Finite Group Databasebeta

← C11×#22439 #14599632

Subgroups — C11×#22439 #14599632

Order 2816.

1466 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic
2C2×C11×#440C212yesmaximal, complemented
3C11×#2341C211yesmaximal, characteristic, complemented
4C11×#2339C211yesmaximal, characteristic, complemented
5C11×#1973C212yesmaximal, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1878C212yesmaximal, complemented
8C11×#1808C211yesmaximal, characteristic, complemented
9C11×#1788C211yesmaximal, characteristic, complemented
10C11×#1788C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C2×C11×#135—28no—
15C2×C11×#135C418yescomplemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×D4×C11C2212yes—
23C11×#440—28no—
24C2×C11×#107C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×#97C2212yes—
31C11×#391C2212yes—
32C11×#390—22no—
33C11×#390C2212yes—
34C11×#386—22no—
35C11×#381—21no—
36C11×#380—21no—
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4C2211yescharacteristic
41C2×C11×#95—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41—42no—
50C2×C11×#41C2×C414yes—
51C2×C11×#41C2×C414yescomplemented
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—22no—
61C23×C4×C11C2311yescharacteristic
62C11×#135—232no—
63C2×C11×Q16—24no—
64C2×C11×Q16C2×C414yescomplemented
65C2×C11×SD16—24no—
66C2×C11×SD16C2×C414yes—
67C2×C11×SD16C2×C414yescomplemented
68C2×C11×SD16D418yes—
69C2×C11×D8—24no—
70C2×C11×D8C2×C414yes—
71C22×C8×C11—24no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2312yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×Q8×C11—24no—
77C4×Q8×C11—42no—
78C4×D4×C11—24no—
79C4×D4×C11—42no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11C2312yes—
91C11×#107—24no—
92C11×#103—24no—
93C11×#103—42no—
94C11×#102—24no—
95C11×#102—42no—
96C11×C22⋊C8—22no—
97C11×#97—24no—
98C11×#95—21no—
99C11×#95—22no—
100C11×#95—21no—
101C11×#95—22no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#22439C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—21no—
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—48no—
113C11×#41—48no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C22×C412yes—
120C2×Q8×C11C22×C412yes—
121C2×Q8×C11C2×D414yes—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11C22×C412yes—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—82no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C11×Q16—28no—
154C11×SD16—28no—
155C11×SD16C22⋊C4116yescomplemented
156C11×D8—28no—
157C2×C8×C11—28no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C2×D414yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—82no—
174C11×C22⋊C4—81no—
175C11×C22⋊C4—81no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—44no—
179C22×#135C2×C1111yescharacteristic
180C2×#440C2×C1112yescomplemented
181#2341C2×C1111yescharacteristic, complemented
182#2339C2×C1111yescharacteristic, complemented
183#1973C2×C1112yescomplemented
184#1879C2×C1112yescomplemented
185#1878C2×C1112yescomplemented
186#1808C2×C1111yescharacteristic, complemented
187#1788C2×C1111yescharacteristic, complemented
188#1788C2×C1111yescharacteristic, complemented
189#1752C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C4×D412yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11C2×C22⋊C414yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—24no—
216D4×C11—48no—
217D4×C11—48no—
218D4×C11—42no—
219D4×C11C2×C22⋊C414yes—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
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—48no—
234C2×C4×C11—48no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—88no—
243C2×C4×C11C4×D412yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)12yes—
248C8×C11—22no—
249C8×C11—42no—
250C8×C11C2×C22⋊C414yes—
251C22×#41C22×C1111yescharacteristic
252C22×#41C22×C1111yescharacteristic
253C2×#135—28no—
254C2×#135C4×C1118yescomplemented
255C22×Q16C22×C1111yescharacteristic
256C22×SD16C22×C1111yescharacteristic
257C22×SD16C22×C1111yescharacteristic
258C22×D8C22×C1111yescharacteristic
259C23×C8C22×C1111yescharacteristic
260C2×C4×Q8C22×C1112yes—
261C2×C4×D4C22×C1112yes—
262#440—28no—
263C2×#107C22×C1112yes—
264C2×#103C22×C1112yes—
265C2×#103C22×C1112yes—
266C2×#102C22×C1112yes—
267C2×#102C22×C1112yes—
268C2×C22⋊C8C22×C1111yescharacteristic
269C2×#97C22×C1112yes—
270#391C22×C1112yes—
271#390—22no—
272#390C22×C1112yes—
273#386—22no—
274#381—21no—
275#380—21no—
276#380C22×C1111yescharacteristic
277#380C22×C1111yescharacteristic
278C4×C22⋊C4—21no—
279C4×C22⋊C4C22×C1111yescharacteristic
280C2×#95—21no—
281#340C22×C1112yes—
282#336C22×C1112yes—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C2×C4×D411yescharacteristic
299C22×C11D4212yes—
300C22×C11#57512yes—
301C22×C11#57611yescharacteristic
302C22×C11#57811yescharacteristic
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—82no—
309C4×C11—82no—
310C4×C11C22×C22⋊C411yescharacteristic
311C4×C11#51811yescharacteristic
312C4×C11#54612yes—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41C2×C4×C1114yes—
320C2×#41C2×C4×C1114yescomplemented
321C22×Q8C23×C1111yescharacteristic
322C22×Q8C23×C1111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C23×C1111yescharacteristic
326C22×D4C23×C1111yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4C23×C1111yescharacteristic
331#135—232no—
332C2×Q16—24no—
333C2×Q16C2×C4×C1114yescomplemented
334C2×SD16—24no—
335C2×SD16C2×C4×C1114yes—
336C2×SD16C2×C4×C1114yescomplemented
337C2×SD16D4×C1118yes—
338C2×D8—24no—
339C2×D8C2×C4×C1114yes—
340C22×C8—24no—
341C22×C8C2×C4×C1114yescomplemented
342C22×C8C23×C1112yes—
343C22×C8C23×C1111yescharacteristic
344C22×C8C23×C1111yescharacteristic
345C4×Q8—24no—
346C4×Q8—42no—
347C4×D4—24no—
348C4×D4—42no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4D4×C1112yes—
358C2×C42—22no—
359C2×C42C23×C1112yes—
360#107—24no—
361#103—24no—
362#103—42no—
363#102—24no—
364#102—42no—
365C22⋊C8—22no—
366#97—24no—
367#95—21no—
368#95—22no—
369#95—21no—
370#95—22no—
371#95D4×C1111yescharacteristic
372#95D4×C1111yescharacteristic
373C2×C11—42no—
374C2×C11—44no—
375C2×C11—82no—
376C2×C11D4×C22⋊C411yescharacteristic
377C2×C11#294311yescharacteristic
378C2×C11#295111yescharacteristic
379C2×C11#326812yes—
380C2×C11#326912yes—
381C24—21no—
382C24—21no—
383C24C2×D4×C1111yescharacteristic
384#41—28no—
385#41—28no—
386#41—44no—
387#41—44no—
388#41—48no—
389#41—48no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8C22×C4×C1112yes—
396C2×Q8C22×C4×C1112yes—
397C2×Q8C2×D4×C1114yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4C22×C4×C1112yes—
408C2×D4C22×C4×C1112yes—
409C2×D4C2×D4×C1114yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—82no—
423C22×C4C22×C4×C1112yes—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C11×#4112yes—
428C22×C4C24×C1111yescharacteristic
429Q16—28no—
430SD16—28no—
431SD16C11×C22⋊C4116yescomplemented
432D8—28no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8C22×C4×C1112yes—
439C2×C8C22×C4×C1112yes—
440C2×C8C2×D4×C1114yes—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—44no—
446C22⋊C4—42no—
447C22⋊C4—44no—
448C22⋊C4—44no—
449C22⋊C4—82no—
450C22⋊C4—81no—
451C22⋊C4—81no—
452C42—22no—
453C42—22no—
454C42—44no—
455C11#2243911yescharacteristic, direct product factor, Sylow
456C23—22no—
457C23—24no—
458C23—22no—
459C23—22no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23C4×D4×C1112yes—
471C23C22×D4×C1111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8C2×C11×C22⋊C414yes—
478D4—22no—
479D4—22no—
480D4—22no—
481D4—24no—
482D4—48no—
483D4—48no—
484D4—42no—
485D4C2×C11×C22⋊C414yes—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—48no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—88no—
509C2×C4C4×D4×C1112yes—
510C2×C4C23×C4×C1111yescharacteristic
511C2×C4C22×D4×C1112yes—
512C2×C4C2×C11×#4111yescharacteristic
513C2×C4C11×H(5,𝔽2)12yes—
514C8—22no—
515C8—42no—
516C8C2×C11×C22⋊C414yes—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—42no—
525C22—42no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22C2×C4×D4×C1111yescharacteristic
533C22D42×C1112yes—
534C22C11×#57512yes—
535C22C11×#57611yescharacteristic
536C22C11×#57811yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—82no—
544C4C22×C11×C22⋊C411yescharacteristic
545C4C11×#51811yescharacteristic
546C4C11×#54612yes—
547C2—42no—
548C2—44no—
549C2—82no—
550C2D4×C11×C22⋊C411yescharacteristic
551C2C11×#294311yescharacteristic
552C2C11×#295111yescharacteristic
553C2C11×#326812yes—
554C2C11×#326912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#135C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#440C2semidirect
3. C11×#2341C2semidirect
4. C11×#2339C2semidirect
5. C11×#1973C2semidirect
6. C11×#1879C2semidirect
7. C11×#1878C2semidirect
8. C11×#1808C2semidirect
9. C11×#1788C2semidirect
10. C11×#1788C2semidirect
11. C11×#1752C2semidirect
15. C2×C11×#135C4semidirect
51. C2×C11×#41C2×C4semidirect
64. C2×C11×Q16C2×C4semidirect
67. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
104. #22439C11direct (N × H)
155. C11×SD16C22⋊C4semidirect
180. C2×#440C2×C11semidirect
181. #2341C2×C11semidirect
182. #2339C2×C11semidirect
183. #1973C2×C11semidirect
184. #1879C2×C11semidirect
185. #1878C2×C11semidirect
186. #1808C2×C11semidirect
187. #1788C2×C11semidirect
188. #1788C2×C11semidirect
189. #1752C2×C11semidirect
254. C2×#135C4×C11semidirect
320. C2×#41C2×C4×C11semidirect
333. C2×Q16C2×C4×C11semidirect
336. C2×SD16C2×C4×C11semidirect
341. C22×C8C2×C4×C11semidirect
431. SD16C11×C22⋊C4semidirect
455. C11#22439direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4402
C11×#23412
C11×#23392
C11×#19732
C11×#18792
C11×#18782
C11×#18082
C11×#17882
C11×#17522
#2243911