Finite Group Databasebeta

← C2×#13078089 #15620613

Subgroups — C2×#13078089 #15620613

Order 2816.

2810 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
1C22×#66971C212yesmaximal, complemented
2C2×#10623256C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
4#13078089C2116yesmaximal, direct product factor
5C2×#10622411C212yesmaximal, complemented
6C2×#10622798C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622461C211yesmaximal, characteristic, complemented
9C2×#10622640C211yesmaximal, characteristic, complemented
10C2×#10622450C211yesmaximal, characteristic, complemented
11C2×#10622416C212yesmaximal, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×Q8×D11C2211yescharacteristic
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2212yes—
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2212yes—
21C22×#4325C2212yes—
22C2×#66971—216no—
23C2×#66971C22116yescomplemented
24C22×#4314C2212yes—
25C22×#4313C2212yes—
26#10623256—24no—
27#10623256C2218yes—
28C4×Q8×D11—24no—
29C4×Q8×D11C2218yescomplemented
30C2×#66948—21no—
31C2×#66948—21no—
32C2×#66946—21no—
33C2×#66946—21no—
34C2×C4⋊C4×D11—21no—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic
38C2×#66927C2211yescharacteristic
39C2×C42×D11—21no—
40C2×C42×D11C2211yescharacteristic
41C2×C4×Dic22—21no—
42C2×C4×Dic22C2211yescharacteristic
43C11×#462C2218yescomplemented
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×#103C2212yes—
46C2×#66899C2212yes—
47#10622798C22116yescomplemented
48C2×#66885C2212yes—
49C2×Dic11⋊C8C2212yes—
50#10622703C2218yescomplemented
51#10622640C2218yescomplemented
52C2×#66873C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622461C2218yescomplemented
55#10622450C2218yescomplemented
56#10622416C22116yescomplemented
57#10622411C22116yescomplemented
58C22×Q8×C11C2312yes—
59C22×Q8×C11C2311yescharacteristic
60C2×#4343—24no—
61C2×#4343—28no—
62C2×#4343—28no—
63C2×#4343C2318yes—
64C2×Q8×D11—22no—
65C2×Q8×D11—24no—
66C2×Q8×D11D418yescomplemented
67C2×Q8×D11C2314yes—
68C22×D44—22no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2312yes—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22—21no—
79C22×Dic22C2311yescharacteristic
80C2×C11×Q16—28no—
81C2×C11×Q16C2318yes—
82C22×C8×C11C2312yes—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8C2314yes—
85C4×Q8×C11—22no—
86C4×Q8×C11C2314yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93#67000—24no—
94#67000C2318yes—
95Q8×Dic11—22no—
96Q8×Dic11C2314yes—
97C2×#4326—28no—
98C2×#4326C2318yes—
99C2×#4325—28no—
100C2×#4325C2318yes—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115#66971—264no—
116C2×#4314—28no—
117C2×#4314C2318yes—
118C2×#4313—28no—
119C2×#4313C2318yes—
120#66948—28no—
121#66948—28no—
122#66946—28no—
123#66946—28no—
124C4⋊C4×D11—28no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11C2314yes—
127#66940—28no—
128#66940—22no—
129#66940C2314yes—
130#66927—22no—
131#66927C2314yes—
132C42×D11—28no—
133C42×D11D414yes—
134C42×D11C2314yes—
135C4×Dic22—22no—
136C4×Dic22—28no—
137C4×Dic22C2314yes—
138C11×C4⋊C8C2314yes—
139C11×#103C2318yes—
140#66899C2318yes—
141#66885C2318yes—
142Dic11⋊C8C2318yes—
143#66873C2318yes—
144C4⋊(C11⋊C8)C2314yes—
145C2×#3037—111nomaximal, Sylow
146C23×D11—22no—
147C23×D11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11C2×D414yes—
154C2×Q8×C11C2414yes—
155C2×Q8×C11C2412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4343—216no—
168#4343—216no—
169#4343—416no—
170Q8×D11—216no—
171Q8×D11—28no—
172Q8×D11C2×D4116yescomplemented
173C2×D44—28no—
174C2×D44—22no—
175C2×D44—24no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—24no—
179C2×D44—44no—
180C2×D44—48no—
181C2×D44—44no—
182C2×D44C2414yes—
183C2×C4×D11—28no—
184C2×C4×D11—28no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—42no—
189C2×C4×D11—44no—
190C2×C4×D11—48no—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2×D414yes—
193C2×C4×D11C2×D414yes—
194C2×C4×D11C2×D412yes—
195C2×C4×D11#4114yes—
196C2×C4×D11C2412yes—
197C2×Dic22—28no—
198C2×Dic22—24no—
199C2×Dic22—21no—
200C2×Dic22—22no—
201C2×Dic22C2×D414yes—
202C2×Dic22C2412yes—
203C11×Q16—216no—
204C2×C8×C11—24no—
205C2×C8×C11C2414yes—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4C2412yes—
211C42×C11—24no—
212C42×C11C2×D412yes—
213C42×C11C2412yes—
214#4326—216no—
215#4325—216no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218C4⋊Dic11—24no—
219C4⋊Dic11—21no—
220C4⋊Dic11C2412yes—
221Dic11⋊C4—24no—
222Dic11⋊C4—24no—
223Dic11⋊C4—24no—
224C4×Dic11—24no—
225C4×Dic11—24no—
226C4×Dic11—24no—
227C4×Dic11C2×D414yes—
228C4×Dic11C2×D412yes—
229C4×Dic11C2×D414yes—
230C4×Dic11C2412yes—
231C2×C11⋊C8—24no—
232C2×C11⋊C8C2414yes—
233#4314—216no—
234#4313—216no—
235C22×#137—112no—
236C2×#532—111no—
237C22×C4×Q8—111no—
238#3037—1116no—
239C2×#464—112no—
240C2×#464—112no—
241C2×#462—111no—
242C2×#462D1111yescharacteristic, complemented
243C2×#460—111no—
244C2×#460—111no—
245C2×#423—111no—
246C2×#417—112no—
247C23×C11C22×D411yescharacteristic
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—24no—
251C22×D11—44no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11#12114yes—
255C22×D11C22×D412yes—
256Q8×C11—24no—
257Q8×C11—22no—
258Q8×C11—24no—
259Q8×C11—24no—
260Q8×C11—44no—
261Q8×C11C22×D414yes—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11#13714yescomplemented
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2511yescharacteristic
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—42no—
282C2×Dic11#12114yes—
283C2×Dic11C22×D412yes—
284C2×Dic11C22×D412yes—
285C2×Dic11C22×D412yes—
286D44—24no—
287D44—24no—
288D44—48no—
289D44—416no—
290D44—44no—
291D44—48no—
292C4×D11—216no—
293C4×D11—28no—
294C4×D11—44no—
295C4×D11—48no—
296C4×D11—416no—
297C4×D11#12118yes—
298C4×D11C22×D414yes—
299C4×D11C2×#4114yes—
300Dic22—24no—
301Dic22—22no—
302Dic22—216no—
303Dic22C22×D414yes—
304C8×C11—24no—
305C11⋊C8—24no—
306C22×#41—112no—
307C23×Q8—111no—
308C2×#137—1116no—
309C2×#137—2216no—
310C22×Q16—112no—
311C22×Q16C2×D1112yes—
312C22×SD16—112no—
313C22×SD16—112no—
314C22×M16—112no—
315#532—118no—
316#532—224no—
317C2×C4⋊Q8C2×D1111yescharacteristic
318C2×#127—111no—
319C2×#124—112no—
320C2×#121—221no—
321C2×#121—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—118no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8—221no—
327C2×C4×Q8—221no—
328C2×C4×Q8—224no—
329C2×C4×Q8C2×D1111yescharacteristic
330C2×C4×D4—221no—
331C2×C4×D4—221no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4—221no—
334C22×C42—111no—
335C22×C42—221no—
336#464—1116no—
337#464—1116no—
338#462—118no—
339#462C2×D1118yescomplemented
340#460—118no—
341#460—118no—
342#423—118no—
343C2×C4⋊C8—112no—
344C2×C4⋊C8—111no—
345C2×C4⋊C8C2×D1111yescharacteristic
346#417—1116no—
347C2×#103—112no—
348C2×#103C2×D1112yes—
349C2×#102—112no—
350C2×#102—112no—
351C22×C11C2×#12112yes—
352C22×C11C2×#13712yes—
353C22×C11#57512yes—
354C22×C11C23×D411yescharacteristic
355C2×D11—28no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—88no—
362C2×D11C2×#12114yes—
363C4×C11—24no—
364C4×C11—22no—
365C4×C11—44no—
366C4×C11—42no—
367C4×C11C2×#12112yes—
368C4×C11C2×#13714yescomplemented
369C4×C11C23×D411yescharacteristic
370C4×C11C22×#4111yescharacteristic
371Dic11—24no—
372Dic11—22no—
373Dic11—22no—
374Dic11—42no—
375Dic11C2×#12114yes—
376C2×#41—118no—
377C2×#41—224no—
378C2×#41—228no—
379C2×#41—228no—
380C22×Q8—118no—
381C22×Q8—114no—
382C22×Q8—111no—
383C22×Q8—221no—
384C22×Q8—222no—
385C22×Q8—224no—
386C22×Q8C22×D1112yes—
387C22×Q8C22×D1111yescharacteristic
388C22×D4—112no—
389C22×D4—222no—
390C22×D4—221no—
391C22×D4—221no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—222no—
396C23×C4—221no—
397C23×C4—221no—
398#137—2264no—
399C2×Q16—28no—
400C2×Q16—118no—
401C2×Q16—228no—
402C2×Q16C22×D1118yes—
403C2×SD16—118no—
404C2×SD16—118no—
405C2×SD16—228no—
406C2×SD16—228no—
407C2×M16—118no—
408C2×M16—228no—
409C22×C8—112no—
410C22×C8C22×D1112yes—
411C4⋊Q8—22no—
412C4⋊Q8C22×D1114yes—
413#127—114no—
414#127—222no—
415#124—118no—
416#124—224no—
417#121—228no—
418#121—228no—
419C4×Q8—22no—
420C4×Q8—114no—
421C4×Q8—114no—
422C4×Q8—114no—
423C4×Q8—228no—
424C4×Q8—228no—
425C4×Q8—222no—
426C4×Q8—222no—
427C4×Q8—222no—
428C4×Q8C22×D1114yes—
429C4×D4—228no—
430C4×D4—228no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—228no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—222no—
444C2×C22⋊C4—222no—
445C2×C42—21no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42—228no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42—221no—
455C2×C42C22×D1111yescharacteristic
456C4⋊C8—118no—
457C4⋊C8—114no—
458C4⋊C8C22×D1114yes—
459#103—118no—
460#103C22×D1118yes—
461#102—118no—
462#102—118no—
463C2×C11#303714yescomplemented
464C2×C11C22×#12111yescharacteristic
465C2×C11C22×#13711yescharacteristic
466C2×C11C2×#57511yescharacteristic
467D11—24no—
468D11—84no—
469C24—111no—
470C24—222no—
471#41—2216no—
472#41—2216no—
473#41—4416no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—1116no—
480C2×Q8—114no—
481C2×Q8—112no—
482C2×Q8—224no—
483C2×Q8—228no—
484C2×Q8—2216no—
485C2×Q8—228no—
486C2×Q8—221no—
487C2×Q8—222no—
488C2×Q8D4×D1114yes—
489C2×Q8C23×D1114yes—
490C2×Q8C23×D1112yes—
491C2×D4—114no—
492C2×D4—228no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—222no—
497C2×D4—224no—
498C2×D4—444no—
499C2×D4—448no—
500C2×D4—444no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—114no—
512C22×C4—114no—
513C22×C4—228no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—224no—
517C22×C4—221no—
518C22×C4—224no—
519C22×C4—221no—
520C22×C4—442no—
521C22×C4—448no—
522C22×C4—444no—
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526Q16—216no—
527Q16—2216no—
528SD16—2216no—
529SD16—2216no—
530M16—2216no—
531C2×C8—24no—
532C2×C8—114no—
533C2×C8—224no—
534C2×C8C23×D1114yes—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—112no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4—224no—
545C4⋊C4C23×D1112yes—
546C22⋊C4—228no—
547C22⋊C4—228no—
548C42—24no—
549C42—114no—
550C42—114no—
551C42—112no—
552C42—112no—
553C42—224no—
554C42—224no—
555C42—224no—
556C42D4×D1112yes—
557C42C23×D1112yes—
558C11C2×#303711yescharacteristic, complemented, Sylow
559C23—114no—
560C23—112no—
561C23—222no—
562C23—222no—
563C23—224no—
564C23—444no—
565C23—444no—
566C23—444no—
567C23C2×D4×D1111yescharacteristic
568Q8—24no—
569Q8—22no—
570Q8—24no—
571Q8—24no—
572Q8—44no—
573Q8—114no—
574Q8—2216no—
575Q8—224no—
576Q8—222no—
577Q8C2×D4×D1114yes—
578D4—224no—
579D4—224no—
580D4—448no—
581D4—4416no—
582D4—448no—
583D4—444no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—114no—
592C2×C4—112no—
593C2×C4—118no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—2216no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—228no—
604C2×C4—222no—
605C2×C4—444no—
606C2×C4—4416no—
607C2×C4—448no—
608C2×C4—442no—
609C2×C4#6697114yescomplemented
610C2×C4C2×D4×D1112yes—
611C2×C4C2×D4×D1112yes—
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4C2×D4×D1112yes—
614C2×C4#41×D1112yes—
615C2×C4C24×D1111yescharacteristic
616C8—24no—
617C8—224no—
618C22—114no—
619C22—228no—
620C22—222no—
621C22—222no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—888no—
626C22D11×#12112yes—
627C22C2×#6697112yes—
628C22#1062330812yes—
629C22C22×D4×D1111yescharacteristic
630C4—22no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—114no—
635C4—222no—
636C4—222no—
637C4—224no—
638C4—442no—
639C4D11×#12112yes—
640C4C2×#6697114yescomplemented
641C4C22×D4×D1111yescharacteristic
642C4C2×#41×D1111yescharacteristic
643C2—224no—
644C2—884no—
645C2#1307808914yesdirect product factor
646C2C2×D11×#12111yescharacteristic
647C2C22×#6697111yescharacteristic
648C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#462D11
hypocenterC11C2×#3037
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
3. C2×C4×Q8×D11C2semidirect
4. #13078089C2direct (N × H)
5. C2×#10622411C2semidirect
6. C2×#10622798C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622461C2semidirect
9. C2×#10622640C2semidirect
10. C2×#10622450C2semidirect
11. C2×#10622416C2semidirect
12. C2×C11×#462C2semidirect
23. C2×#66971C22semidirect
29. C4×Q8×D11C22semidirect
43. C11×#462C22semidirect
47. #10622798C22semidirect
50. #10622703C22semidirect
51. #10622640C22semidirect
54. #10622461C22semidirect
55. #10622450C22semidirect
56. #10622416C22semidirect
57. #10622411C22semidirect
66. C2×Q8×D11D4semidirect
172. Q8×D11C2×D4semidirect
242. C2×#462D11semidirect
269. C2×C4×C11#137semidirect
339. #462C2×D11semidirect
368. C4×C11C2×#137semidirect
463. C2×C11#3037semidirect
558. C11C2×#3037semidirect
609. C2×C4#66971semidirect
640. C4C2×#66971semidirect
645. C2#13078089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×#106232562
C2×C4×Q8×D112
#130780892
C2×#106224112
C2×#106227982
C2×#106227032
C2×#106224612
C2×#106226402
C2×#106224502
C2×#106224162
C2×C11×#4622
C2×#303711