Finite Group Databasebeta

← C11×#22601 #14599794

Subgroups — C11×#22601 #14599794

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#432C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1940C212yesmaximal, complemented
5C11×#1917C212yesmaximal, complemented
6C11×#1916C212yesmaximal, complemented
7C11×#1817C211yesmaximal, characteristic
8C11×#1817C211yesmaximal, characteristic
9C11×#1797C211yesmaximal, characteristic
10C11×#1771C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic
12C22×C11×C4⋊C4C411yescharacteristic
13C22×C11×C4⋊C4C411yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#432—24no—
18C11×#431—24no—
19C2×C11×C4⋊C8C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C2×C11×#97C2212yes—
28C2×C4×C8×C11C2212yes—
29C4×C11×C4⋊C4C411yescharacteristic
30C4×C11×C4⋊C4C411yescharacteristic
31C4×C11×C4⋊C4C411yescharacteristic
32C4×C11×C4⋊C4C411yescharacteristic
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C2×C11×#95C411yescharacteristic
38C2×C11×#95C411yescharacteristic
39C11×#336C2212yes—
40C11×#336C2212yes—
41C11×#336C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11—24no—
71C2×C42×C11C2×C411yescharacteristic
72C2×C42×C11C2×C411yescharacteristic
73C2×C42×C11C2×C411yescharacteristic
74C2×C42×C11C2×C411yescharacteristic
75C2×C42×C11C2×C411yescharacteristic
76C2×C42×C11C2×C411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×C4⋊C8—24no—
84C11×C4⋊C8—24no—
85C11×C4⋊C8—24no—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8—22no—
89C11×C22⋊C8D414yes—
90C11×#97—24no—
91C11×#97—24no—
92C4×C8×C11—24no—
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
96C11×#95C2×C411yescharacteristic
97C11×#95C2×C411yescharacteristic
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101#22601C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C22×C411yescharacteristic
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11M1614yes—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11C2×D414yes—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4M1614yes—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—22no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11#4114yes—
175C2×#432C2×C1111yescharacteristic
176C2×#431C2×C1111yescharacteristic
177C2×C4×C4⋊C4C2×C1111yescharacteristic
178#1940C2×C1112yescomplemented
179#1917C2×C1112yescomplemented
180#1916C2×C1112yescomplemented
181#1817C2×C1111yescharacteristic
182#1817C2×C1111yescharacteristic
183#1797C2×C1111yescharacteristic
184#1771C2×C1112yescomplemented
185#1749C2×C1111yescharacteristic
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11C4×D412yes—
191C23×C11C2×M1612yes—
192C23×C11#13112yes—
193C23×C11C23×C411yescharacteristic
194C2×C4×C11—28no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
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—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11#11712yes—
234C2×C4×C11#11712yes—
235C2×C4×C11C4×D412yes—
236C2×C4×C11C2×M1612yes—
237C2×C4×C11C2×M1612yes—
238C2×C4×C11C2×M1612yes—
239C2×C4×C11C2×M1612yes—
240C2×C4×C11C2×M1612yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4112yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C112−1+412yes—
245C8×C11—24no—
246C8×C11—42no—
247C8×C11—42no—
248C8×C11—42no—
249C22×C4⋊C4C4×C1111yescharacteristic
250C22×C4⋊C4C4×C1111yescharacteristic
251C22×C42C22×C1111yescharacteristic
252C22×C42C22×C1111yescharacteristic
253C22×C42C22×C1111yescharacteristic
254#432—24no—
255#431—24no—
256C2×C4⋊C8C22×C1112yes—
257C2×C4⋊C8C22×C1112yes—
258C2×C4⋊C8C22×C1112yes—
259C2×C22⋊C8C22×C1111yescharacteristic
260C2×C22⋊C8C22×C1111yescharacteristic
261C2×C22⋊C8C22×C1111yescharacteristic
262C2×C22⋊C8C22×C1111yescharacteristic
263C2×#97C22×C1112yes—
264C2×#97C22×C1112yes—
265C2×C4×C8C22×C1112yes—
266C4×C4⋊C4C4×C1111yescharacteristic
267C4×C4⋊C4C4×C1111yescharacteristic
268C4×C4⋊C4C4×C1111yescharacteristic
269C4×C4⋊C4C4×C1111yescharacteristic
270C4×C4⋊C4C22×C1111yescharacteristic
271C4×C4⋊C4C22×C1111yescharacteristic
272C4×C4⋊C4C22×C1111yescharacteristic
273C4×C4⋊C4C22×C1111yescharacteristic
274C2×#95C4×C1111yescharacteristic
275C2×#95C4×C1111yescharacteristic
276#336C22×C1112yes—
277#336C22×C1112yes—
278#336C22×C1112yes—
279#336C22×C1112yes—
280#336C22×C1112yes—
281#336C22×C1112yes—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11#43514yes—
289C22×C11C2×#11711yescharacteristic
290C22×C11C2×C4×D411yescharacteristic
291C22×C11#51911yescharacteristic
292C22×C11C22×M1611yescharacteristic
293C22×C11C22×M1611yescharacteristic
294C22×C11C2×#13111yescharacteristic
295C22×C11#56811yescharacteristic
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11#54712yes—
310C4×C11#55212yes—
311C23×C4C2×C4×C1111yescharacteristic
312C23×C4C2×C4×C1111yescharacteristic
313C23×C4C2×C4×C1111yescharacteristic
314C23×C4C2×C4×C1111yescharacteristic
315C23×C4C2×C4×C1111yescharacteristic
316C23×C4C2×C4×C1111yescharacteristic
317C23×C4C23×C1111yescharacteristic
318C22×C8C23×C1112yes—
319C22×C8C23×C1112yes—
320C22×C8C23×C1112yes—
321C22×C8C23×C1112yes—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4C2×C4×C1111yescharacteristic
325C2×C4⋊C4C2×C4×C1111yescharacteristic
326C2×C4⋊C4C2×C4×C1111yescharacteristic
327C2×C4⋊C4C2×C4×C1111yescharacteristic
328C2×C4⋊C4C2×C4×C1111yescharacteristic
329C2×C4⋊C4C2×C4×C1111yescharacteristic
330C2×C4⋊C4C2×C4×C1111yescharacteristic
331C2×C4⋊C4C2×C4×C1111yescharacteristic
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42C2×C4×C1111yescharacteristic
338C2×C42C2×C4×C1111yescharacteristic
339C2×C42C2×C4×C1111yescharacteristic
340C2×C42C2×C4×C1111yescharacteristic
341C2×C42C2×C4×C1111yescharacteristic
342C2×C42C2×C4×C1111yescharacteristic
343C2×C42C23×C1111yescharacteristic
344C2×C42C23×C1111yescharacteristic
345C2×C42C23×C1111yescharacteristic
346C2×C42C23×C1111yescharacteristic
347C2×C42C23×C1111yescharacteristic
348C2×C42C23×C1111yescharacteristic
349C4⋊C8—24no—
350C4⋊C8—24no—
351C4⋊C8—24no—
352C22⋊C8—22no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355C22⋊C8D4×C1114yes—
356#97—24no—
357#97—24no—
358C4×C8—24no—
359#95C2×C4×C1111yescharacteristic
360#95C2×C4×C1111yescharacteristic
361#95C2×C4×C1111yescharacteristic
362#95C2×C4×C1111yescharacteristic
363#95C2×C4×C1111yescharacteristic
364#95C2×C4×C1111yescharacteristic
365#95C2×C4×C1111yescharacteristic
366#95C2×C4×C1111yescharacteristic
367C2×C11—24no—
368C2×C11#234411yescharacteristic
369C2×C11#292011yescharacteristic
370C2×C11#292411yescharacteristic
371C2×C11C2×#43511yescharacteristic
372C2×C11D4×M1611yescharacteristic
373C2×C11#298311yescharacteristic
374C2×C11#298411yescharacteristic
375C24C22×C4×C1111yescharacteristic
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4C11×M1614yes—
396C22×C4C22×C4×C1111yescharacteristic
397C22×C4C22×C4×C1111yescharacteristic
398C22×C4C22×C4×C1111yescharacteristic
399C22×C4C22×C4×C1111yescharacteristic
400C22×C4C22×C4×C1111yescharacteristic
401C22×C4C22×C4×C1111yescharacteristic
402C22×C4C22×C4×C1111yescharacteristic
403C22×C4C22×C4×C1111yescharacteristic
404C22×C4C22×C4×C1111yescharacteristic
405C22×C4C22×C4×C1111yescharacteristic
406C22×C4C22×C4×C1111yescharacteristic
407C22×C4C22×C4×C1111yescharacteristic
408C22×C4C22×C4×C1111yescharacteristic
409C22×C4C2×D4×C1112yes—
410C22×C4C11×#4112yes—
411C22×C4C24×C1111yescharacteristic
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8C2×D4×C1114yes—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4C11×M1614yes—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—22no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42—22no—
443C42—21no—
444C42—21no—
445C42—21no—
446C42—21no—
447C42C11×#4114yes—
448C11#2260111yescharacteristic, direct product factor, Sylow
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23C4×D4×C1112yes—
454C23C2×C11×M1612yes—
455C23C11×#13112yes—
456C23C23×C4×C1111yescharacteristic
457C2×C4—28no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—28no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4C11×#11712yes—
497C2×C4C11×#11712yes—
498C2×C4C4×D4×C1112yes—
499C2×C4C2×C11×M1612yes—
500C2×C4C2×C11×M1612yes—
501C2×C4C2×C11×M1612yes—
502C2×C4C2×C11×M1612yes—
503C2×C4C2×C11×M1612yes—
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C2×C11×#4112yes—
506C2×C4C2×C11×#4111yescharacteristic
507C2×C4C11×2−1+412yes—
508C8—24no—
509C8—42no—
510C8—42no—
511C8—42no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22C11×#43514yes—
519C22C2×C11×#11711yescharacteristic
520C22C2×C4×D4×C1111yescharacteristic
521C22C11×#51911yescharacteristic
522C22C22×C11×M1611yescharacteristic
523C22C22×C11×M1611yescharacteristic
524C22C2×C11×#13111yescharacteristic
525C22C11×#56811yescharacteristic
526C4—22no—
527C4—22no—
528C4—22no—
529C4—22no—
530C4—22no—
531C4—22no—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4C11×#54712yes—
540C4C11×#55212yes—
541C2—24no—
542C2C11×#234411yescharacteristic
543C2C11×#292011yescharacteristic
544C2C11×#292411yescharacteristic
545C2C2×C11×#43511yescharacteristic
546C2D4×C11×M1611yescharacteristic
547C2C11×#298311yescharacteristic
548C2C11×#298411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1940C2semidirect
5. C11×#1917C2semidirect
6. C11×#1916C2semidirect
10. C11×#1771C2semidirect
101. #22601C11direct (N × H)
178. #1940C2×C11semidirect
179. #1917C2×C11semidirect
180. #1916C2×C11semidirect
184. #1771C2×C11semidirect
448. C11#22601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C2×C11×#4312
C2×C4×C11×C4⋊C42
C11×#19402
C11×#19172
C11×#19162
C11×#18172
C11×#17972
C11×#17712
C11×#17492
#2260111