Finite Group Databasebeta

← C11×#22480 #14599673

Subgroups — C11×#22480 #14599673

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2D4×C11×M16C212yesmaximal
3C11×#1998C212yesmaximal, complemented
4C11×#1901C212yesmaximal, complemented
5C11×#1901C212yesmaximal, complemented
6C11×#1822C211yesmaximal, characteristic, complemented
7C11×#1821C211yesmaximal, characteristic, complemented
8C11×#1801C211yesmaximal, characteristic, complemented
9C4×C11×#101C211yesmaximal, characteristic, complemented
10C11×#1742C211yesmaximal, characteristic, complemented
11C2×C11×#343C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C22×C11×M16C2212yes—
14C11×#552—22no—
15C11×#552—22no—
16C11×#552—22no—
17C11×#552—22no—
18C2×C11×#126C412yes—
19C2×C11×#125C412yes—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123C412yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C412yes—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#436—22no—
30C11×#435—22no—
31C11×#435—22no—
32C8×D4×C11—22no—
33C11×#423C2212yes—
34C2×C11×#101C2212yes—
35C2×C11×#101C2212yes—
36C11×#407C2212yes—
37C11×#407C2212yes—
38C4×C11×M16C2212yes—
39C11×#343C2212yes—
40C11×#343C2212yes—
41C11×#343C2212yes—
42C11×#343C2212yes—
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#343C2211yescharacteristic
46C11×#343C2211yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16—42no—
57C2×C11×M16—42no—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C2×C11×M16C2312yes—
61C2×C11×M16C2312yes—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C11×#126—24no—
65C11×#126—24no—
66C11×#125—24no—
67C11×#125—24no—
68C11×#125—22no—
69C11×#125—22no—
70C11×#123—24no—
71C11×#123—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×D4×C11D412yes—
79C4×D4×C11D412yes—
80C4×D4×C11D412yes—
81C4×D4×C11D412yes—
82C11×#117—22no—
83C11×#117—22no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4C2×C412yes—
91C2×C11×C4⋊C4C2×C412yes—
92C2×C11×C4⋊C4C2×C412yes—
93C2×C11×C4⋊C4C2×C412yes—
94C2×C11×C4⋊C4C2×C412yes—
95C2×C11×C4⋊C4C2×C412yes—
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2×C412yes—
101C2×C11×C22⋊C4C2×C412yes—
102C2×C11×C22⋊C4C2×C412yes—
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C42×C11C2×C412yes—
106C2×C42×C11C2×C412yes—
107C2×C42×C11C2311yescharacteristic
108C11×C4⋊C8—22no—
109C11×C4⋊C8—22no—
110C11×#101—24no—
111C11×#101—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11×#97—22no—
117C4×C8×C11—22no—
118#22480C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11C22×C411yescharacteristic
120C24×C11C22×C411yescharacteristic
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×D4×C11—42no—
126C2×D4×C11C22⋊C412yes—
127C2×D4×C11C22⋊C412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—44no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—44no—
158C11×M16—44no—
159C11×M16#4114yes—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—44no—
165C2×C8×C11—44no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C22⋊C412yes—
178C11×C4⋊C4C22⋊C412yes—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4C22⋊C411yescharacteristic
184C11×C22⋊C4C22⋊C411yescharacteristic
185C11×C22⋊C4C22⋊C411yescharacteristic
186C11×C22⋊C4C22⋊C411yescharacteristic
187C11×C22⋊C4C22⋊C412yes—
188C11×C22⋊C4C22⋊C412yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195C2×#552C2×C1111yescharacteristic
196D4×M16C2×C1112yes—
197#1998C2×C1112yescomplemented
198#1901C2×C1112yescomplemented
199#1901C2×C1112yescomplemented
200#1822C2×C1111yescharacteristic, complemented
201#1821C2×C1111yescharacteristic, complemented
202#1801C2×C1111yescharacteristic, complemented
203C4×#101C2×C1111yescharacteristic, complemented
204#1742C2×C1111yescharacteristic, complemented
205C2×#343C2×C1111yescharacteristic, complemented
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C2×C22⋊C412yes—
215C23×C11C2×C22⋊C411yescharacteristic
216C23×C11C2×C22⋊C411yescharacteristic
217C23×C11C23×C411yescharacteristic
218Q8×C11—42no—
219Q8×C11—42no—
220D4×C11—24no—
221D4×C11—42no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C8×C11—24no—
258C8×C11—42no—
259C8×C11—42no—
260C8×C11—42no—
261C22×M16C22×C1112yes—
262C22×M16C22×C1112yes—
263#552—22no—
264#552—22no—
265#552—22no—
266#552—22no—
267C2×#126C4×C1112yes—
268C2×#125C4×C1112yes—
269C2×#125C22×C1111yescharacteristic
270C2×#123C4×C1112yes—
271C2×C22⋊Q8C22×C1111yescharacteristic
272C2×C22⋊Q8C22×C1111yescharacteristic
273C2×C4×Q8C22×C1111yescharacteristic
274C2×C4×D4C22×C1111yescharacteristic
275C2×#117C4×C1112yes—
276C2×#117C22×C1111yescharacteristic
277C22×C4⋊C4C22×C1111yescharacteristic
278#436—22no—
279#435—22no—
280#435—22no—
281C8×D4—22no—
282#423C22×C1112yes—
283C2×#101C22×C1112yes—
284C2×#101C22×C1112yes—
285#407C22×C1112yes—
286#407C22×C1112yes—
287C4×M16C22×C1112yes—
288#343C22×C1111yescharacteristic
289#343C22×C1111yescharacteristic
290#343C22×C1111yescharacteristic
291#343C22×C1112yes—
292#343C22×C1112yes—
293#343C22×C1112yes—
294#343C22×C1112yes—
295#343C22×C1111yescharacteristic
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—22no—
302C22×C11—21no—
303C22×C11—22no—
304C22×C11—21no—
305C22×C11—22no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11#41312yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C4×#4111yescharacteristic
313C22×C11#52011yescharacteristic
314C4×C11—21no—
315C4×C11—22no—
316C4×C11—21no—
317C4×C11—22no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11#54612yes—
325C4×C11#54712yes—
326C22×Q8C23×C1111yescharacteristic
327C22×D4C2×C4×C1111yescharacteristic
328C23×C4C2×C4×C1112yes—
329C23×C4C23×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16C23×C1112yes—
338C2×M16C23×C1112yes—
339C2×M16C23×C1112yes—
340C2×M16C23×C1112yes—
341C22×C8—22no—
342C22×C8—22no—
343#126—24no—
344#126—24no—
345#125—24no—
346#125—24no—
347#125—22no—
348#125—22no—
349#123—24no—
350#123—24no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×D4D4×C1112yes—
358C4×D4D4×C1112yes—
359C4×D4D4×C1112yes—
360C4×D4D4×C1112yes—
361#117—22no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366#117—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C2×C4×C1112yes—
370C2×C4⋊C4C2×C4×C1112yes—
371C2×C4⋊C4C2×C4×C1112yes—
372C2×C4⋊C4C2×C4×C1112yes—
373C2×C4⋊C4C2×C4×C1112yes—
374C2×C4⋊C4C2×C4×C1112yes—
375C2×C4⋊C4C2×C4×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C22⋊C4C2×C4×C1112yes—
380C2×C22⋊C4C2×C4×C1112yes—
381C2×C22⋊C4C2×C4×C1112yes—
382C2×C22⋊C4C2×C4×C1111yescharacteristic
383C2×C22⋊C4C2×C4×C1111yescharacteristic
384C2×C42C2×C4×C1112yes—
385C2×C42C2×C4×C1112yes—
386C2×C42C23×C1111yescharacteristic
387C4⋊C8—22no—
388C4⋊C8—22no—
389#101—24no—
390#101—42no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#97—22no—
396C4×C8—22no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—22no—
400C2×C11—41no—
401C2×C11—42no—
402C2×C11#233911yescharacteristic
403C2×C11C2×#41311yescharacteristic
404C2×C11#288911yescharacteristic
405C24C22×C4×C1111yescharacteristic
406C24C22×C4×C1111yescharacteristic
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×D4—42no—
412C2×D4C11×C22⋊C412yes—
413C2×D4C11×C22⋊C412yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4C22×C4×C1112yes—
424C22×C4C22×C4×C1111yescharacteristic
425C22×C4C22×C4×C1111yescharacteristic
426C22×C4C22×C4×C1112yes—
427C22×C4C22×C4×C1112yes—
428C22×C4C22×C4×C1112yes—
429C22×C4C22×C4×C1111yescharacteristic
430C22×C4C22×C4×C1111yescharacteristic
431C22×C4C2×D4×C1112yes—
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1112yes—
434C22×C4C2×D4×C1112yes—
435C22×C4C24×C1111yescharacteristic
436M16—22no—
437M16—22no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—44no—
444M16—44no—
445M16C11×#4114yes—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—44no—
451C2×C8—44no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4C11×C22⋊C412yes—
464C4⋊C4C11×C22⋊C412yes—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4C11×C22⋊C411yescharacteristic
470C22⋊C4C11×C22⋊C411yescharacteristic
471C22⋊C4C11×C22⋊C411yescharacteristic
472C22⋊C4C11×C22⋊C411yescharacteristic
473C22⋊C4C11×C22⋊C412yes—
474C22⋊C4C11×C22⋊C412yes—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42C2×D4×C1112yes—
480C42C2×D4×C1112yes—
481C11#2248011yescharacteristic, direct product factor, Sylow
482C23—21no—
483C23—21no—
484C23—22no—
485C23—21no—
486C23—21no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C11×C22⋊C412yes—
491C23C2×C11×C22⋊C411yescharacteristic
492C23C2×C11×C22⋊C411yescharacteristic
493C23C23×C4×C1111yescharacteristic
494Q8—42no—
495Q8—42no—
496D4—24no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4C2×C11×C22⋊C411yescharacteristic
524C2×C4C2×C11×C22⋊C411yescharacteristic
525C2×C4C2×C11×C22⋊C411yescharacteristic
526C2×C4C2×C11×C22⋊C411yescharacteristic
527C2×C4C2×C11×C22⋊C412yes—
528C2×C4C2×C11×C22⋊C412yes—
529C2×C4C22×D4×C1112yes—
530C2×C4C2×C11×#4112yes—
531C2×C4C11×H(5,𝔽2)11yescharacteristic
532C2×C4C11×2−1+411yescharacteristic
533C8—24no—
534C8—42no—
535C8—42no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22C11×#41312yes—
552C22C22×C11×C22⋊C411yescharacteristic
553C22C4×C11×#4111yescharacteristic
554C22C11×#52011yescharacteristic
555C4—21no—
556C4—22no—
557C4—21no—
558C4—22no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4C11×#54612yes—
566C4C11×#54712yes—
567C2—21no—
568C2—21no—
569C2—22no—
570C2—41no—
571C2—42no—
572C2C11×#233911yescharacteristic
573C2C2×C11×#41311yescharacteristic
574C2C11×#288911yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1998C2semidirect
4. C11×#1901C2semidirect
5. C11×#1901C2semidirect
6. C11×#1822C2semidirect
7. C11×#1821C2semidirect
8. C11×#1801C2semidirect
9. C4×C11×#101C2semidirect
10. C11×#1742C2semidirect
11. C2×C11×#343C2semidirect
118. #22480C11direct (N × H)
197. #1998C2×C11semidirect
198. #1901C2×C11semidirect
199. #1901C2×C11semidirect
200. #1822C2×C11semidirect
201. #1821C2×C11semidirect
202. #1801C2×C11semidirect
203. C4×#101C2×C11semidirect
204. #1742C2×C11semidirect
205. C2×#343C2×C11semidirect
481. C11#22480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
D4×C11×M162
C11×#19982
C11×#19012
C11×#18222
C11×#18212
C11×#18012
C4×C11×#1012
C11×#17422
C2×C11×#3432
#2248011