Finite Group Databasebeta

← C11×#23616 #14600809

Subgroups — C11×#23616 #14600809

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#424C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic
4C2×C11×#416C211yesmaximal, characteristic
5C11×#2317C211yesmaximal, characteristic, complemented
6C11×#2311C211yesmaximal, characteristic
7C11×#2068C212yesmaximal, complemented
8C11×#2067C212yesmaximal, complemented
9C11×#2066C212yesmaximal, complemented
10C11×#2065C212yesmaximal, complemented
11C2×C11×#340C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#428—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C11×#424—24no—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×C4⋊C8C2212yes—
25C11×#417—24no—
26C11×#416—24no—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2212yes—
33C11×#391C2212yes—
34C11×#390C2212yes—
35C11×#389C2212yes—
36C11×#389C2212yes—
37C11×#386—22no—
38C11×#385—22no—
39C11×#384—21no—
40C11×#382—21no—
41C11×#380—21no—
42C11×#380—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41Q814yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C2×C11×M16—22no—
59C2×C11×M16—22no—
60C2×C11×M16D414yes—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2312yes—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117D414yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—21no—
90C2×C42×C11C2312yes—
91C11×#107—24no—
92C11×#106—24no—
93C11×C4⋊C8—24no—
94C11×C4⋊C8—24no—
95C11×#103—24no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#102—24no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#95—22no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#23616C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C2×Q812yes—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—81no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×Q812yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C11×M16—28no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—44no—
161C2×C8×C11C2×D414yes—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—82no—
173C11×C4⋊C4—82no—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—82no—
179C11×C22⋊C4—82no—
180C42×C11—24no—
181C42×C11—22no—
182C42×C11—22no—
183C2×#428C2×C1111yescharacteristic, complemented
184C2×#424C2×C1111yescharacteristic, complemented
185C2×#417C2×C1111yescharacteristic
186C2×#416C2×C1111yescharacteristic
187#2317C2×C1111yescharacteristic, complemented
188#2311C2×C1111yescharacteristic
189#2068C2×C1112yescomplemented
190#2067C2×C1112yescomplemented
191#2066C2×C1112yescomplemented
192#2065C2×C1112yescomplemented
193C2×#340C2×C1111yescharacteristic, complemented
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11#12112yes—
206C23×C11#12112yes—
207C23×C11C22⋊Q812yes—
208C23×C11C22×D411yescharacteristic
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—41no—
212Q8×C11—41no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—48no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—48no—
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—84no—
241C2×C4×C11—84no—
242C2×C4×C11#12114yes—
243C2×C4×C11#12112yes—
244C2×C4×C11#12112yes—
245C2×C4×C11C22⋊Q814yes—
246C2×C4×C11C22⋊Q814yes—
247C2×C4×C11C22⋊Q812yes—
248C2×C4×C11#12614yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C8×C11—24no—
256C8×C11—41no—
257C8×C11—41no—
258C22×#41C22×C1111yescharacteristic
259C22×M16C22×C1111yescharacteristic
260C23×C8C22×C1111yescharacteristic
261C2×#117C22×C1111yescharacteristic
262C2×#117C22×C1111yescharacteristic
263C22×C4⋊C4C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265#428—24no—
266C2×#107C22×C1112yes—
267C2×#106C22×C1112yes—
268#424—24no—
269C2×C4⋊C8C22×C1112yes—
270C2×C4⋊C8C22×C1112yes—
271#417—24no—
272#416—24no—
273C2×#103C22×C1111yescharacteristic
274C2×#103C22×C1112yes—
275C2×#103C22×C1111yescharacteristic
276C2×#102C22×C1111yescharacteristic
277C2×#102C22×C1112yes—
278C2×#102C22×C1111yescharacteristic
279#391C22×C1112yes—
280#390C22×C1112yes—
281#389C22×C1112yes—
282#389C22×C1112yes—
283#386—22no—
284#385—22no—
285#384—21no—
286#382—21no—
287#380—21no—
288#380—21no—
289#340C22×C1112yes—
290#340C22×C1112yes—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11#39614yes—
305C22×C11C2×#12111yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×C22⋊Q811yescharacteristic
308C22×C11#57611yescharacteristic
309C22×C11#57711yescharacteristic
310C22×C11#57711yescharacteristic
311C22×C11#57811yescharacteristic
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11—82no—
319C4×C11#39614yes—
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×C22⋊Q811yescharacteristic
322C4×C11C2×C22⋊Q811yescharacteristic
323C4×C11C2×#12611yescharacteristic
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41Q8×C1114yes—
330C22×Q8C23×C1111yescharacteristic
331C22×D4—21no—
332C22×D4C23×C1111yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4C23×C1111yescharacteristic
337C2×M16—22no—
338C2×M16—22no—
339C2×M16D4×C1114yes—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8C23×C1111yescharacteristic
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1112yes—
346#117—22no—
347#117—22no—
348#117—22no—
349#117D4×C1114yes—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4D4×C1111yescharacteristic
360C2×C4⋊C4C23×C1112yes—
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4D4×C1112yes—
368C2×C42—21no—
369C2×C42C23×C1112yes—
370#107—24no—
371#106—24no—
372C4⋊C8—24no—
373C4⋊C8—24no—
374#103—24no—
375#103—22no—
376#103—22no—
377#102—24no—
378#102—22no—
379#102—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384C2×C11—24no—
385C2×C11—82no—
386C2×C11C2×#39611yescharacteristic
387C2×C11#304511yescharacteristic
388C2×C11#304611yescharacteristic
389C2×C11#306211yescharacteristic
390C2×C11#306311yescharacteristic
391C2×C11#308311yescharacteristic
392C2×C11#308411yescharacteristic
393C24—21no—
394C24C2×D4×C1111yescharacteristic
395#41—28no—
396#41—28no—
397#41—44no—
398#41—44no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8C2×Q8×C1112yes—
405C2×D4—24no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4C2×Q8×C1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4C2×D4×C1112yes—
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1112yes—
432C22×C4C2×D4×C1112yes—
433C22×C4C2×Q8×C1112yes—
434C22×C4C11×#4112yes—
435C22×C4C11×#4112yes—
436C22×C4C11×#4112yes—
437C22×C4C24×C1111yescharacteristic
438M16—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—44no—
448C2×C8C2×D4×C1114yes—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—82no—
460C4⋊C4—82no—
461C4⋊C4C2×D4×C1112yes—
462C4⋊C4C2×D4×C1112yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—82no—
466C22⋊C4—82no—
467C42—24no—
468C42—22no—
469C42—22no—
470C11#2361611yescharacteristic, direct product factor, Sylow
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23C11×#12112yes—
483C23C11×#12112yes—
484C23C11×C22⋊Q812yes—
485C23C22×D4×C1111yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490D4—22no—
491D4—22no—
492D4—48no—
493D4—41no—
494D4—41no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4C11×#12114yes—
520C2×C4C11×#12112yes—
521C2×C4C11×#12112yes—
522C2×C4C11×C22⋊Q814yes—
523C2×C4C11×C22⋊Q814yes—
524C2×C4C11×C22⋊Q812yes—
525C2×C4C11×#12614yes—
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×Q8×C1111yescharacteristic
529C2×C4C2×C11×#4111yescharacteristic
530C2×C4C2×C11×#4111yescharacteristic
531C2×C4C2×C11×#4111yescharacteristic
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22C11×#39614yes—
549C22C2×C11×#12111yescharacteristic
550C22C2×C11×#12111yescharacteristic
551C22C2×C11×C22⋊Q811yescharacteristic
552C22C11×#57611yescharacteristic
553C22C11×#57711yescharacteristic
554C22C11×#57711yescharacteristic
555C22C11×#57811yescharacteristic
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—82no—
562C4—82no—
563C4C11×#39614yes—
564C4C2×C11×#12111yescharacteristic
565C4C2×C11×C22⋊Q811yescharacteristic
566C4C2×C11×C22⋊Q811yescharacteristic
567C4C2×C11×#12611yescharacteristic
568C2—24no—
569C2—82no—
570C2C2×C11×#39611yescharacteristic
571C2C11×#304511yescharacteristic
572C2C11×#304611yescharacteristic
573C2C11×#306211yescharacteristic
574C2C11×#306311yescharacteristic
575C2C11×#308311yescharacteristic
576C2C11×#308411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
2. C2×C11×#424C2semidirect
5. C11×#2317C2semidirect
7. C11×#2068C2semidirect
8. C11×#2067C2semidirect
9. C11×#2066C2semidirect
10. C11×#2065C2semidirect
11. C2×C11×#340C2semidirect
105. #23616C11direct (N × H)
183. C2×#428C2×C11semidirect
184. C2×#424C2×C11semidirect
187. #2317C2×C11semidirect
189. #2068C2×C11semidirect
190. #2067C2×C11semidirect
191. #2066C2×C11semidirect
192. #2065C2×C11semidirect
193. C2×#340C2×C11semidirect
470. C11#23616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4242
C2×C11×#4172
C2×C11×#4162
C11×#23172
C11×#23112
C11×#20682
C11×#20672
C11×#20662
C11×#20652
C2×C11×#3402
#2361611