Finite Group Databasebeta

← C11×#22995 #14600188

Subgroups — C11×#22995 #14600188

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C4×C11×D8C212yesmaximal, complemented
3C11×#2366C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic, complemented
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1934C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2212yes—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4—21no—
19C11×#459C418yescomplemented
20C4×C11×D8—28no—
21C2×C11×#107C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C4×C8×C11C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#390—21no—
31C11×#390C2212yes—
32C11×#389C2212yes—
33C11×#386—22no—
34C11×#385—22no—
35C11×#384C2211yescharacteristic
36C11×#380—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C2×C11×D8—24no—
51C2×C11×D8—24no—
52C2×C11×D8C2×C418yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×#127—22no—
57C11×#127C2×C414yescomplemented
58C4×D4×C11—24no—
59C4×D4×C11—24no—
60C4×D4×C11—22no—
61C4×D4×C11—42no—
62C4×D4×C11—42no—
63C4×D4×C11—44no—
64C4×D4×C11C2×C414yescomplemented
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—44no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#107—24no—
84C11×C4⋊C8C2×C414yescomplemented
85C11×#102—22no—
86C11×#102—24no—
87C11×#102—42no—
88C11×#102C2×C418yescomplemented
89C11×#102D414yescomplemented
90C4×C8×C11—24no—
91C4×C8×C11—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95D412yes—
95#22995C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C24×C11—22no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—81no—
111C2×D4×C11—81no—
112C2×D4×C11C22×C414yes—
113C2×D4×C11C22×C412yes—
114C2×D4×C11C2×D412yes—
115C2×D4×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11—82no—
128C22×C4×C11—82no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C11×D8—216no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C22×C414yes—
143C2×C8×C11C2×D412yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4D814yescomplemented
155C11×C4⋊C4C22×C412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—82no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—42no—
165C42×C11C22×C412yes—
166C42×C11#4112yes—
167C2×#459C2×C1111yescharacteristic
168C2×C4×D8C2×C1112yescomplemented
169#2366C2×C1111yescharacteristic, complemented
170D4×C4⋊C4C2×C1111yescharacteristic, complemented
171#1957C2×C1111yescharacteristic, complemented
172#1947C2×C1111yescharacteristic, complemented
173#1934C2×C1112yescomplemented
174#1879C2×C1112yescomplemented
175#1862C2×C1112yescomplemented
176C8×C4⋊C4C2×C1111yescharacteristic, complemented
177C4×#102C2×C1111yescharacteristic, complemented
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11C22×D411yescharacteristic
193D4×C11—24no—
194D4×C11—22no—
195D4×C11—24no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—48no—
201D4×C11—84no—
202D4×C11C4×D414yescomplemented
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—48no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—88no—
224C2×C4×C11—88no—
225C2×C4×C11C4×D412yes—
226C2×C4×C11C4×D412yes—
227C2×C4×C11C2×D814yes—
228C2×C4×C11C2×D812yes—
229C2×C4×C11#13512yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C8×C11—24no—
237C8×C11—22no—
238C8×C11—41no—
239C22×D8C22×C1112yes—
240C2×#127C22×C1111yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C22×C1112yes—
243C2×C4×D4C22×C1112yes—
244C2×C4×D4C22×C1111yescharacteristic
245C22×C4⋊C4—21no—
246#459C4×C1118yescomplemented
247C4×D8—28no—
248C2×#107C22×C1112yes—
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×#102C22×C1111yescharacteristic
251C2×#102C22×C1112yes—
252C2×#102C22×C1112yes—
253C2×#102C22×C1112yes—
254C2×#102C22×C1111yescharacteristic
255C2×C4×C8C22×C1112yes—
256C2×C4×C8C22×C1111yescharacteristic
257#390—21no—
258#390C22×C1112yes—
259#389C22×C1112yes—
260#386—22no—
261#385—22no—
262#384C22×C1111yescharacteristic
263#380—21no—
264C4×C4⋊C4C22×C1111yescharacteristic
265C4×C4⋊C4C22×C1111yescharacteristic
266#340C22×C1111yescharacteristic
267#340C22×C1112yes—
268#340C22×C1111yescharacteristic
269#336C22×C1112yes—
270C22×C11—24no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11D4211yescharacteristic
286C22×C11#54811yescharacteristic
287C22×C11C22×D811yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11#57611yescharacteristic
290C22×C11#57711yescharacteristic
291C4×C11—22no—
292C4×C11—24no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11C4×D814yescomplemented
299C4×C11C2×C4×D411yescharacteristic
300C4×C11#52011yescharacteristic
301C4×C11#54711yescharacteristic
302C4×C11#55311yescharacteristic
303C22×D4—21no—
304C22×D4—21no—
305C22×D4C23×C1112yes—
306C22×D4C23×C1111yescharacteristic
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—22no—
310C2×D8—24no—
311C2×D8—24no—
312C2×D8C2×C4×C1118yescomplemented
313C22×C8C23×C1111yescharacteristic
314C22×C8C23×C1112yes—
315C22×C8C23×C1111yescharacteristic
316#127—22no—
317#127C2×C4×C1114yescomplemented
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—42no—
322C4×D4—42no—
323C4×D4—44no—
324C4×D4C2×C4×C1114yescomplemented
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4D4×C1111yescharacteristic
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C42—21no—
341C2×C42C23×C1112yes—
342C2×C42C23×C1111yescharacteristic
343#107—24no—
344C4⋊C8C2×C4×C1114yescomplemented
345#102—22no—
346#102—24no—
347#102—42no—
348#102C2×C4×C1118yescomplemented
349#102D4×C1114yescomplemented
350C4×C8—24no—
351C4×C8—22no—
352#95—21no—
353#95—22no—
354#95D4×C1112yes—
355C2×C11—44no—
356C2×C11—84no—
357C2×C11#236111yescharacteristic
358C2×C11C2×C4×D811yescharacteristic
359C2×C11#294611yescharacteristic
360C2×C11D4×D811yescharacteristic
361C2×C11#328411yescharacteristic
362C2×C11#335811yescharacteristic
363C2×C11#336111yescharacteristic
364C24—21no—
365C24—22no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—81no—
379C2×D4—81no—
380C2×D4C22×C4×C1114yes—
381C2×D4C22×C4×C1112yes—
382C2×D4C2×D4×C1112yes—
383C2×D4C11×#4112yes—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1112yes—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C24×C1111yescharacteristic
402D8—216no—
403C2×C8—22no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8C22×C4×C1114yes—
411C2×C8C2×D4×C1112yes—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—44no—
420C4⋊C4—42no—
421C4⋊C4—81no—
422C4⋊C4C11×D814yescomplemented
423C4⋊C4C22×C4×C1112yes—
424C4⋊C4C2×D4×C1112yes—
425C22⋊C4—24no—
426C22⋊C4—44no—
427C22⋊C4—44no—
428C22⋊C4—44no—
429C22⋊C4—82no—
430C42—22no—
431C42—22no—
432C42—42no—
433C42C22×C4×C1112yes—
434C42C11×#4112yes—
435C11#2299511yescharacteristic, direct product factor, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23C22×D4×C1111yescharacteristic
451D4—24no—
452D4—22no—
453D4—24no—
454D4—22no—
455D4—22no—
456D4—42no—
457D4—42no—
458D4—48no—
459D4—84no—
460D4C4×D4×C1114yescomplemented
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—48no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—88no—
482C2×C4—88no—
483C2×C4C4×D4×C1112yes—
484C2×C4C4×D4×C1112yes—
485C2×C4C2×C11×D814yes—
486C2×C4C2×C11×D812yes—
487C2×C4C11×#13512yes—
488C2×C4C23×C4×C1111yescharacteristic
489C2×C4C22×D4×C1111yescharacteristic
490C2×C4C2×C11×#4111yescharacteristic
491C2×C4C2×C11×#4111yescharacteristic
492C2×C4C11×H(5,𝔽2)11yescharacteristic
493C2×C4C11×2−1+411yescharacteristic
494C8—24no—
495C8—22no—
496C8—41no—
497C22—24no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—82no—
508C22—82no—
509C22—82no—
510C22—82no—
511C22C2×C4×D4×C1111yescharacteristic
512C22D42×C1111yescharacteristic
513C22C11×#54811yescharacteristic
514C22C22×C11×D811yescharacteristic
515C22C2×C11×#13511yescharacteristic
516C22C11×#57611yescharacteristic
517C22C11×#57711yescharacteristic
518C4—22no—
519C4—24no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—82no—
524C4—81no—
525C4C4×C11×D814yescomplemented
526C4C2×C4×D4×C1111yescharacteristic
527C4C11×#52011yescharacteristic
528C4C11×#54711yescharacteristic
529C4C11×#55311yescharacteristic
530C2—44no—
531C2—84no—
532C2C11×#236111yescharacteristic
533C2C2×C4×C11×D811yescharacteristic
534C2C11×#294611yescharacteristic
535C2D4×C11×D811yescharacteristic
536C2C11×#328411yescharacteristic
537C2C11×#335811yescharacteristic
538C2C11×#336111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×D8C2semidirect
3. C11×#2366C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#1957C2semidirect
6. C11×#1947C2semidirect
7. C11×#1934C2semidirect
8. C11×#1879C2semidirect
9. C11×#1862C2semidirect
10. C8×C11×C4⋊C4C2semidirect
11. C4×C11×#102C2semidirect
19. C11×#459C4semidirect
52. C2×C11×D8C2×C4semidirect
57. C11×#127C2×C4semidirect
64. C4×D4×C11C2×C4semidirect
84. C11×C4⋊C8C2×C4semidirect
88. C11×#102C2×C4semidirect
89. C11×#102D4semidirect
95. #22995C11direct (N × H)
154. C11×C4⋊C4D8semidirect
168. C2×C4×D8C2×C11semidirect
169. #2366C2×C11semidirect
170. D4×C4⋊C4C2×C11semidirect
171. #1957C2×C11semidirect
172. #1947C2×C11semidirect
173. #1934C2×C11semidirect
174. #1879C2×C11semidirect
175. #1862C2×C11semidirect
176. C8×C4⋊C4C2×C11semidirect
177. C4×#102C2×C11semidirect
202. D4×C11C4×D4semidirect
246. #459C4×C11semidirect
298. C4×C11C4×D8semidirect
312. C2×D8C2×C4×C11semidirect
317. #127C2×C4×C11semidirect
324. C4×D4C2×C4×C11semidirect
344. C4⋊C8C2×C4×C11semidirect
348. #102C2×C4×C11semidirect
349. #102D4×C11semidirect
422. C4⋊C4C11×D8semidirect
435. C11#22995direct (N × H)
460. D4C4×D4×C11semidirect
525. C4C4×C11×D8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C4×C11×D82
C11×#23662
D4×C11×C4⋊C42
C11×#19572
C11×#19472
C11×#19342
C11×#18792
C11×#18622
C8×C11×C4⋊C42
C4×C11×#1022
#2299511