Finite Group Databasebeta

← C2×#13080858 #15630614

Subgroups — C2×#13080858 #15630614

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×#10623094C211yesmaximal, characteristic, complemented
2#13080858C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622648C212yesmaximal, complemented
5C2×#10622621C211yesmaximal, characteristic, complemented
6C2×#10622652C212yesmaximal, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622830C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622828C212yesmaximal, complemented
12C2×D42×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11—21no—
14C23×D4×C11C2212yes—
15D42×C11—24no—
16D42×C11C2218yescomplemented
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C11×#120—22no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66991—21no—
24C22×#4323C2211yescharacteristic
25C22×#4323C2212yescomplemented
26C2×#66983C2212yescomplemented
27C2×#66979C2212yescomplemented
28C22×#4318C2212yescomplemented
29#10623094—24no—
30#10623094C2218yescomplemented
31C2×#66945—21no—
32C2×#66938—22no—
33C2×C4×D44C2211yescharacteristic, complemented
34C2×#66922C2211yescharacteristic, complemented
35#10622830C22116yescomplemented
36#10622828C22116yescomplemented
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66896C2212yescomplemented
40C2×#66896C2212yescomplemented
41C2×#66896C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2212yescomplemented
43#10622685C2218yescomplemented
44#10622683C2218yescomplemented
45#10622652C22116yescomplemented
46#10622648C22116yescomplemented
47C4×#4323C2218yescomplemented
48#10622625C2218yescomplemented
49#10622621C2218yescomplemented
50C2×#66873C2211yescharacteristic, complemented
51C2×#66872C2212yescomplemented
52C2×#66871C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C25×C11—22no—
56C22×D4×C11—28no—
57C22×D4×C11—22no—
58C22×D4×C11—28no—
59C22×D4×C11—22no—
60C22×D4×C11—21no—
61C22×D4×C11—24no—
62C22×D4×C11—21no—
63C22×D4×C11—44no—
64C22×D4×C11—48no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2312yes—
67C22×D4×C11C2318yes—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2312yes—
71C22×C22⋊D11—22no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22—21no—
75C11×#127—22no—
76C11×#127C2314yes—
77C11×#121—24no—
78C11×#121—28no—
79C11×#121C2318yes—
80C11×#120—216no—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C4×D4×C11C2314yes—
84C4×D4×C11C2314yes—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—22no—
92#66991—28no—
93C2×#4323—24no—
94C2×#4323—44no—
95C2×#4323C2314yes—
96C2×#4323C2318yescomplemented
97#66983—24no—
98#66983C2318yescomplemented
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—22no—
101#66979—24no—
102#66979C2318yescomplemented
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4×Dic11—22no—
107C2×#4318—44no—
108C2×#4318C2318yescomplemented
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66945—28no—
113#66938—216no—
114C4×D44—22no—
115C4×D44C2314yescomplemented
116#66922—22no—
117#66922C2314yescomplemented
118#66896C2314yes—
119#66896C2318yes—
120#66896C2318yescomplemented
121#66896C2318yescomplemented
122#66896C2318yescomplemented
123C22⋊(C11⋊C8)C2318yescomplemented
124#66873C2314yescomplemented
125#66872C2318yescomplemented
126#66871C2314yescomplemented
127C4⋊(C11⋊C8)C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3325—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11—22no—
132C24×C11—28no—
133C24×C11—48no—
134C24×C11—48no—
135C24×C11—84no—
136C24×C11C2×D412yes—
137C23×D11—21no—
138C2×D4×C11—216no—
139C2×D4×C11—28no—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—28no—
143C2×D4×C11—22no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—48no—
150C2×D4×C11—416no—
151C2×D4×C11—48no—
152C2×D4×C11—432no—
153C2×D4×C11—48no—
154C2×D4×C11—44no—
155C2×D4×C11—82no—
156C2×D4×C11C2×D414yes—
157C2×D4×C11#4114yes—
158C2×D4×C11C2414yes—
159C2×D4×C11C2412yes—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2414yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—28no—
172C2×C22⋊D11—84no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C2×Dic22—24no—
182C2×Dic22—82no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2×D414yes—
185C11×C4⋊C4C2412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—28no—
188C11×C22⋊C4C2×D418yes—
189C42×C11C2×D412yes—
190C42×C11C2412yes—
191C22⋊Dic11—28no—
192#4323—28no—
193#4323—48no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11C2412yes—
200C4⋊Dic11C2414yes—
201C4×Dic11—28no—
202#4318—48no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2412yes—
208C2×C11⋊C8C2414yes—
209C2×#555—111no—
210C2×D42D1111yescharacteristic, complemented
211#3325—1116no—
212C2×#486—111no—
213C2×#482—112no—
214C2×#476—111no—
215C2×#469—112no—
216C2×#459—111no—
217C2×#447—112no—
218C2×C4×D8—111no—
219C2×#436—111no—
220C2×#418—112no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—416no—
228C23×C11—416no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—44no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11—88no—
235C23×C11—832no—
236C23×C11C22×D414yes—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242D4×C11—24no—
243D4×C11—28no—
244D4×C11—24no—
245D4×C11—22no—
246D4×C11—24no—
247D4×C11—416no—
248D4×C11—416no—
249D4×C11—44no—
250D4×C11—48no—
251D4×C11—84no—
252D4×C11C2×#4114yes—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—42no—
260C2×C4×C11—48no—
261C2×C4×C11AGL(1,ℤ/8)14yes—
262C2×C4×C11C22×D414yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D412yes—
266C2×C4×C11C2×#4112yes—
267C2×C4×C11H(5,𝔽2)12yes—
268C2×C4×C11C2511yescharacteristic
269C22⋊D11—88no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—42no—
273C2×Dic11—44no—
274D44—22no—
275D44—22no—
276D44—42no—
277C4×D11—48no—
278Dic22—84no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—24no—
282C23×D4—21no—
283C23×D4C2×D1112yes—
284C22×D8—111no—
285C22×D8—112no—
286C22×M16—112no—
287#555—118no—
288#555—224no—
289D42—24no—
290D42C2×D1118yescomplemented
291C2×C4⋊Q8—111no—
292C2×#127C2×D1111yescharacteristic
293C2×#124—222no—
294C2×#121—21no—
295C2×#121—112no—
296C2×#121—221no—
297C2×#121C2×D1112yes—
298C2×#120—22no—
299C2×C4×D4—111no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×C4×D4C2×D1111yescharacteristic
302C2×#117—112no—
303C2×#117—221no—
304#486—118no—
305#482—1116no—
306#476—118no—
307#469—1116no—
308#459—118no—
309#447—1116no—
310C4×D8—118no—
311#436—118no—
312C2×#107—111no—
313C2×#106—112no—
314C2×C4⋊C8—111no—
315#418—1116no—
316C2×#102—112no—
317C2×#102—112no—
318C2×#102—112no—
319C2×#102—111no—
320C2×#102—112no—
321C2×#102—111no—
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—42no—
329C22×C11—48no—
330C22×C11—48no—
331C22×C11—42no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—832no—
336C22×C11—88no—
337C22×C11#54612yes—
338C22×C11C2×AGL(1,ℤ/8)12yes—
339C22×C11#57612yes—
340C22×C11C23×D411yescharacteristic
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—84no—
345C4×C11—24no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11#54612yes—
349C4×C11C2×AGL(1,ℤ/8)14yes—
350C4×C11C22×#4111yescharacteristic
351C4×C11C2×H(5,𝔽2)11yescharacteristic
352Dic11—42no—
353Dic11—44no—
354C25—22no—
355C22×Q8—221no—
356C22×D4—28no—
357C22×D4—22no—
358C22×D4—28no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—24no—
362C22×D4—21no—
363C22×D4—44no—
364C22×D4—48no—
365C22×D4—111no—
366C22×D4—222no—
367C22×D4C22⋊D1111yescharacteristic
368C22×D4C22×D1112yes—
369C22×D4C22×D1118yes—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—221no—
373C23×C4C22×D1112yes—
374C2×D8—114no—
375C2×D8—118no—
376C2×D8—224no—
377C2×D8—444no—
378C2×M16—118no—
379C2×M16—444no—
380C22×C8—111no—
381C22×C8—112no—
382C22×C8—111no—
383C4⋊Q8—114no—
384C4⋊Q8—222no—
385#127—22no—
386#127C22×D1114yes—
387#124—2216no—
388#121—24no—
389#121—28no—
390#121—118no—
391#121—228no—
392#121—224no—
393#121C22×D1118yes—
394#120—216no—
395C4×D4—22no—
396C4×D4—114no—
397C4×D4—222no—
398C4×D4C22⋊D1114yes—
399C4×D4C22×D1114yes—
400C4×D4C22×D1114yes—
401#117—118no—
402#117—224no—
403#117—228no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22⋊D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4C22⋊D1112yes—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417#107—114no—
418#106—118no—
419C4⋊C8—114no—
420#102—114no—
421#102—118no—
422#102—118no—
423#102—118no—
424#102—118no—
425#102—114no—
426C22⋊C8—118no—
427C4×C8—114no—
428C2×C11—44no—
429C2×C11—44no—
430C2×C11—84no—
431C2×C11#332514yescomplemented
432C2×C11C2×#54611yescharacteristic
433C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
434C2×C11C2×#57611yescharacteristic
435D11—82no—
436C24—21no—
437C24—22no—
438C24—28no—
439C24—48no—
440C24—48no—
441C24—84no—
442C24—221no—
443C24C2×C22⋊D1112yes—
444C2×Q8—224no—
445C2×Q8—882no—
446C2×D4—216no—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—28no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—48no—
458C2×D4—416no—
459C2×D4—48no—
460C2×D4—432no—
461C2×D4—48no—
462C2×D4—44no—
463C2×D4—82no—
464C2×D4—112no—
465C2×D4—228no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—221no—
469C2×D4—884no—
470C2×D4#434114yes—
471C2×D4C2×C22⋊D1114yes—
472C2×D4C23×D1114yes—
473C2×D4C23×D1112yes—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—44no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—224no—
482C22×C4—444no—
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C23×D1114yes—
488C22×C4C23×D1111yescharacteristic
489D8—228no—
490D8—448no—
491M16—448no—
492C2×C8—112no—
493C2×C8—112no—
494C2×C8—114no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—224no—
498C4⋊C4—21no—
499C4⋊C4—114no—
500C4⋊C4—112no—
501C4⋊C4—221no—
502C4⋊C4—222no—
503C4⋊C4—224no—
504C4⋊C4C2×C22⋊D1114yes—
505C4⋊C4C23×D1112yes—
506C22⋊C4—24no—
507C22⋊C4—28no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—224no—
511C22⋊C4C2×C22⋊D1118yes—
512C42—228no—
513C42C2×C22⋊D1112yes—
514C42C23×D1112yes—
515C11C2×#332511yescharacteristic, complemented, Sylow
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—416no—
523C23—416no—
524C23—42no—
525C23—42no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—88no—
530C23—832no—
531C23—222no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23C22×C22⋊D1114yes—
536C23C22×C22⋊D1111yescharacteristic
537Q8—884no—
538D4—28no—
539D4—24no—
540D4—24no—
541D4—22no—
542D4—24no—
543D4—416no—
544D4—416no—
545D4—48no—
546D4—44no—
547D4—84no—
548D4—222no—
549D4—222no—
550D4—442no—
551D4—888no—
552D4C2×#434114yes—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—48no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—442no—
564C2×C4—444no—
565C2×C4—448no—
566C2×C4#6698514yes—
567C2×C4C2×#434112yes—
568C2×C4#6703712yes—
569C2×C4C22×C22⋊D1114yes—
570C2×C4C22×C22⋊D1112yes—
571C2×C4C22×C22⋊D1112yes—
572C2×C4C22×C22⋊D1111yescharacteristic
573C2×C4C24×D1111yescharacteristic
574C8—222no—
575C8—222no—
576C8—224no—
577C22—24no—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—48no—
582C22—48no—
583C22—42no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—832no—
589C22—88no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22—884no—
594C22C2×#6698512yes—
595C22#1062333712yes—
596C22#1062336612yes—
597C22C23×C22⋊D1111yescharacteristic
598C4—24no—
599C4—22no—
600C4—42no—
601C4—442no—
602C4—444no—
603C4C2×#6698514yes—
604C4#1062333712yes—
605C4C22×#434111yescharacteristic
606C4C2×#6703711yescharacteristic
607C2—44no—
608C2—44no—
609C2—84no—
610C2—882no—
611C2#1308085814yesdirect product factor
612C2C2×#1062333711yescharacteristic
613C2C22×#6698511yescharacteristic
614C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. #13080858C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622621C2semidirect
6. C2×#10622652C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622830C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622828C2semidirect
12. C2×D42×C11C2semidirect
16. D42×C11C22semidirect
25. C22×#4323C22semidirect
26. C2×#66983C22semidirect
27. C2×#66979C22semidirect
28. C22×#4318C22semidirect
30. #10623094C22semidirect
33. C2×C4×D44C22semidirect
34. C2×#66922C22semidirect
35. #10622830C22semidirect
36. #10622828C22semidirect
39. C2×#66896C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622685C22semidirect
44. #10622683C22semidirect
45. #10622652C22semidirect
46. #10622648C22semidirect
47. C4×#4323C22semidirect
48. #10622625C22semidirect
49. #10622621C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
96. C2×#4323C23semidirect
98. #66983C23semidirect
102. #66979C23semidirect
108. C2×#4318C23semidirect
115. C4×D44C23semidirect
117. #66922C23semidirect
120. #66896C23semidirect
121. #66896C23semidirect
122. #66896C23semidirect
123. C22⋊(C11⋊C8)C23semidirect
124. #66873C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. C4⋊(C11⋊C8)C23semidirect
128. C4×C11⋊C8C23semidirect
210. C2×D42D11semidirect
290. D42C2×D11semidirect
431. C2×C11#3325semidirect
515. C11C2×#3325semidirect
611. C2#13080858direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
#130808582
C2×#106226832
C2×#106226482
C2×#106226212
C2×#106226522
C2×#106226852
C2×#106228302
C2×C4×#43232
C2×#106226252
C2×#106228282
C2×D42×C112
C2×#332511