Finite Group Databasebeta

← C2×#13078538 #15621550

Subgroups — C2×#13078538 #15621550

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×#10623137C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13078538C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic, complemented
7C2×#10622475C212yesmaximal, complemented
8C2×#10622387C212yesmaximal, complemented
9C2×#10622474C212yesmaximal, complemented
10C2×#10622384C212yesmaximal, complemented
11C2×#10622339C211yesmaximal, characteristic, complemented
12C2×C11×#481C211yesmaximal, characteristic, complemented
13C22×#4341C2211yescharacteristic
14C23×C4×D11—21no—
15C23×C4×D11C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×#66990—21no—
20C2×D4×Dic11—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C22×Dic11⋊C4—21no—
24C22×#4313C2212yes—
25#10623137—24no—
26#10623137C2218yes—
27C2×#66950C2211yescharacteristic
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×#66936—21no—
36C2×(C22⋊D11)⋊C4—21no—
37C11×#481C2218yescomplemented
38C2×C11×#106C2212yescomplemented
39C2×C11×#102C2212yescomplemented
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×#66896C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66882C2212yescomplemented
45C2×#66880C2212yescomplemented
46#10622647C2218yescomplemented
47#10622583C2218yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66872C2212yescomplemented
50C2×#66871C2212yescomplemented
51#10622475C22116yescomplemented
52#10622474C22116yescomplemented
53#10622387C22116yescomplemented
54#10622384C22116yescomplemented
55#10622339C2218yescomplemented
56#10622335C2218yescomplemented
57C24×D11D411yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C23×Dic11D411yescharacteristic
67C2×#4341—22no—
68C2×#4341—28no—
69C2×#4341C2314yes—
70C22×C4×D11—28no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—28no—
74C22×C4×D11—48no—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D414yes—
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2314yes—
80C22×C4×D11C2311yescharacteristic
81C22×Dic22C2311yescharacteristic
82C22×C8×C11C2312yes—
83C11×#121—22no—
84C11×#121C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93#66991—22no—
94#66991C2314yes—
95#66990—28no—
96D4×Dic11—28no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2311yescharacteristic
105#66977—22no—
106#66977C2314yes—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—28no—
111C2×C4×Dic11—21no—
112C22×C11⋊C8C2312yes—
113C2×#4313—28no—
114C2×#4313C2318yes—
115#66950—22no—
116#66950C2314yes—
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#66936—28no—
126(C22⋊D11)⋊C4—28no—
127C11×#106C2318yescomplemented
128C11×#102C2318yescomplemented
129C11×C22⋊C8C2314yes—
130#66896C2318yescomplemented
131C22⋊(C11⋊C8)C2314yes—
132(C2×D11)⋊C8C2318yes—
133#66882C2318yescomplemented
134#66880C2318yescomplemented
135#66874C2318yescomplemented
136#66872C2318yescomplemented
137#66871C2318yescomplemented
138C2×#3092—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—24no—
142C23×D11—24no—
143C23×D11—24no—
144C23×D11C2×D414yes—
145C23×D11C2×D411yescharacteristic
146C23×D11C2×D411yescharacteristic
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—24no—
150C2×D4×C11—44no—
151C2×D4×C11C2412yes—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—44no—
164C2×C22⋊D11—44no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—21no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—44no—
172C22×Dic11—44no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D414yes—
175C22×Dic11C2×D411yescharacteristic
176#4341—216no—
177#4341—48no—
178C2×C4×D11—24no—
179C2×C4×D11—216no—
180C2×C4×D11—216no—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—28no—
184C2×C4×D11—24no—
185C2×C4×D11—432no—
186C2×C4×D11—48no—
187C2×C4×D11—48no—
188C2×C4×D11C2×D414yes—
189C2×C4×D11C2×D414yes—
190C2×C4×D11C2×D412yes—
191C2×C4×D11C2×D412yes—
192C2×C4×D11#4118yes—
193C2×C4×D11C2412yes—
194C2×C4×D11C2412yes—
195C2×Dic22—21no—
196C2×Dic22—24no—
197C2×Dic22C2412yes—
198C2×C8×C11—24no—
199C2×C8×C11C2414yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4C2414yes—
204C11×C4⋊C4C2412yes—
205C11×C22⋊C4—24no—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—22no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2412yes—
215C4⋊Dic11C2414yes—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218Dic11⋊C4—24no—
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×#484—111no—
228C2×#481—111no—
229C2×#481D1111yescharacteristic, complemented
230C2×#483—112no—
231C2×#480—112no—
232C2×#428—112no—
233C2×#417—112no—
234C2×#407—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11#13714yes—
242C23×C11C22×D412yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—232no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—28no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—28no—
251C22×D11—28no—
252C22×D11#12314yes—
253C22×D11AGL(1,ℤ/8)14yes—
254C22×D11C22×D412yes—
255C22×D11C22×D412yes—
256D4×C11—24no—
257D4×C11—48no—
258D4×C11—42no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—48no—
265C2×C4×C11—44no—
266C2×C4×C11—42no—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4114yes—
270C2×C4×C11C2511yescharacteristic
271C22⋊D11—48no—
272C22⋊D11—48no—
273C2×Dic11—22no—
274C2×Dic11—28no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—48no—
279C2×Dic11—42no—
280C2×Dic11—44no—
281C2×Dic11—42no—
282C2×Dic11—48no—
283C2×Dic11#12314yes—
284C2×Dic11C22×D412yes—
285C2×Dic11C22×D412yes—
286C4×D11—28no—
287C4×D11—24no—
288C4×D11—24no—
289C4×D11—28no—
290C4×D11—416no—
291C4×D11—416no—
292C4×D11#12318yes—
293C4×D11C2×#4118yes—
294Dic22—24no—
295Dic22—42no—
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⋊Q8—111no—
307C2×#121—111no—
308C2×#121C2×D1111yescharacteristic
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#484—118no—
324#483—1116no—
325#481—118no—
326#481C2×D1118yescomplemented
327#480—1116no—
328#428—1116no—
329C2×#107—112no—
330C2×#107—112no—
331C2×#106—112no—
332C2×#106C2×D1112yescomplemented
333#417—1116no—
334C2×#103—112no—
335C2×#103—112no—
336C2×#102—112no—
337C2×#102C2×D1112yescomplemented
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×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—84no—
349C22×C11C2×#12312yes—
350C22×C11C2×AGL(1,ℤ/8)12yes—
351C22×C11C2×#13714yes—
352C22×C11C2×#13712yes—
353C22×C11C23×D411yescharacteristic
354C2×D11—232no—
355C2×D11—28no—
356C2×D11—28no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11C2×#12314yes—
362C2×D11C2×AGL(1,ℤ/8)14yes—
363C4×C11—22no—
364C4×C11—44no—
365C4×C11—42no—
366C4×C11C2×#12312yes—
367C4×C11C22×#4112yes—
368Dic11—22no—
369Dic11—42no—
370Dic11—44no—
371Dic11—42no—
372Dic11C2×#12314yes—
373C25—111no—
374C2×#41—114no—
375C2×#41—222no—
376C2×#41—228no—
377C22×Q8—111no—
378C22×D4—21no—
379C22×D4—221no—
380C22×D4—221no—
381C22×D4C22×D1111yescharacteristic
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—228no—
392C23×C4—222no—
393C23×C4—222no—
394C23×C4—221no—
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—114no—
404C22⋊Q8—114no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407#121—22no—
408#121—114no—
409#121—222no—
410#121C22×D1114yes—
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—112no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—118no—
422C2×C4⋊C4—118no—
423C2×C4⋊C4—224no—
424C2×C4⋊C4—228no—
425C2×C4⋊C4—224no—
426C2×C4⋊C4—228no—
427C2×C4⋊C4—228no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
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#107—118no—
445#106—118no—
446#106C22×D1118yescomplemented
447#103—118no—
448#103—118no—
449#102—118no—
450#102C22×D1118yescomplemented
451C22⋊C8—114no—
452C22⋊C8—118no—
453C22⋊C8C22×D1114yes—
454C2×C11—24no—
455C2×C11—82no—
456C2×C11#309214yescomplemented
457C2×C11C22×#12311yescharacteristic
458C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
459C2×C11C22×#13711yescharacteristic
460D11—24no—
461D11—24no—
462C24—21no—
463C24—111no—
464C24—111no—
465C24—114no—
466C24—224no—
467C24—224no—
468C24—224no—
469C24D4×D1111yescharacteristic
470#41—2216no—
471#41—448no—
472C2×Q8—112no—
473C2×Q8—221no—
474C2×Q8—224no—
475C2×D4—24no—
476C2×D4—21no—
477C2×D4—24no—
478C2×D4—44no—
479C2×D4—224no—
480C2×D4—224no—
481C2×D4—444no—
482C2×D4—444no—
483C2×D4C23×D1112yes—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—111no—
490C22×C4—112no—
491C22×C4—118no—
492C22×C4—112no—
493C22×C4—114no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—112no—
499C22×C4—224no—
500C22×C4—2216no—
501C22×C4—2216no—
502C22×C4—224no—
503C22×C4—228no—
504C22×C4—228no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—448no—
513C22×C4—4432no—
514C22×C4—448no—
515C22×C4—444no—
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—21no—
529C4⋊C4—114no—
530C4⋊C4—112no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—222no—
536C4⋊C4—221no—
537C4⋊C4—224no—
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—22no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—114no—
554C23—114no—
555C23—112no—
556C23—112no—
557C23—228no—
558C23—228no—
559C23—2232no—
560C23—228no—
561C23—222no—
562C23—222no—
563C23—222no—
564C23—222no—
565C23#6696814yes—
566C23C2×D4×D1112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—224no—
569Q8—442no—
570D4—24no—
571D4—48no—
572D4—42no—
573D4—448no—
574D4—448no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—114no—
584C2×C4—112no—
585C2×C4—118no—
586C2×C4—118no—
587C2×C4—112no—
588C2×C4—228no—
589C2×C4—228no—
590C2×C4—228no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—4416no—
598C2×C4—4416no—
599C2×C4—448no—
600C2×C4—448no—
601C2×C4—444no—
602C2×C4—442no—
603C2×C4—442no—
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—42no—
614C22—42no—
615C22—42no—
616C22—84no—
617C22—114no—
618C22—114no—
619C22—2232no—
620C22—228no—
621C22—228no—
622C22—222no—
623C22—222no—
624C22—222no—
625C22—222no—
626C22D11×#12312yes—
627C22C2×#6696814yes—
628C22C2×#6696812yes—
629C22D11×AGL(1,ℤ/8)12yes—
630C22C22×D4×D1111yescharacteristic
631C4—22no—
632C4—44no—
633C4—42no—
634C4—114no—
635C4—222no—
636C4—444no—
637C4—442no—
638C4—442no—
639C4D11×#12312yes—
640C4C2×#41×D1112yes—
641C2—24no—
642C2—82no—
643C2—224no—
644C2—224no—
645C2#1307853814yesdirect product factor
646C2C2×D11×#12311yescharacteristic
647C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
648C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
prime radicalC2×#10623137C2
hypercenterC2×#481D11
hypocenterC11C2×#3092
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13078538C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622647C2semidirect
7. C2×#10622475C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622474C2semidirect
10. C2×#10622384C2semidirect
11. C2×#10622339C2semidirect
12. C2×C11×#481C2semidirect
34. C2×C4⋊C4×D11C22semidirect
37. C11×#481C22semidirect
38. C2×C11×#106C22semidirect
39. C2×C11×#102C22semidirect
41. C2×#66896C22semidirect
44. C2×#66882C22semidirect
45. C2×#66880C22semidirect
46. #10622647C22semidirect
47. #10622583C22semidirect
48. C2×#66874C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
51. #10622475C22semidirect
52. #10622474C22semidirect
53. #10622387C22semidirect
54. #10622384C22semidirect
55. #10622339C22semidirect
56. #10622335C22semidirect
127. C11×#106C23semidirect
128. C11×#102C23semidirect
130. #66896C23semidirect
133. #66882C23semidirect
134. #66880C23semidirect
135. #66874C23semidirect
136. #66872C23semidirect
137. #66871C23semidirect
229. C2×#481D11semidirect
326. #481C2×D11semidirect
332. C2×#106C2×D11semidirect
337. C2×#102C2×D11semidirect
446. #106C22×D11semidirect
450. #102C22×D11semidirect
456. C2×C11#3092semidirect
546. C11C2×#3092semidirect
645. C2#13078538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231372
C22×C4⋊C4×D112
#130785382
C2×#106223352
C2×#106225832
C2×#106226472
C2×#106224752
C2×#106223872
C2×#106224742
C2×#106223842
C2×#106223392
C2×C11×#4812
C2×#309211