Finite Group Databasebeta

← C2×#13080915 #15630676

Subgroups — C2×#13080915 #15630676

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2#13080915C2116yesmaximal, direct product factor
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622583C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622650C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622579C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C22×#4339C2212yes—
15C11×#547—24no—
16C11×#547C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C2×#66991—21no—
25C22×#4324C2212yes—
26C22×#4323C2211yescharacteristic
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29#10623082—24no—
30#10623082C2218yescomplemented
31C2×C4⋊C4×D11—21no—
32C2×#66936—22no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622706C2218yescomplemented
38#10622700C2218yescomplemented
39#10622655C22116yescomplemented
40#10622650C22116yescomplemented
41#10622632C2218yescomplemented
42C4×#4323C2218yescomplemented
43#10622625C2218yescomplemented
44#10622583C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48#10622579C22116yescomplemented
49C2×#66873C2212yes—
50C2×#66873C2211yescharacteristic
51C2×#66871C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C22×C22⋊D11—22no—
65C2×#4339—24no—
66C2×#4339—28no—
67C2×#4339—44no—
68C2×#4339C2318yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×Dic22C2312yes—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C11×#123—216no—
76C11×C22⋊Q8—28no—
77C11×#121—24no—
78C11×#121C2318yes—
79C4×D4×C11—22no—
80C4×D4×C11D414yes—
81C4×D4×C11C2314yes—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2318yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—22no—
95#66991—28no—
96C2×#4324—44no—
97C2×#4324C2318yes—
98C2×#4323—24no—
99C2×#4323C2314yes—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104#66977—24no—
105#66977C2318yes—
106C2×Dic11⋊C4—22no—
107C2×#4318—44no—
108C2×#4318C2318yes—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112C4⋊C4×D11—28no—
113#66936—216no—
114C4×D44—22no—
115C4×D44C2314yes—
116#66922—22no—
117#66922C2314yes—
118#66896C2314yes—
119C22⋊(C11⋊C8)C2318yes—
120#66874C2318yes—
121#66874C2318yes—
122#66874C2318yes—
123#66873C2314yes—
124#66873C2318yes—
125#66871C2314yes—
126#66871C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3330—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D412yes—
132C23×D11—21no—
133C11×#41—432no—
134C2×Q8×C11—24no—
135C2×Q8×C11—44no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—48no—
142C2×D4×C11C2×D414yes—
143C2×D4×C11C2412yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—48no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—48no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162#4339—216no—
163#4339—48no—
164#4339—416no—
165C2×D44—21no—
166C2×D44—22no—
167C2×D44#4114yescomplemented
168C2×D44C2412yes—
169C2×C4×D11—24no—
170C2×C4×D11—28no—
171C2×C4×D11—48no—
172C2×C4×D11—44no—
173C2×Dic22—22no—
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22C2414yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4C2×D414yes—
182C11×C4⋊C4C2412yes—
183C11×C4⋊C4C2414yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4C2×D418yes—
187C42×C11C2×D412yes—
188C42×C11C2412yes—
189C22⋊Dic11—28no—
190#4324—48no—
191#4323—28no—
192(C2×D11)⋊C4—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2412yes—
197Dic11⋊C4—28no—
198#4318—48no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—24no—
202C2×C11⋊C8C2412yes—
203C2×C11⋊C8C2412yes—
204C2×C11⋊C8C2414yes—
205C2×#547—111no—
206C2×#547D1111yescharacteristic, complemented
207#3330—1116no—
208C2×#487—111no—
209C2×#484—112no—
210C2×#474—111no—
211C2×#468—112no—
212C2×#461—111no—
213C2×#449—112no—
214C2×C4×D8—111no—
215C2×#436—111no—
216C2×#417—112no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11C22×D414yes—
225C23×C11C22×D411yescharacteristic
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—42no—
229C22×D11—42no—
230Q8×C11—48no—
231D4×C11—28no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—416no—
235D4×C11—42no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11AGL(1,ℤ/8)14yes—
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11H(5,𝔽2)12yes—
254C2×C4×C11C2511yescharacteristic
255C22⋊D11—416no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260D44—24no—
261D44—22no—
262D44C2×#4114yescomplemented
263C4×D11—416no—
264C4×D11—48no—
265Dic22—24no—
266Dic22—24no—
267Dic22—44no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—24no—
271C22×#41—21no—
272C22×#41—112no—
273C22×SD16—112no—
274C22×D8—111no—
275C22×M16—112no—
276#547—24no—
277#547—118no—
278#547—224no—
279#547C2×D1118yescomplemented
280C2×C4⋊Q8—111no—
281C2×C4⋊Q8C2×D1111yescharacteristic
282C2×#123—22no—
283C2×#123—222no—
284C2×C22⋊Q8—21no—
285C2×C22⋊Q8—112no—
286C2×#121—221no—
287C2×#121C2×D1112yes—
288C2×C4×D4—111no—
289C2×C4×D4C2×D1111yescharacteristic
290C2×C4×D4C2×D1111yescharacteristic
291C22×C4⋊C4—221no—
292C22×C4⋊C4C2×D1112yes—
293#487—118no—
294#484—1116no—
295#474—118no—
296#468—1116no—
297#461—118no—
298#449—1116no—
299C4×D8—118no—
300#436—118no—
301C2×#107—111no—
302C2×#107—112no—
303C2×C4⋊C8—111no—
304#417—1116no—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—112no—
311C2×C22⋊C8—112no—
312C2×C4×C8—111no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—48no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—84no—
321C22×C11#54612yes—
322C22×C11C2×AGL(1,ℤ/8)12yes—
323C22×C11#57812yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—24no—
326C2×D11—48no—
327C2×D11—42no—
328C2×D11—42no—
329C4×C11—24no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—44no—
333C4×C11#54612yes—
334C4×C11C2×AGL(1,ℤ/8)14yes—
335C4×C11C22×#4111yescharacteristic
336C4×C11C2×H(5,𝔽2)11yescharacteristic
337Dic11—44no—
338Dic11—42no—
339C2×#41—28no—
340C2×#41—48no—
341C2×#41—118no—
342C2×#41—228no—
343C2×#41—224no—
344C2×#41—444no—
345C22×Q8—21no—
346C22×Q8—112no—
347C22×D4—22no—
348C22×D4—111no—
349C22×D4—222no—
350C22×D4C22⋊D1111yescharacteristic
351C22×D4C22×D1111yescharacteristic
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—221no—
355C23×C4—222no—
356C23×C4C22×D1112yes—
357C2×SD16—118no—
358C2×SD16—444no—
359C2×D8—114no—
360C2×D8—224no—
361C2×M16—118no—
362C2×M16—444no—
363C22×C8—111no—
364C22×C8—112no—
365C22×C8—111no—
366C4⋊Q8—22no—
367C4⋊Q8—114no—
368C4⋊Q8—222no—
369C4⋊Q8C22×D1114yes—
370#123—216no—
371#123—2216no—
372C22⋊Q8—28no—
373C22⋊Q8—118no—
374C22⋊Q8—224no—
375#121—24no—
376#121—228no—
377#121C22×D1118yes—
378C4×D4—22no—
379C4×D4—114no—
380C4×D4—222no—
381C4×D4C22⋊D1114yes—
382C4×D4C22×D1114yes—
383C4×D4C22×D1114yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1112yes—
395C2×C4⋊C4C22×D1118yes—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4C22⋊D1112yes—
401C2×C42C22×D1111yescharacteristic
402#107—114no—
403#107—118no—
404C4⋊C8—114no—
405#103—118no—
406#103—118no—
407#103—118no—
408#102—114no—
409#102—114no—
410#102—118no—
411C22⋊C8—118no—
412C4×C8—114no—
413C2×C11—44no—
414C2×C11—82no—
415C2×C11#333014yescomplemented
416C2×C11C2×#54611yescharacteristic
417C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
418C2×C11C2×#57811yescharacteristic
419D11—44no—
420C24—21no—
421C24—221no—
422C24C2×C22⋊D1112yes—
423#41—432no—
424#41—2216no—
425#41—448no—
426#41—4416no—
427C2×Q8—24no—
428C2×Q8—44no—
429C2×Q8—114no—
430C2×Q8—222no—
431C2×Q8—224no—
432C2×Q8—224no—
433C2×D4—28no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—48no—
439C2×D4—114no—
440C2×D4—112no—
441C2×D4—228no—
442C2×D4—222no—
443C2×D4—221no—
444C2×D4—448no—
445C2×D4C2×C22⋊D1114yes—
446C2×D4C23×D1112yes—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—28no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—48no—
454C22×C4—44no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—228no—
459C22×C4—448no—
460C22×C4—444no—
461C22×C4C2×C22⋊D1114yes—
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C23×D1114yes—
466C22×C4C23×D1111yescharacteristic
467SD16—448no—
468D8—228no—
469M16—448no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—114no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—224no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—28no—
479C4⋊C4—24no—
480C4⋊C4—112no—
481C4⋊C4—221no—
482C4⋊C4—224no—
483C4⋊C4—228no—
484C4⋊C4—224no—
485C4⋊C4C2×C22⋊D1114yes—
486C4⋊C4C23×D1112yes—
487C4⋊C4C23×D1114yes—
488C22⋊C4—24no—
489C22⋊C4—28no—
490C22⋊C4—228no—
491C22⋊C4—224no—
492C22⋊C4C2×C22⋊D1118yes—
493C42C2×C22⋊D1112yes—
494C42C23×D1112yes—
495C11C2×#333011yescharacteristic, complemented, Sylow
496C23—24no—
497C23—24no—
498C23—24no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—224no—
504C23—222no—
505C23—442no—
506C23—442no—
507C23C22×C22⋊D1114yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—48no—
510Q8—224no—
511Q8—224no—
512Q8—444no—
513D4—28no—
514D4—22no—
515D4—22no—
516D4—416no—
517D4—42no—
518D4—114no—
519D4—224no—
520D4—222no—
521D4—4416no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—416no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—222no—
534C2×C4—224no—
535C2×C4—4416no—
536C2×C4—442no—
537C2×C4—444no—
538C2×C4—448no—
539C2×C4#6698514yes—
540C2×C4#41×D1112yes—
541C2×C4#6704212yes—
542C2×C4C22×C22⋊D1112yes—
543C2×C4C22×C22⋊D1114yes—
544C2×C4C22×C22⋊D1112yes—
545C2×C4C22×C22⋊D1111yescharacteristic
546C2×C4C24×D1111yescharacteristic
547C8—222no—
548C8—222no—
549C8—224no—
550C22—24no—
551C22—24no—
552C22—24no—
553C22—48no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—84no—
558C22—224no—
559C22—448no—
560C22—442no—
561C22—442no—
562C22C2×#6698512yes—
563C22#1062336012yes—
564C22#1062336912yes—
565C22C23×C22⋊D1111yescharacteristic
566C4—24no—
567C4—22no—
568C4—42no—
569C4—44no—
570C4—444no—
571C4—442no—
572C4C2×#6698514yes—
573C4#1062336012yes—
574C4C2×#41×D1111yescharacteristic
575C4C2×#6704211yescharacteristic
576C2—44no—
577C2—82no—
578C2—444no—
579C2#1308091514yesdirect product factor
580C2C2×#1062336011yescharacteristic
581C2C22×#6698511yescharacteristic
582C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623082C2semidirect
2. #13080915C2direct (N × H)
3. C2×#10622706C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622650C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622579C2semidirect
12. C2×C11×#547C2semidirect
16. C11×#547C22semidirect
30. #10623082C22semidirect
37. #10622706C22semidirect
38. #10622700C22semidirect
39. #10622655C22semidirect
40. #10622650C22semidirect
41. #10622632C22semidirect
42. C4×#4323C22semidirect
43. #10622625C22semidirect
44. #10622583C22semidirect
48. #10622579C22semidirect
167. C2×D44#41semidirect
206. C2×#547D11semidirect
262. D44C2×#41semidirect
279. #547C2×D11semidirect
415. C2×C11#3330semidirect
495. C11C2×#3330semidirect
579. C2#13080915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230822
#130809152
C2×#106227062
C2×#106225832
C2×#106227002
C2×#106226552
C2×#106226322
C2×#106226502
C2×C4×#43232
C2×#106226252
C2×#106225792
C2×C11×#5472
C2×#333011