Finite Group Databasebeta

← C2×#13073578 #14923799

Subgroups — C2×#13073578 #14923799

Order 2816.

4326 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C212yesmaximal, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13073578C2116yesmaximal, direct product factor
4C2×#10622593C211yesmaximal, characteristic, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622557C212yesmaximal, complemented
9C2×#10622833C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C22×C11⋊#95C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C2×C11×#121—28no—
21C2×C11×#121C2218yescomplemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C2×#66992—216no—
29C2×#66992C22116yescomplemented
30C2×C4×C22⋊D11—28no—
31C2×C4×C22⋊D11C2218yescomplemented
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37#10622836C2218yescomplemented
38#10622835C2218yescomplemented
39#10622833C22116yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45C2×C11⋊#95C2218yescomplemented
46#10622606C2218yescomplemented
47#10622593C2218yescomplemented
48#10622569C22116yescomplemented
49#10622557C22116yescomplemented
50C25×C11C2312yes—
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C22×D4×C11—28no—
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11—24no—
57C22×D4×C11—44no—
58C22×D4×C11C2318yes—
59C22×D4×C11C2314yes—
60C23×C4×C11—44no—
61C23×C4×C11D418yescomplemented
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—24no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—28no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11D418yescomplemented
72C22×C22⋊D11C2318yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11—28no—
75C23×Dic11—28no—
76C23×Dic11—44no—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2312yes—
80C23×Dic11C2318yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2312yes—
83C22×C4×D11—24no—
84C22×C4×D11—44no—
85C22×C4×D11C2314yes—
86C11×#121—232no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C22⋊C4—28no—
90C2×C11×C22⋊C4C2318yes—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—28no—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11—44no—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2318yes—
97C2×C22⋊Dic11C2318yes—
98C2×C22⋊Dic11C2318yes—
99#66992—264no—
100C4×C22⋊D11—232no—
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—28no—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2318yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11C2314yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C11⋊#95C2314yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11C2×D414yes—
127C24×C11C2×D414yes—
128C24×C11#4114yes—
129C24×C11C2414yes—
130C24×C11C2412yes—
131C24×C11C2411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11C2×D414yes—
137C23×D11C2412yes—
138C2×D4×C11—216no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—28no—
142C2×D4×C11—48no—
143C2×D4×C11—416no—
144C2×D4×C11—432no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—416no—
151C22×C4×C11—48no—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D4116yescomplemented
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—232no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—432no—
165C2×C22⋊D11C2×D4116yescomplemented
166C22×Dic11—216no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—24no—
172C22×Dic11—216no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—24no—
179C22×Dic11—48no—
180C22×Dic11—432no—
181C22×Dic11C2×D414yes—
182C22×Dic11#4118yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C22×Dic11C2414yes—
188C2×C4×D11—28no—
189C2×C4×D11—48no—
190C2×C4×D11—416no—
191C11×C4⋊C4—28no—
192C11×C22⋊C4—216no—
193C22⋊Dic11—216no—
194C22⋊Dic11—216no—
195C22⋊Dic11—28no—
196C22⋊Dic11—48no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—28no—
199Dic11⋊C4—216no—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202C22×#121—112no—
203C22×#121D1111yescharacteristic, complemented
204C22×C4×D4—111no—
205#2543—1116no—
206C2×#398—111no—
207C2×#397—111no—
208C2×#394—111no—
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95—111no—
214C23×C11—28no—
215C23×C11—28no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11—48no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11#121116yes—
235C23×C11C22×D414yes—
236C23×C11C22×D412yes—
237C23×C11C22×D414yes—
238C23×C11C22×D412yes—
239C23×C11C2×#4114yes—
240C23×C11C2×#4112yes—
241C23×C11C2×#4114yes—
242C23×C11H(5,𝔽2)14yes—
243C23×C11C2511yescharacteristic
244C22×D11—28no—
245C22×D11—216no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—44no—
251C22×D11—44no—
252C22×D11—48no—
253C22×D11C22×D414yes—
254D4×C11—416no—
255D4×C11—432no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—416no—
264C2×C4×C11—48no—
265C2×C4×C11C22×D414yes—
266C2×C4×C11C22×D414yes—
267C22⋊D11—232no—
268C22⋊D11—432no—
269C2×Dic11—28no—
270C2×Dic11—216no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—432no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11—48no—
286C2×Dic11C22×D414yes—
287C2×Dic11C2×#4118yes—
288C4×D11—416no—
289C23×D4—111no—
290C23×D4—112no—
291C23×D4C2×D1112yes—
292C23×D4C2×D1111yescharacteristic
293C24×C4—112no—
294C24×C4—111no—
295C24×C4C2×D1111yescharacteristic
296C2×#121—28no—
297C2×#121—1116no—
298C2×#121—2216no—
299C2×#121C2×D1118yescomplemented
300C2×C4×D4—118no—
301C2×C4×D4—228no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—112no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—111no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313#398—118no—
314#397—118no—
315#394—118no—
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—118no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—28no—
329C22×C11—28no—
330C22×C11—232no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—816no—
339C22×C11C2×#12118yes—
340C22×C11C2×#12114yes—
341C22×C11#53214yes—
342C22×C11#53414yes—
343C22×C11#54618yes—
344C22×C11#55318yes—
345C22×C11C23×D411yescharacteristic
346C22×C11C23×D411yescharacteristic
347C22×C11C22×#4111yescharacteristic
348C22×C11C22×#4112yes—
349C22×C11C2×H(5,𝔽2)12yes—
350C2×D11—24no—
351C2×D11—28no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—416no—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—44no—
359Dic11—24no—
360Dic11—28no—
361Dic11—42no—
362Dic11—42no—
363Dic11—44no—
364C25—111no—
365C25C22×D1112yes—
366C25C22×D1111yescharacteristic
367C22×D4—28no—
368C22×D4—28no—
369C22×D4—28no—
370C22×D4—24no—
371C22×D4—44no—
372C22×D4—118no—
373C22×D4—114no—
374C22×D4—118no—
375C22×D4—228no—
376C22×D4—224no—
377C22×D4—224no—
378C22×D4—228no—
379C22×D4—444no—
380C22×D4C22×D1118yes—
381C22×D4C22×D1114yes—
382C23×C4—44no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—112no—
388C23×C4—118no—
389C23×C4—114no—
390C23×C4—228no—
391C23×C4—228no—
392C23×C4—224no—
393C23×C4—444no—
394C23×C4—444no—
395C23×C4C22⋊D1118yescomplemented
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1114yes—
400#121—232no—
401#121—2264no—
402C4×D4—2232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4C22×D1114yes—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—444no—
422C2×C22⋊C4C22×D1118yes—
423C2×C42—114no—
424C2×C42—224no—
425#95—118no—
426#95—114no—
427#95—114no—
428#95—118no—
429#95—118no—
430C2×C11—28no—
431C2×C11—84no—
432C2×C11#254318yescomplemented
433C2×C11C22×#12111yescharacteristic
434C2×C11C2×#53211yescharacteristic
435C2×C11C2×#53411yescharacteristic
436C2×C11C2×#54612yes—
437C2×C11C2×#55312yes—
438D11—44no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—114no—
449C24—112no—
450C24—222no—
451C24—224no—
452C24—224no—
453C24—222no—
454C24D4×D1114yes—
455C24#434114yes—
456C24C2×C22⋊D1114yes—
457C24C23×D1114yes—
458C24C23×D1112yes—
459C24C23×D1111yescharacteristic
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—28no—
464C2×D4—48no—
465C2×D4—416no—
466C2×D4—432no—
467C2×D4—1116no—
468C2×D4—2216no—
469C2×D4—2232no—
470C2×D4—228no—
471C2×D4—228no—
472C2×D4—2216no—
473C2×D4—448no—
474C2×D4—4432no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—48no—
481C22×C4—416no—
482C22×C4—114no—
483C22×C4—118no—
484C22×C4—114no—
485C22×C4—112no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—2216no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—2216no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—228no—
503C22×C4—448no—
504C22×C4—4416no—
505C22×C4—448no—
506C22×C4—4432no—
507C22×C4C2×C22⋊D1114yes—
508C22×C4C2×C22⋊D1114yes—
509C22×C4C2×C22⋊D11116yescomplemented
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C4⋊C4—28no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C22⋊C4—216no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C22⋊C4—2216no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C42—228no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—28no—
526C23—28no—
527C23—216no—
528C23—216no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—48no—
539C23—48no—
540C23—48no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—48no—
545C23—114no—
546C23—228no—
547C23—2216no—
548C23—222no—
549C23—224no—
550C23—224no—
551C23—222no—
552C23—444no—
553C23—444no—
554C23—448no—
555C23#66991116yes—
556C23C2×D4×D1114yes—
557C23C2×D4×D1112yes—
558C23C2×#434114yes—
559C23C2×#434112yes—
560C23#6703714yes—
561C23#41×D1114yes—
562C23C22×C22⋊D1114yes—
563C23C22×C22⋊D1112yes—
564C23C24×D1111yescharacteristic
565D4—416no—
566D4—432no—
567D4—2232no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—416no—
577C2×C4—48no—
578C2×C4—114no—
579C2×C4—118no—
580C2×C4—228no—
581C2×C4—2216no—
582C2×C4—224no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—4416no—
594C2×C4—4432no—
595C2×C4—444no—
596C2×C4—444no—
597C2×C4—448no—
598C2×C4C22×C22⋊D1114yes—
599C2×C4C22×C22⋊D1114yes—
600C22—28no—
601C22—24no—
602C22—24no—
603C22—232no—
604C22—28no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—816no—
613C22—228no—
614C22—224no—
615C22—444no—
616C22—442no—
617C22—442no—
618C22—4416no—
619C22#1062313218yes—
620C22#1062314118yes—
621C22C2×#6699118yes—
622C22C2×#6699114yes—
623C22#1062333514yes—
624C22#1062336314yes—
625C22C22×D4×D1111yescharacteristic
626C22C22×#434111yescharacteristic
627C22C2×#6703712yes—
628C22C2×#41×D1112yes—
629C22C23×C22⋊D1111yescharacteristic
630C4—24no—
631C4—24no—
632C4—44no—
633C4—228no—
634C4—224no—
635C4—442no—
636C4—442no—
637C4—444no—
638C2—28no—
639C2—84no—
640C2—444no—
641C2#1307357818yesdirect product factor
642C2C22×#6699111yescharacteristic
643C2C2×#1062336311yescharacteristic
644C2C2×#1062333511yescharacteristic
645C2C2×#1062314112yes—
646C2C2×#1062313212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13073578C2direct (N × H)
4. C2×#10622593C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622557C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622569C2semidirect
11. C22×C11⋊#95C2semidirect
12. C22×C11×#121C2semidirect
21. C2×C11×#121C22semidirect
29. C2×#66992C22semidirect
31. C2×C4×C22⋊D11C22semidirect
37. #10622836C22semidirect
38. #10622835C22semidirect
39. #10622833C22semidirect
45. C2×C11⋊#95C22semidirect
46. #10622606C22semidirect
47. #10622593C22semidirect
48. #10622569C22semidirect
49. #10622557C22semidirect
61. C23×C4×C11D4semidirect
71. C22×C22⋊D11D4semidirect
154. C22×C4×C11C2×D4semidirect
165. C2×C22⋊D11C2×D4semidirect
203. C22×#121D11semidirect
299. C2×#121C2×D11semidirect
395. C23×C4C22⋊D11semidirect
432. C2×C11#2543semidirect
509. C22×C4C2×C22⋊D11semidirect
524. C11C2×#2543semidirect
641. C2#13073578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×C4×C22⋊D112
#130735782
C2×#106225932
C2×#106226062
C2×#106228352
C2×#106228362
C2×#106225572
C2×#106228332
C2×#106225692
C22×C11⋊#952
C22×C11×#1212
C2×#254311