Finite Group Databasebeta

← C2×#13078083 #15620607

Subgroups — C2×#13078083 #15620607

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×#66968C212yesmaximal, complemented
2C2×#10623247C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
4#13078083C2116yesmaximal, direct product factor
5C2×#10622380C212yesmaximal, complemented
6C2×#10622779C212yesmaximal, complemented
7C2×#10622462C211yesmaximal, characteristic, complemented
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622688C211yesmaximal, characteristic, complemented
10C2×#10622450C211yesmaximal, characteristic, complemented
11C2×#10622384C212yesmaximal, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2211yescharacteristic
14C22×#4341C2212yes—
15C22×C11×SD16C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2212yes—
20C2×#66991—21no—
21C2×#66991—21no—
22C2×#66989C2212yes—
23C2×D4×Dic11—21no—
24C2×D4×Dic11—21no—
25C22×#4324C2212yes—
26C2×#66968—216no—
27C2×#66968C22116yescomplemented
28C22×Dic44C2212yes—
29C22×#4313C2212yes—
30#10623247—24no—
31#10623247C2218yes—
32C4×Q8×D11—24no—
33C4×Q8×D11C2218yescomplemented
34C2×C4⋊C4×D11—21no—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic
38C2×C42×D11—21no—
39C2×C42×D11C2211yescharacteristic
40C2×#66922C2211yescharacteristic
41C2×C4×Dic22—21no—
42C2×C4×Dic22C2211yescharacteristic
43C11×#460C2218yescomplemented
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×#102C2212yes—
46C2×#66896C2212yes—
47#10622779C22116yescomplemented
48C2×#66880C2212yes—
49C2×Dic11⋊C8C2212yes—
50#10622688C2218yescomplemented
51#10622644C2218yescomplemented
52C2×#66874C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622462C2218yescomplemented
55#10622450C2218yescomplemented
56#10622384C22116yescomplemented
57#10622380C22116yescomplemented
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2312yes—
62C22×C22⋊D11—22no—
63C23×Dic11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—24no—
66C2×Q8×D11D418yescomplemented
67C2×Q8×D11C2314yes—
68C2×#4341—28no—
69C2×#4341—24no—
70C2×#4341—28no—
71C2×#4341C2318yes—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22—21no—
78C22×Dic22C2312yes—
79C22×Dic22C2311yescharacteristic
80C2×C11×SD16—28no—
81C2×C11×SD16C2318yes—
82C22×C8×C11C2312yes—
83C11×#127—22no—
84C11×#127C2314yes—
85C4×Q8×C11—22no—
86C4×Q8×C11C2314yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93Q8×Dic11—22no—
94Q8×Dic11C2314yes—
95C2×#4326—28no—
96C2×#4326C2318yes—
97#66991—28no—
98#66991—28no—
99#66989—24no—
100#66989C2318yes—
101D4×Dic11—28no—
102D4×Dic11—28no—
103C2×#4324—28no—
104C2×#4324C2318yes—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D411yescharacteristic
116C2×C4×Dic11D411yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2312yes—
119#66968—264no—
120C2×Dic44—28no—
121C2×Dic44C2318yes—
122C2×#4313—28no—
123C2×#4313C2318yes—
124C4⋊C4×D11—28no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11C2314yes—
127#66940—28no—
128#66940—22no—
129#66940C2314yes—
130C42×D11—28no—
131C42×D11D414yes—
132C42×D11C2314yes—
133#66922—22no—
134#66922C2314yes—
135C4×Dic22—22no—
136C4×Dic22—28no—
137C4×Dic22C2314yes—
138C11×C4⋊C8C2314yes—
139C11×#102C2318yes—
140#66896C2318yes—
141#66880C2318yes—
142Dic11⋊C8C2318yes—
143#66874C2318yes—
144C4⋊(C11⋊C8)C2314yes—
145C2×#3037—111nomaximal, Sylow
146C24×C11—22no—
147C23×D11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11C2×D414yes—
151C2×Q8×C11C2412yes—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—22no—
156C2×D4×C11—24no—
157C2×D4×C11—44no—
158C2×D4×C11—44no—
159C2×D4×C11C2414yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—28no—
166C2×C22⋊D11—48no—
167C22×Dic11—28no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—48no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175Q8×D11—216no—
176Q8×D11—28no—
177Q8×D11C2×D4116yescomplemented
178#4341—216no—
179#4341—216no—
180#4341—416no—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—42no—
186C2×C4×D11—44no—
187C2×C4×D11C2×D414yes—
188C2×C4×D11C2×D414yes—
189C2×C4×D11C2×D414yes—
190C2×C4×D11C2×D412yes—
191C2×C4×D11#4114yes—
192C2×C4×D11C2412yes—
193C2×Dic22—28no—
194C2×Dic22—24no—
195C2×Dic22—21no—
196C2×Dic22—24no—
197C2×Dic22—22no—
198C2×Dic22—22no—
199C2×Dic22—24no—
200C2×Dic22C2×D414yes—
201C2×Dic22C2414yes—
202C2×Dic22C2412yes—
203C11×SD16—216no—
204C2×C8×C11—24no—
205C2×C8×C11C2414yes—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C2412yes—
209C42×C11—24no—
210C42×C11C2×D412yes—
211C42×C11C2412yes—
212C22⋊Dic11—28no—
213C22⋊Dic11—28no—
214#4326—216no—
215#4324—216no—
216C4⋊Dic11—24no—
217C4⋊Dic11—21no—
218C4⋊Dic11—24no—
219C4⋊Dic11—24no—
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—
233Dic44—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×#462—111no—
243C2×#460—111no—
244C2×#460D1111yescharacteristic, complemented
245C2×#423—111no—
246C2×#417—112no—
247C23×C11—24no—
248C23×C11—44no—
249C23×C11—44no—
250C23×C11—44no—
251C23×C11C22×D411yescharacteristic
252C22×D11—22no—
253C22×D11—22no—
254C22×D11#12114yes—
255C22×D11C22×D412yes—
256Q8×C11—24no—
257Q8×C11—22no—
258Q8×C11C22×D414yes—
259D4×C11—24no—
260D4×C11—24no—
261D4×C11—48no—
262D4×C11—44no—
263D4×C11—48no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
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
276C22⋊D11—416no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—44no—
284C2×Dic11—42no—
285C2×Dic11—416no—
286C2×Dic11#12114yes—
287C2×Dic11C22×D412yes—
288C2×Dic11C22×D412yes—
289C2×Dic11C22×D412yes—
290C4×D11—216no—
291C4×D11—28no—
292C4×D11—44no—
293C4×D11—48no—
294C4×D11#12118yes—
295C4×D11C22×D414yes—
296C4×D11C2×#4114yes—
297Dic22—24no—
298Dic22—22no—
299Dic22—216no—
300Dic22—24no—
301Dic22—24no—
302Dic22—44no—
303Dic22C22×D414yes—
304C8×C11—24no—
305C11⋊C8—24no—
306C22×#41—112no—
307C23×Q8—111no—
308C2×#137—1116no—
309C2×#137—2216no—
310C22×Q16—112no—
311C22×Q16—112no—
312C22×SD16—112no—
313C22×SD16C2×D1112yes—
314C22×M16—112no—
315#532—118no—
316#532—224no—
317C2×C4⋊Q8—111no—
318C2×#127C2×D1111yescharacteristic
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#462—118no—
340#460—118no—
341#460C2×D1118yescomplemented
342#423—118no—
343C2×C4⋊C8—112no—
344C2×C4⋊C8—111no—
345C2×C4⋊C8C2×D1111yescharacteristic
346#417—1116no—
347C2×#103—112no—
348C2×#103—112no—
349C2×#102—112no—
350C2×#102C2×D1112yes—
351C22×C11—44no—
352C22×C11—44no—
353C22×C11—44no—
354C22×C11—88no—
355C22×C11C2×#12112yes—
356C22×C11C2×#13712yes—
357C22×C11#57512yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—28no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11C2×#12114yes—
363C4×C11—24no—
364C4×C11—22no—
365C4×C11—42no—
366C4×C11C2×#12112yes—
367C4×C11C2×#13714yescomplemented
368C4×C11C23×D411yescharacteristic
369C4×C11C22×#4111yescharacteristic
370Dic11—24no—
371Dic11—22no—
372Dic11—22no—
373Dic11—44no—
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—112no—
384C22×Q8—221no—
385C22×Q8—222no—
386C22×Q8—224no—
387C22×Q8C22×D1111yescharacteristic
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—222no—
391C22×D4C22×D1112yes—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—222no—
398#137—2264no—
399C2×Q16—118no—
400C2×Q16—118no—
401C2×Q16—228no—
402C2×Q16—228no—
403C2×SD16—28no—
404C2×SD16—118no—
405C2×SD16—228no—
406C2×SD16C22×D1118yes—
407C2×M16—118no—
408C2×M16—228no—
409C22×C8—112no—
410C22×C8C22×D1112yes—
411C4⋊Q8—114no—
412C4⋊Q8—222no—
413#127—22no—
414#127C22×D1114yes—
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—111no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
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#103—118no—
461#102—118no—
462#102C22×D1118yes—
463C2×C11—84no—
464C2×C11#303714yescomplemented
465C2×C11C22×#12111yescharacteristic
466C2×C11C22×#13711yescharacteristic
467C2×C11C2×#57511yescharacteristic
468D11—24no—
469C24—22no—
470C24—111no—
471#41—2216no—
472#41—2216no—
473#41—4416no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—1116no—
477C2×Q8—114no—
478C2×Q8—112no—
479C2×Q8—114no—
480C2×Q8—224no—
481C2×Q8—228no—
482C2×Q8—2216no—
483C2×Q8—228no—
484C2×Q8—221no—
485C2×Q8—222no—
486C2×Q8—222no—
487C2×Q8—224no—
488C2×Q8—224no—
489C2×Q8D4×D1114yes—
490C2×Q8C23×D1112yes—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—22no—
495C2×D4—24no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—228no—
499C2×D4—448no—
500C2×D4C23×D1114yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—111no—
504C22×C4—112no—
505C22×C4—114no—
506C22×C4—114no—
507C22×C4—112no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—224no—
513C22×C4—228no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—221no—
517C22×C4—224no—
518C22×C4—221no—
519C22×C4—222no—
520C22×C4—442no—
521C22×C4—444no—
522C22×C4—448no—
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526Q16—2216no—
527Q16—2216no—
528SD16—216no—
529SD16—2216no—
530M16—2216no—
531C2×C8—24no—
532C2×C8—114no—
533C2×C8—224no—
534C2×C8C23×D1114yes—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—112no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—221no—
542C4⋊C4—224no—
543C4⋊C4—224no—
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—24no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—114no—
564C23—112no—
565C23—222no—
566C23—222no—
567C23C2×D4×D1111yescharacteristic
568Q8—24no—
569Q8—22no—
570Q8—114no—
571Q8—2216no—
572Q8—224no—
573Q8—222no—
574Q8—224no—
575Q8—224no—
576Q8—444no—
577Q8C2×D4×D1114yes—
578D4—24no—
579D4—24no—
580D4—48no—
581D4—48no—
582D4—44no—
583D4—4416no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—114no—
590C2×C4—112no—
591C2×C4—118no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—2216no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—228no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—444no—
605C2×C4—448no—
606C2×C4—4416no—
607C2×C4—442no—
608C2×C4—444no—
609C2×C4#6696814yescomplemented
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—44no—
619C22—44no—
620C22—44no—
621C22—88no—
622C22—114no—
623C22—228no—
624C22—222no—
625C22—222no—
626C22D11×#12112yes—
627C22C2×#6696812yes—
628C22#1062330412yes—
629C22C22×D4×D1111yescharacteristic
630C4—22no—
631C4—24no—
632C4—42no—
633C4—114no—
634C4—222no—
635C4—222no—
636C4—224no—
637C4—442no—
638C4—444no—
639C4D11×#12112yes—
640C4C2×#6696814yescomplemented
641C4C22×D4×D1111yescharacteristic
642C4C2×#41×D1111yescharacteristic
643C2—84no—
644C2—224no—
645C2#1307808314yesdirect product factor
646C2C2×D11×#12111yescharacteristic
647C2C22×#6696811yescharacteristic
648C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×#10623247C2
hypercenterC2×#460D11
hypocenterC11C2×#3037
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
3. C2×C4×Q8×D11C2semidirect
4. #13078083C2direct (N × H)
5. C2×#10622380C2semidirect
6. C2×#10622779C2semidirect
7. C2×#10622462C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622688C2semidirect
10. C2×#10622450C2semidirect
11. C2×#10622384C2semidirect
12. C2×C11×#460C2semidirect
27. C2×#66968C22semidirect
33. C4×Q8×D11C22semidirect
43. C11×#460C22semidirect
47. #10622779C22semidirect
50. #10622688C22semidirect
51. #10622644C22semidirect
54. #10622462C22semidirect
55. #10622450C22semidirect
56. #10622384C22semidirect
57. #10622380C22semidirect
66. C2×Q8×D11D4semidirect
177. Q8×D11C2×D4semidirect
244. C2×#460D11semidirect
269. C2×C4×C11#137semidirect
341. #460C2×D11semidirect
367. C4×C11C2×#137semidirect
464. C2×C11#3037semidirect
558. C11C2×#3037semidirect
609. C2×C4#66968semidirect
640. C4C2×#66968semidirect
645. C2#13078083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C2×#106232472
C2×C4×Q8×D112
#130780832
C2×#106223802
C2×#106227792
C2×#106224622
C2×#106226442
C2×#106226882
C2×#106224502
C2×#106223842
C2×C11×#4602
C2×#303711