Finite Group Databasebeta

← C2×C11×#3181 #14637880

Subgroups — C2×C11×#3181 #14637880

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#529C211yesmaximal, characteristic
3C11×#3181C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#497C211yesmaximal, characteristic, complemented
6C2×C11×#491C211yesmaximal, characteristic, complemented
7C2×C11×#489C211yesmaximal, characteristic, complemented
8C2×C11×#467C212yesmaximal, complemented
9C2×C11×#465C212yesmaximal
10C2×C11×#441C212yesmaximal, complemented
11C2×C11×#440C212yesmaximal, complemented
12C22×C11×#97C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C23×C8×C11C2212yes—
16C11×#533—24no—
17C11×#533C2218yescomplemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C11×#529—24no—
21C11×#529C2218yes—
22C2×C11×#126—21no—
23C2×C11×#125—21no—
24C2×C11×#125C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2212yes—
30C2×C11×#121C2211yescharacteristic
31C2×C4×Q8×C11—21no—
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×Q8×C11C2212yes—
34C2×C4×D4×C11—21no—
35C2×C4×D4×C11C2211yescharacteristic
36C2×C11×#117—21no—
37C2×C11×#117—21no—
38C22×C42×C11C2211yescharacteristic
39C11×#501C2218yescomplemented
40C11×#497C2218yescomplemented
41C11×#491C2218yescomplemented
42C11×#489C2218yescomplemented
43C11×#467C22116yescomplemented
44C11×#465C22116yes—
45C11×#441C22116yescomplemented
46C11×#440C22116yescomplemented
47C2×C11×#107C2212yes—
48C2×C11×#106C2212yes—
49C2×C11×#103C2212yes—
50C2×C11×#103C2212yes—
51C2×C11×#103C2212yes—
52C2×C11×#102C2212yes—
53C2×C11×#97C2211yescharacteristic
54C2×C11×#97C2212yes—
55C2×C11×#97C2211yescharacteristic
56C2×C11×#97C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×Q8×C11C2312yes—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C2×C11×Q16—28no—
67C2×C11×Q16C2318yes—
68C2×C11×SD16—28no—
69C2×C11×SD16C2318yes—
70C22×C8×C11—28no—
71C22×C8×C11C2312yes—
72C22×C8×C11C2318yes—
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yes—
77C11×C4⋊Q8C2314yes—
78C11×#126—28no—
79C11×#125—28no—
80C11×#125—22no—
81C11×#125C2314yes—
82C11×#124—22no—
83C11×#124C2314yes—
84C11×#123—28no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8C2314yes—
89C11×C22⋊Q8C2318yes—
90C11×#121—22no—
91C11×#121C2314yes—
92C4×Q8×C11—28no—
93C4×Q8×C11—22no—
94C4×Q8×C11—24no—
95C4×Q8×C11C2314yes—
96C4×Q8×C11C2318yes—
97C4×D4×C11—28no—
98C4×D4×C11—22no—
99C4×D4×C11C2314yes—
100C11×#117—28no—
101C11×#117—28no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11—21no—
121C2×C42×C11—22no—
122C2×C42×C11D411yescharacteristic
123C2×C42×C11D411yescharacteristic
124C2×C42×C11D414yes—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2314yes—
128C11×#107C2318yes—
129C11×#106C2318yes—
130C11×#103C2318yes—
131C11×#103C2318yes—
132C11×#103C2318yes—
133C11×#102C2318yes—
134C11×#97C2314yes—
135C11×#97C2314yes—
136C11×#97C2318yes—
137C2×#3181C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—24no—
146C2×Q8×C11—44no—
147C2×Q8×C11C2412yes—
148C2×Q8×C11C2414yes—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—24no—
152C2×D4×C11—44no—
153C2×D4×C11C2412yes—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—42no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D414yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C11×Q16—216no—
175C11×SD16—216no—
176C2×C8×C11—216no—
177C2×C8×C11—24no—
178C2×C8×C11#4118yes—
179C2×C8×C11C2414yes—
180C2×C8×C11C2414yes—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—28no—
188C11×C4⋊C4—28no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4C2414yes—
194C11×C4⋊C4C2412yes—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—28no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C42×C11—24no—
203C42×C11—28no—
204C42×C11C2×D414yes—
205C42×C11C2×D412yes—
206C42×C11C2×D414yes—
207C42×C11C2×D412yes—
208C42×C11C2412yes—
209C42×C11C2412yes—
210C2×#533C2×C1111yescharacteristic, complemented
211C2×#529C2×C1111yescharacteristic
212#3181C2×C11116yesdirect product factor
213C2×#501C2×C1111yescharacteristic, complemented
214C2×#497C2×C1111yescharacteristic, complemented
215C2×#491C2×C1111yescharacteristic, complemented
216C2×#489C2×C1111yescharacteristic, complemented
217C2×#467C2×C1112yescomplemented
218C2×#465C2×C1112yes—
219C2×#441C2×C1112yescomplemented
220C2×#440C2×C1112yescomplemented
221C22×#97C2×C1111yescharacteristic, complemented
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11#13714yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—24no—
234Q8×C11—48no—
235Q8×C11—42no—
236Q8×C11—44no—
237D4×C11—24no—
238D4×C11—48no—
239D4×C11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11—42no—
256C2×C4×C11—44no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—44no—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4114yes—
267C2×C4×C11C2511yescharacteristic
268C8×C11—24no—
269C8×C11C2×#4118yes—
270C22×Q16C22×C1112yes—
271C22×SD16C22×C1112yes—
272C23×C8C22×C1112yes—
273#533—24no—
274#533C22×C1118yescomplemented
275C2×C4⋊Q8C22×C1111yescharacteristic
276C2×C4⋊Q8C22×C1111yescharacteristic
277#529—24no—
278#529C22×C1118yes—
279C2×#126—21no—
280C2×#125—21no—
281C2×#125C22×C1111yescharacteristic
282C2×#124C22×C1111yescharacteristic
283C2×#123—21no—
284C2×C22⋊Q8—21no—
285C2×C22⋊Q8C22×C1111yescharacteristic
286C2×C22⋊Q8C22×C1112yes—
287C2×#121C22×C1111yescharacteristic
288C2×C4×Q8—21no—
289C2×C4×Q8C22×C1111yescharacteristic
290C2×C4×Q8C22×C1112yes—
291C2×C4×D4—21no—
292C2×C4×D4C22×C1111yescharacteristic
293C2×#117—21no—
294C2×#117—21no—
295C22×C42C22×C1111yescharacteristic
296#501C22×C1118yescomplemented
297#497C22×C1118yescomplemented
298#491C22×C1118yescomplemented
299#489C22×C1118yescomplemented
300#467C22×C11116yescomplemented
301#465C22×C11116yes—
302#441C22×C11116yescomplemented
303#440C22×C11116yescomplemented
304C2×#107C22×C1112yes—
305C2×#106C22×C1112yes—
306C2×#103C22×C1112yes—
307C2×#103C22×C1112yes—
308C2×#103C22×C1112yes—
309C2×#102C22×C1112yes—
310C2×#97C22×C1111yescharacteristic
311C2×#97C22×C1111yescharacteristic
312C2×#97C22×C1112yes—
313C2×#97C22×C1118yescomplemented
314C22×C11—28no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—84no—
321C22×C11#53212yes—
322C22×C11C2×#13714yes—
323C22×C11C2×#13712yes—
324C22×C11#57512yes—
325C22×C11C23×D411yescharacteristic
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—44no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—44no—
336C4×C11#53212yes—
337C4×C11C22×#4112yes—
338C22×Q8—21no—
339C22×Q8C23×C1111yescharacteristic
340C22×Q8C23×C1112yes—
341C22×D4—21no—
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C23×C4D4×C1111yescharacteristic
345C23×C4D4×C1111yescharacteristic
346C23×C4C23×C1111yescharacteristic
347C2×Q16—28no—
348C2×Q16C23×C1118yes—
349C2×SD16—28no—
350C2×SD16C23×C1118yes—
351C22×C8—28no—
352C22×C8C23×C1112yes—
353C22×C8C23×C1118yes—
354C22×C8C23×C1112yes—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8C23×C1114yes—
358C4⋊Q8C23×C1114yes—
359#126—28no—
360#125—28no—
361#125—22no—
362#125C23×C1114yes—
363#124—22no—
364#124C23×C1114yes—
365#123—28no—
366C22⋊Q8—28no—
367C22⋊Q8—22no—
368C22⋊Q8—24no—
369C22⋊Q8C23×C1114yes—
370C22⋊Q8C23×C1118yes—
371#121—22no—
372#121C23×C1114yes—
373C4×Q8—28no—
374C4×Q8—22no—
375C4×Q8—24no—
376C4×Q8C23×C1114yes—
377C4×Q8C23×C1118yes—
378C4×D4—28no—
379C4×D4—22no—
380C4×D4C23×C1114yes—
381#117—28no—
382#117—28no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1112yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—22no—
403C2×C42D4×C1111yescharacteristic
404C2×C42D4×C1111yescharacteristic
405C2×C42D4×C1114yes—
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408C2×C42C23×C1114yes—
409#107C23×C1118yes—
410#106C23×C1118yes—
411#103C23×C1118yes—
412#103C23×C1118yes—
413#103C23×C1118yes—
414#102C23×C1118yes—
415#97C23×C1118yes—
416#97C23×C1114yes—
417#97C23×C1114yes—
418C2×C11—24no—
419C2×C11—82no—
420C2×C11#318114yesdirect product factor
421C2×C11C2×#53211yescharacteristic
422C2×C11C22×#13711yescharacteristic
423C2×C11C2×#57511yescharacteristic
424C24—21no—
425C24C2×D4×C1111yescharacteristic
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—24no—
432C2×Q8—44no—
433C2×Q8C24×C1112yes—
434C2×Q8C24×C1114yes—
435C2×D4—24no—
436C2×D4—21no—
437C2×D4—24no—
438C2×D4—44no—
439C2×D4C24×C1112yes—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—42no—
449C22×C4—44no—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1112yes—
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1114yes—
457C22×C4C2×D4×C1114yes—
458C22×C4C24×C1112yes—
459C22×C4C24×C1111yescharacteristic
460Q16—216no—
461SD16—216no—
462C2×C8—24no—
463C2×C8—216no—
464C2×C8C11×#4118yes—
465C2×C8C24×C1114yes—
466C2×C8C24×C1114yes—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—28no—
474C4⋊C4—28no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4C24×C1114yes—
480C4⋊C4C24×C1112yes—
481C4⋊C4C24×C1112yes—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C42—24no—
489C42—28no—
490C42C2×D4×C1114yes—
491C42C2×D4×C1112yes—
492C42C2×D4×C1114yes—
493C42C2×D4×C1112yes—
494C42C24×C1112yes—
495C42C24×C1112yes—
496C11C2×#318111yescharacteristic, direct product factor, Sylow
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23C11×#13714yes—
504C23C22×D4×C1112yes—
505C23C22×D4×C1111yescharacteristic
506Q8—24no—
507Q8—24no—
508Q8—24no—
509Q8—48no—
510Q8—42no—
511Q8—44no—
512D4—24no—
513D4—48no—
514D4—42no—
515C2×C4—22no—
516C2×C4—28no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—44no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4C22×D4×C1112yes—
536C2×C4C22×D4×C1112yes—
537C2×C4C22×D4×C1112yes—
538C2×C4C22×D4×C1112yes—
539C2×C4C22×D4×C1112yes—
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C2×C11×#4114yes—
542C2×C4C25×C1111yescharacteristic
543C8—24no—
544C8C2×C11×#4118yes—
545C22—28no—
546C22—22no—
547C22—22no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—84no—
552C22C11×#53212yes—
553C22C2×C11×#13714yes—
554C22C2×C11×#13712yes—
555C22C11×#57512yes—
556C22C23×D4×C1111yescharacteristic
557C4—22no—
558C4—22no—
559C4—22no—
560C4—22no—
561C4—22no—
562C4—42no—
563C4—44no—
564C4—42no—
565C4—42no—
566C4—44no—
567C4C11×#53212yes—
568C4C22×C11×#4112yes—
569C2—24no—
570C2—82no—
571C2C11×#318114yesdirect product factor
572C2C2×C11×#53211yescharacteristic
573C2C22×C11×#13711yescharacteristic
574C2C2×C11×#57511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#533C2semidirect
3. C11×#3181C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#497C2semidirect
6. C2×C11×#491C2semidirect
7. C2×C11×#489C2semidirect
8. C2×C11×#467C2semidirect
10. C2×C11×#441C2semidirect
11. C2×C11×#440C2semidirect
12. C22×C11×#97C2semidirect
17. C11×#533C22semidirect
39. C11×#501C22semidirect
40. C11×#497C22semidirect
41. C11×#491C22semidirect
42. C11×#489C22semidirect
43. C11×#467C22semidirect
45. C11×#441C22semidirect
46. C11×#440C22semidirect
56. C2×C11×#97C22semidirect
137. C2×#3181C11direct (N × H)
210. C2×#533C2×C11semidirect
212. #3181C2×C11direct (N × H)
213. C2×#501C2×C11semidirect
214. C2×#497C2×C11semidirect
215. C2×#491C2×C11semidirect
216. C2×#489C2×C11semidirect
217. C2×#467C2×C11semidirect
219. C2×#441C2×C11semidirect
220. C2×#440C2×C11semidirect
221. C22×#97C2×C11semidirect
274. #533C22×C11semidirect
296. #501C22×C11semidirect
297. #497C22×C11semidirect
298. #491C22×C11semidirect
299. #489C22×C11semidirect
300. #467C22×C11semidirect
302. #441C22×C11semidirect
303. #440C22×C11semidirect
313. C2×#97C22×C11semidirect
420. C2×C11#3181direct (N × H)
496. C11C2×#3181direct (N × H)
571. C2C11×#3181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#5292
C11×#31812
C2×C11×#5012
C2×C11×#4972
C2×C11×#4912
C2×C11×#4892
C2×C11×#4672
C2×C11×#4652
C2×C11×#4412
C2×C11×#4402
C22×C11×#972
C2×#318111