2×#121C2×D1111yescharacteristic
297C2×C4×D4—111no—
298C2×C4×D4—111no—
299C2×C4×D4—221no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—221no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C42—111no—
304#498—1116no—
305#486—1116no—
306#481—118no—
307#481—118no—
308#481—118no—
309#481C2×D1118yescomplemented
310#476—1116no—
311#476—1116no—
312#431—118no—
313C2×#106—112no—
314C2×#106—112no—
315C2×#106—112no—
316C2×#106C2×D1112yes—
317C2×C4⋊C8—112no—
318C2×#102—112no—
319C2×#102—112no—
320C2×#102—112no—
321C2×#102C2×D1112yes—
322C2×C22⋊C8—111no—
323C2×C22⋊C8C2×D1111yescharacteristic
324C2×C4×C8—112no—
325C22×C11—22no—
326C22×C11—28no—
327C22×C11—22no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—84no—
332C22×C11#53612yes—
333C22×C11C22×SD1614yes—
334C22×C11C22×SD1612yes—
335C22×C11C2×AGL(1,ℤ/8)12yes—
336C22×C11C23×D411yescharacteristic
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—84no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—44no—
344C4×C11#53612yes—
345C4×C11C2×2−1+412yes—
346Dic11—22no—
347Dic11—42no—
348Dic11—44no—
349Dic11C22×SD1614yes—
350Dic11C22×SD1614yes—
351Dic11C2×AGL(1,ℤ/8)14yes—
352C2×#41—228no—
353C2×#41—448no—
354C22×Q8—221no—
355C22×Q8—228no—
356C22×Q8—222no—
357C22×Q8—222no—
358C22×Q8—448no—
359C22×D4—21no—
360C22×D4—111no—
361C22×D4—221no—
362C22×D4—221no—
363C22×D4—221no—
364C22×D4C22×D1111yescharacteristic
365C23×C4—21no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—221no—
369C23×C4—221no—
370C23×C4—221no—
371C23×C4C22×D1111yescharacteristic
372C22×C8—112no—
373C22×C8C22×D1112yes—
374C4⋊Q8—118no—
375C4⋊Q8—118no—
376C4⋊Q8—114no—
377C4⋊Q8—224no—
378C4⋊Q8—228no—
379C4⋊Q8—228no—
380C4⋊Q8—224no—
381C4⋊Q8—222no—
382#127—114no—
383#127—222no—
384#124—228no—
385#121—22no—
386#121—114no—
387#121—228no—
388#121—222no—
389#121C22×D1114yes—
390C4×D4—114no—
391C4×D4—114no—
392C4×D4—228no—
393C4×D4—222no—
394C4×D4—222no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—228no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1112yes—
407C2×C4⋊C4C22×D1114yes—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—114no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—114no—
419#106—118no—
420#106—118no—
421#106—118no—
422#106C22×D1118yes—
423C4⋊C8—118no—
424#102—118no—
425#102—118no—
426#102—118no—
427#102C22×D1118yes—
428C22⋊C8—114no—
429C22⋊C8C22×D1114yes—
430C4×C8—118no—
431C2×C11—24no—
432C2×C11—82no—
433C2×C11#322714yescomplemented
434C2×C11C2×#53611yescharacteristic
435C2×C11C23×SD1611yescharacteristic
436C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
437D11—82no—
438C24—21no—
439C24—221no—
440C24D4×D1111yescharacteristic
441#41—4432no—
442C2×Q8—224no—
443C2×Q8—228no—
444C2×Q8—228no—
445C2×Q8—448no—
446C2×Q8—444no—
447C2×Q8—4432no—
448C2×Q8—448no—
449C2×D4—24no—
450C2×D4—21no—
451C2×D4—24no—
452C2×D4—44no—
453C2×D4—112no—
454C2×D4—224no—
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—221no—
458C2×D4—224no—
459C2×D4—444no—
460C2×D4—444no—
461C2×D4—444no—
462C2×D4C23×D1112yes—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—44no—
468C22×C4—118no—
469C22×C4—114no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—114no—
474C22×C4—111no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4—444no—
484C22×C4D4×D1112yes—
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1112yes—
487C22×C4C23×D1111yescharacteristic
488C2×C8—24no—
489C2×C8—114no—
490C2×C8—224no—
491C2×C8C23×D1114yes—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—114no—
496C4⋊C4—112no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—222no—
502C4⋊C4—221no—
503C4⋊C4C23×D1114yes—
504C4⋊C4C23×D1112yes—
505C22⋊C4—24no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C42—114no—
510C42—112no—
511C42—114no—
512C42—112no—
513C42—112no—
514C42—112no—
515C11C2×#322711yescharacteristic, complemented, Sylow
516C23—22no—
517C23—22no—
518C23—22no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—222no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23SD16×D1114yes—
527C23C2×D4×D1112yes—
528C23C2×D4×D1111yescharacteristic
529Q8—4416no—
530Q8—448no—
531Q8—4416no—
532D4—24no—
533D4—48no—
534D4—42no—
535D4—224no—
536D4—448no—
537D4—448no—
538D4—448no—
539D4—442no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—114no—
549C2×C4—114no—
550C2×C4—1116no—
551C2×C4—114no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—228no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—448no—
561C2×C4—448no—
562C2×C4—448no—
563C2×C4—442no—
564C2×C4—444no—
565C2×C4C2×D4×D1112yes—
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#6704314yes—
568C2×C4C24×D1111yescharacteristic
569C8—24no—
570C8—224no—
571C22—22no—
572C22—28no—
573C22—22no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—884no—
582C22#1062317912yes—
583C22C2×SD16×D1114yes—
584C22C2×SD16×D1112yes—
585C22D11×AGL(1,ℤ/8)12yes—
586C22C22×D4×D1111yescharacteristic
587C4—22no—
588C4—42no—
589C4—44no—
590C4—114no—
591C4—114no—
592C4—114no—
593C4—222no—
594C4—442no—
595C4—444no—
596C4#1062317912yes—
597C4C2×#6704312yes—
598C2—24no—
599C2—82no—
600C2—882no—
601C2#1307974214yesdirect product factor
602C2C2×#1062317911yescharacteristic
603C2C22×SD16×D1111yescharacteristic
604C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
hypercenterC2×#481D11
hypocenterC11C2×#3227
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#66941C2semidirect
3. #13079742C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622348C2semidirect
7. C2×#10622581C2semidirect
8. C2×#10622647C2semidirect
9. C2×#10622483C2semidirect
10. C2×#10622374C2semidirect
11. C2×#10622331C2semidirect
12. C2×C11×#481C2semidirect
33. C2×#66941C22semidirect
36. C11×#481C22semidirect
46. #10622647C22semidirect
47. #10622581C22semidirect
51. #10622483C22semidirect
52. #10622468C22semidirect
53. #10622374C22semidirect
54. #10622373C22semidirect
55. #10622348C22semidirect
56. #10622331C22semidirect
222. C2×#481D11semidirect
309. #481C2×D11semidirect
433. C2×C11#3227semidirect
515. C11C2×#3227semidirect
601. C2#13079742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C22×#669412
#130797422
C2×#106224682
C2×#106223732
C2×#106223482
C2×#106225812
C2×#106226472
C2×#106224832
C2×#106223742
C2×#106223312
C2×C11×#4812
C2×#322711