Finite Group Databasebeta

← C2×C11×#1901 #14598181

Subgroups — C2×C11×#1901 #14598181

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic
3C22×C11×#101C212yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic
5C11×#1901C218yesmaximal, direct product factor
6C2×C11×#343C212yesmaximal, complemented
7C23×Q8×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C22×C11×M16—22no—
10C22×C11×M16—21no—
11C22×C11×M16—28no—
12C22×C11×M16C2214yes—
13C22×C11×M16C2212yes—
14C22×C11×M16C2212yes—
15C23×C8×C11—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—22no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8C414yes—
23C2×C11×C22⋊Q8C2214yes—
24C22×C11×C4⋊C4C412yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C412yes—
27C2×C11×#101—28no—
28C2×C11×#101C2218yescomplemented
29C11×#407—22no—
30C11×#407C2214yes—
31C2×C11×C22⋊C8—21no—
32C2×C11×C22⋊C8—21no—
33C11×#343C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—24no—
40C22×Q8×C11—24no—
41C22×Q8×C11C2×C412yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11C2×C412yes—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C412yes—
48C23×C4×C11C2×C412yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D412yes—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D412yes—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C2×C11×M16—216no—
58C2×C11×M16—28no—
59C2×C11×M16—24no—
60C2×C11×M16—24no—
61C2×C11×M16—22no—
62C2×C11×M16—216no—
63C2×C11×M16—22no—
64C2×C11×M16—24no—
65C2×C11×M16—24no—
66C2×C11×M16D418yes—
67C2×C11×M16C2314yes—
68C2×C11×M16C2314yes—
69C22×C8×C11—28no—
70C22×C8×C11—24no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—24no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2×C418yes—
89C2×C11×C4⋊C4C2×C412yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4C2×C418yes—
95C11×#101—216no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—24no—
98C2×#1901C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—42no—
102C24×C11C22⋊C411yescharacteristic
103C24×C11C22⋊C412yes—
104C24×C11C22⋊C411yescharacteristic
105C24×C11C22×C412yes—
106C24×C11C22×C411yescharacteristic
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—28no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—24no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11—44no—
117C2×Q8×C11—44no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C22×C4×C11—24no—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—28no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—28no—
138C22×C4×C11—44no—
139C22×C4×C11C22⋊C412yes—
140C22×C4×C11C22⋊C412yes—
141C22×C4×C11C22⋊C412yes—
142C22×C4×C11C22⋊C412yes—
143C22×C4×C11C22⋊C412yes—
144C22×C4×C11C22⋊C411yescharacteristic
145C22×C4×C11C22⋊C411yescharacteristic
146C22×C4×C11C22×C414yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11#4114yes—
160C22×C4×C11C2411yescharacteristic
161C11×M16—216no—
162C11×M16—28no—
163C11×M16—24no—
164C11×M16—24no—
165C11×M16—24no—
166C11×M16—44no—
167C11×M16C2×D418yes—
168C2×C8×C11—216no—
169C2×C8×C11—28no—
170C2×C8×C11—24no—
171C2×C8×C11—24no—
172C2×C8×C11—44no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C23×M16C2×C1111yescharacteristic
182C22×C22⋊Q8C2×C1111yescharacteristic
183C22×#101C2×C1112yescomplemented
184C2×#407C2×C1111yescharacteristic
185#1901C2×C1118yesdirect product factor
186C2×#343C2×C1112yescomplemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—416no—
201C23×C11#10114yescomplemented
202C23×C11C2×C22⋊C412yes—
203C23×C11C2×C22⋊C411yescharacteristic
204C23×C11C2×C22⋊C412yes—
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11C4×D414yes—
207C23×C11C23×C411yescharacteristic
208Q8×C11—42no—
209Q8×C11—44no—
210Q8×C11—42no—
211Q8×C11—44no—
212Q8×C11—44no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—28no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C4×D414yes—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11#12114yes—
243C2×C4×C11#12114yes—
244C2×C4×C11#12312yes—
245C2×C4×C11#12312yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4112yes—
250C8×C11—28no—
251C8×C11—44no—
252C23×Q8C22×C1111yescharacteristic
253C24×C4C22×C1111yescharacteristic
254C22×M16—22no—
255C22×M16—21no—
256C22×M16—28no—
257C22×M16C22×C1112yes—
258C22×M16C22×C1114yes—
259C22×M16C22×C1112yes—
260C23×C8—21no—
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—22no—
264C2×C22⋊Q8—21no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—22no—
267C2×C22⋊Q8C4×C1114yes—
268C2×C22⋊Q8C22×C1114yes—
269C22×C4⋊C4C4×C1112yes—
270C22×C4⋊C4C22×C1111yescharacteristic
271C22×C22⋊C4C4×C1112yes—
272C2×#101—28no—
273C2×#101C22×C1118yescomplemented
274#407—22no—
275#407C22×C1114yes—
276C2×C22⋊C8—21no—
277C2×C22⋊C8—21no—
278#343C22×C1118yescomplemented
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—28no—
285C22×C11—28no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—48no—
291C22×C11—48no—
292C22×C11—44no—
293C22×C11#38612yes—
294C22×C11#38612yes—
295C22×C11C2×#10112yes—
296C22×C11C2×#10114yescomplemented
297C22×C11#41312yes—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11C2×C4×D412yes—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—44no—
303C4×C11—44no—
304C4×C11#38612yes—
305C4×C11#38612yes—
306C4×C11C2×#12011yescharacteristic
307C4×C11C2×#12112yes—
308C4×C11C2×#12311yescharacteristic
309C25C2×C4×C1111yescharacteristic
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—24no—
315C22×Q8—24no—
316C22×Q8C2×C4×C1112yes—
317C22×Q8C23×C1112yes—
318C23×C4—24no—
319C23×C4—24no—
320C23×C4C2×C4×C1112yes—
321C23×C4C2×C4×C1111yescharacteristic
322C23×C4C2×C4×C1112yes—
323C23×C4C2×C4×C1112yes—
324C23×C4D4×C1111yescharacteristic
325C23×C4D4×C1112yes—
326C23×C4D4×C1111yescharacteristic
327C23×C4D4×C1111yescharacteristic
328C23×C4D4×C1111yescharacteristic
329C23×C4D4×C1112yes—
330C23×C4C23×C1112yes—
331C23×C4C23×C1111yescharacteristic
332C2×M16—216no—
333C2×M16—28no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—22no—
337C2×M16—216no—
338C2×M16—22no—
339C2×M16—24no—
340C2×M16—24no—
341C2×M16D4×C1118yes—
342C2×M16C23×C1114yes—
343C2×M16C23×C1114yes—
344C22×C8—28no—
345C22×C8—24no—
346C22×C8—22no—
347C22×C8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2×C4×C1118yes—
364C2×C4⋊C4C2×C4×C1112yes—
365C2×C4⋊C4C23×C1112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4C2×C4×C1118yes—
370#101—216no—
371C22⋊C8—24no—
372C22⋊C8—24no—
373C2×C11—22no—
374C2×C11—22no—
375C2×C11—24no—
376C2×C11—42no—
377C2×C11#190114yesdirect product factor
378C2×C11C2×#38611yescharacteristic
379C2×C11C22×#10111yescharacteristic
380C2×C11C2×#41311yescharacteristic
381C24—24no—
382C24—24no—
383C24—42no—
384C24C11×C22⋊C411yescharacteristic
385C24C11×C22⋊C412yes—
386C24C11×C22⋊C411yescharacteristic
387C24C22×C4×C1112yes—
388C24C22×C4×C1111yescharacteristic
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—28no—
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—24no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—44no—
399C2×Q8—44no—
400C2×Q8—42no—
401C2×Q8—42no—
402C22×C4—24no—
403C22×C4—28no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—28no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—28no—
420C22×C4—44no—
421C22×C4C11×C22⋊C412yes—
422C22×C4C11×C22⋊C411yescharacteristic
423C22×C4C11×C22⋊C411yescharacteristic
424C22×C4C11×C22⋊C412yes—
425C22×C4C11×C22⋊C412yes—
426C22×C4C11×C22⋊C412yes—
427C22×C4C11×C22⋊C412yes—
428C22×C4C22×C4×C1114yes—
429C22×C4C22×C4×C1112yes—
430C22×C4C22×C4×C1114yes—
431C22×C4C22×C4×C1111yescharacteristic
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1112yes—
434C22×C4C2×D4×C1112yes—
435C22×C4C2×D4×C1112yes—
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1114yes—
441C22×C4C11×#4114yes—
442C22×C4C24×C1111yescharacteristic
443M16—216no—
444M16—28no—
445M16—24no—
446M16—24no—
447M16—24no—
448M16—44no—
449M16C2×D4×C1118yes—
450C2×C8—216no—
451C2×C8—28no—
452C2×C8—24no—
453C2×C8—24no—
454C2×C8—44no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C22⋊C4—28no—
462C22⋊C4—28no—
463C11C2×#190111yescharacteristic, direct product factor, Sylow
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—42no—
476C23—42no—
477C23—416no—
478C23C11×#10114yescomplemented
479C23C2×C11×C22⋊C412yes—
480C23C2×C11×C22⋊C411yescharacteristic
481C23C2×C11×C22⋊C412yes—
482C23C2×C11×C22⋊C411yescharacteristic
483C23C4×D4×C1114yes—
484C23C23×C4×C1111yescharacteristic
485Q8—42no—
486Q8—44no—
487Q8—44no—
488Q8—44no—
489Q8—42no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—28no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4C2×C11×C22⋊C412yes—
513C2×C4C2×C11×C22⋊C412yes—
514C2×C4C2×C11×C22⋊C411yescharacteristic
515C2×C4C2×C11×C22⋊C411yescharacteristic
516C2×C4C4×D4×C1114yes—
517C2×C4C11×#12012yes—
518C2×C4C11×#12012yes—
519C2×C4C11×#12114yes—
520C2×C4C11×#12114yes—
521C2×C4C11×#12312yes—
522C2×C4C11×#12312yes—
523C2×C4C22×D4×C1112yes—
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C22×D4×C1111yescharacteristic
526C2×C4C2×C11×#4112yes—
527C8—28no—
528C8—44no—
529C22—28no—
530C22—28no—
531C22—22no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—44no—
543C22C11×#38612yes—
544C22C11×#38612yes—
545C22C2×C11×#10112yes—
546C22C2×C11×#10114yescomplemented
547C22C11×#41312yes—
548C22C22×C11×C22⋊C411yescharacteristic
549C22C2×C4×D4×C1112yes—
550C4—22no—
551C4—22no—
552C4—44no—
553C4—44no—
554C4C11×#38612yes—
555C4C11×#38612yes—
556C4C2×C11×#12011yescharacteristic
557C4C2×C11×#12112yes—
558C4C2×C11×#12311yescharacteristic
559C2—22no—
560C2—22no—
561C2—24no—
562C2—42no—
563C2C11×#190114yesdirect product factor
564C2C2×C11×#38611yescharacteristic
565C2C22×C11×#10111yescharacteristic
566C2C2×C11×#41311yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11C2×C4
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
3. C22×C11×#101C2semidirect
5. C11×#1901C2direct (N × H)
6. C2×C11×#343C2semidirect
28. C2×C11×#101C22semidirect
33. C11×#343C22semidirect
98. C2×#1901C11direct (N × H)
183. C22×#101C2×C11semidirect
185. #1901C2×C11direct (N × H)
186. C2×#343C2×C11semidirect
201. C23×C11#101semidirect
273. C2×#101C22×C11semidirect
278. #343C22×C11semidirect
296. C22×C11C2×#101semidirect
377. C2×C11#1901direct (N × H)
463. C11C2×#1901direct (N × H)
478. C23C11×#101semidirect
546. C22C2×C11×#101semidirect
563. C2C11×#1901direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×M162
C22×C11×C22⋊Q82
C22×C11×#1012
C2×C11×#4072
C11×#19012
C2×C11×#3432
C2×#190111