Finite Group Databasebeta

← C2×#13073573 #14923798

Subgroups — C2×#13073573 #14923798

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×#66948C211yesmaximal, characteristic, complemented
2C22×#66937C212yesmaximal, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13073573C2116yesmaximal, direct product factor
5C2×#10622593C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622282C212yesmaximal, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2212yes—
14C23×C22⋊D11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×D44C2212yes—
17C23×D44C2211yescharacteristic
18C23×C4×D11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66948—28no—
32C2×#66948C2218yescomplemented
33C2×#66937—216no—
34C2×#66937C22116yescomplemented
35C2×(C22⋊D11)⋊C4—28no—
36C2×(C22⋊D11)⋊C4C2218yescomplemented
37C11×#397C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43#10622593C2218yescomplemented
44#10622573C2218yescomplemented
45#10622571C22116yescomplemented
46#10622285C2218yescomplemented
47#10622282C22116yescomplemented
48#10622278C22116yescomplemented
49D11×#95C2218yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—24no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11D418yescomplemented
63C22×C22⋊D11C2318yes—
64C22×C22⋊D11C2314yes—
65C23×Dic11—24no—
66C23×Dic11—44no—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2314yes—
72C22×D44—28no—
73C22×D44—28no—
74C22×D44—28no—
75C22×D44—24no—
76C22×D44—44no—
77C22×D44C2318yes—
78C22×D44C2314yes—
79C22×C4×D11—28no—
80C22×C4×D11—28no—
81C22×C4×D11—44no—
82C22×C4×D11—44no—
83C22×C4×D11D418yescomplemented
84C22×C4×D11C2318yes—
85C22×C4×D11C2314yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4—28no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2318yes—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—28no—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11C2314yes—
108#66948—232no—
109#66937—264no—
110(C22⋊D11)⋊C4—232no—
111C11×#95C2314yes—
112C11×#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11C2×D414yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11C2×D414yes—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C23×D11C2414yes—
137C23×D11C2412yes—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—216no—
154C2×C22⋊D11—232no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C2×C22⋊D11C2×D4116yescomplemented
160C22×Dic11—28no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—48no—
169C22×Dic11—416no—
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D414yes—
172C22×Dic11#4118yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C2×D44—216no—
178C2×D44—216no—
179C2×D44—216no—
180C2×D44—28no—
181C2×D44—48no—
182C2×D44—416no—
183C2×D44—432no—
184C2×C4×D11—216no—
185C2×C4×D11—216no—
186C2×C4×D11—416no—
187C2×C4×D11—48no—
188C2×C4×D11—48no—
189C2×C4×D11—432no—
190C2×C4×D11C2×D4116yescomplemented
191C11×C4⋊C4—28no—
192C11×C22⋊C4—216no—
193C11×C22⋊C4—28no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—48no—
199Dic11⋊C4—216no—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202C22×#121—111no—
203C22×#121—112no—
204C22×C4×D4—111no—
205#2543—1116no—
206C2×#398—111no—
207C2×#397D1111yescharacteristic, complemented
208C2×#394—111no—
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95—111no—
214C23×C11—28no—
215C23×C11—216no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—48no—
223C23×C11C22×D414yes—
224C23×C11C22×D412yes—
225C23×C11C22×D412yes—
226C23×C11C2×#4112yes—
227C23×C11C2×#4114yes—
228C23×C11H(5,𝔽2)14yes—
229C23×C11C2511yescharacteristic
230C22×D11—28no—
231C22×D11—28no—
232C22×D11—216no—
233C22×D11—216no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11#121116yes—
251C22×D11C22×D414yes—
252C22×D11C22×D414yes—
253C22×D11C2×#4114yes—
254C2×C4×C11—28no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—48no—
265C2×C4×C11—44no—
266C2×C4×C11—48no—
267C2×C4×C11C22×D414yes—
268C22⋊D11—232no—
269C22⋊D11—432no—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—216no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—416no—
281C2×Dic11—44no—
282C2×Dic11C22×D414yes—
283C2×Dic11C22×D414yes—
284C2×Dic11C2×#4118yes—
285D44—416no—
286D44—432no—
287C4×D11—416no—
288C4×D11—432no—
289C23×D4—111no—
290C23×D4—112no—
291C23×D4—112no—
292C23×D4—111no—
293C24×C4—111no—
294C24×C4—111no—
295C24×C4—112no—
296C2×#121—118no—
297C2×#121—1116no—
298C2×#121—2216no—
299C2×#121—228no—
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—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313#398—118no—
314#397C2×D1118yescomplemented
315#394—118no—
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—118no—
324C2×#95C2×D1111yescharacteristic
325C2×#95C2×D1112yes—
326C22×C11—24no—
327C22×C11—28no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—416no—
332C22×C11C2×#12114yes—
333C22×C11#53214yes—
334C22×C11#53414yes—
335C22×C11#54618yes—
336C22×C11#55318yes—
337C22×C11C23×D411yescharacteristic
338C22×C11C23×D411yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4112yes—
341C22×C11C2×H(5,𝔽2)12yes—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—28no—
345C2×D11—28no—
346C2×D11—232no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—816no—
355C2×D11C2×#12118yes—
356C4×C11—24no—
357C4×C11—44no—
358C4×C11—42no—
359C4×C11—44no—
360Dic11—24no—
361Dic11—24no—
362Dic11—28no—
363Dic11—42no—
364C25—111no—
365C25—112no—
366C25C22×D1111yescharacteristic
367C22×D4—118no—
368C22×D4—114no—
369C22×D4—118no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—228no—
373C22×D4—228no—
374C22×D4—228no—
375C22×D4—228no—
376C22×D4—224no—
377C22×D4—224no—
378C22×D4—228no—
379C22×D4—224no—
380C22×D4—444no—
381C22×D4—444no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—118no—
386C23×C4—114no—
387C23×C4—111no—
388C23×C4—114no—
389C23×C4—118no—
390C23×C4—228no—
391C23×C4—228no—
392C23×C4—224no—
393C23×C4—444no—
394C23×C4—444no—
395C23×C4—444no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1112yes—
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400#121—2264no—
401#121—2232no—
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—24no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
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—444no—
421C2×C22⋊C4C22×D1114yes—
422C2×C22⋊C4C22×D1118yes—
423C2×C42—114no—
424C2×C42—224no—
425#95—118no—
426#95—114no—
427#95—118no—
428#95C22×D1114yes—
429#95C22×D1118yes—
430C2×C11—44no—
431C2×C11#254318yescomplemented
432C2×C11C22×#12111yescharacteristic
433C2×C11C2×#53211yescharacteristic
434C2×C11C2×#53411yescharacteristic
435C2×C11C2×#54612yes—
436C2×C11C2×#55312yes—
437D11—28no—
438D11—84no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—24no—
443C24—114no—
444C24—114no—
445C24—114no—
446C24—112no—
447C24—114no—
448C24—224no—
449C24—224no—
450C24—224no—
451C24—224no—
452C24—224no—
453C24—224no—
454C24—224no—
455C24—224no—
456C24—224no—
457C24D4×D1114yes—
458C24C23×D1112yes—
459C24C23×D1111yescharacteristic
460C2×D4—1116no—
461C2×D4—2216no—
462C2×D4—2216no—
463C2×D4—2216no—
464C2×D4—2216no—
465C2×D4—228no—
466C2×D4—2232no—
467C2×D4—228no—
468C2×D4—2216no—
469C2×D4—228no—
470C2×D4—448no—
471C2×D4—4416no—
472C2×D4—4432no—
473C2×D4—448no—
474C2×D4—4432no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—114no—
485C22×C4—114no—
486C22×C4—118no—
487C22×C4—114no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—1116no—
491C22×C4—112no—
492C22×C4—2216no—
493C22×C4—2216no—
494C22×C4—228no—
495C22×C4—222no—
496C22×C4—224no—
497C22×C4—222no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—224no—
502C22×C4—4416no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—4432no—
506C22×C4—448no—
507C22×C4—4416no—
508C22×C4D4×D1114yes—
509C22×C4C23×D1114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C4⋊C4—28no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C22⋊C4—216no—
517C22⋊C4—28no—
518C22⋊C4—2216no—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C42—228no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—28no—
526C23—216no—
527C23—22no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—48no—
532C23—44no—
533C23—44no—
534C23—1116no—
535C23—114no—
536C23—114no—
537C23—114no—
538C23—2216no—
539C23—228no—
540C23—2216no—
541C23—224no—
542C23—224no—
543C23—228no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—448no—
552C23—448no—
553C23—448no—
554C23—448no—
555C23—448no—
556C23—448no—
557C23—448no—
558C23C2×D4×D1114yes—
559C23C2×D4×D1112yes—
560C23C2×D4×D1112yes—
561C23#41×D1112yes—
562C23#41×D1114yes—
563C23#6704214yes—
564C23C24×D1111yescharacteristic
565D4—2232no—
566D4—4416no—
567D4—4432no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—48no—
580C2×C4—48no—
581C2×C4—44no—
582C2×C4—114no—
583C2×C4—114no—
584C2×C4—118no—
585C2×C4—228no—
586C2×C4—228no—
587C2×C4—2216no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—4416no—
596C2×C4—4432no—
597C2×C4—4416no—
598C2×C4—444no—
599C2×C4C2×D4×D1114yes—
600C22—28no—
601C22—24no—
602C22—44no—
603C22—42no—
604C22—42no—
605C22—416no—
606C22—118no—
607C22—228no—
608C22—224no—
609C22—224no—
610C22—2232no—
611C22—228no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—8816no—
620C22D11×#12114yes—
621C22#1062318414yes—
622C22#1062318518yes—
623C22#1062319914yes—
624C22#1062324018yes—
625C22C22×D4×D1111yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C2×#41×D1111yescharacteristic
628C22C2×#41×D1112yes—
629C22C2×#6704212yes—
630C4—24no—
631C4—42no—
632C4—44no—
633C4—44no—
634C4—224no—
635C4—228no—
636C4—224no—
637C4—442no—
638C2—44no—
639C2—228no—
640C2—884no—
641C2#1307357318yesdirect product factor
642C2C2×D11×#12111yescharacteristic
643C2C2×#1062319911yescharacteristic
644C2C2×#1062318411yescharacteristic
645C2C2×#1062318512yes—
646C2C2×#1062324012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66937C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13073573C2direct (N × H)
5. C2×#10622593C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622571C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#397C2semidirect
32. C2×#66948C22semidirect
34. C2×#66937C22semidirect
36. C2×(C22⋊D11)⋊C4C22semidirect
37. C11×#397C22semidirect
43. #10622593C22semidirect
44. #10622573C22semidirect
45. #10622571C22semidirect
46. #10622285C22semidirect
47. #10622282C22semidirect
48. #10622278C22semidirect
49. D11×#95C22semidirect
62. C22×C22⋊D11D4semidirect
83. C22×C4×D11D4semidirect
159. C2×C22⋊D11C2×D4semidirect
190. C2×C4×D11C2×D4semidirect
207. C2×#397D11semidirect
314. #397C2×D11semidirect
431. C2×C11#2543semidirect
524. C11C2×#2543semidirect
641. C2#13073573direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669372
C22×(C22⋊D11)⋊C42
#130735732
C2×#106225932
C2×#106222852
C2×#106225732
C2×#106222822
C2×#106222782
C2×#106225712
C2×D11×#952
C2×C11×#3972
C2×#254311