Finite Group Databasebeta

← C11×#13949 #14591142

Subgroups — C11×#13949 #14591142

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#387C212yesmaximal
2C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#1442C212yesmaximal
4C11×#1441C212yesmaximal
5C11×#1436C212yesmaximal
6C11×C4⋊#95C211yesmaximal, characteristic
7C11×C4⋊#95C211yesmaximal, characteristic
8C11×#1434C211yesmaximal, characteristic
9C11×#1434C211yesmaximal, characteristic
10C11×#1434C211yesmaximal, characteristic
11C4×C11×#95C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#387—28no—
21C4×C11×C4⋊C4C418yescomplemented
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C4⋊C4Q814yes—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—24no—
63C2×C42×C11—24no—
64C2×C42×C11—42no—
65C2×C42×C11—42no—
66C2×C42×C11—42no—
67C2×C42×C11C2×C414yes—
68C2×C42×C11C2×C414yes—
69C2×C42×C11C2×C414yes—
70C11×#95—24no—
71C11×#95—24no—
72C11×#95—24no—
73C11×#95—24no—
74C11×#95—24no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—24no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—42no—
83C11×#95C2×C414yes—
84C11×#95C2×C414yes—
85#13949C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11C2411yescharacteristic
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×Q812yes—
144C22×C4×C11C2×Q812yes—
145C22×C4×C11C2×Q812yes—
146C22×C4×C11#4114yes—
147C22×C4×C11#4114yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—48no—
154C11×C4⋊C4—48no—
155C11×C4⋊C4C4⋊C4116yescomplemented
156C42×C11—28no—
157C42×C11—44no—
158C42×C11—44no—
159C42×C11—48no—
160C2×#387C2×C1112yes—
161C2×C4×C4⋊C4C2×C1111yescharacteristic
162#1442C2×C1112yes—
163#1441C2×C1112yes—
164#1436C2×C1112yes—
165C4⋊#95C2×C1111yescharacteristic
166C4⋊#95C2×C1111yescharacteristic
167#1434C2×C1111yescharacteristic
168#1434C2×C1111yescharacteristic
169#1434C2×C1111yescharacteristic
170C4×#95C2×C1111yescharacteristic
171C23×C11C23×C411yescharacteristic
172C23×C11C22×D411yescharacteristic
173C23×C11C22×Q811yescharacteristic
174C23×C11C2×#4111yescharacteristic
175C23×C11C2×#4111yescharacteristic
176C23×C11C2×#4111yescharacteristic
177C23×C11C2×#4111yescharacteristic
178C23×C11C2×#4112yes—
179C23×C11C2×#4112yes—
180C23×C11H(5,𝔽2)12yes—
181C23×C112−1+412yes—
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—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11C2×C4⋊C414yes—
243C2×C4×C11C2×C4⋊C414yes—
244C2×C4×C11C2×C4⋊C414yes—
245C2×C4×C11#11714yes—
246C2×C4×C11#11714yes—
247C22×C4⋊C4C22×C1112yes—
248C22×C4⋊C4C22×C1112yes—
249C22×C4⋊C4C22×C1111yescharacteristic
250C22×C4⋊C4C22×C1111yescharacteristic
251C22×C42C22×C1112yes—
252C22×C42C22×C1111yescharacteristic
253C22×C42C22×C1111yescharacteristic
254C22×C42C22×C1111yescharacteristic
255#387—28no—
256C4×C4⋊C4C4×C1118yescomplemented
257C2×#95C22×C1111yescharacteristic
258C2×#95C22×C1111yescharacteristic
259C2×#95C22×C1112yes—
260C2×#95C22×C1111yescharacteristic
261C2×#95C22×C1111yescharacteristic
262C2×#95C22×C1112yes—
263C2×#95C22×C1112yes—
264C2×#95C22×C1112yes—
265C2×#95C22×C1112yes—
266C2×#95C22×C1112yes—
267C2×#95C22×C1112yes—
268C2×#95C22×C1112yes—
269C2×#95C22×C1112yes—
270C2×#95C22×C1111yescharacteristic
271C2×#95C22×C1111yescharacteristic
272C22×C11C22×C4⋊C411yescharacteristic
273C22×C11C2×#11711yescharacteristic
274C22×C11C2×#11711yescharacteristic
275C22×C11C4×#4111yescharacteristic
276C22×C11C4×#4111yescharacteristic
277C22×C11#51811yescharacteristic
278C22×C11#51911yescharacteristic
279C22×C11#52912yes—
280C22×C11#52912yes—
281C22×C11#53211yescharacteristic
282C22×C11#53211yescharacteristic
283C22×C11#53311yescharacteristic
284C22×C11#53311yescharacteristic
285C22×C11#53912yes—
286C22×C11#53912yes—
287C22×C11#54612yes—
288C22×C11#54812yes—
289C22×C11#55112yes—
290C22×C11#55212yes—
291C22×C11#55312yes—
292C22×C11#55412yes—
293C22×C11#55612yes—
294C22×C11#55712yes—
295C4×C11—24no—
296C4×C11—24no—
297C4×C11—24no—
298C4×C11—24no—
299C4×C11—24no—
300C4×C11—44no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11—82no—
305C4×C11—82no—
306C23×C4C23×C1112yes—
307C23×C4C23×C1112yes—
308C23×C4C23×C1111yescharacteristic
309C23×C4C23×C1111yescharacteristic
310C23×C4C23×C1112yes—
311C23×C4C23×C1112yes—
312C23×C4C23×C1111yescharacteristic
313C23×C4C23×C1111yescharacteristic
314C23×C4C23×C1111yescharacteristic
315C23×C4C23×C1111yescharacteristic
316C23×C4C23×C1111yescharacteristic
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4C2×C4×C1114yes—
326C2×C4⋊C4C2×C4×C1114yes—
327C2×C4⋊C4D4×C1114yes—
328C2×C4⋊C4Q8×C1114yes—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42C2×C4×C1114yes—
337C2×C42C2×C4×C1114yes—
338C2×C42C2×C4×C1114yes—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—22no—
345#95—22no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—22no—
350#95—22no—
351#95—42no—
352#95C2×C4×C1114yes—
353#95C2×C4×C1114yes—
354C2×C11#228511yescharacteristic
355C2×C11#229811yescharacteristic
356C2×C11#231311yescharacteristic
357C2×C11#234911yescharacteristic
358C2×C11#235111yescharacteristic
359C2×C11#235311yescharacteristic
360C2×C11#235611yescharacteristic
361C2×C11#255812yes—
362C2×C11#256012yes—
363C2×C11#258812yes—
364C2×C11#259012yes—
365C24C24×C1111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C22×C4×C1112yes—
413C22×C4C22×C4×C1112yes—
414C22×C4C22×C4×C1112yes—
415C22×C4C22×C4×C1112yes—
416C22×C4C22×C4×C1112yes—
417C22×C4C22×C4×C1112yes—
418C22×C4C22×C4×C1112yes—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1112yes—
421C22×C4C2×D4×C1112yes—
422C22×C4C2×Q8×C1112yes—
423C22×C4C2×Q8×C1112yes—
424C22×C4C2×Q8×C1112yes—
425C22×C4C11×#4114yes—
426C22×C4C11×#4114yes—
427C22×C4C11×#4112yes—
428C22×C4C11×#4112yes—
429C22×C4C11×#4112yes—
430C22×C4C11×#4112yes—
431C4⋊C4—28no—
432C4⋊C4—48no—
433C4⋊C4—48no—
434C4⋊C4C11×C4⋊C4116yescomplemented
435C42—28no—
436C42—44no—
437C42—44no—
438C42—48no—
439C11#1394911yescharacteristic, direct product factor, Sylow
440C23C23×C4×C1111yescharacteristic
441C23C22×D4×C1111yescharacteristic
442C23C22×Q8×C1111yescharacteristic
443C23C2×C11×#4111yescharacteristic
444C23C2×C11×#4111yescharacteristic
445C23C2×C11×#4111yescharacteristic
446C23C2×C11×#4111yescharacteristic
447C23C2×C11×#4112yes—
448C23C2×C11×#4112yes—
449C23C11×H(5,𝔽2)12yes—
450C23C11×2−1+412yes—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4C2×C11×C4⋊C414yes—
512C2×C4C2×C11×C4⋊C414yes—
513C2×C4C2×C11×C4⋊C414yes—
514C2×C4C11×#11714yes—
515C2×C4C11×#11714yes—
516C22C22×C11×C4⋊C411yescharacteristic
517C22C2×C11×#11711yescharacteristic
518C22C2×C11×#11711yescharacteristic
519C22C4×C11×#4111yescharacteristic
520C22C4×C11×#4111yescharacteristic
521C22C11×#51811yescharacteristic
522C22C11×#51911yescharacteristic
523C22C11×#52912yes—
524C22C11×#52912yes—
525C22C11×#53211yescharacteristic
526C22C11×#53211yescharacteristic
527C22C11×#53311yescharacteristic
528C22C11×#53311yescharacteristic
529C22C11×#53912yes—
530C22C11×#53912yes—
531C22C11×#54612yes—
532C22C11×#54812yes—
533C22C11×#55112yes—
534C22C11×#55212yes—
535C22C11×#55312yes—
536C22C11×#55412yes—
537C22C11×#55612yes—
538C22C11×#55712yes—
539C4—24no—
540C4—24no—
541C4—24no—
542C4—24no—
543C4—24no—
544C4—42no—
545C4—44no—
546C4—44no—
547C4—42no—
548C4—82no—
549C4—82no—
550C2C11×#228511yescharacteristic
551C2C11×#229811yescharacteristic
552C2C11×#231311yescharacteristic
553C2C11×#234911yescharacteristic
554C2C11×#235111yescharacteristic
555C2C11×#235311yescharacteristic
556C2C11×#235611yescharacteristic
557C2C11×#255812yes—
558C2C11×#256012yes—
559C2C11×#258812yes—
560C2C11×#259012yes—
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
21. C4×C11×C4⋊C4C4semidirect
85. #13949C11direct (N × H)
155. C11×C4⋊C4C4⋊C4semidirect
256. C4×C4⋊C4C4×C11semidirect
434. C4⋊C4C11×C4⋊C4semidirect
439. C11#13949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3872
C2×C4×C11×C4⋊C42
C11×#14422
C11×#14412
C11×#14362
C11×C4⋊#952
C11×#14342
C4×C11×#952
#1394911