Finite Group Databasebeta

← C2×C11×#1964 #14598404

Subgroups — C2×C11×#1964 #14598404

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C22×C11×#99C214yesmaximal, complemented
3C2×C11×#380C211yesmaximal, characteristic, complemented
4C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#1964C218yesmaximal, direct product factor
6C23×D4×C11C411yescharacteristic, complemented
7C23×D4×C11C2212yes—
8C24×C4×C11C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#121—21no—
11C2×C11×#121—21no—
12C2×C11×#121—21no—
13C2×C11×#121—22no—
14C2×C11×#121—22no—
15C2×C11×#121C414yescomplemented
16C2×C11×#121C2214yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C411yescharacteristic, complemented
19C22×C11×C22⋊C4C412yescomplemented
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C42×C11—21no—
23C2×C11×#99—216no—
24C2×C11×#99C22116yescomplemented
25C11×#380—22no—
26C11×#380C2214yescomplemented
27C4×C11×C22⋊C4—22no—
28C4×C11×C22⋊C4C2214yescomplemented
29C2×C11×#95—21no—
30C2×C11×#95—21no—
31C25×C11C2×C412yes—
32C25×C11C2311yescharacteristic
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—28no—
38C22×D4×C11—28no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—44no—
43C22×D4×C11C2×C414yes—
44C22×D4×C11C2×C414yescomplemented
45C22×D4×C11C2314yes—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—44no—
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C412yes—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D412yes—
58C23×C4×C11D412yes—
59C23×C4×C11C2312yes—
60C11×#121—24no—
61C11×#121—24no—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—24no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—44no—
73C2×C11×C4⋊C4C2×C414yescomplemented
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4C2×C418yescomplemented
82C2×C11×C22⋊C4D418yescomplemented
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C42×C11—24no—
86C2×C42×C11—44no—
87C11×#99—232no—
88C11×#95—24no—
89C11×#95—24no—
90C2×#1964C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—28no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11—44no—
97C24×C11—44no—
98C24×C11C22×C411yescharacteristic
99C24×C11C22×C414yes—
100C24×C11C22×C411yescharacteristic
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D414yes—
106C24×C11#4114yes—
107C24×C11C2411yescharacteristic
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—216no—
111C2×D4×C11—28no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—44no—
118C2×D4×C11—48no—
119C2×D4×C11—48no—
120C2×D4×C11—48no—
121C2×D4×C11—48no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11C22⋊C412yes—
149C22×C4×C11C22⋊C412yes—
150C22×C4×C11C22⋊C412yes—
151C22×C4×C11C22⋊C411yescharacteristic
152C22×C4×C11C22⋊C411yescharacteristic
153C22×C4×C11C22⋊C411yescharacteristic
154C22×C4×C11C22⋊C412yes—
155C22×C4×C11C22⋊C412yes—
156C22×C4×C11C22⋊C412yes—
157C22×C4×C11C22⋊C411yescharacteristic
158C22×C4×C11C22×C414yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—48no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4C2×D418yescomplemented
175C42×C11—48no—
176C22×#121C2×C1111yescharacteristic
177C22×#99C2×C1114yescomplemented
178C2×#380C2×C1111yescharacteristic, complemented
179C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
180#1964C2×C1118yesdirect product factor
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—41no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—816no—
208C23×C11C2×C22⋊C411yescharacteristic
209C23×C11C2×C22⋊C411yescharacteristic
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C4×D414yes—
213C23×C11C4×D414yes—
214C23×C11#12114yes—
215C23×C11#12114yes—
216C23×C11#12412yes—
217C23×C11#12412yes—
218C23×C11#12712yes—
219C23×C11#12712yes—
220C23×C11C23×C411yescharacteristic
221C23×C11C22×D411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×D412yes—
224C23×C11C2×#4112yes—
225D4×C11—48no—
226D4×C11—48no—
227D4×C11—44no—
228D4×C11—44no—
229D4×C11—48no—
230D4×C11—48no—
231D4×C11—48no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
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—28no—
243C2×C4×C11—28no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—416no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—88no—
259C2×C4×C11#9914yescomplemented
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C2×C22⋊C412yes—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C412yes—
264C23×D4C4×C1111yescharacteristic, complemented
265C23×D4C22×C1112yes—
266C24×C4C22×C1111yescharacteristic
267C2×#121—21no—
268C2×#121—21no—
269C2×#121—21no—
270C2×#121—21no—
271C2×#121—22no—
272C2×#121—22no—
273C2×#121C4×C1114yescomplemented
274C2×#121C22×C1114yes—
275C22×C4⋊C4—21no—
276C22×C4⋊C4C4×C1111yescharacteristic, complemented
277C22×C22⋊C4C4×C1112yescomplemented
278C22×C22⋊C4C22×C1112yes—
279C22×C22⋊C4C22×C1112yes—
280C22×C42—21no—
281C2×#99—216no—
282C2×#99C22×C11116yescomplemented
283#380—22no—
284#380C22×C1114yescomplemented
285C4×C22⋊C4—22no—
286C4×C22⋊C4C22×C1114yescomplemented
287C2×#95—21no—
288C2×#95—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—28no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—24no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—88no—
315C22×C11—88no—
316C22×C11—88no—
317C22×C11#39012yes—
318C22×C11#39012yes—
319C22×C11#39012yes—
320C22×C11#39012yes—
321C22×C11C2×#9912yes—
322C22×C11#41012yes—
323C22×C11C22×C22⋊C411yescharacteristic
324C22×C11C2×C4×D412yes—
325C22×C11C2×#12112yes—
326C22×C11C2×#12411yescharacteristic
327C22×C11C2×#12711yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—48no—
332C4×C11—44no—
333C4×C11—84no—
334C4×C11C2×#9914yescomplemented
335C25C2×C4×C1112yes—
336C25C23×C1111yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—28no—
342C22×D4—28no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—44no—
347C22×D4C2×C4×C1114yes—
348C22×D4C2×C4×C1114yescomplemented
349C22×D4C23×C1114yes—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—44no—
353C23×C4C2×C4×C1112yes—
354C23×C4C2×C4×C1111yescharacteristic
355C23×C4C2×C4×C1111yescharacteristic
356C23×C4C2×C4×C1112yes—
357C23×C4D4×C1111yescharacteristic
358C23×C4D4×C1111yescharacteristic
359C23×C4D4×C1111yescharacteristic
360C23×C4D4×C1111yescharacteristic
361C23×C4D4×C1112yes—
362C23×C4D4×C1112yes—
363C23×C4C23×C1112yes—
364#121—24no—
365#121—24no—
366#121—24no—
367#121—24no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×C4×C1114yescomplemented
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4C2×C4×C1118yescomplemented
386C2×C22⋊C4D4×C1118yescomplemented
387C2×C22⋊C4C23×C1114yes—
388C2×C22⋊C4C23×C1114yes—
389C2×C42—24no—
390C2×C42—44no—
391#99—232no—
392#95—24no—
393#95—24no—
394C2×C11—22no—
395C2×C11—21no—
396C2×C11—22no—
397C2×C11—22no—
398C2×C11—21no—
399C2×C11—22no—
400C2×C11—22no—
401C2×C11—84no—
402C2×C11#196414yesdirect product factor
403C2×C11C2×#39011yescharacteristic
404C2×C11C22×#9911yescharacteristic
405C2×C11C2×#41011yescharacteristic
406C24—22no—
407C24—22no—
408C24—28no—
409C24—42no—
410C24—42no—
411C24—44no—
412C24—44no—
413C24C22×C4×C1111yescharacteristic
414C24C22×C4×C1114yes—
415C24C22×C4×C1111yescharacteristic
416C24C2×D4×C1111yescharacteristic
417C24C2×D4×C1111yescharacteristic
418C24C2×D4×C1111yescharacteristic
419C24C2×D4×C1111yescharacteristic
420C24C2×D4×C1114yes—
421C24C11×#4114yes—
422C24C24×C1111yescharacteristic
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—216no—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—28no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—44no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4C11×C22⋊C411yescharacteristic
464C22×C4C11×C22⋊C411yescharacteristic
465C22×C4C11×C22⋊C411yescharacteristic
466C22×C4C11×C22⋊C412yes—
467C22×C4C11×C22⋊C412yes—
468C22×C4C11×C22⋊C412yes—
469C22×C4C11×C22⋊C412yes—
470C22×C4C11×C22⋊C412yes—
471C22×C4C11×C22⋊C412yes—
472C22×C4C11×C22⋊C411yescharacteristic
473C22×C4C22×C4×C1114yes—
474C22×C4C22×C4×C1112yes—
475C22×C4C22×C4×C1112yes—
476C22×C4C2×D4×C1112yes—
477C22×C4C2×D4×C1112yes—
478C22×C4C2×D4×C1112yes—
479C22×C4C2×D4×C1112yes—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—48no—
483C22⋊C4—28no—
484C22⋊C4—24no—
485C22⋊C4—28no—
486C22⋊C4—28no—
487C22⋊C4—28no—
488C22⋊C4—44no—
489C22⋊C4C2×D4×C1118yescomplemented
490C42—48no—
491C11C2×#196411yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—28no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—48no—
506C23—41no—
507C23—41no—
508C23—48no—
509C23—41no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23—816no—
519C23C2×C11×C22⋊C411yescharacteristic
520C23C2×C11×C22⋊C411yescharacteristic
521C23C2×C11×C22⋊C411yescharacteristic
522C23C2×C11×C22⋊C411yescharacteristic
523C23C4×D4×C1114yes—
524C23C4×D4×C1114yes—
525C23C11×#12114yes—
526C23C11×#12114yes—
527C23C11×#12412yes—
528C23C11×#12412yes—
529C23C11×#12712yes—
530C23C11×#12712yes—
531C23C23×C4×C1111yescharacteristic
532C23C22×D4×C1111yescharacteristic
533C23C22×D4×C1111yescharacteristic
534C23C22×D4×C1112yes—
535C23C2×C11×#4112yes—
536D4—48no—
537D4—48no—
538D4—44no—
539D4—48no—
540D4—48no—
541D4—44no—
542D4—48no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—28no—
554C2×C4—28no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—416no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—88no—
570C2×C4C11×#9914yescomplemented
571C2×C4C2×C11×C22⋊C412yes—
572C2×C4C2×C11×C22⋊C412yes—
573C2×C4C2×C11×C22⋊C412yes—
574C2×C4C2×C11×C22⋊C412yes—
575C22—28no—
576C22—24no—
577C22—28no—
578C22—24no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—44no—
592C22—44no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—88no—
601C22—88no—
602C22—88no—
603C22C11×#39012yes—
604C22C11×#39012yes—
605C22C11×#39012yes—
606C22C11×#39012yes—
607C22C2×C11×#9912yes—
608C22C11×#41012yes—
609C22C22×C11×C22⋊C411yescharacteristic
610C22C2×C4×D4×C1112yes—
611C22C2×C11×#12112yes—
612C22C2×C11×#12411yescharacteristic
613C22C2×C11×#12711yescharacteristic
614C4—22no—
615C4—22no—
616C4—22no—
617C4—48no—
618C4—44no—
619C4—84no—
620C4C2×C11×#9914yescomplemented
621C2—22no—
622C2—21no—
623C2—22no—
624C2—22no—
625C2—21no—
626C2—22no—
627C2—22no—
628C2—84no—
629C2C11×#196414yesdirect product factor
630C2C2×C11×#39011yescharacteristic
631C2C22×C11×#9911yescharacteristic
632C2C2×C11×#41011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C2×C11×#380C2semidirect
4. C2×C4×C11×C22⋊C4C2semidirect
5. C11×#1964C2direct (N × H)
6. C23×D4×C11C4semidirect
15. C2×C11×#121C4semidirect
18. C22×C11×C4⋊C4C4semidirect
19. C22×C11×C22⋊C4C4semidirect
24. C2×C11×#99C22semidirect
26. C11×#380C22semidirect
28. C4×C11×C22⋊C4C22semidirect
44. C22×D4×C11C2×C4semidirect
73. C2×C11×C4⋊C4C2×C4semidirect
81. C2×C11×C22⋊C4C2×C4semidirect
82. C2×C11×C22⋊C4D4semidirect
90. C2×#1964C11direct (N × H)
174. C11×C22⋊C4C2×D4semidirect
177. C22×#99C2×C11semidirect
178. C2×#380C2×C11semidirect
179. C2×C4×C22⋊C4C2×C11semidirect
180. #1964C2×C11direct (N × H)
259. C2×C4×C11#99semidirect
264. C23×D4C4×C11semidirect
273. C2×#121C4×C11semidirect
276. C22×C4⋊C4C4×C11semidirect
277. C22×C22⋊C4C4×C11semidirect
282. C2×#99C22×C11semidirect
284. #380C22×C11semidirect
286. C4×C22⋊C4C22×C11semidirect
334. C4×C11C2×#99semidirect
348. C22×D4C2×C4×C11semidirect
377. C2×C4⋊C4C2×C4×C11semidirect
385. C2×C22⋊C4C2×C4×C11semidirect
386. C2×C22⋊C4D4×C11semidirect
402. C2×C11#1964direct (N × H)
489. C22⋊C4C2×D4×C11semidirect
491. C11C2×#1964direct (N × H)
570. C2×C4C11×#99semidirect
620. C4C2×C11×#99semidirect
629. C2C11×#1964direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C11×#992
C2×C11×#3802
C2×C4×C11×C22⋊C42
C11×#19642
C2×#196411