Finite Group Databasebeta

← C2×#13076617 #14959924

Subgroups — C2×#13076617 #14959924

Order 2816.

3322 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3#13076617C2116yesmaximal, direct product factor
4C2×#10622599C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622561C212yesmaximal, complemented
7C2×#10622574C212yesmaximal, complemented
8C2×#10622572C212yesmaximal, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622280C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66991—28no—
24C2×#66991C2218yescomplemented
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34C2×#66947—28no—
35C2×#66947C2218yescomplemented
36C11×#394C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38#10622836C2218yescomplemented
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622599C2218yescomplemented
43#10622574C22116yescomplemented
44#10622573C22116yescomplemented
45#10622572C22116yescomplemented
46#10622561C22116yescomplemented
47#10622290C2218yescomplemented
48#10622280C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—28no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11C2318yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C22×D44—24no—
72C22×D44—44no—
73C22×D44C2314yes—
74C22×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87#66991—232no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—44no—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2318yes—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—44no—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2318yes—
106#66947—232no—
107C11×#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2813—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11C2414yes—
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11C2×D414yes—
131C23×D11C2412yes—
132C23×D11C2412yes—
133C2×D4×C11—28no—
134C2×D4×C11—48no—
135C2×D4×C11—416no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—216no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—432no—
157C2×C22⋊D11—432no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11C2×D414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C2×D44—28no—
173C2×D44—48no—
174C2×D44—416no—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C4⋊C4—28no—
179C11×C22⋊C4—48no—
180C11×C22⋊C4—48no—
181C22⋊Dic11—216no—
182C22⋊Dic11—48no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—28no—
189C4⋊Dic11—48no—
190Dic11⋊C4—28no—
191Dic11⋊C4—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2813—1116no—
195C2×#400—111no—
196C2×#399—111no—
197C2×#396—112no—
198C2×#394—112no—
199C2×#394—112no—
200C2×#394D1111yescharacteristic, complemented
201C2×#392—111no—
202C2×#392—112no—
203C2×#380—111no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D412yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)14yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224C22×D11—28no—
225C22×D11—28no—
226C22×D11—28no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D414yes—
244D4×C11—416no—
245C2×C4×C11—28no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—48no—
258C2×C4×C11C22×D414yes—
259C22⋊D11—432no—
260C22⋊D11—432no—
261C2×Dic11—28no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—44no—
272C2×Dic11—48no—
273C2×Dic11—48no—
274C2×Dic11C22×D414yes—
275D44—416no—
276C4×D11—416no—
277C23×D4—112no—
278C23×D4—112no—
279C23×D4—111no—
280C23×D4C2×D1111yescharacteristic
281C24×C4—111no—
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4C2×D1112yes—
299C22×C22⋊C4C2×D1112yes—
300#400—118no—
301#399—118no—
302#396—1116no—
303#394—1116no—
304#394—1116no—
305#394C2×D1118yescomplemented
306#392—118no—
307#392—1116no—
308#380—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95C2×D1111yescharacteristic
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—816no—
321C22×C11#53414yes—
322C22×C11#53514yes—
323C22×C11#53714yes—
324C22×C11#56018yes—
325C22×C11#56218yes—
326C22×C11C23×D411yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×H(5,𝔽2)11yescharacteristic
329C22×C11C2×H(5,𝔽2)12yes—
330C22×C11C2×2−1+411yescharacteristic
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—416no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—88no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—44no—
347Dic11—24no—
348Dic11—42no—
349Dic11—44no—
350Dic11—44no—
351C25—111no—
352C25—111no—
353C25C22×D1112yes—
354C22×D4—24no—
355C22×D4—44no—
356C22×D4—118no—
357C22×D4—118no—
358C22×D4—114no—
359C22×D4—224no—
360C22×D4—228no—
361C22×D4—444no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4C22×D1114yes—
368C23×C4—111no—
369C23×C4—118no—
370C23×C4—114no—
371C23×C4—111no—
372C23×C4—112no—
373C23×C4—112no—
374C23×C4—444no—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—444no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4C22×D1114yes—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—228no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4C22×D1118yes—
408C2×C22⋊C4C22×D1118yes—
409#95—114no—
410#95—118no—
411#95—118no—
412#95C22×D1114yes—
413C2×C11—84no—
414C2×C11#281318yescomplemented
415C2×C11C2×#53411yescharacteristic
416C2×C11C2×#53511yescharacteristic
417C2×C11C2×#53711yescharacteristic
418C2×C11C2×#56012yes—
419C2×C11C2×#56212yes—
420D11—44no—
421D11—82no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—114no—
430C24—112no—
431C24—112no—
432C24—222no—
433C24—224no—
434C24—224no—
435C24—222no—
436C24—222no—
437C24—224no—
438C24—222no—
439C24—224no—
440C24—222no—
441C24C23×D1114yes—
442C24C23×D1111yescharacteristic
443C2×D4—28no—
444C2×D4—48no—
445C2×D4—416no—
446C2×D4—228no—
447C2×D4—2216no—
448C2×D4—448no—
449C2×D4—4416no—
450C2×D4—448no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4432no—
456C2×D4—4432no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—1116no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—4416no—
482C22×C4—448no—
483C22×C4D4×D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C4⋊C4—448no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—2216no—
498C22⋊C4—228no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C11C2×#281311yescharacteristic, complemented, Sylow
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—48no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23—114no—
518C23—228no—
519C23—228no—
520C23—222no—
521C23—224no—
522C23—224no—
523C23—222no—
524C23—228no—
525C23—222no—
526C23—224no—
527C23—222no—
528C23—224no—
529C23—222no—
530C23—448no—
531C23—448no—
532C23—444no—
533C23—444no—
534C23—448no—
535C23—448no—
536C23—444no—
537C23C2×D4×D1112yes—
538C23#6703714yes—
539C23#6703712yes—
540C23#6704214yes—
541C23#6704312yes—
542C23C24×D1111yescharacteristic
543D4—416no—
544D4—4416no—
545D4—4432no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—114no—
561C2×C4—228no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—448no—
573C2×C4—448no—
574C2×C4—444no—
575C2×C4C2×D4×D1114yes—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—816no—
584C22—224no—
585C22—224no—
586C22—224no—
587C22—444no—
588C22—444no—
589C22—4416no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22—444no—
594C22—444no—
595C22—888no—
596C22#1062312014yes—
597C22#1062313914yes—
598C22#1062315118yes—
599C22#1062319818yes—
600C22#1062320514yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703712yes—
603C22C2×#6703711yescharacteristic
604C22C2×#6704212yes—
605C22C2×#6704311yescharacteristic
606C4—24no—
607C4—42no—
608C4—42no—
609C4—44no—
610C4—224no—
611C4—444no—
612C4—442no—
613C4—444no—
614C2—84no—
615C2—444no—
616C2—882no—
617C2#1307661718yesdirect product factor
618C2C2×#1062312011yescharacteristic
619C2C2×#1062320511yescharacteristic
620C2C2×#1062313911yescharacteristic
621C2C2×#1062315112yes—
622C2C2×#1062319812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66991C2semidirect
3. #13076617C2direct (N × H)
4. C2×#10622599C2semidirect
5. C2×#10622290C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#394C2semidirect
24. C2×#66991C22semidirect
35. C2×#66947C22semidirect
36. C11×#394C22semidirect
38. #10622836C22semidirect
42. #10622599C22semidirect
43. #10622574C22semidirect
44. #10622573C22semidirect
45. #10622572C22semidirect
46. #10622561C22semidirect
47. #10622290C22semidirect
48. #10622280C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
200. C2×#394D11semidirect
305. #394C2×D11semidirect
414. C2×C11#2813semidirect
502. C11C2×#2813semidirect
617. C2#13076617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669912
#130766172
C2×#106225992
C2×#106222902
C2×#106225612
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106222802
C2×C11×#3942
C2×#281311