Finite Group Databasebeta

← C2×C11×#1282 #14585116

Subgroups — C2×C11×#1282 #14585116

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊C8C211yesmaximal, characteristic
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
4C11×#1282C214yesmaximal, direct product factor
5C24×C4×C11C2211yescharacteristic
6C23×C8×C11—21no—
7C23×C8×C11C412yescomplemented
8C22×C11×C22⋊C4C412yes—
9C22×C42×C11—21no—
10C2×C11×C22⋊C8—21no—
11C2×C11×C22⋊C8—21no—
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C11×C22⋊C8—21no—
15C2×C11×C22⋊C8—21no—
16C2×C11×C22⋊C8—21no—
17C2×C11×C22⋊C8C412yescomplemented
18C2×C11×C22⋊C8C412yescomplemented
19C2×C11×C22⋊C8C412yescomplemented
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C4×C11×C22⋊C4—21no—
23C4×C11×C22⋊C4—21no—
24C4×C11×C22⋊C4C412yes—
25C4×C11×C22⋊C4C2212yes—
26C2×C11×#95—21no—
27C25×C11C2×C411yescharacteristic
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11Q811yescharacteristic
42C23×C4×C11Q811yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C8×C11—22no—
45C22×C8×C11—22no—
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11—44no—
50C22×C8×C11—44no—
51C22×C8×C11C2×C414yescomplemented
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4C818yescomplemented
55C2×C11×C22⋊C4C2×C414yes—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11—44no—
59C11×C22⋊C8—22no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11×C22⋊C8—22no—
63C11×C22⋊C8—22no—
64C11×C22⋊C8—22no—
65C11×C22⋊C8—22no—
66C11×C22⋊C8C2×C414yescomplemented
67C11×#95—22no—
68C11×#95—22no—
69C2×#1282C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—42no—
71C24×C11—42no—
72C24×C11C4211yescharacteristic
73C24×C11C4211yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C24×C11C4⋊C411yescharacteristic
77C24×C11C4⋊C411yescharacteristic
78C24×C11C2×C814yes—
79C24×C11M1614yes—
80C24×C11C22×C411yescharacteristic
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—28no—
85C22×C4×C11—24no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—44no—
98C22×C4×C11—44no—
99C22×C4×C11C4211yescharacteristic
100C22×C4×C11C4211yescharacteristic
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C411yescharacteristic
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22⋊C411yescharacteristic
110C22×C4×C11C22⋊C411yescharacteristic
111C22×C4×C11C4⋊C411yescharacteristic
112C22×C4×C11C4⋊C411yescharacteristic
113C22×C4×C11C4⋊C411yescharacteristic
114C22×C4×C11C4⋊C411yescharacteristic
115C22×C4×C11C4⋊C411yescharacteristic
116C22×C4×C11C4⋊C411yescharacteristic
117C22×C4×C11C4⋊C411yescharacteristic
118C22×C4×C11C4⋊C411yescharacteristic
119C22×C4×C11C4⋊C411yescharacteristic
120C22×C4×C11C4⋊C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×Q811yescharacteristic
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11—44no—
130C2×C8×C11—44no—
131C2×C8×C11—44no—
132C2×C8×C11—44no—
133C2×C8×C11—44no—
134C2×C8×C11—44no—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4C2×C818yescomplemented
138C42×C11—44no—
139C42×C11—44no—
140C22×C22⋊C8C2×C1111yescharacteristic
141C22×C22⋊C8C2×C1111yescharacteristic
142C2×C4×C22⋊C4C2×C1111yescharacteristic
143#1282C2×C1114yesdirect product factor
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—48no—
158C23×C11—48no—
159C23×C11—41no—
160C23×C11#9511yescharacteristic
161C23×C11#9511yescharacteristic
162C23×C11#9511yescharacteristic
163C23×C11#9511yescharacteristic
164C23×C11C4×C812yes—
165C23×C11C4×C812yes—
166C23×C11#9712yes—
167C23×C11#9712yes—
168C23×C11C22⋊C814yes—
169C23×C11C22⋊C814yes—
170C23×C11C4⋊C814yes—
171C23×C11C4⋊C814yes—
172C23×C11C2×C4211yescharacteristic
173C23×C11C2×C22⋊C411yescharacteristic
174C23×C11C2×C4⋊C411yescharacteristic
175C23×C11C22×C812yes—
176C23×C11C2×M1612yes—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—28no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—44no—
206C2×C4×C11—416no—
207C2×C4×C11—44no—
208C2×C4×C11#9511yescharacteristic
209C2×C4×C11#9511yescharacteristic
210C2×C4×C11#9511yescharacteristic
211C2×C4×C11#9511yescharacteristic
212C2×C4×C11#9914yes—
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C4⋊C411yescharacteristic
216C2×C4×C11C2×C4⋊C411yescharacteristic
217C8×C11—44no—
218C8×C11—44no—
219C24×C4C22×C1111yescharacteristic
220C23×C8—21no—
221C23×C8C4×C1112yescomplemented
222C22×C22⋊C4C4×C1112yes—
223C22×C42—21no—
224C2×C22⋊C8—21no—
225C2×C22⋊C8—21no—
226C2×C22⋊C8—21no—
227C2×C22⋊C8—21no—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230C2×C22⋊C8—21no—
231C2×C22⋊C8C4×C1112yescomplemented
232C2×C22⋊C8C4×C1112yescomplemented
233C2×C22⋊C8C4×C1112yescomplemented
234C2×C22⋊C8C22×C1112yes—
235C2×C22⋊C8C22×C1112yes—
236C4×C22⋊C4—21no—
237C4×C22⋊C4—21no—
238C4×C22⋊C4C4×C1112yes—
239C4×C22⋊C4C22×C1112yes—
240C2×#95—21no—
241C22×C11—28no—
242C22×C11—24no—
243C22×C11—24no—
244C22×C11—28no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11#33612yes—
264C22×C11#33612yes—
265C22×C11#33612yes—
266C22×C11#33612yes—
267C22×C11#34212yes—
268C22×C11#34412yes—
269C22×C11C2×#9511yescharacteristic
270C22×C11C2×C4×C811yescharacteristic
271C22×C11C2×#9711yescharacteristic
272C22×C11C2×C22⋊C812yes—
273C22×C11C2×C4⋊C812yes—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—48no—
281C4×C11#34212yes—
282C4×C11C2×#9912yes—
283C25C2×C4×C1111yescharacteristic
284C23×C4—22no—
285C23×C4—44no—
286C23×C4C2×C4×C1111yescharacteristic
287C23×C4C2×C4×C1111yescharacteristic
288C23×C4C2×C4×C1111yescharacteristic
289C23×C4C2×C4×C1111yescharacteristic
290C23×C4C2×C4×C1111yescharacteristic
291C23×C4D4×C1111yescharacteristic
292C23×C4D4×C1111yescharacteristic
293C23×C4D4×C1111yescharacteristic
294C23×C4D4×C1111yescharacteristic
295C23×C4D4×C1111yescharacteristic
296C23×C4D4×C1111yescharacteristic
297C23×C4Q8×C1111yescharacteristic
298C23×C4Q8×C1111yescharacteristic
299C23×C4C23×C1111yescharacteristic
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—44no—
306C22×C8—44no—
307C22×C8C2×C4×C1114yescomplemented
308C2×C22⋊C4—22no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4C8×C1118yescomplemented
311C2×C22⋊C4C2×C4×C1114yes—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—44no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317C22⋊C8—22no—
318C22⋊C8—22no—
319C22⋊C8—22no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322C22⋊C8C2×C4×C1114yescomplemented
323#95—22no—
324#95—22no—
325C2×C11—22no—
326C2×C11—22no—
327C2×C11—22no—
328C2×C11—22no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—22no—
332C2×C11#128214yesdirect product factor
333C2×C11C2×#33611yescharacteristic
334C2×C11C2×#34211yescharacteristic
335C2×C11C2×#34411yescharacteristic
336C24—42no—
337C24—42no—
338C24C42×C1111yescharacteristic
339C24C42×C1111yescharacteristic
340C24C11×C22⋊C411yescharacteristic
341C24C11×C22⋊C411yescharacteristic
342C24C11×C4⋊C411yescharacteristic
343C24C11×C4⋊C411yescharacteristic
344C24C2×C8×C1114yes—
345C24C11×M1614yes—
346C24C22×C4×C1111yescharacteristic
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—28no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4C42×C1111yescharacteristic
366C22×C4C42×C1111yescharacteristic
367C22×C4C11×C22⋊C411yescharacteristic
368C22×C4C11×C22⋊C411yescharacteristic
369C22×C4C11×C22⋊C411yescharacteristic
370C22×C4C11×C22⋊C411yescharacteristic
371C22×C4C11×C22⋊C411yescharacteristic
372C22×C4C11×C22⋊C411yescharacteristic
373C22×C4C11×C22⋊C411yescharacteristic
374C22×C4C11×C22⋊C411yescharacteristic
375C22×C4C11×C22⋊C411yescharacteristic
376C22×C4C11×C22⋊C411yescharacteristic
377C22×C4C11×C4⋊C411yescharacteristic
378C22×C4C11×C4⋊C411yescharacteristic
379C22×C4C11×C4⋊C411yescharacteristic
380C22×C4C11×C4⋊C411yescharacteristic
381C22×C4C11×C4⋊C411yescharacteristic
382C22×C4C11×C4⋊C411yescharacteristic
383C22×C4C11×C4⋊C411yescharacteristic
384C22×C4C11×C4⋊C411yescharacteristic
385C22×C4C11×C4⋊C411yescharacteristic
386C22×C4C11×C4⋊C411yescharacteristic
387C22×C4C22×C4×C1111yescharacteristic
388C22×C4C22×C4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×Q8×C1111yescharacteristic
393C2×C8—24no—
394C2×C8—24no—
395C2×C8—44no—
396C2×C8—44no—
397C2×C8—44no—
398C2×C8—44no—
399C2×C8—44no—
400C2×C8—44no—
401C22⋊C4—28no—
402C22⋊C4—24no—
403C22⋊C4C2×C8×C1118yescomplemented
404C42—44no—
405C42—44no—
406C11C2×#128211yescharacteristic, direct product factor, Sylow
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—48no—
421C23—48no—
422C23—41no—
423C23C11×#9511yescharacteristic
424C23C11×#9511yescharacteristic
425C23C11×#9511yescharacteristic
426C23C11×#9511yescharacteristic
427C23C4×C8×C1112yes—
428C23C4×C8×C1112yes—
429C23C11×#9712yes—
430C23C11×#9712yes—
431C23C11×C22⋊C814yes—
432C23C11×C22⋊C814yes—
433C23C11×C4⋊C814yes—
434C23C11×C4⋊C814yes—
435C23C2×C42×C1111yescharacteristic
436C23C2×C11×C22⋊C411yescharacteristic
437C23C2×C11×C4⋊C411yescharacteristic
438C23C22×C8×C1112yes—
439C23C2×C11×M1612yes—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—28no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—416no—
471C2×C4C11×#9511yescharacteristic
472C2×C4C11×#9511yescharacteristic
473C2×C4C11×#9511yescharacteristic
474C2×C4C11×#9511yescharacteristic
475C2×C4C11×#9914yes—
476C2×C4C2×C11×C22⋊C411yescharacteristic
477C2×C4C2×C11×C22⋊C411yescharacteristic
478C2×C4C2×C11×C4⋊C411yescharacteristic
479C2×C4C2×C11×C4⋊C411yescharacteristic
480C8—44no—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—28no—
495C22—24no—
496C22—24no—
497C22—28no—
498C22—42no—
499C22—42no—
500C22—44no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22C11×#33612yes—
505C22C11×#33612yes—
506C22C11×#33612yes—
507C22C11×#33612yes—
508C22C11×#34212yes—
509C22C11×#34412yes—
510C22C2×C11×#9511yescharacteristic
511C22C2×C4×C8×C1111yescharacteristic
512C22C2×C11×#9711yescharacteristic
513C22C2×C11×C22⋊C812yes—
514C22C2×C11×C4⋊C812yes—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—48no—
522C4C11×#34212yes—
523C4C2×C11×#9912yes—
524C2—22no—
525C2—22no—
526C2—22no—
527C2—22no—
528C2—21no—
529C2—21no—
530C2—22no—
531C2C11×#128214yesdirect product factor
532C2C2×C11×#33611yescharacteristic
533C2C2×C11×#34211yescharacteristic
534C2C2×C11×#34411yescharacteristic
subgroupG/H
centerC22×C4×C11C22⋊C4
commutatorC22C2×C4×C8×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11#95
prime radicalC25×C11C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1282C2direct (N × H)
7. C23×C8×C11C4semidirect
17. C2×C11×C22⋊C8C4semidirect
18. C2×C11×C22⋊C8C4semidirect
19. C2×C11×C22⋊C8C4semidirect
51. C22×C8×C11C2×C4semidirect
54. C2×C11×C22⋊C4C8semidirect
66. C11×C22⋊C8C2×C4semidirect
69. C2×#1282C11direct (N × H)
137. C11×C22⋊C4C2×C8semidirect
143. #1282C2×C11direct (N × H)
221. C23×C8C4×C11semidirect
231. C2×C22⋊C8C4×C11semidirect
232. C2×C22⋊C8C4×C11semidirect
233. C2×C22⋊C8C4×C11semidirect
307. C22×C8C2×C4×C11semidirect
310. C2×C22⋊C4C8×C11semidirect
322. C22⋊C8C2×C4×C11semidirect
332. C2×C11#1282direct (N × H)
403. C22⋊C4C2×C8×C11semidirect
406. C11C2×#1282direct (N × H)
531. C2C11×#1282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊C82
C2×C4×C11×C22⋊C42
C11×#12822
C2×#128211