Finite Group Databasebeta

← C2×#13079602 #15625019

Subgroups — C2×#13079602 #15625019

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic, complemented
2C22×#67000C211yesmaximal, characteristic, complemented
3#13079602C2116yesmaximal, direct product factor
4C2×#10622789C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622432C212yesmaximal, complemented
7C2×#10622778C212yesmaximal, complemented
8C2×#10622840C211yesmaximal, characteristic, complemented
9C2×#10622345C211yesmaximal, characteristic, complemented
10C2×#10622649C211yesmaximal, characteristic, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#448C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4341—21no—
15C23×D44C2211yescharacteristic
16C22×C11×SD16C2212yescomplemented
17C2×C11×#121C2211yescharacteristic
18C2×#67000—21no—
19C2×#67000—21no—
20C2×#67000—24no—
21C2×#67000C2212yes—
22C2×#67000C2212yes—
23C2×#67000C2218yescomplemented
24C22×#4325C2212yescomplemented
25C2×#66993C2211yescharacteristic, complemented
26C2×#66992—21no—
27C2×D4×Dic11C2211yescharacteristic, complemented
28C22×#4323C2212yes—
29C2×#66983C2211yescharacteristic
30C22×(C2×D11)⋊C4—21no—
31C22×(C2×D11)⋊C4—21no—
32C22×C4×Dic11C2211yescharacteristic
33C22×D88C2212yes—
34#10623127—24no—
35#10623127C2218yescomplemented
36C2×#66946C2211yescharacteristic, complemented
37C2×#66941C2211yescharacteristic, complemented
38C2×#66938—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C11×#448C2218yescomplemented
41C2×C11×#103C2212yescomplemented
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622840C2218yescomplemented
44C2×#66899C2212yescomplemented
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622789C22116yescomplemented
47#10622778C22116yescomplemented
48C2×#66885C2212yes—
49C2×#66879C2212yescomplemented
50C2×Dic11⋊C8C2212yescomplemented
51#10622649C2218yescomplemented
52C2×#66873C2212yes—
53#10622432C22116yescomplemented
54#10622408C22116yescomplemented
55#10622345C2218yescomplemented
56#10622332C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11—44no—
61C22×Q8×C11C2312yes—
62C22×Q8×C11C2314yes—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11D411yescharacteristic
72C23×Dic11D411yescharacteristic
73C2×#4341—28no—
74C2×#4341—48no—
75C22×D44—21no—
76C22×D44—22no—
77C22×D44—44no—
78C22×D44C2312yes—
79C22×D44C2311yescharacteristic
80C22×D44C2314yes—
81C22×C4×D11—21no—
82C22×Dic22—21no—
83C2×C11×SD16—44no—
84C2×C11×SD16C2318yescomplemented
85C22×C8×C11C2312yes—
86C11×#121—22no—
87C11×#121C2314yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91#67000—24no—
92#67000—24no—
93#67000—28no—
94#67000—28no—
95#67000C2318yes—
96#67000C2318yes—
97C2×#4325—44no—
98C2×#4325C2318yescomplemented
99#66993—22no—
100#66993C2314yescomplemented
101#66992—28no—
102D4×Dic11—22no—
103D4×Dic11C2314yescomplemented
104C2×#4323—44no—
105C2×#4323C2318yes—
106#66983—22no—
107#66983C2314yes—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—28no—
115C2×(C2×D11)⋊C4—28no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11D411yescharacteristic
119C2×C4×Dic11D411yescharacteristic
120C2×C4×Dic11D414yes—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2314yes—
124C22×C11⋊C8C2312yes—
125C2×D88—44no—
126C2×D88C2318yes—
127#66946—22no—
128#66946C2314yescomplemented
129#66941—22no—
130#66941C2314yescomplemented
131#66938—28no—
132(C22⋊D11)⋊C4—28no—
133C11×#103C2318yescomplemented
134C11×C22⋊C8C2314yes—
135#66899C2318yescomplemented
136C22⋊(C11⋊C8)C2314yes—
137#66885C2318yes—
138#66879C2318yescomplemented
139Dic11⋊C8C2318yescomplemented
140#66873C2318yes—
141C2×#3213—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—24no—
145C23×D11—22no—
146C23×D11—21no—
147C23×D11—44no—
148C23×D11—44no—
149C23×D11—44no—
150C2×Q8×C11—24no—
151C2×Q8×C11—22no—
152C2×Q8×C11—24no—
153C2×Q8×C11—24no—
154C2×Q8×C11—48no—
155C2×Q8×C11—44no—
156C2×Q8×C11—48no—
157C2×Q8×C11C2414yes—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11—24no—
161C2×D4×C11—44no—
162C2×D4×C11C2412yes—
163C22×C4×C11—24no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—44no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—44no—
176C2×C22⋊D11—44no—
177C2×C22⋊D11—44no—
178C22×Dic11—24no—
179C22×Dic11—24no—
180C22×Dic11—21no—
181C22×Dic11—42no—
182C22×Dic11—44no—
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D414yes—
188C22×Dic11C2×D414yes—
189#4341—432no—
190C2×D44—21no—
191C2×D44—24no—
192C2×D44—22no—
193C2×D44—24no—
194C2×D44—24no—
195C2×D44—24no—
196C2×D44—48no—
197C2×D44—44no—
198C2×D44—48no—
199C2×D44C2414yes—
200C2×D44C2412yes—
201C2×C4×D11—24no—
202C2×C4×D11—44no—
203C2×Dic22—24no—
204C2×Dic22—44no—
205C11×SD16—48no—
206C2×C8×C11—24no—
207C2×C8×C11C2414yes—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C2412yes—
210C11×C22⋊C4—24no—
211C22⋊Dic11—24no—
212#4325—48no—
213#4323—48no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—28no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—24no—
220C4⋊Dic11—21no—
221C4⋊Dic11C2412yes—
222Dic11⋊C4—24no—
223C4×Dic11C2×D414yes—
224C4×Dic11C2×D414yes—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227C4×Dic11C2412yes—
228C4×Dic11C2412yes—
229C2×C11⋊C8—24no—
230C2×C11⋊C8C2414yes—
231D88—48no—
232C2×#532—111no—
233C22×#124—111no—
234#3213—1116no—
235C2×#496—112no—
236C2×#489—112no—
237C2×#463—112no—
238C2×#463—112no—
239C2×#448—111no—
240C2×#448D1111yescharacteristic, complemented
241C2×#447—111no—
242C2×#447—111no—
243C2×#432—111no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11AGL(1,ℤ/8)14yes—
251C23×C11C22×D412yes—
252C23×C11C22×D411yescharacteristic
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—48no—
256C22×D11—48no—
257C22×D11—44no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—48no—
261C22×D11—44no—
262C22×D11—42no—
263C22×D11—44no—
264C22×D11—816no—
265Q8×C11—24no—
266Q8×C11—24no—
267Q8×C11—48no—
268Q8×C11—44no—
269D4×C11—24no—
270D4×C11—48no—
271D4×C11—42no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—48no—
278C2×C4×C11—44no—
279C2×C4×C11—42no—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11H(5,𝔽2)14yes—
283C2×C4×C11C2511yescharacteristic
284C22⋊D11—48no—
285C22⋊D11—48no—
286C22⋊D11—48no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—28no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—44no—
294C2×Dic11—48no—
295C2×Dic11—42no—
296C2×Dic11C22×D412yes—
297C2×Dic11C22×D412yes—
298C2×Dic11C22×D412yes—
299C2×Dic11C22×D412yes—
300D44—24no—
301D44—24no—
302D44—24no—
303D44—48no—
304D44—42no—
305D44—44no—
306C4×D11—48no—
307Dic22—48no—
308C8×C11—24no—
309C11⋊C8—24no—
310C22×#41—221no—
311C23×Q8C2×D1111yescharacteristic
312C23×D4—111no—
313C22×SD16—112no—
314C22×SD16C2×D1112yescomplemented
315C22×D8—112no—
316C22×D8—112no—
317#532—118no—
318#532—224no—
319C2×C4⋊Q8—111no—
320C2×#127—111no—
321C2×#124—112no—
322C2×#124—112no—
323C2×#124—118no—
324C2×#124—221no—
325C2×#124—221no—
326C2×#124—221no—
327C2×#124—224no—
328C2×#121—111no—
329C2×#121—221no—
330C2×#121C2×D1111yescharacteristic
331C2×C4×D4—111no—
332C2×C4×D4—111no—
333C2×C4×D4—221no—
334C22×C22⋊C4—221no—
335C22×C22⋊C4—221no—
336C22×C42—111no—
337#496—1116no—
338#489—1116no—
339#463—1116no—
340#463—1116no—
341#448—118no—
342#448C2×D1118yescomplemented
343#447—118no—
344#447—118no—
345#432—118no—
346C2×C4⋊C8—112no—
347C2×#103—112no—
348C2×#103C2×D1112yescomplemented
349C2×#102—112no—
350C2×#102—112no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8C2×D1111yescharacteristic
353C2×#97—112no—
354C22×C11—22no—
355C22×C11—28no—
356C22×C11—22no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—84no—
361C22×C11#53512yes—
362C22×C11C2×AGL(1,ℤ/8)14yes—
363C22×C11C2×AGL(1,ℤ/8)12yes—
364C22×C11#57512yes—
365C22×C11C23×D411yescharacteristic
366C2×D11—44no—
367C2×D11—42no—
368C2×D11—44no—
369C2×D11—42no—
370C2×D11—44no—
371C2×D11—42no—
372C2×D11—816no—
373C2×D11—84no—
374C2×D11—88no—
375C4×C11—22no—
376C4×C11—44no—
377C4×C11—42no—
378C4×C11#53512yes—
379C4×C11C2×H(5,𝔽2)12yes—
380Dic11—22no—
381Dic11—22no—
382Dic11—22no—
383Dic11—22no—
384Dic11—42no—
385C25—221no—
386C2×#41—228no—
387C2×#41—448no—
388C22×Q8—22no—
389C22×Q8—21no—
390C22×Q8—44no—
391C22×Q8—221no—
392C22×Q8C22×D1112yes—
393C22×Q8C22×D1114yes—
394C22×D4—21no—
395C22×D4—111no—
396C22×D4—112no—
397C22×D4—114no—
398C22×D4—221no—
399C22×D4—221no—
400C22×D4—221no—
401C22×D4—222no—
402C22×D4—221no—
403C22×D4—444no—
404C22×D4C22×D1111yescharacteristic
405C23×C4—21no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—221no—
409C23×C4—221no—
410C23×C4C22×D1111yescharacteristic
411C2×SD16—44no—
412C2×SD16—118no—
413C2×SD16—444no—
414C2×SD16C22×D1118yescomplemented
415C2×D8—118no—
416C2×D8—118no—
417C2×D8—444no—
418C2×D8—444no—
419C22×C8—112no—
420C22×C8C22×D1112yes—
421C4⋊Q8—114no—
422C4⋊Q8—222no—
423#127—114no—
424#127—222no—
425#124—118no—
426#124—118no—
427#124—228no—
428#124—224no—
429#124—228no—
430#124—228no—
431#124—224no—
432#121—22no—
433#121—114no—
434#121—228no—
435#121—222no—
436#121C22×D1114yes—
437C4×D4—114no—
438C4×D4—114no—
439C4×D4—228no—
440C4×D4—222no—
441C4×D4—222no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4C22×D1111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—228no—
447C2×C22⋊C4—228no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—114no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—114no—
461C4⋊C8—118no—
462#103—118no—
463#103C22×D1118yescomplemented
464#102—118no—
465#102—118no—
466C22⋊C8—114no—
467C22⋊C8C22×D1114yes—
468#97—118no—
469C2×C11—24no—
470C2×C11—82no—
471C2×C11#321314yescomplemented
472C2×C11C2×#53511yescharacteristic
473C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
474C2×C11C2×#57511yescharacteristic
475D11—82no—
476D11—84no—
477C24—21no—
478C24—224no—
479C24—222no—
480C24—221no—
481C24—444no—
482C24—444no—
483C24—444no—
484C24D4×D1111yescharacteristic
485#41—4432no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—48no—
491C2×Q8—44no—
492C2×Q8—48no—
493C2×Q8—224no—
494C2×Q8—444no—
495C2×Q8C23×D1114yes—
496C2×D4—24no—
497C2×D4—21no—
498C2×D4—24no—
499C2×D4—44no—
500C2×D4—114no—
501C2×D4—112no—
502C2×D4—224no—
503C2×D4—224no—
504C2×D4—224no—
505C2×D4—221no—
506C2×D4—224no—
507C2×D4—222no—
508C2×D4—224no—
509C2×D4—224no—
510C2×D4—224no—
511C2×D4—448no—
512C2×D4—444no—
513C2×D4—448no—
514C2×D4—444no—
515C2×D4—444no—
516C2×D4—444no—
517C2×D4C23×D1112yes—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—44no—
523C22×C4—114no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—114no—
529C22×C4—224no—
530C22×C4—224no—
531C22×C4—224no—
532C22×C4—221no—
533C22×C4—444no—
534C22×C4—442no—
535C22×C4—444no—
536C22×C4D4×D1112yes—
537C22×C4D4×D1111yescharacteristic
538C22×C4C23×D1112yes—
539C22×C4C23×D1111yescharacteristic
540SD16—48no—
541SD16—448no—
542D8—448no—
543D8—448no—
544C2×C8—24no—
545C2×C8—114no—
546C2×C8—224no—
547C2×C8C23×D1114yes—
548C4⋊C4—21no—
549C4⋊C4—112no—
550C4⋊C4—224no—
551C4⋊C4—221no—
552C4⋊C4C23×D1112yes—
553C22⋊C4—24no—
554C22⋊C4—228no—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—228no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C42—112no—
562C42—114no—
563C42—114no—
564C42—112no—
565C42—112no—
566C42—112no—
567C11C2×#321311yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—22no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—224no—
575C23—222no—
576C23—448no—
577C23—448no—
578C23—442no—
579C23—448no—
580C23—444no—
581C23—442no—
582C23—444no—
583C23—444no—
584C23—442no—
585C23—8816no—
586C23#6696714yes—
587C23C2×D4×D1112yes—
588C23C2×D4×D1111yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—48no—
592Q8—44no—
593Q8—448no—
594D4—24no—
595D4—48no—
596D4—42no—
597D4—224no—
598D4—224no—
599D4—224no—
600D4—448no—
601D4—448no—
602D4—448no—
603D4—448no—
604D4—444no—
605D4—442no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—48no—
612C2×C4—42no—
613C2×C4—44no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—228no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—448no—
625C2×C4—444no—
626C2×C4—448no—
627C2×C4—442no—
628C2×C4C2×D4×D1112yes—
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4#6703714yes—
631C2×C4C24×D1111yescharacteristic
632C8—24no—
633C8—224no—
634C22—28no—
635C22—22no—
636C22—22no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—84no—
641C22—444no—
642C22—442no—
643C22—442no—
644C22—444no—
645C22—442no—
646C22—444no—
647C22—8816no—
648C22—888no—
649C22—884no—
650C22#1062312312yes—
651C22C2×#6696714yes—
652C22C2×#6696712yes—
653C22#1062330812yes—
654C22C22×D4×D1111yescharacteristic
655C4—22no—
656C4—44no—
657C4—42no—
658C4—222no—
659C4—222no—
660C4—222no—
661C4—222no—
662C4—442no—
663C4#1062312312yes—
664C4C2×#6703712yes—
665C2—24no—
666C2—82no—
667C2—884no—
668C2—882no—
669C2#1307960214yesdirect product factor
670C2C2×#1062312311yescharacteristic
671C2C22×#6696711yescharacteristic
672C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
hypercenterC2×#448D11
hypocenterC11C2×#3213
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#10623127C2semidirect
2. C22×#67000C2semidirect
3. #13079602C2direct (N × H)
4. C2×#10622789C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622432C2semidirect
7. C2×#10622778C2semidirect
8. C2×#10622840C2semidirect
9. C2×#10622345C2semidirect
10. C2×#10622649C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#448C2semidirect
16. C22×C11×SD16C22semidirect
23. C2×#67000C22semidirect
24. C22×#4325C22semidirect
25. C2×#66993C22semidirect
27. C2×D4×Dic11C22semidirect
35. #10623127C22semidirect
36. C2×#66946C22semidirect
37. C2×#66941C22semidirect
40. C11×#448C22semidirect
41. C2×C11×#103C22semidirect
43. #10622840C22semidirect
44. C2×#66899C22semidirect
46. #10622789C22semidirect
47. #10622778C22semidirect
49. C2×#66879C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. #10622649C22semidirect
53. #10622432C22semidirect
54. #10622408C22semidirect
55. #10622345C22semidirect
56. #10622332C22semidirect
84. C2×C11×SD16C23semidirect
98. C2×#4325C23semidirect
100. #66993C23semidirect
103. D4×Dic11C23semidirect
128. #66946C23semidirect
130. #66941C23semidirect
133. C11×#103C23semidirect
135. #66899C23semidirect
138. #66879C23semidirect
139. Dic11⋊C8C23semidirect
240. C2×#448D11semidirect
314. C22×SD16C2×D11semidirect
342. #448C2×D11semidirect
348. C2×#103C2×D11semidirect
414. C2×SD16C22×D11semidirect
463. #103C22×D11semidirect
471. C2×C11#3213semidirect
567. C11C2×#3213semidirect
669. C2#13079602direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C22×#670002
#130796022
C2×#106227892
C2×#106224082
C2×#106224322
C2×#106227782
C2×#106228402
C2×#106223452
C2×#106226492
C2×#106223322
C2×C11×#4482
C2×#321311