Finite Group Databasebeta

← C2×#13080855 #15630611

Subgroups — C2×#13080855 #15630611

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic, complemented
3#13080855C2116yesmaximal, direct product factor
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622479C212yesmaximal, complemented
6C2×#10622478C212yesmaximal, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622386C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622383C212yesmaximal, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×D4×D11C2212yes—
14C23×D44—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000—22no—
18C22×#4323C2211yescharacteristic
19C2×#66983—21no—
20C22×D88C2212yescomplemented
21C22×#4313C2212yescomplemented
22#10623265—24no—
23#10623265C2218yescomplemented
24D4×D44—24no—
25D4×D44C2218yescomplemented
26C2×#66948—21no—
27C2×#66948C2212yes—
28C2×#66948C2212yescomplemented
29C2×#66945—21no—
30C2×#66945C2212yescomplemented
31C2×#66935—22no—
32C2×#66927C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic, complemented
35C11×#476C2218yescomplemented
36C2×C11×#106C2212yescomplemented
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×#102C2212yes—
39C2×#66896C2211yescharacteristic
40C2×#66885C2212yescomplemented
41C2×(C2×D11)⋊C8C2212yescomplemented
42#10622701C2218yescomplemented
43C4×#4323C2218yescomplemented
44C2×#66873C2212yescomplemented
45C2×#66873C2211yescharacteristic, complemented
46C2×#66873C2212yescomplemented
47C2×#66871C2211yescharacteristic, complemented
48C2×C4×C11⋊C8C2211yescharacteristic, complemented
49#10622479C22116yescomplemented
50#10622478C22116yescomplemented
51#10622456C2218yescomplemented
52#10622451C2218yescomplemented
53#10622386C22116yescomplemented
54#10622383C22116yescomplemented
55C24×D11—22no—
56C22×Q8×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C2×D4×D11—28no—
61C2×D4×D11—24no—
62C2×D4×D11—44no—
63C2×D4×D11C2318yes—
64C22×D44—22no—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—28no—
69C22×D44—48no—
70C22×D44D411yescharacteristic
71C22×D44C2312yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11C2312yes—
75C22×C8×C11C2312yes—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yescomplemented
78C4×D4×C11—22no—
79C4×D4×C11C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85#67000—216no—
86C2×#4323—24no—
87C2×#4323C2314yes—
88#66983—28no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4D412yes—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4×Dic11—22no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×D88—44no—
100C2×D88C2318yescomplemented
101C2×#4313—44no—
102C2×#4313C2318yescomplemented
103#66948—28no—
104#66948—24no—
105#66948—24no—
106#66948C2318yes—
107#66948C2318yescomplemented
108#66945—24no—
109#66945—28no—
110#66945C2318yescomplemented
111#66935—216no—
112#66927—22no—
113#66927C2314yes—
114C4×D44—22no—
115C4×D44D414yes—
116C4×D44C2314yes—
117C4×D44C2314yescomplemented
118C11×#106C2318yescomplemented
119C11×C4⋊C8C2314yescomplemented
120C11×#102C2318yes—
121#66896C2314yes—
122#66885C2318yescomplemented
123(C2×D11)⋊C8C2318yescomplemented
124#66873C2314yescomplemented
125#66873C2318yescomplemented
126#66873C2318yescomplemented
127#66871C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3325—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—28no—
134C23×D11—48no—
135C23×D11—48no—
136C23×D11—84no—
137C23×D11C2×D412yes—
138C2×Q8×C11—24no—
139C2×Q8×C11—82no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11#4114yes—
143C2×D4×C11C2412yes—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—48no—
153C22×Dic11—21no—
154C22×Dic11C2×D412yes—
155D4×D11—216no—
156D4×D11—48no—
157D4×D11—416no—
158C2×D44—28no—
159C2×D44—28no—
160C2×D44—24no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—24no—
167C2×D44—22no—
168C2×D44—24no—
169C2×D44—48no—
170C2×D44—432no—
171C2×D44—44no—
172C2×D44—82no—
173C2×D44—84no—
174C2×D44C2×D414yes—
175C2×D44C2414yes—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2414yes—
183C2×C8×C11—24no—
184C2×C8×C11C2414yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2412yes—
189C11×C4⋊C4C2414yes—
190C11×C22⋊C4—24no—
191C42×C11C2×D412yes—
192C42×C11C2412yes—
193#4323—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4C2×D418yes—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D414yes—
201C4⋊Dic11C2412yes—
202C4×Dic11—28no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2412yes—
207D88—48no—
208#4313—48no—
209C2×#555—111no—
210C2×D42—111no—
211#3325—1116no—
212C2×#486—111no—
213C2×#482—112no—
214C2×#476D1111yescharacteristic, complemented
215C2×#469—112no—
216C2×#459—111no—
217C2×#447—112no—
218C2×C4×D8—111no—
219C2×#436—111no—
220C2×#418—112no—
221C23×C11—24no—
222C23×C11—22no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11C22×D411yescharacteristic
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—22no—
230C22×D11—24no—
231C22×D11—416no—
232C22×D11—416no—
233C22×D11—44no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—44no—
237C22×D11—42no—
238C22×D11—44no—
239C22×D11—88no—
240C22×D11—832no—
241C22×D11C22×D414yes—
242Q8×C11—84no—
243D4×C11—24no—
244D4×C11—22no—
245D4×C11C2×#4114yes—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11AGL(1,ℤ/8)14yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—416no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263C2×Dic11C22×D414yes—
264D44—28no—
265D44—22no—
266D44—24no—
267D44—22no—
268D44—24no—
269D44—416no—
270D44—42no—
271D44—44no—
272D44—48no—
273D44—84no—
274D44—88no—
275C4×D11—28no—
276C4×D11—24no—
277C4×D11—24no—
278C4×D11—48no—
279C8×C11—24no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C23×D4—112no—
283C23×D4—221no—
284C22×D8—111no—
285C22×D8—112no—
286C22×M16—112no—
287#555—118no—
288#555—224no—
289D42—118no—
290D42—224no—
291C2×C4⋊Q8C2×D1111yescharacteristic, complemented
292C2×#127—111no—
293C2×#124—222no—
294C2×#121—112no—
295C2×#121—112no—
296C2×#121—221no—
297C2×#121—221no—
298C2×#120—222no—
299C2×C4×D4—111no—
300C2×C4×D4—111no—
301C2×C4×D4C2×D1111yescharacteristic
302C2×#117—112no—
303C2×#117—221no—
304#486—118no—
305#482—1116no—
306#476C2×D1118yescomplemented
307#469—1116no—
308#459—118no—
309#447—1116no—
310C4×D8—118no—
311#436—118no—
312C2×#107—111no—
313C2×#106C2×D1112yescomplemented
314C2×C4⋊C8C2×D1111yescharacteristic, complemented
315#418—1116no—
316C2×#102—111no—
317C2×#102—112no—
318C2×#102—112no—
319C2×#102—112no—
320C2×#102—111no—
321C2×#102C2×D1112yes—
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—24no—
325C22×C11—42no—
326C22×C11—48no—
327C22×C11—42no—
328C22×C11#54612yes—
329C22×C11C2×AGL(1,ℤ/8)12yes—
330C22×C11#57612yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—24no—
335C2×D11—48no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—42no—
342C2×D11—832no—
343C2×D11—84no—
344C2×D11—88no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—44no—
348C4×C11#54612yes—
349C4×C11C2×AGL(1,ℤ/8)14yes—
350C4×C11C22×#4111yescharacteristic
351C4×C11C2×H(5,𝔽2)11yescharacteristic
352Dic11—24no—
353Dic11—42no—
354C25—222no—
355C22×Q8—21no—
356C22×D4—118no—
357C22×D4—111no—
358C22×D4—111no—
359C22×D4—112no—
360C22×D4—228no—
361C22×D4—222no—
362C22×D4—222no—
363C22×D4—224no—
364C22×D4—222no—
365C22×D4—228no—
366C22×D4—221no—
367C22×D4—221no—
368C22×D4—448no—
369C22×D4—444no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—112no—
373C23×C4—221no—
374C2×D8—114no—
375C2×D8—118no—
376C2×D8—224no—
377C2×D8—444no—
378C2×M16—118no—
379C2×M16—444no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8C22×D1112yes—
383C4⋊Q8—22no—
384C4⋊Q8C22×D1114yescomplemented
385#127—114no—
386#127—222no—
387#124—2216no—
388#121—118no—
389#121—118no—
390#121—224no—
391#121—224no—
392#121—228no—
393#121—228no—
394#120—2216no—
395C4×D4—22no—
396C4×D4—114no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—222no—
400C4×D4C22×D1114yes—
401#117—118no—
402#117—228no—
403#117—224no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4C22×D1112yes—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417#107—114no—
418#106C22×D1118yescomplemented
419C4⋊C8C22×D1114yescomplemented
420#102—114no—
421#102—118no—
422#102—118no—
423#102—114no—
424#102—118no—
425#102C22×D1118yes—
426C22⋊C8—118no—
427C4×C8—114no—
428C2×C11—44no—
429C2×C11#332514yescomplemented
430C2×C11C2×#54611yescharacteristic
431C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
432C2×C11C2×#57611yescharacteristic
433D11—44no—
434D11—82no—
435D11—84no—
436C24—21no—
437C24—112no—
438C24—228no—
439C24—221no—
440C24—222no—
441C24—448no—
442C24—448no—
443C24—884no—
444C2×Q8—24no—
445C2×Q8—82no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—114no—
449C2×D4—114no—
450C2×D4—112no—
451C2×D4—228no—
452C2×D4—228no—
453C2×D4—228no—
454C2×D4—2216no—
455C2×D4—224no—
456C2×D4—221no—
457C2×D4—224no—
458C2×D4—222no—
459C2×D4—224no—
460C2×D4—222no—
461C2×D4—224no—
462C2×D4—222no—
463C2×D4—224no—
464C2×D4—4432no—
465C2×D4—448no—
466C2×D4—448no—
467C2×D4—4416no—
468C2×D4—448no—
469C2×D4—444no—
470C2×D4—882no—
471C2×D4—884no—
472C2×D4#434314yes—
473C2×D4C23×D1112yes—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—44no—
478C22×C4—112no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—221no—
484C22×C4—224no—
485C22×C4—444no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489D8—228no—
490D8—448no—
491M16—448no—
492C2×C8—24no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8C23×D1114yes—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—114no—
502C4⋊C4—112no—
503C4⋊C4—221no—
504C4⋊C4C23×D1114yes—
505C4⋊C4C23×D1112yes—
506C22⋊C4—24no—
507C22⋊C4—118no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—228no—
511C22⋊C4—224no—
512C42—228no—
513C42D4×D1112yes—
514C42C23×D1112yes—
515C11C2×#332511yescharacteristic, complemented, Sylow
516C23—24no—
517C23—22no—
518C23—42no—
519C23—42no—
520C23—114no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—222no—
525C23—224no—
526C23—4416no—
527C23—4416no—
528C23—442no—
529C23—444no—
530C23—442no—
531C23—444no—
532C23—444no—
533C23—442no—
534C23—888no—
535C23—8832no—
536C23C2×D4×D1111yescharacteristic
537Q8—84no—
538D4—24no—
539D4—22no—
540D4—228no—
541D4—222no—
542D4—224no—
543D4—222no—
544D4—224no—
545D4—4416no—
546D4—4416no—
547D4—448no—
548D4—444no—
549D4—442no—
550D4—884no—
551D4—888no—
552D4C2×#434314yes—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—114no—
560C2×C4—224no—
561C2×C4—228no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—442no—
566C2×C4—448no—
567C2×C4#6696714yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4C2×#434312yes—
572C2×C4#6704212yes—
573C2×C4C24×D1111yescharacteristic
574C8—24no—
575C8—222no—
576C8—222no—
577C22—24no—
578C22—48no—
579C22—42no—
580C22—42no—
581C22—224no—
582C22—224no—
583C22—224no—
584C22—448no—
585C22—444no—
586C22—442no—
587C22—442no—
588C22—444no—
589C22—442no—
590C22—444no—
591C22—8832no—
592C22—888no—
593C22—884no—
594C22#1062316112yes—
595C22C2×#6696712yes—
596C22#1062330512yes—
597C22C22×D4×D1111yescharacteristic
598C4—22no—
599C4—42no—
600C4—44no—
601C4—224no—
602C4—442no—
603C4#1062316112yes—
604C4C2×#6696714yes—
605C4C22×#434311yescharacteristic
606C4C2×#6704211yescharacteristic
607C2—44no—
608C2—444no—
609C2—884no—
610C2—882no—
611C2#1308085514yesdirect product factor
612C2C2×#1062316111yescharacteristic
613C2C22×#6696711yescharacteristic
614C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
hypercenterC2×#476D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×D4×D44C2semidirect
3. #13080855C2direct (N × H)
4. C2×#10622701C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622478C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622386C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622383C2semidirect
12. C2×C11×#476C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
20. C22×D88C22semidirect
21. C22×#4313C22semidirect
23. #10623265C22semidirect
25. D4×D44C22semidirect
28. C2×#66948C22semidirect
30. C2×#66945C22semidirect
34. C2×C4×D44C22semidirect
35. C11×#476C22semidirect
36. C2×C11×#106C22semidirect
37. C2×C11×C4⋊C8C22semidirect
40. C2×#66885C22semidirect
41. C2×(C2×D11)⋊C8C22semidirect
42. #10622701C22semidirect
43. C4×#4323C22semidirect
44. C2×#66873C22semidirect
45. C2×#66873C22semidirect
46. C2×#66873C22semidirect
47. C2×#66871C22semidirect
48. C2×C4×C11⋊C8C22semidirect
49. #10622479C22semidirect
50. #10622478C22semidirect
51. #10622456C22semidirect
52. #10622451C22semidirect
53. #10622386C22semidirect
54. #10622383C22semidirect
77. C11×C4⋊Q8C23semidirect
100. C2×D88C23semidirect
102. C2×#4313C23semidirect
107. #66948C23semidirect
110. #66945C23semidirect
117. C4×D44C23semidirect
118. C11×#106C23semidirect
119. C11×C4⋊C8C23semidirect
122. #66885C23semidirect
123. (C2×D11)⋊C8C23semidirect
124. #66873C23semidirect
125. #66873C23semidirect
126. #66873C23semidirect
127. #66871C23semidirect
128. C4×C11⋊C8C23semidirect
214. C2×#476D11semidirect
291. C2×C4⋊Q8C2×D11semidirect
306. #476C2×D11semidirect
313. C2×#106C2×D11semidirect
314. C2×C4⋊C8C2×D11semidirect
384. C4⋊Q8C22×D11semidirect
418. #106C22×D11semidirect
419. C4⋊C8C22×D11semidirect
429. C2×C11#3325semidirect
515. C11C2×#3325semidirect
611. C2#13080855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×D4×D442
#130808552
C2×#106227012
C2×#106224792
C2×#106224782
C2×#106224562
C2×#106223862
C2×C4×#43232
C2×#106224512
C2×#106223832
C2×C11×#4762
C2×#332511