Finite Group Databasebeta

← C2×#13066952 #14719628

Subgroups — C2×#13066952 #14719628

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13066952C218yesmaximal, direct product factor
4C2×#10622107C212yesmaximal, complemented
5C2×#10622106C212yesmaximal, complemented
6C2×C11×#407C211yesmaximal, characteristic, complemented
7C24×C4×C11C2211yescharacteristic
8C23×C22⋊D11C411yescharacteristic
9C23×C4×D11C411yescharacteristic
10C22×C11×M16—21no—
11C22×C22⋊Dic11C411yescharacteristic
12C2×C4×C22⋊D11—21no—
13C2×C4×C22⋊D11—21no—
14C2×C4×C22⋊D11—22no—
15C2×C4×C22⋊D11—21no—
16C2×C4×C22⋊D11—21no—
17C2×C4×C22⋊D11—22no—
18C2×C4×C22⋊D11C414yes—
19C2×C4×C22⋊D11C2214yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C411yescharacteristic
23C22×#4318—21no—
24C11×#407—22no—
25C11×#407C2214yescomplemented
26C2×C11×C22⋊C8—21no—
27C2×C11×C22⋊C8C2212yes—
28#10622820—22no—
29#10622820C2214yescomplemented
30C2×C22⋊(C11⋊C8)—21no—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622107C2218yescomplemented
33#10622106C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C24×D11C2×C411yescharacteristic
36C23×C4×C11—44no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C412yes—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D412yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—21no—
48C22×C22⋊D11—21no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11C2×C414yes—
53C23×Dic11C2×C411yescharacteristic
54C23×Dic11C2×C411yescharacteristic
55C23×Dic11C2×C411yescharacteristic
56C22×C4×D11—22no—
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—44no—
60C22×C4×D11C2×C414yes—
61C2×C11×M16—24no—
62C2×C11×M16—44no—
63C22×C8×C11—22no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11C2×C414yes—
68C4×C22⋊D11—24no—
69C4×C22⋊D11—24no—
70C4×C22⋊D11—24no—
71C4×C22⋊D11—24no—
72C4×C22⋊D11—24no—
73C4×C22⋊D11—24no—
74C4×C22⋊D11—24no—
75C4×C22⋊D11—24no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4C2×C412yes—
81C2×(C2×D11)⋊C4C2312yes—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4C2×C412yes—
87C2×Dic11⋊C4C2312yes—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2×C414yes—
92C2×#4318—24no—
93C2×#4318—44no—
94C22×C11⋊C8—22no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8C2314yes—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)C2314yes—
101C2×#1465—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11C22⋊C411yescharacteristic
107C24×C11C22⋊C411yescharacteristic
108C24×C11C22⋊C412yes—
109C24×C11C22×C411yescharacteristic
110C24×C11C22×C412yes—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—22no—
114C23×D11—42no—
115C23×D11—42no—
116C23×D11M1614yescomplemented
117C23×D11C22×C412yes—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—44no—
124C22×C4×C11—44no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C22⋊C411yescharacteristic
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22⋊C412yes—
131C22×C4×C11C22⋊C412yes—
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22⋊C412yes—
134C22×C4×C11C22⋊C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—216no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—24no—
151C2×C22⋊D11—24no—
152C2×C22⋊D11—28no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11M1614yescomplemented
163C22×Dic11C22×C412yes—
164C22×Dic11C22×C412yes—
165C22×Dic11C22×C412yes—
166C2×C4×D11—24no—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—44no—
172C11×M16—48no—
173C2×C8×C11—24no—
174C2×C8×C11—44no—
175C22⋊Dic11—24no—
176C22⋊Dic11—24no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—22no—
185C4×Dic11—24no—
186C4×Dic11—24no—
187#4318—48no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—44no—
190C22×C4×D4—111no—
191C2×#407—111no—
192C2×#407D1111yescharacteristic, complemented
193#1465—118no—
194C2×#324—112no—
195C2×#323—112no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11C2×C22⋊C412yes—
214C23×C11C2×C22⋊C412yes—
215C23×C11C2×C22⋊C411yescharacteristic
216C23×C11C2×C22⋊C411yescharacteristic
217C23×C11C2×M1612yes—
218C23×C11C2×M1612yes—
219C23×C11C23×C411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—48no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—48no—
231C22×D11—42no—
232C22×D11C2×M1614yescomplemented
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11#9914yes—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C22⋊D11—216no—
258C22⋊D11—216no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11C2×M1614yescomplemented
272C4×D11—48no—
273C4×D11—48no—
274C8×C11—44no—
275C11⋊C8—44no—
276C23×D4—111no—
277C24×C4—111no—
278C24×C4C2×D1111yescharacteristic
279C22×M16—21no—
280C22×M16—221no—
281C2×C4×D4—114no—
282C2×C4×D4—114no—
283C2×C4×D4—221no—
284C2×C4×D4—221no—
285C2×C4×D4—222no—
286C2×C4×D4—221no—
287C2×C4×D4—221no—
288C2×C4×D4—222no—
289C22×C4⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—111no—
292C22×C42—111no—
293#407—22no—
294#407—114no—
295#407—222no—
296#407C2×D1114yescomplemented
297C2×C22⋊C8—21no—
298C2×C22⋊C8—112no—
299C2×C22⋊C8—221no—
300C2×C22⋊C8C2×D1112yes—
301#324—118no—
302#323—118no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—48no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11#40712yes—
321C22×C11#40712yes—
322C22×C11C2×#9912yes—
323C22×C11#41312yes—
324C22×C11C22×C22⋊C411yescharacteristic
325C22×C11C22×M1611yescharacteristic
326C22×C11C22×M1611yescharacteristic
327C2×D11—24no—
328C2×D11—44no—
329C2×D11—48no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—48no—
333C2×D11—44no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11C2×#9914yes—
340Dic11—24no—
341Dic11—42no—
342Dic11—42no—
343C25—111no—
344C25C4×D1111yescharacteristic
345C22×D4—114no—
346C22×D4—224no—
347C22×D4—224no—
348C22×D4—222no—
349C22×D4—221no—
350C22×D4—221no—
351C23×C4—44no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—114no—
356C23×C4—222no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4—444no—
360C23×C4C4×D1111yescharacteristic
361C23×C4C4×D1112yes—
362C23×C4D4411yescharacteristic
363C23×C4D4411yescharacteristic
364C23×C4D4412yes—
365C23×C4C22⋊D1111yescharacteristic
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22⋊D1112yes—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370C2×M16—24no—
371C2×M16—44no—
372C2×M16—224no—
373C2×M16—444no—
374C22×C8—22no—
375C22×C8—222no—
376C4×D4—224no—
377C4×D4—224no—
378C4×D4—224no—
379C4×D4—224no—
380C4×D4—224no—
381C4×D4—224no—
382C4×D4—224no—
383C4×D4—224no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C42—114no—
401C2×C42—222no—
402C2×C42—221no—
403C2×C42—221no—
404C22⋊C8—24no—
405C22⋊C8—22no—
406C22⋊C8—114no—
407C22⋊C8—222no—
408C22⋊C8—224no—
409C22⋊C8C22×D1114yes—
410C2×C11—21no—
411C2×C11—21no—
412C2×C11—22no—
413C2×C11—42no—
414C2×C11—42no—
415C2×C11#146514yescomplemented
416C2×C11C2×#40711yescharacteristic
417C2×C11C22×#9911yescharacteristic
418C2×C11C2×#41311yescharacteristic
419D11—44no—
420C24—22no—
421C24—22no—
422C24—42no—
423C24—42no—
424C24—114no—
425C24—112no—
426C24—222no—
427C24—221no—
428C24—221no—
429C24—442no—
430C24—442no—
431C24(C2×D11)⋊C411yescharacteristic
432C24(C2×D11)⋊C411yescharacteristic
433C24(C2×D11)⋊C412yes—
434C24C2×C4×D1111yescharacteristic
435C24C2×C4×D1112yes—
436C2×D4—228no—
437C2×D4—228no—
438C2×D4—2216no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—224no—
442C2×D4—224no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—444no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4—444no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4(C2×D11)⋊C412yes—
473C22×C4(C2×D11)⋊C412yes—
474C22×C4(C2×D11)⋊C412yes—
475C22×C4(C2×D11)⋊C411yescharacteristic
476C22×C4(C2×D11)⋊C412yes—
477C22×C4(C2×D11)⋊C412yes—
478C22×C4(C2×D11)⋊C411yescharacteristic
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×D4412yes—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4412yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1112yes—
489C22×C4C23×D1111yescharacteristic
490M16—48no—
491M16—448no—
492C2×C8—24no—
493C2×C8—44no—
494C2×C8—224no—
495C2×C8—444no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C22⋊C4—224no—
501C22⋊C4—224no—
502C22⋊C4—222no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C42—224no—
507C42—224no—
508C11C2×#146511yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—48no—
525C23—48no—
526C23—114no—
527C23—224no—
528C23—224no—
529C23—222no—
530C23—222no—
531C23—442no—
532C23—442no—
533C23—448no—
534C23—442no—
535C23—442no—
536C23—448no—
537C23—442no—
538C23—442no—
539C23M16×D1112yes—
540C23M16×D1112yes—
541C23C2×(C2×D11)⋊C412yes—
542C23C2×(C2×D11)⋊C412yes—
543C23C2×(C2×D11)⋊C411yescharacteristic
544C23C2×(C2×D11)⋊C411yescharacteristic
545C23C22×C4×D1111yescharacteristic
546D4—2216no—
547D4—2216no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—114no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—448no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—448no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4#6687014yes—
581C2×C4C2×(C2×D11)⋊C412yes—
582C2×C4C2×(C2×D11)⋊C411yescharacteristic
583C2×C4C2×(C2×D11)⋊C411yescharacteristic
584C2×C4C2×(C2×D11)⋊C412yes—
585C2×C4C22×D4411yescharacteristic
586C2×C4C22×C22⋊D1111yescharacteristic
587C8—44no—
588C8—444no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—24no—
594C22—24no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—48no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—224no—
607C22—444no—
608C22—448no—
609C22—444no—
610C22—442no—
611C22—442no—
612C22—448no—
613C22C2×#6687012yes—
614C22#1062273912yes—
615C22#1062273912yes—
616C22#1062274512yes—
617C22C2×M16×D1111yescharacteristic
618C22C2×M16×D1111yescharacteristic
619C22C22×(C2×D11)⋊C411yescharacteristic
620C4—21no—
621C4—21no—
622C4—22no—
623C4—21no—
624C4—21no—
625C4—224no—
626C4—442no—
627C4—442no—
628C4C2×#6687014yes—
629C2—22no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—444no—
635C2#1306695214yesdirect product factor
636C2C2×#1062273911yescharacteristic
637C2C22×#6687011yescharacteristic
638C2C2×#1062274511yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11C2×#1465
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622820C2semidirect
3. #13066952C2direct (N × H)
4. C2×#10622107C2semidirect
5. C2×#10622106C2semidirect
6. C2×C11×#407C2semidirect
25. C11×#407C22semidirect
29. #10622820C22semidirect
32. #10622107C22semidirect
33. #10622106C22semidirect
116. C23×D11M16semidirect
162. C22×Dic11M16semidirect
192. C2×#407D11semidirect
232. C22×D11C2×M16semidirect
271. C2×Dic11C2×M16semidirect
296. #407C2×D11semidirect
415. C2×C11#1465semidirect
508. C11C2×#1465semidirect
635. C2#13066952direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228202
#130669522
C2×#106221072
C2×#106221062
C2×C11×#4072
C2×#146511