Finite Group Databasebeta

← C2×#13078735 #15621964

Subgroups — C2×#13078735 #15621964

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13078735C2116yesmaximal, direct product factor
4C2×#10622580C211yesmaximal, characteristic, complemented
5C2×#10622488C212yesmaximal, complemented
6C2×#10622375C212yesmaximal, complemented
7C2×#10622351C211yesmaximal, characteristic, complemented
8C2×#10622653C211yesmaximal, characteristic, complemented
9C2×#10622502C212yesmaximal, complemented
10C2×#10622370C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#480C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C23×Dic22C2211yescharacteristic
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×#66992—21no—
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2212yes—
21C2×#66983C2211yescharacteristic
22C22×Dic11⋊C4—21no—
23C22×C4×Dic11—21no—
24C22×C4×Dic11C2211yescharacteristic
25C22×#4314C2212yes—
26#10623127—24no—
27#10623127C2218yes—
28C2×#66946C2211yescharacteristic
29C2×#66941C2211yescharacteristic
30C2×#66940—24no—
31C2×#66940—21no—
32C2×#66940—21no—
33C2×#66940C2212yes—
34C2×#66940C2212yes—
35C2×#66940C2218yescomplemented
36C2×#66938—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C11×#480C2218yescomplemented
39C2×C11×#107C2212yes—
40C2×C11×#102C2212yes—
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622653C2218yescomplemented
47C2×#66874C2212yes—
48#10622580C2218yescomplemented
49C2×#66873C2212yes—
50C2×#66871C2212yes—
51#10622502C22116yescomplemented
52#10622488C22116yescomplemented
53#10622375C22116yescomplemented
54#10622370C22116yescomplemented
55#10622351C2218yescomplemented
56#10622332C2218yescomplemented
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—28no—
75C22×Dic22—21no—
76C22×Dic22C2314yes—
77C22×Dic22C2312yes—
78C22×C8×C11C2312yes—
79C11×#121—22no—
80C11×#121C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11—21no—
88#66993—22no—
89#66993C2314yes—
90#66992—28no—
91D4×Dic11—22no—
92D4×Dic11C2314yes—
93C2×#4324—28no—
94C2×#4324C2318yes—
95#66983—22no—
96#66983C2314yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—28no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—28no—
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D414yes—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2314yes—
113C22×C11⋊C8C2312yes—
114C2×#4314—28no—
115C2×#4314C2318yes—
116#66946—22no—
117#66946C2314yes—
118#66941—22no—
119#66941C2314yes—
120#66940—24no—
121#66940—24no—
122#66940—28no—
123#66940—28no—
124#66940C2318yes—
125#66940C2318yes—
126#66938—28no—
127(C22⋊D11)⋊C4—28no—
128C11×#107C2318yes—
129C11×#102C2318yes—
130C11×C22⋊C8C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#66880C2318yes—
133#66879C2318yes—
134Dic11⋊C8C2318yes—
135#66874C2318yes—
136#66873C2318yes—
137#66871C2318yes—
138C2×#3112—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—24no—
145C2×D4×C11—44no—
146C2×D4×C11C2412yes—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11—44no—
162C22×Dic11—28no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—44no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D414yes—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D414yes—
175C22×Dic11C2×D411yescharacteristic
176#4341—432no—
177C2×D44—21no—
178C2×D44—24no—
179C2×D44C2412yes—
180C2×C4×D11—24no—
181C2×C4×D11—44no—
182C2×Dic22—28no—
183C2×Dic22—216no—
184C2×Dic22—216no—
185C2×Dic22—24no—
186C2×Dic22—24no—
187C2×Dic22—22no—
188C2×Dic22—24no—
189C2×Dic22—44no—
190C2×Dic22#4118yescomplemented
191C2×Dic22C2414yes—
192C2×C8×C11—24no—
193C2×C8×C11C2414yes—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2414yes—
198C11×C4⋊C4C2412yes—
199C11×C22⋊C4—24no—
200C22⋊Dic11—24no—
201#4324—216no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—28no—
208Dic11⋊C4—28no—
209C4×Dic11—28no—
210C4×Dic11—28no—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2×D412yes—
214C4×Dic11C2×D412yes—
215C4×Dic11C2412yes—
216C4×Dic11C2412yes—
217C2×C11⋊C8—24no—
218C2×C11⋊C8C2414yes—
219#4314—216no—
220C2×#532—111no—
221C22×C4×Q8—111no—
222#3112—1116no—
223C2×#480—111no—
224C2×#480D1111yescharacteristic, complemented
225C2×#477—112no—
226C2×#460—112no—
227C2×#448—111no—
228C2×#448—111no—
229C2×#440—112no—
230C2×#440—112no—
231C2×#432—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11AGL(1,ℤ/8)14yes—
239C23×C11C22×D412yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245D4×C11—24no—
246D4×C11—48no—
247D4×C11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2511yescharacteristic
260C22⋊D11—48no—
261C22⋊D11—48no—
262C22⋊D11—48no—
263C2×Dic11—216no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—28no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—28no—
271C2×Dic11—22no—
272C2×Dic11—48no—
273C2×Dic11—42no—
274C2×Dic11#13714yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278C2×Dic11C22×D412yes—
279D44—24no—
280D44—42no—
281C4×D11—48no—
282Dic22—216no—
283Dic22—28no—
284Dic22—24no—
285Dic22—48no—
286Dic22C2×#4118yescomplemented
287C8×C11—24no—
288C11⋊C8—24no—
289C22×#41—221no—
290C23×Q8—111no—
291C22×SD16—112no—
292C22×SD16—112no—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8—111no—
296C2×#127—111no—
297C2×#124—221no—
298C2×#121—111no—
299C2×#121—221no—
300C2×#121C2×D1111yescharacteristic
301C2×C4×Q8—112no—
302C2×C4×Q8—118no—
303C2×C4×Q8—112no—
304C2×C4×Q8—221no—
305C2×C4×Q8—221no—
306C2×C4×Q8—224no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4—221no—
310C22×C4⋊C4—221no—
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C42—111no—
313C22×C42—221no—
314#480—118no—
315#480C2×D1118yescomplemented
316#477—1116no—
317#460—1116no—
318#448—118no—
319#448—118no—
320#440—1116no—
321#440—1116no—
322#432—118no—
323C2×#107—112no—
324C2×#107C2×D1112yes—
325C2×C4⋊C8—112no—
326C2×#103—112no—
327C2×#103—112no—
328C2×#102—112no—
329C2×#102C2×D1112yes—
330C2×C22⋊C8—111no—
331C2×C22⋊C8C2×D1111yescharacteristic
332C2×#97—112no—
333C22×C11—28no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—84no—
340C22×C11#52512yes—
341C22×C11C2×AGL(1,ℤ/8)14yes—
342C22×C11C2×AGL(1,ℤ/8)12yes—
343C22×C11C2×#13712yes—
344C22×C11C23×D411yescharacteristic
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—84no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11#52512yes—
353C4×C11C22×#4112yes—
354Dic11—28no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11C2×#13714yes—
360C2×#41—228no—
361C2×#41—448no—
362C22×Q8—112no—
363C22×Q8—114no—
364C22×Q8—221no—
365C22×Q8—228no—
366C22×Q8—222no—
367C22×Q8—221no—
368C22×D4—21no—
369C22×D4—111no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—221no—
378C23×C4—221no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×SD16—118no—
382C2×SD16—118no—
383C2×SD16—228no—
384C2×SD16—228no—
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C4⋊Q8—114no—
388C4⋊Q8—222no—
389#127—114no—
390#127—222no—
391#124—228no—
392#121—22no—
393#121—114no—
394#121—228no—
395#121—222no—
396#121C22×D1114yes—
397C4×Q8—118no—
398C4×Q8—118no—
399C4×Q8—228no—
400C4×Q8—224no—
401C4×Q8—228no—
402C4×Q8—224no—
403C4×D4—114no—
404C4×D4—114no—
405C4×D4—228no—
406C4×D4—222no—
407C4×D4—222no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1112yes—
416C2×C4⋊C4C22×D1114yes—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—114no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—114no—
428C2×C42—228no—
429C2×C42—222no—
430C2×C42—222no—
431#107—118no—
432#107C22×D1118yes—
433C4⋊C8—118no—
434#103—118no—
435#103—118no—
436#102—118no—
437#102C22×D1118yes—
438C22⋊C8—114no—
439C22⋊C8C22×D1114yes—
440#97—118no—
441C2×C11—24no—
442C2×C11—82no—
443C2×C11#311214yescomplemented
444C2×C11C2×#52511yescharacteristic
445C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C22×#13711yescharacteristic
447D11—82no—
448C24—21no—
449C24—221no—
450C24D4×D1111yescharacteristic
451#41—4432no—
452C2×Q8—118no—
453C2×Q8—114no—
454C2×Q8—224no—
455C2×Q8—2216no—
456C2×Q8—228no—
457C2×Q8—2216no—
458C2×Q8—224no—
459C2×Q8—222no—
460C2×Q8—224no—
461C2×Q8—444no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—24no—
465C2×D4—44no—
466C2×D4—112no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—221no—
471C2×D4—224no—
472C2×D4—444no—
473C2×D4—444no—
474C2×D4—444no—
475C2×D4C23×D1112yes—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—44no—
481C22×C4—111no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—228no—
491C22×C4—224no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—444no—
496C22×C4—444no—
497C22×C4D4×D1112yes—
498C22×C4D4×D1111yescharacteristic
499C22×C4C23×D1112yes—
500C22×C4C23×D1111yescharacteristic
501SD16—2216no—
502SD16—2216no—
503C2×C8—24no—
504C2×C8—114no—
505C2×C8—224no—
506C2×C8C23×D1114yes—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—112no—
511C4⋊C4—228no—
512C4⋊C4—228no—
513C4⋊C4—224no—
514C4⋊C4—221no—
515C4⋊C4C23×D1114yes—
516C4⋊C4C23×D1112yes—
517C22⋊C4—24no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C42—114no—
522C42—112no—
523C42—114no—
524C42—112no—
525C42—112no—
526C42—112no—
527C42—228no—
528C42—228no—
529C11C2×#311211yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—222no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23#6696414yes—
541C23C2×D4×D1112yes—
542C23C2×D4×D1111yescharacteristic
543Q8—118no—
544Q8—2216no—
545Q8—228no—
546Q8—224no—
547Q8—448no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—224no—
552D4—448no—
553D4—448no—
554D4—448no—
555D4—442no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—114no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—112no—
569C2×C4—228no—
570C2×C4—2216no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—228no—
574C2×C4—222no—
575C2×C4—228no—
576C2×C4—224no—
577C2×C4—222no—
578C2×C4—448no—
579C2×C4—448no—
580C2×C4—442no—
581C2×C4C2×D4×D1112yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#41×D1114yes—
584C2×C4C24×D1111yescharacteristic
585C8—24no—
586C8—224no—
587C22—28no—
588C22—22no—
589C22—22no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—84no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062318712yes—
599C22C2×#6696414yes—
600C22C2×#6696412yes—
601C22D11×#13712yes—
602C22C22×D4×D1111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—114no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—228no—
611C4—442no—
612C4#1062318712yes—
613C4C2×#41×D1112yes—
614C2—24no—
615C2—82no—
616C2—882no—
617C2#1307873514yesdirect product factor
618C2C2×#1062318711yescharacteristic
619C2C22×#6696411yescharacteristic
620C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
hypercenterC2×#480D11
hypocenterC11C2×#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13078735C2direct (N × H)
4. C2×#10622580C2semidirect
5. C2×#10622488C2semidirect
6. C2×#10622375C2semidirect
7. C2×#10622351C2semidirect
8. C2×#10622653C2semidirect
9. C2×#10622502C2semidirect
10. C2×#10622370C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#480C2semidirect
35. C2×#66940C22semidirect
38. C11×#480C22semidirect
46. #10622653C22semidirect
48. #10622580C22semidirect
51. #10622502C22semidirect
52. #10622488C22semidirect
53. #10622375C22semidirect
54. #10622370C22semidirect
55. #10622351C22semidirect
56. #10622332C22semidirect
190. C2×Dic22#41semidirect
224. C2×#480D11semidirect
286. Dic22C2×#41semidirect
315. #480C2×D11semidirect
443. C2×C11#3112semidirect
529. C11C2×#3112semidirect
617. C2#13078735direct (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×#669402
#130787352
C2×#106225802
C2×#106224882
C2×#106223752
C2×#106223512
C2×#106226532
C2×#106225022
C2×#106223702
C2×#106223322
C2×C11×#4802
C2×#311211