Finite Group Databasebeta

← C11×#23617 #14600810

Subgroups — C11×#23617 #14600810

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#423C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic
4C2×C11×#417C211yesmaximal, characteristic
5C11×#2297C211yesmaximal, characteristic
6C2×C11×#389C211yesmaximal, characteristic, complemented
7C11×#2068C212yesmaximal, complemented
8C11×#2067C212yesmaximal, complemented
9C11×#2066C212yesmaximal, complemented
10C11×#2065C212yesmaximal, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#428—24no—
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C11×#423—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2212yes—
26C11×#417—24no—
27C11×#417—24no—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C11×#391C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#390C2211yescharacteristic
36C11×#389—21no—
37C11×#389—21no—
38C11×#389C2212yes—
39C11×#389C2212yes—
40C11×#386—21no—
41C11×#386—21no—
42C4×C11×C22⋊C4—21no—
43C4×C11×C22⋊C4—21no—
44C2×C11×#95—21no—
45C11×#340C2212yes—
46C11×#340C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41Q814yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16D414yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—44no—
80C2×C11×C4⋊C4D414yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—21no—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#107—24no—
98C11×#106—24no—
99C11×C4⋊C8—24no—
100C11×C4⋊C8—24no—
101C11×#103—24no—
102C11×#103—24no—
103C11×#102—24no—
104C11×#102—24no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111#23617C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C24×C11C2×D411yescharacteristic
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—44no—
117C11×#41—44no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11C2×Q812yes—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11C2×Q812yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×Q812yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C11×M16—28no—
166C11×M16—44no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—44no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—44no—
184C11×C4⋊C4C2×D414yes—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C2×#428C2×C1111yescharacteristic, complemented
198C2×#423C2×C1111yescharacteristic, complemented
199C2×#417C2×C1111yescharacteristic
200C2×#417C2×C1111yescharacteristic
201#2297C2×C1111yescharacteristic
202C2×#389C2×C1111yescharacteristic, complemented
203#2068C2×C1112yescomplemented
204#2067C2×C1112yescomplemented
205#2066C2×C1112yescomplemented
206#2065C2×C1112yescomplemented
207#1736C2×C1111yescharacteristic, complemented
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11#12112yes—
220C23×C11#12112yes—
221C23×C11C22⋊Q812yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—48no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—48no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—84no—
262C2×C4×C11#12114yes—
263C2×C4×C11#12112yes—
264C2×C4×C11#12112yes—
265C2×C4×C11C22⋊Q814yes—
266C2×C4×C11C22⋊Q814yes—
267C2×C4×C11C22⋊Q812yes—
268C2×C4×C11#12614yes—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11#13712yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C8×C11—24no—
278C8×C11—42no—
279C22×#41C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C22×M16C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C22×C4⋊C4—21no—
284C22×C4⋊C4C22×C1111yescharacteristic
285C22×C4⋊C4C22×C1111yescharacteristic
286C22×C42C22×C1111yescharacteristic
287#428—24no—
288C2×#107C22×C1112yes—
289C2×#106C22×C1112yes—
290#423—24no—
291C2×C4⋊C8C22×C1112yes—
292C2×C4⋊C8C22×C1112yes—
293#417—24no—
294#417—24no—
295C2×#103C22×C1112yes—
296C2×#103C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299#391C22×C1111yescharacteristic
300#391C22×C1111yescharacteristic
301#390C22×C1111yescharacteristic
302#390C22×C1111yescharacteristic
303#389—21no—
304#389—21no—
305#389C22×C1112yes—
306#389C22×C1112yes—
307#386—21no—
308#386—21no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C2×#95—21no—
312#340C22×C1112yes—
313#340C22×C1112yes—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#39614yes—
328C22×C11C2×#12111yescharacteristic
329C22×C11C2×#12111yescharacteristic
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11#57511yescharacteristic
334C22×C11#57511yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—42no—
338C4×C11—44no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—82no—
344C4×C11#39614yes—
345C4×C11C2×#12111yescharacteristic
346C4×C11C2×C22⋊Q811yescharacteristic
347C4×C11C2×C22⋊Q811yescharacteristic
348C4×C11C2×#12611yescharacteristic
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41Q8×C1114yes—
355C22×Q8C23×C1111yescharacteristic
356C22×D4—21no—
357C22×D4C23×C1111yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4D4×C1111yescharacteristic
362C23×C4D4×C1111yescharacteristic
363C23×C4C23×C1111yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16D4×C1114yes—
370C22×C8C23×C1112yes—
371C22×C8C23×C1112yes—
372#117—22no—
373#117—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4D4×C1114yes—
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1112yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—21no—
395C2×C42D4×C1111yescharacteristic
396C2×C42D4×C1111yescharacteristic
397C2×C42C23×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399#107—24no—
400#106—24no—
401C4⋊C8—24no—
402C4⋊C8—24no—
403#103—24no—
404#103—24no—
405#102—24no—
406#102—24no—
407#95—22no—
408#95—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413C2×C11—24no—
414C2×C11—82no—
415C2×C11C2×#39611yescharacteristic
416C2×C11#303611yescharacteristic
417C2×C11#303711yescharacteristic
418C2×C11#305511yescharacteristic
419C2×C11#305611yescharacteristic
420C2×C11#307911yescharacteristic
421C2×C11#308011yescharacteristic
422C24—21no—
423C24C2×D4×C1111yescharacteristic
424#41—28no—
425#41—28no—
426#41—44no—
427#41—44no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C2×Q8×C1112yes—
434C2×D4—24no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4C2×Q8×C1112yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1112yes—
470C22×C4C2×Q8×C1112yes—
471C22×C4C11×#4112yes—
472C22×C4C11×#4112yes—
473C22×C4C11×#4112yes—
474C22×C4C24×C1111yescharacteristic
475M16—28no—
476M16—44no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8C2×D4×C1114yes—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—44no—
492C4⋊C4—42no—
493C4⋊C4—44no—
494C4⋊C4C2×D4×C1114yes—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C11#2361711yescharacteristic, direct product factor, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C11×#12112yes—
520C23C11×#12112yes—
521C23C11×C22⋊Q812yes—
522C23C22×D4×C1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527D4—22no—
528D4—22no—
529D4—48no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—48no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—48no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—84no—
562C2×C4C11×#12114yes—
563C2×C4C11×#12112yes—
564C2×C4C11×#12112yes—
565C2×C4C11×C22⋊Q814yes—
566C2×C4C11×C22⋊Q814yes—
567C2×C4C11×C22⋊Q812yes—
568C2×C4C11×#12614yes—
569C2×C4C11×AGL(1,ℤ/8)12yes—
570C2×C4C11×#13712yes—
571C2×C4C22×D4×C1111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×Q8×C1111yescharacteristic
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C2×C11×#4111yescharacteristic
577C8—24no—
578C8—42no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22C11×#39614yes—
593C22C2×C11×#12111yescharacteristic
594C22C2×C11×#12111yescharacteristic
595C22C2×C11×C22⋊Q811yescharacteristic
596C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
597C22C2×C11×#13711yescharacteristic
598C22C11×#57511yescharacteristic
599C22C11×#57511yescharacteristic
600C4—22no—
601C4—22no—
602C4—42no—
603C4—44no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—82no—
609C4C11×#39614yes—
610C4C2×C11×#12111yescharacteristic
611C4C2×C11×C22⋊Q811yescharacteristic
612C4C2×C11×C22⋊Q811yescharacteristic
613C4C2×C11×#12611yescharacteristic
614C2—24no—
615C2—82no—
616C2C2×C11×#39611yescharacteristic
617C2C11×#303611yescharacteristic
618C2C11×#303711yescharacteristic
619C2C11×#305511yescharacteristic
620C2C11×#305611yescharacteristic
621C2C11×#307911yescharacteristic
622C2C11×#308011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×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×#428C2semidirect
2. C2×C11×#423C2semidirect
6. C2×C11×#389C2semidirect
7. C11×#2068C2semidirect
8. C11×#2067C2semidirect
9. C11×#2066C2semidirect
10. C11×#2065C2semidirect
11. C11×#1736C2semidirect
111. #23617C11direct (N × H)
197. C2×#428C2×C11semidirect
198. C2×#423C2×C11semidirect
202. C2×#389C2×C11semidirect
203. #2068C2×C11semidirect
204. #2067C2×C11semidirect
205. #2066C2×C11semidirect
206. #2065C2×C11semidirect
207. #1736C2×C11semidirect
507. C11#23617direct (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×#4232
C2×C11×#4172
C11×#22972
C2×C11×#3892
C11×#20682
C11×#20672
C11×#20662
C11×#20652
C11×#17362
#2361711