Finite Group Databasebeta

← C11×#23574 #14600767

Subgroups — C11×#23574 #14600767

Order 2816.

1228 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#440C212yesmaximal, complemented
3C4×C11×#121C211yesmaximal, characteristic
4C11×#2057C211yesmaximal, characteristic, complemented
5C11×#2043C211yesmaximal, characteristic, complemented
6C11×#2036C212yesmaximal, complemented
7C11×#2023C211yesmaximal, characteristic, complemented
8C11×#2013C211yesmaximal, characteristic, complemented
9C11×#2000C212yesmaximal
10C11×#1763C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C11×#533—28no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C22×C42×C11C2211yescharacteristic
26C11×#440—28no—
27C2×C11×#107C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2212yes—
33C2×C11×#97C2212yes—
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#386—21no—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11C2312yes—
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×SD16—24no—
54C2×C11×SD16—24no—
55C2×C11×SD16—24no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×#125—28no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×#121—22no—
65C11×#121—22no—
66C4×Q8×C11—28no—
67C4×Q8×C11—24no—
68C4×Q8×C11D418yescomplemented
69C4×D4×C11—24no—
70C4×D4×C11—44no—
71C11×#117—28no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—22no—
89C2×C42×C11—24no—
90C2×C42×C11—21no—
91C2×C42×C11D411yescharacteristic
92C2×C42×C11D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C11×#107—24no—
96C11×#103—24no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#102—24no—
100C11×C22⋊C8—24no—
101C11×#97—24no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105#23574C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11C2×D414yes—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11#4112yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—41no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×SD16—216no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11#4114yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4#4112yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—42no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—28no—
176C42×C11—22no—
177C42×C11—42no—
178C42×C11C2×D414yes—
179C2×#533C2×C1111yescharacteristic, complemented
180C2×#440C2×C1112yescomplemented
181C4×#121C2×C1111yescharacteristic
182#2057C2×C1111yescharacteristic, complemented
183#2043C2×C1111yescharacteristic, complemented
184#2036C2×C1112yescomplemented
185#2023C2×C1111yescharacteristic, complemented
186#2013C2×C1111yescharacteristic, complemented
187#2000C2×C1112yes—
188#1763C2×C1112yescomplemented
189#1749C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—48no—
208Q8×C11—42no—
209Q8×C11—42no—
210D4×C11—24no—
211D4×C11—48no—
212D4×C11—42no—
213C2×C4×C11—28no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—84no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12012yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4111yescharacteristic
252C8×C11—24no—
253C8×C11—42no—
254C22×SD16C22×C1112yes—
255#533—28no—
256C2×C4⋊Q8C22×C1111yescharacteristic
257C2×C4⋊Q8C22×C1111yescharacteristic
258C2×#125—21no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8C22×C1112yes—
261C2×#121C22×C1111yescharacteristic
262C2×C4×Q8—21no—
263C2×C4×Q8C22×C1112yes—
264C2×C4×D4—21no—
265C2×C4×D4C22×C1111yescharacteristic
266C2×#117—21no—
267C22×C42C22×C1111yescharacteristic
268#440—28no—
269C2×#107C22×C1112yes—
270C2×#103C22×C1112yes—
271C2×#103C22×C1112yes—
272C2×#103C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×C22⋊C8C22×C1112yes—
275C2×#97C22×C1112yes—
276#390C22×C1111yescharacteristic
277#389C22×C1111yescharacteristic
278#388—21no—
279#386—21no—
280#380C22×C1111yescharacteristic
281C4×C4⋊C4C22×C1111yescharacteristic
282C4×C22⋊C4—21no—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#336C22×C1111yescharacteristic
286#336C22×C1111yescharacteristic
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#52511yescharacteristic
303C22×C11#53211yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11C2×#13711yescharacteristic
306C22×C11C2×#13711yescharacteristic
307C22×C11#57511yescharacteristic
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—44no—
315C4×C11—44no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11#52512yes—
319C4×C11#53212yes—
320C22×Q8—21no—
321C22×Q8C23×C1112yes—
322C22×D4—21no—
323C22×D4C23×C1111yescharacteristic
324C23×C4—21no—
325C23×C4D4×C1111yescharacteristic
326C23×C4D4×C1111yescharacteristic
327C23×C4C23×C1111yescharacteristic
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—24no—
331C22×C8C23×C1112yes—
332C22×C8C23×C1112yes—
333C4⋊Q8—24no—
334C4⋊Q8—24no—
335#125—28no—
336C22⋊Q8—28no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339#121—22no—
340#121—22no—
341C4×Q8—28no—
342C4×Q8—24no—
343C4×Q8D4×C1118yescomplemented
344C4×D4—24no—
345C4×D4—44no—
346#117—28no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1112yes—
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—21no—
366C2×C42D4×C1111yescharacteristic
367C2×C42D4×C1111yescharacteristic
368C2×C42C23×C1111yescharacteristic
369C2×C42C23×C1111yescharacteristic
370#107—24no—
371#103—24no—
372#103—24no—
373#103—24no—
374#102—24no—
375C22⋊C8—24no—
376#97—24no—
377#95—21no—
378#95—21no—
379#95—21no—
380C2×C11—42no—
381C2×C11—82no—
382C2×C11#238811yescharacteristic
383C2×C11#300411yescharacteristic
384C2×C11#300611yescharacteristic
385C2×C11#311011yescharacteristic
386C2×C11#311611yescharacteristic
387C2×C11#318111yescharacteristic
388C2×C11#318211yescharacteristic
389C24—21no—
390C24C2×D4×C1111yescharacteristic
391C2×Q8—24no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8C2×D4×C1114yes—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4C11×#4112yes—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—41no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C24×C1111yescharacteristic
431SD16—216no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8C11×#4114yes—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—28no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4C2×D4×C1114yes—
449C4⋊C4C11×#4112yes—
450C22⋊C4—28no—
451C22⋊C4—24no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C42—22no—
457C42—22no—
458C42—28no—
459C42—22no—
460C42—42no—
461C42C2×D4×C1114yes—
462C11#2357411yescharacteristic, direct product factor, Sylow
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C11×#13712yes—
477C23C22×D4×C1111yescharacteristic
478Q8—24no—
479Q8—24no—
480Q8—48no—
481Q8—42no—
482Q8—42no—
483D4—24no—
484D4—48no—
485D4—42no—
486C2×C4—28no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—84no—
517C2×C4C11×#12012yes—
518C2×C4C11×#12012yes—
519C2×C4C11×AGL(1,ℤ/8)12yes—
520C2×C4C11×#13712yes—
521C2×C4C22×D4×C1112yes—
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C2×C11×#4112yes—
524C2×C4C2×C11×#4111yescharacteristic
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C2×C11×#12011yescharacteristic
542C22C11×#52511yescharacteristic
543C22C11×#53211yescharacteristic
544C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
545C22C2×C11×#13711yescharacteristic
546C22C2×C11×#13711yescharacteristic
547C22C11×#57511yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—22no—
552C4—41no—
553C4—44no—
554C4—44no—
555C4—42no—
556C4—81no—
557C4—81no—
558C4C11×#52512yes—
559C4C11×#53212yes—
560C2—42no—
561C2—82no—
562C2C11×#238811yescharacteristic
563C2C11×#300411yescharacteristic
564C2C11×#300611yescharacteristic
565C2C11×#311011yescharacteristic
566C2C11×#311611yescharacteristic
567C2C11×#318111yescharacteristic
568C2C11×#318211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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×#533C2semidirect
2. C2×C11×#440C2semidirect
4. C11×#2057C2semidirect
5. C11×#2043C2semidirect
6. C11×#2036C2semidirect
7. C11×#2023C2semidirect
8. C11×#2013C2semidirect
10. C11×#1763C2semidirect
11. C11×#1749C2semidirect
68. C4×Q8×C11D4semidirect
105. #23574C11direct (N × H)
179. C2×#533C2×C11semidirect
180. C2×#440C2×C11semidirect
182. #2057C2×C11semidirect
183. #2043C2×C11semidirect
184. #2036C2×C11semidirect
185. #2023C2×C11semidirect
186. #2013C2×C11semidirect
188. #1763C2×C11semidirect
189. #1749C2×C11semidirect
343. C4×Q8D4×C11semidirect
462. C11#23574direct (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×#4402
C4×C11×#1212
C11×#20572
C11×#20432
C11×#20362
C11×#20232
C11×#20132
C11×#20002
C11×#17632
C11×#17492
#2357411