Finite Group Databasebeta

← C11×#22127 #14599320

Subgroups — C11×#22127 #14599320

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C11×#2331C211yesmaximal, characteristic, complemented
3C11×#2319C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C11×#1949C211yesmaximal, characteristic, complemented
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic
9C11×#1934C211yesmaximal, characteristic
10C11×#1926C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1921C211yesmaximal, characteristic, complemented
13C11×#1918C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic
15C11×#1768C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#474C418yescomplemented
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#391—21no—
32C11×#391—21no—
33C11×#390C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#388—21no—
41C11×#387—21no—
42C11×#387—21no—
43C11×#382C2211yescharacteristic
44C11×#381—21no—
45C11×#380—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#376C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2×C414yes—
69C4×D4×C11—22no—
70C4×D4×C11C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
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—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C11×#107—41no—
95C11×#107C2×C414yes—
96C11×#107C2×C414yes—
97C11×#106—41no—
98C11×C4⋊C8—22no—
99C11×C4⋊C8C2×C414yes—
100C11×#102—41no—
101C11×#102—41no—
102C11×#102C2×C414yes—
103C11×#102C2×C414yes—
104C11×#97—41no—
105C4×C8×C11—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#22127C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—81no—
123C2×Q8×C11—81no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22×C412yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—81no—
180C11×C22⋊C4—81no—
181C11×C22⋊C4—81no—
182C11×C22⋊C4—81no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—81no—
188C42×C11—81no—
189C42×C11—81no—
190C42×C11C22×C412yes—
191C42×C11#4112yes—
192C2×#474C2×C1111yescharacteristic
193#2331C2×C1111yescharacteristic, complemented
194#2319C2×C1111yescharacteristic
195#1987C2×C1111yescharacteristic, complemented
196#1949C2×C1111yescharacteristic, complemented
197#1943C2×C1111yescharacteristic, complemented
198#1942C2×C1111yescharacteristic, complemented
199#1936C2×C1111yescharacteristic
200#1934C2×C1111yescharacteristic
201#1926C2×C1111yescharacteristic
202#1925C2×C1111yescharacteristic
203#1921C2×C1111yescharacteristic, complemented
204#1918C2×C1111yescharacteristic, complemented
205#1804C2×C1111yescharacteristic
206#1768C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—84no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
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—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—84no—
258C2×C4×C11C4×D412yes—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—41no—
269C8×C11—41no—
270C2×C4⋊Q8C22×C1111yescharacteristic
271C2×C4×D4C22×C1111yescharacteristic
272#474C4×C1118yescomplemented
273C2×#107C22×C1111yescharacteristic
274C2×#107C22×C1111yescharacteristic
275C2×#107C22×C1111yescharacteristic
276C2×#106C22×C1111yescharacteristic
277C2×C4⋊C8C22×C1111yescharacteristic
278C2×C4⋊C8C22×C1111yescharacteristic
279C2×#102C22×C1111yescharacteristic
280C2×#102C22×C1111yescharacteristic
281C2×#102C22×C1111yescharacteristic
282C2×#102C22×C1111yescharacteristic
283C2×#97C22×C1111yescharacteristic
284C2×C4×C8C22×C1111yescharacteristic
285#391—21no—
286#391—21no—
287#390C22×C1111yescharacteristic
288#390C22×C1111yescharacteristic
289#389C22×C1111yescharacteristic
290#389C22×C1111yescharacteristic
291#389C22×C1111yescharacteristic
292#389C22×C1111yescharacteristic
293#388—21no—
294#388—21no—
295#387—21no—
296#387—21no—
297#382C22×C1111yescharacteristic
298#381—21no—
299#380—21no—
300C4×C4⋊C4C22×C1111yescharacteristic
301C4×C4⋊C4C22×C1111yescharacteristic
302C4×C4⋊C4C22×C1111yescharacteristic
303#376C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#336C22×C1111yescharacteristic
313#336C22×C1111yescharacteristic
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×C4×D411yescharacteristic
322C22×C11#53611yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57811yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#51911yescharacteristic
342C4×C11#52011yescharacteristic
343C4×C11#54111yescharacteristic
344C4×C11#54211yescharacteristic
345C22×Q8—21no—
346C22×D4C23×C1111yescharacteristic
347C23×C4—21no—
348C22×C8C23×C1111yescharacteristic
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351C22×C8C23×C1111yescharacteristic
352C4⋊Q8—22no—
353C4⋊Q8C2×C4×C1114yes—
354C4×D4—22no—
355C4×D4C2×C4×C1114yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42C23×C1111yescharacteristic
377C2×C42C23×C1111yescharacteristic
378C2×C42C23×C1111yescharacteristic
379#107—41no—
380#107C2×C4×C1114yes—
381#107C2×C4×C1114yes—
382#106—41no—
383C4⋊C8—22no—
384C4⋊C8C2×C4×C1114yes—
385#102—41no—
386#102—41no—
387#102C2×C4×C1114yes—
388#102C2×C4×C1114yes—
389#97—41no—
390C4×C8—41no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95D4×C1111yescharacteristic
401#95D4×C1111yescharacteristic
402#95D4×C1111yescharacteristic
403#95D4×C1111yescharacteristic
404C2×C11—82no—
405C2×C11#232311yescharacteristic
406C2×C11#294711yescharacteristic
407C2×C11#294811yescharacteristic
408C2×C11#324111yescharacteristic
409C2×C11#324311yescharacteristic
410C2×C11#325711yescharacteristic
411C2×C11#326211yescharacteristic
412C24—21no—
413C2×Q8—24no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C22×C4×C1112yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C22×C4×C1112yes—
450C2×C8C22×C4×C1112yes—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4C22×C4×C1112yes—
468C4⋊C4C22×C4×C1112yes—
469C4⋊C4C22×C4×C1112yes—
470C22⋊C4—24no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—81no—
482C42C22×C4×C1112yes—
483C42C11×#4112yes—
484C11#2212711yescharacteristic, direct product factor, Sylow
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×D4×C1111yescharacteristic
493Q8—84no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4C4×D4×C1112yes—
537C2×C4C4×D4×C1112yes—
538C2×C4C23×C4×C1111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C11×H(5,𝔽2)11yescharacteristic
541C2×C4C11×2−1+411yescharacteristic
542C2×C4C11×2−1+411yescharacteristic
543C2×C4C11×2−1+411yescharacteristic
544C8—22no—
545C8—22no—
546C8—41no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×C4×D4×C1111yescharacteristic
556C22C11×#53611yescharacteristic
557C22C11×#53711yescharacteristic
558C22C11×#57611yescharacteristic
559C22C11×#57611yescharacteristic
560C22C11×#57711yescharacteristic
561C22C11×#57811yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C11×#51911yescharacteristic
576C4C11×#52011yescharacteristic
577C4C11×#54111yescharacteristic
578C4C11×#54211yescharacteristic
579C2—82no—
580C2C11×#232311yescharacteristic
581C2C11×#294711yescharacteristic
582C2C11×#294811yescharacteristic
583C2C11×#324111yescharacteristic
584C2C11×#324311yescharacteristic
585C2C11×#325711yescharacteristic
586C2C11×#326211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2331C2semidirect
4. C11×#1987C2semidirect
5. C11×#1949C2semidirect
6. C11×#1943C2semidirect
7. C11×#1942C2semidirect
12. C11×#1921C2semidirect
13. C11×#1918C2semidirect
15. C11×#1768C2semidirect
18. C11×#474C4semidirect
119. #22127C11direct (N × H)
193. #2331C2×C11semidirect
195. #1987C2×C11semidirect
196. #1949C2×C11semidirect
197. #1943C2×C11semidirect
198. #1942C2×C11semidirect
203. #1921C2×C11semidirect
204. #1918C2×C11semidirect
206. #1768C2×C11semidirect
272. #474C4×C11semidirect
484. C11#22127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C11×#23312
C11×#23192
C11×#19872
C11×#19492
C11×#19432
C11×#19422
C11×#19362
C11×#19342
C11×#19262
C11×#19252
C11×#19212
C11×#19182
C11×#18042
C11×#17682
#2212711