Finite Group Databasebeta

← C2×#13073549 #14924940

Subgroups — C2×#13073549 #14924940

Order 2816.

4566 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66931C212yesmaximal, complemented
3C22×#66992C212yesmaximal, complemented
4C22×D4×Dic11C211yesmaximal, characteristic, complemented
5#13073549C2116yesmaximal, direct product factor
6C2×#10622290C211yesmaximal, characteristic, complemented
7C2×#10622562C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622834C212yesmaximal, complemented
10C2×#10622570C212yesmaximal, complemented
11C2×#10622262C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C24×Dic11C2212yes—
18C23×Dic22C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66992—216no—
26C2×#66992C22116yescomplemented
27C2×D4×Dic11—28no—
28C2×D4×Dic11C2218yescomplemented
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2212yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2212yes—
34C22×Dic11⋊C4C2212yes—
35C22×Dic11⋊C4C2212yes—
36C22×C4×Dic11C2212yes—
37C22×C4×Dic11C2211yescharacteristic
38C2×#66938—28no—
39C2×#66938C2218yescomplemented
40C2×#66931—216no—
41C2×#66931C22116yescomplemented
42C11×#392C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44#10622836C2218yescomplemented
45#10622834C22116yescomplemented
46C2×C11⋊#95C2211yescharacteristic
47#10622570C22116yescomplemented
48#10622562C2218yescomplemented
49#10622290C2218yescomplemented
50#10622262C2218yescomplemented
51C25×C11C2311yescharacteristic
52C25×C11C2312yes—
53C24×D11C2311yescharacteristic
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11—24no—
57C22×D4×C11—28no—
58C22×D4×C11—44no—
59C22×D4×C11C2314yes—
60C22×D4×C11C2318yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—28no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—44no—
69C22×C22⋊D11C2314yes—
70C22×C22⋊D11C2318yes—
71C23×Dic11—28no—
72C23×Dic11—28no—
73C23×Dic11—28no—
74C23×Dic11C2318yes—
75C23×Dic11C2312yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C22×Dic22—28no—
81C22×Dic22—24no—
82C22×Dic22C2314yes—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95#66992—264no—
96D4×Dic11—232no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×C4⋊Dic11—28no—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11C2318yes—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—28no—
108C2×Dic11⋊C4D4116yescomplemented
109C2×Dic11⋊C4C2318yes—
110C2×Dic11⋊C4C2318yes—
111C2×C4×Dic11—44no—
112C2×C4×Dic11D418yescomplemented
113C2×C4×Dic11C2318yes—
114C2×C4×Dic11C2314yes—
115#66938—232no—
116#66931—264no—
117C11×#95C2314yes—
118C11⋊#95C2314yes—
119C2×#2540—111nomaximal, Sylow
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—22no—
127C24×C11—24no—
128C24×C11—24no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11#4118yes—
132C24×C11C2412yes—
133C24×C11C2414yes—
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—24no—
137C23×D11—24no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11C2412yes—
141C2×D4×C11—232no—
142C2×D4×C11—216no—
143C2×D4×C11—216no—
144C2×D4×C11—28no—
145C2×D4×C11—216no—
146C2×D4×C11—48no—
147C2×D4×C11—432no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D418yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—432no—
164C2×C22⋊D11—416no—
165C22×Dic11—216no—
166C22×Dic11—216no—
167C22×Dic11—216no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—22no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—432no—
178C22×Dic11C2×D414yes—
179C22×Dic11C2×D418yes—
180C22×Dic11C2×D414yes—
181C22×Dic11C2×D418yes—
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2414yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C2×Dic22—216no—
188C2×Dic22—28no—
189C2×Dic22—416no—
190C11×C22⋊C4—216no—
191C11×C22⋊C4—28no—
192C22⋊Dic11—216no—
193C22⋊Dic11—28no—
194C22⋊Dic11—216no—
195C22⋊Dic11—216no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—216no—
199C4⋊Dic11—216no—
200C4⋊Dic11—28no—
201Dic11⋊C4—216no—
202Dic11⋊C4C2×D4132yescomplemented
203C4×Dic11—48no—
204C4×Dic11C2×D4116yescomplemented
205C22×#124—111no—
206C22×C22⋊Q8—112no—
207C22×#121—112no—
208C22×C4×D4—111no—
209#2540—1116no—
210C2×#399—111no—
211C2×#399—111no—
212C2×#392—111no—
213C2×#392D1111yescharacteristic, complemented
214C2×#390—112no—
215C2×#390—112no—
216C2×C4×C4⋊C4—111no—
217C23×C11—216no—
218C23×C11—216no—
219C23×C11—216no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—48no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11—44no—
236C23×C11—44no—
237C23×C11—44no—
238C23×C11—48no—
239C23×C11—48no—
240C23×C11C22×D412yes—
241C23×C11C22×D414yes—
242C23×C11C2×#4118yes—
243C23×C11C2×#4114yes—
244C23×C11H(5,𝔽2)12yes—
245C23×C112−1+412yes—
246C23×C11C2511yescharacteristic
247C22×D11—22no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11—44no—
255C22×D11—48no—
256C22×D11—48no—
257D4×C11—232no—
258D4×C11—432no—
259C2×C4×C11—28no—
260C2×C4×C11—216no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—44no—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D418yes—
269C22⋊D11—432no—
270C22⋊D11—416no—
271C2×Dic11—28no—
272C2×Dic11—216no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—44no—
283C2×Dic11—48no—
284C2×Dic11—432no—
285C2×Dic11#127116yes—
286C2×Dic11C22×D414yes—
287C2×Dic11C22×D418yes—
288C2×Dic11C22×D414yes—
289C2×Dic11C22×D418yes—
290Dic22—416no—
291C23×Q8—111no—
292C23×D4—111no—
293C23×D4—112no—
294C23×D4C2×D1111yescharacteristic
295C23×D4C2×D1112yes—
296C24×C4—112no—
297C2×#124—118no—
298C2×#124—228no—
299C2×C22⋊Q8—1116no—
300C2×C22⋊Q8—2216no—
301C2×#121—1116no—
302C2×#121—2216no—
303C2×C4×D4—118no—
304C2×C4×D4—228no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4—112no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—111no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—111no—
316C22×C22⋊C4C2×D1111yescharacteristic
317C22×C22⋊C4C2×D1112yes—
318C22×C42—111no—
319C22×C42—112no—
320#399—118no—
321#399—118no—
322#392—118no—
323#392C2×D1118yescomplemented
324#390—1116no—
325#390—1116no—
326C4×C4⋊C4—118no—
327C2×#95—111no—
328C2×#95C2×D1111yescharacteristic
329C22×C11—28no—
330C22×C11—28no—
331C22×C11—28no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—432no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—88no—
343C22×C11#52514yes—
344C22×C11C2×#12714yes—
345C22×C11#53714yes—
346C22×C11#54618yes—
347C22×C11#54818yes—
348C22×C11C23×D411yescharacteristic
349C22×C11C23×D412yes—
350C22×C11C22×#4112yes—
351C22×C11C2×H(5,𝔽2)11yescharacteristic
352C22×C11C2×2−1+411yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—88no—
359C4×C11—24no—
360C4×C11—28no—
361C4×C11—42no—
362Dic11—24no—
363Dic11—28no—
364Dic11—42no—
365Dic11—44no—
366Dic11C2×#12718yes—
367C25—111no—
368C25C22×D1111yescharacteristic
369C25C22×D1112yes—
370C22×Q8—114no—
371C22×Q8—228no—
372C22×Q8—224no—
373C22×D4—28no—
374C22×D4—28no—
375C22×D4—24no—
376C22×D4—28no—
377C22×D4—44no—
378C22×D4—114no—
379C22×D4—118no—
380C22×D4—228no—
381C22×D4—228no—
382C22×D4—224no—
383C22×D4—228no—
384C22×D4—444no—
385C22×D4C22×D1114yes—
386C22×D4C22×D1118yes—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—112no—
390C23×C4—118no—
391C23×C4—111no—
392C23×C4—112no—
393C23×C4—228no—
394C23×C4—228no—
395C23×C4—228no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399#124—2232no—
400C22⋊Q8—2264no—
401#121—2264no—
402C4×D4—2232no—
403C2×C4⋊C4—1116no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—118no—
407C2×C4⋊C4—118no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—228no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—224no—
425C2×C22⋊C4—228no—
426C2×C22⋊C4—224no—
427C2×C22⋊C4C22×D1118yes—
428C2×C22⋊C4C22×D1114yes—
429C2×C42—118no—
430C2×C42—114no—
431C2×C42—118no—
432C2×C42—444no—
433#95—114no—
434#95C22×D1114yes—
435C2×C11—48no—
436C2×C11—82no—
437C2×C11#254018yescomplemented
438C2×C11C2×#52511yescharacteristic
439C2×C11C22×#12711yescharacteristic
440C2×C11C2×#53711yescharacteristic
441C2×C11C2×#54612yes—
442C2×C11C2×#54812yes—
443D11—82no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—22no—
451C24—24no—
452C24—24no—
453C24—22no—
454C24—22no—
455C24—112no—
456C24—222no—
457C24—224no—
458C24—224no—
459C24—222no—
460C24—222no—
461C24#434118yes—
462C24C23×D1112yes—
463C24C23×D1114yes—
464C24C23×D1111yescharacteristic
465C2×Q8—2216no—
466C2×Q8—228no—
467C2×Q8—4416no—
468C2×D4—232no—
469C2×D4—216no—
470C2×D4—216no—
471C2×D4—28no—
472C2×D4—216no—
473C2×D4—48no—
474C2×D4—432no—
475C2×D4—2216no—
476C2×D4—2216no—
477C2×D4—228no—
478C2×D4—2216no—
479C2×D4—4416no—
480C2×D4—448no—
481C2×D4—4432no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—114no—
488C22×C4—118no—
489C22×C4—112no—
490C22×C4—114no—
491C22×C4—118no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—114no—
496C22×C4—2216no—
497C22×C4—2216no—
498C22×C4—2216no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—224no—
502C22×C4—222no—
503C22×C4—224no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—4432no—
509C22×C4D4×D1114yes—
510C22×C4D4×D1118yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1114yes—
514C4⋊C4—1132no—
515C4⋊C4—2216no—
516C4⋊C4—228no—
517C4⋊C4—2216no—
518C22⋊C4—216no—
519C22⋊C4—28no—
520C22⋊C4—228no—
521C22⋊C4—2216no—
522C22⋊C4—2216no—
523C22⋊C4—2216no—
524C22⋊C4—228no—
525C22⋊C4—2216no—
526C22⋊C4—228no—
527C42—1116no—
528C42—448no—
529C11C2×#254011yescharacteristic, complemented, Sylow
530C23—216no—
531C23—216no—
532C23—216no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—22no—
544C23—48no—
545C23—48no—
546C23—48no—
547C23—48no—
548C23—44no—
549C23—44no—
550C23—48no—
551C23—48no—
552C23—44no—
553C23—222no—
554C23—224no—
555C23—224no—
556C23—222no—
557C23—222no—
558C23—444no—
559C23—444no—
560C23—448no—
561C23—448no—
562C23—444no—
563C23C2×D4×D1112yes—
564C23C2×D4×D1114yes—
565C23C2×#434118yes—
566C23C2×#434114yes—
567C23#6703712yes—
568C23#6704312yes—
569C23C24×D1111yescharacteristic
570Q8—4416no—
571D4—232no—
572D4—432no—
573D4—4416no—
574D4—4432no—
575C2×C4—28no—
576C2×C4—216no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—44no—
583C2×C4—1116no—
584C2×C4—114no—
585C2×C4—118no—
586C2×C4—114no—
587C2×C4—118no—
588C2×C4—2216no—
589C2×C4—228no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—4432no—
600C2×C4—448no—
601C2×C4—444no—
602C2×C4C2×D4×D1114yes—
603C2×C4C2×D4×D1118yes—
604C22—28no—
605C22—28no—
606C22—28no—
607C22—44no—
608C22—44no—
609C22—432no—
610C22—44no—
611C22—44no—
612C22—42no—
613C22—42no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—88no—
618C22—442no—
619C22—442no—
620C22—444no—
621C22—444no—
622C22—442no—
623C22—888no—
624C22#1062311714yes—
625C22#1062312218yes—
626C22#1062312918yes—
627C22#1062313914yes—
628C22D11×#12714yes—
629C22C22×D4×D1111yescharacteristic
630C22C22×D4×D1112yes—
631C22C22×#434112yes—
632C22C2×#6703711yescharacteristic
633C22C2×#6704311yescharacteristic
634C4—28no—
635C4—24no—
636C4—42no—
637C4—118no—
638C4—224no—
639C4—228no—
640C4—444no—
641C4—442no—
642C2—48no—
643C2—82no—
644C2—882no—
645C2#1307354918yesdirect product factor
646C2C2×#1062311711yescharacteristic
647C2C2×D11×#12711yescharacteristic
648C2C2×#1062313911yescharacteristic
649C2C2×#1062312212yes—
650C2C2×#1062312912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66931C2semidirect
3. C22×#66992C2semidirect
4. C22×D4×Dic11C2semidirect
5. #13073549C2direct (N × H)
6. C2×#10622290C2semidirect
7. C2×#10622562C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622262C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66992C22semidirect
28. C2×D4×Dic11C22semidirect
39. C2×#66938C22semidirect
41. C2×#66931C22semidirect
42. C11×#392C22semidirect
44. #10622836C22semidirect
45. #10622834C22semidirect
47. #10622570C22semidirect
48. #10622562C22semidirect
49. #10622290C22semidirect
50. #10622262C22semidirect
108. C2×Dic11⋊C4D4semidirect
112. C2×C4×Dic11D4semidirect
202. Dic11⋊C4C2×D4semidirect
204. C4×Dic11C2×D4semidirect
213. C2×#392D11semidirect
323. #392C2×D11semidirect
437. C2×C11#2540semidirect
529. C11C2×#2540semidirect
645. C2#13073549direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669312
C22×#669922
C22×D4×Dic112
#130735492
C2×#106222902
C2×#106225622
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106222622
C2×C11×#3922
C2×#254011