Finite Group Databasebeta

← C2×#13078543 #15621555

Subgroups — C2×#13078543 #15621555

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13078543C2116yesmaximal, direct product factor
4C2×#10622657C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622581C211yesmaximal, characteristic, complemented
7C2×#10622418C212yesmaximal, complemented
8C2×#10622495C212yesmaximal, complemented
9C2×#10622494C212yesmaximal, complemented
10C2×#10622416C212yesmaximal, complemented
11C2×#10622339C211yesmaximal, characteristic, complemented
12C2×C11×#484C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C23×C4×D11—21no—
15C23×C4×D11C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4—21no—
22C22×#4313C2212yes—
23#10623158—24no—
24#10623158C2218yes—
25C2×#66948C2211yescharacteristic
26C2×#66947—21no—
27C2×#66946—21no—
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11—24no—
30C2×C4⋊C4×D11—21no—
31C2×C4⋊C4×D11—21no—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2218yescomplemented
35C2×#66935—21no—
36C2×(C22⋊D11)⋊C4—21no—
37C11×#484C2218yescomplemented
38C2×C11×#107C2212yescomplemented
39C2×C11×#103C2212yescomplemented
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×#66899C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66885C2212yescomplemented
44C2×(C2×D11)⋊C8C2212yes—
45C2×#66881C2212yescomplemented
46#10622657C2218yescomplemented
47#10622581C2218yescomplemented
48C2×#66873C2212yescomplemented
49C2×#66872C2212yescomplemented
50C2×#66871C2212yescomplemented
51#10622495C22116yescomplemented
52#10622494C22116yescomplemented
53#10622418C22116yescomplemented
54#10622416C22116yescomplemented
55#10622348C2218yescomplemented
56#10622339C2218yescomplemented
57C24×D11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C23×Dic11D411yescharacteristic
64C2×#4343—22no—
65C2×#4343—28no—
66C2×#4343C2314yes—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—28no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—28no—
74C22×C4×D11—21no—
75C22×C4×D11—48no—
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11D414yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2314yes—
81C22×C4×D11C2311yescharacteristic
82C22×C8×C11C2312yes—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92#66999—22no—
93#66999C2314yes—
94#66983—22no—
95#66983C2314yes—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—28no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2312yes—
111C2×#4313—28no—
112C2×#4313C2318yes—
113#66948—22no—
114#66948C2314yes—
115#66947—28no—
116#66946—28no—
117#66945—22no—
118#66945C2314yes—
119C4⋊C4×D11—24no—
120C4⋊C4×D11—24no—
121C4⋊C4×D11—28no—
122C4⋊C4×D11—28no—
123C4⋊C4×D11C2318yes—
124C4⋊C4×D11C2318yes—
125#66935—28no—
126(C22⋊D11)⋊C4—28no—
127C11×#107C2318yescomplemented
128C11×#103C2318yescomplemented
129C11×C22⋊C8C2314yes—
130#66899C2318yescomplemented
131C22⋊(C11⋊C8)C2314yes—
132#66885C2318yescomplemented
133(C2×D11)⋊C8C2318yes—
134#66881C2318yescomplemented
135#66873C2318yescomplemented
136#66872C2318yescomplemented
137#66871C2318yescomplemented
138C2×#3092—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—24no—
141C23×D11—24no—
142C23×D11—24no—
143C23×D11—21no—
144C23×D11C2×D414yes—
145C23×D11C2×D411yescharacteristic
146C23×D11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—24no—
149C2×Q8×C11C2412yes—
150C22×C4×C11—24no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—44no—
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—44no—
167C22×Dic11C2×D414yes—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170#4343—216no—
171#4343—48no—
172C2×D44—24no—
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—24no—
176C2×D44—44no—
177C2×D44—44no—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—216no—
181C2×C4×D11—216no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—28no—
185C2×C4×D11—28no—
186C2×C4×D11—24no—
187C2×C4×D11—432no—
188C2×C4×D11—48no—
189C2×C4×D11—44no—
190C2×C4×D11—48no—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2×D414yes—
193C2×C4×D11C2×D412yes—
194C2×C4×D11C2×D412yes—
195C2×C4×D11#4118yes—
196C2×C4×D11C2412yes—
197C2×C4×D11C2412yes—
198C2×C8×C11—24no—
199C2×C8×C11C2414yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4C2412yes—
205C11×C4⋊C4C2414yes—
206C11×C22⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—22no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2414yes—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219C4×Dic11—24no—
220C2×C11⋊C8—24no—
221C2×C11⋊C8C2414yes—
222#4313—216no—
223C2×#525—111no—
224C23×C4⋊C4—111no—
225#3092—1116no—
226C2×#484—111no—
227C2×#484D1111yescharacteristic, complemented
228C2×#481—111no—
229C2×#481—111no—
230C2×#483—112no—
231C2×#480—112no—
232C2×#428—112no—
233C2×#417—112no—
234C2×#407—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11#13714yes—
238C23×C11C22×D412yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—232no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—28no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—28no—
247C22×D11—28no—
248C22×D11—22no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11#12314yes—
253C22×D11AGL(1,ℤ/8)14yes—
254C22×D11C22×D412yes—
255C22×D11C22×D412yes—
256Q8×C11—24no—
257Q8×C11—42no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—48no—
265C2×C4×C11—42no—
266C2×C4×C11—44no—
267C2×C4×C11—42no—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4114yes—
271C2×C4×C11C2511yescharacteristic
272C22⋊D11—48no—
273C2×Dic11—22no—
274C2×Dic11—28no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—48no—
278C2×Dic11—44no—
279C2×Dic11—42no—
280C2×Dic11#12314yes—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283D44—24no—
284D44—48no—
285D44—48no—
286D44—42no—
287C4×D11—28no—
288C4×D11—24no—
289C4×D11—24no—
290C4×D11—28no—
291C4×D11—416no—
292C4×D11—416no—
293C4×D11—48no—
294C4×D11#12318yes—
295C4×D11C2×#4118yes—
296C8×C11—24no—
297C11⋊C8—24no—
298C22×#41—111no—
299C24×C4—111no—
300C24×C4—221no—
301C22×M16—112no—
302#525—118no—
303#525—224no—
304C2×#123—221no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8C2×D1111yescharacteristic
307C2×#121—111no—
308C2×#121—111no—
309C2×#120—221no—
310C2×C4×D4—221no—
311C2×C4×D4—221no—
312C2×#117—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—112no—
315C22×C4⋊C4—118no—
316C22×C4⋊C4—112no—
317C22×C4⋊C4—221no—
318C22×C4⋊C4—221no—
319C22×C4⋊C4—224no—
320C22×C4⋊C4—221no—
321C22×C4⋊C4C2×D1111yescharacteristic
322#484—118no—
323#484C2×D1118yescomplemented
324#483—1116no—
325#481—118no—
326#481—118no—
327#480—1116no—
328#428—1116no—
329C2×#107—112no—
330C2×#107C2×D1112yescomplemented
331C2×#106—112no—
332C2×#106—112no—
333#417—1116no—
334C2×#103—112no—
335C2×#103C2×D1112yescomplemented
336C2×#102—112no—
337C2×#102—112no—
338#407—118no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—112no—
341C2×C22⋊C8C2×D1111yescharacteristic
342C22×C11—28no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11C2×#12312yes—
346C22×C11C2×AGL(1,ℤ/8)12yes—
347C22×C11C2×#13714yes—
348C22×C11C2×#13712yes—
349C22×C11C23×D411yescharacteristic
350C2×D11—232no—
351C2×D11—28no—
352C2×D11—28no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—84no—
361C2×D11C2×#12314yes—
362C2×D11C2×AGL(1,ℤ/8)14yes—
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—44no—
366C4×C11—42no—
367C4×C11C2×#12312yes—
368C4×C11C22×#4112yes—
369Dic11—22no—
370Dic11—44no—
371Dic11—42no—
372Dic11C2×#12314yes—
373C25—111no—
374C2×#41—114no—
375C2×#41—222no—
376C2×#41—228no—
377C22×Q8C22×D1111yescharacteristic
378C22×D4—111no—
379C22×D4—221no—
380C22×D4—221no—
381C22×D4—221no—
382C23×C4—21no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—114no—
388C23×C4—111no—
389C23×C4—114no—
390C23×C4—228no—
391C23×C4—221no—
392C23×C4—228no—
393C23×C4—222no—
394C23×C4—222no—
395C23×C4—221no—
396C23×C4—448no—
397C23×C4C22×D1111yescharacteristic
398C2×M16—118no—
399C2×M16—228no—
400C22×C8—112no—
401C22×C8C22×D1112yes—
402#123—228no—
403C22⋊Q8—22no—
404C22⋊Q8—114no—
405C22⋊Q8—222no—
406C22⋊Q8C22×D1114yes—
407#121—114no—
408#121—114no—
409#121—222no—
410#121—222no—
411#120—228no—
412C4×D4—228no—
413C4×D4—228no—
414#117—114no—
415#117—222no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—118no—
423C2×C4⋊C4—118no—
424C2×C4⋊C4—224no—
425C2×C4⋊C4—228no—
426C2×C4⋊C4—224no—
427C2×C4⋊C4—228no—
428C2×C4⋊C4—228no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22×D1112yes—
435C2×C4⋊C4C22×D1114yes—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—221no—
443#107—118no—
444#107C22×D1118yescomplemented
445#106—118no—
446#106—118no—
447#103—118no—
448#103C22×D1118yescomplemented
449#102—118no—
450#102—118no—
451C22⋊C8—114no—
452C22⋊C8—118no—
453C22⋊C8C22×D1114yes—
454C2×C11—24no—
455C2×C11#309214yescomplemented
456C2×C11C22×#12311yescharacteristic
457C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
458C2×C11C22×#13711yescharacteristic
459D11—24no—
460D11—24no—
461D11—82no—
462C24—111no—
463C24—111no—
464C24—114no—
465C24—224no—
466C24—224no—
467C24—224no—
468C24—221no—
469C24D4×D1111yescharacteristic
470#41—2216no—
471#41—448no—
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8C23×D1112yes—
475C2×D4—112no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—224no—
479C2×D4—221no—
480C2×D4—224no—
481C2×D4—444no—
482C2×D4—444no—
483C2×D4—444no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—111no—
491C22×C4—112no—
492C22×C4—118no—
493C22×C4—112no—
494C22×C4—114no—
495C22×C4—111no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—224no—
501C22×C4—2216no—
502C22×C4—2216no—
503C22×C4—224no—
504C22×C4—224no—
505C22×C4—228no—
506C22×C4—228no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—444no—
513C22×C4—448no—
514C22×C4—4432no—
515C22×C4—448no—
516C22×C4—444no—
517C22×C4D4×D1112yes—
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521M16—2216no—
522C2×C8—24no—
523C2×C8—114no—
524C2×C8—224no—
525C2×C8C23×D1114yes—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—24no—
529C4⋊C4—21no—
530C4⋊C4—114no—
531C4⋊C4—112no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—222no—
537C4⋊C4—221no—
538C4⋊C4C23×D1114yes—
539C4⋊C4C23×D1112yes—
540C22⋊C4—24no—
541C22⋊C4—224no—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C42—224no—
546C11C2×#309211yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—114no—
550C23—114no—
551C23—112no—
552C23—112no—
553C23—228no—
554C23—228no—
555C23—2232no—
556C23—228no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23—222no—
561C23—222no—
562C23—442no—
563C23—442no—
564C23—442no—
565C23#6697114yes—
566C23C2×D4×D1112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—24no—
569Q8—42no—
570D4—224no—
571D4—448no—
572D4—448no—
573D4—448no—
574D4—442no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—48no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—114no—
586C2×C4—112no—
587C2×C4—118no—
588C2×C4—118no—
589C2×C4—112no—
590C2×C4—228no—
591C2×C4—228no—
592C2×C4—228no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—448no—
599C2×C4—4416no—
600C2×C4—4416no—
601C2×C4—448no—
602C2×C4—442no—
603C2×C4—444no—
604C2×C4C2×D4×D1112yes—
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4#41×D1114yes—
607C2×C4C24×D1111yescharacteristic
608C8—24no—
609C8—224no—
610C22—28no—
611C22—22no—
612C22—22no—
613C22—114no—
614C22—114no—
615C22—2232no—
616C22—228no—
617C22—228no—
618C22—222no—
619C22—222no—
620C22—222no—
621C22—222no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—884no—
626C22D11×#12312yes—
627C22C2×#6697114yes—
628C22C2×#6697112yes—
629C22D11×AGL(1,ℤ/8)12yes—
630C22C22×D4×D1111yescharacteristic
631C4—22no—
632C4—44no—
633C4—42no—
634C4—42no—
635C4—114no—
636C4—222no—
637C4—444no—
638C4—442no—
639C4D11×#12312yes—
640C4C2×#41×D1112yes—
641C2—24no—
642C2—224no—
643C2—224no—
644C2—882no—
645C2#1307854314yesdirect product factor
646C2C2×D11×#12311yescharacteristic
647C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
648C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC2×#10623158C2
hypercenterC2×#484D11
hypocenterC11C2×#3092
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13078543C2direct (N × H)
4. C2×#10622657C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622581C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622495C2semidirect
9. C2×#10622494C2semidirect
10. C2×#10622416C2semidirect
11. C2×#10622339C2semidirect
12. C2×C11×#484C2semidirect
34. C2×C4⋊C4×D11C22semidirect
37. C11×#484C22semidirect
38. C2×C11×#107C22semidirect
39. C2×C11×#103C22semidirect
41. C2×#66899C22semidirect
43. C2×#66885C22semidirect
45. C2×#66881C22semidirect
46. #10622657C22semidirect
47. #10622581C22semidirect
48. C2×#66873C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
51. #10622495C22semidirect
52. #10622494C22semidirect
53. #10622418C22semidirect
54. #10622416C22semidirect
55. #10622348C22semidirect
56. #10622339C22semidirect
127. C11×#107C23semidirect
128. C11×#103C23semidirect
130. #66899C23semidirect
132. #66885C23semidirect
134. #66881C23semidirect
135. #66873C23semidirect
136. #66872C23semidirect
137. #66871C23semidirect
227. C2×#484D11semidirect
323. #484C2×D11semidirect
330. C2×#107C2×D11semidirect
335. C2×#103C2×D11semidirect
444. #107C22×D11semidirect
448. #103C22×D11semidirect
455. C2×C11#3092semidirect
546. C11C2×#3092semidirect
645. C2#13078543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C22×C4⋊C4×D112
#130785432
C2×#106226572
C2×#106223482
C2×#106225812
C2×#106224182
C2×#106224952
C2×#106224942
C2×#106224162
C2×#106223392
C2×C11×#4842
C2×#309211