Finite Group Databasebeta

← C11×#33561 #14610754

Subgroups — C11×#33561 #14610754

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3028C212yesmaximal, complemented
3C11×#3018C211yesmaximal, characteristic
4C11×#2201C214yesmaximal, complemented
5C11×#2198C214yesmaximal, complemented
6C11×#2126C211yesmaximal, characteristic, complemented
7C11×#2123C212yesmaximal, complemented
8C11×#585C2211yescharacteristic
9C11×#575—21no—
10C11×#563—21no—
11C11×#563C2212yescomplemented
12C11×#559C2212yescomplemented
13Q82×C11—21no—
14C11×#556—22no—
15D4×Q8×C11—22no—
16C11×#542—24no—
17C11×#536—21no—
18C11×#536—22no—
19C11×#536C2212yes—
20C11×#533—21no—
21C11×#532C2211yescharacteristic
22C11×#458—24no—
23C11×#458C2218yes—
24C11×#456—21no—
25C11×#455C2212yes—
26C11×#454—21no—
27C11×#453C2212yes—
28C2×C11×#104—21no—
29C11×#413C2211yescharacteristic
30C11×#410—22no—
31C11×#410C2212yes—
32C11×#354C2212yescomplemented
33C11×#353C2212yescomplemented
34C11×#352C2218yescomplemented
35C11×2−1+4—21no—
36C11×2−1+4—41no—
37C11×H(5,𝔽2)—22no—
38C11×H(5,𝔽2)—41no—
39C11×H(5,𝔽2)C2312yes—
40C2×C11×#41—22no—
41C2×C11×#41—21no—
42C2×C11×#41—42no—
43C2×C11×#41D411yescharacteristic
44C2×C11×#41C2311yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11D412yes—
47C11×#137—22no—
48C11×#137—41no—
49C11×AGL(1,ℤ/8)—22no—
50C11×AGL(1,ℤ/8)—41no—
51C11×#135—42no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—42no—
59C11×C4⋊Q8D411yescharacteristic
60C11×#127C2311yescharacteristic
61C11×#126—24no—
62C11×#126—24no—
63C11×#125—22no—
64C11×#124—22no—
65C11×#124—22no—
66C11×#124—24no—
67C11×#124—42no—
68C11×#124D411yescharacteristic
69C11×#124C2311yescharacteristic
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—28no—
73C11×#123D414yes—
74C11×#123C2314yes—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—44no—
82C11×#121—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—24no—
85C4×Q8×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—24no—
88C11×#117—22no—
89C11×#117—21no—
90C11×#117—22no—
91C11×#117D412yes—
92C2×C42×C11D411yescharacteristic
93C11×#104—22no—
94C11×#104—22no—
95C11×#101—21no—
96C11×#100C2312yes—
97C11×#99—22no—
98C11×#99—28no—
99C11×#99C2314yes—
100#33561C1111yesmaximal, characteristic, direct product factor, Sylow
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—42no—
108C11×#41—41no—
109C11×#41—44no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41—41no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—81no—
125C2×Q8×C11—81no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D411yescharacteristic
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—42no—
134C2×D4×C11—44no—
135C2×D4×C11—41no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×D411yescharacteristic
138C2×D4×C11C2411yescharacteristic
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C11×Q16—42no—
148C11×SD16—42no—
149C11×SD16—42no—
150C11×D8—42no—
151C11×M16—22no—
152C11×M16—41no—
153C2×C8×C11—41no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—48no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4C2×D414yes—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—21no—
178C42×C11—42no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181#3550C2×C1111yescharacteristic, complemented
182#3028C2×C1112yescomplemented
183#3018C2×C1111yescharacteristic
184#2201C2×C1114yescomplemented
185#2198C2×C1114yescomplemented
186#2126C2×C1111yescharacteristic, complemented
187#2123C2×C1112yescomplemented
188C23×C11—24no—
189C23×C11—21no—
190C23×C11—41no—
191C23×C11#12011yescharacteristic
192C23×C11C22×D412yes—
193Q8×C11—22no—
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—44no—
197Q8×C11—42no—
198Q8×C11—41no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—82no—
202Q8×C11—82no—
203D4×C11—22no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—44no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—41no—
213D4×C11—81no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11—82no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C8×C11—42no—
238#585C22×C1111yescharacteristic
239#575—21no—
240#563—21no—
241#563C22×C1112yescomplemented
242#559C22×C1112yescomplemented
243Q82—21no—
244#556—22no—
245D4×Q8—22no—
246#542—24no—
247#536—21no—
248#536—22no—
249#536C22×C1112yes—
250#533—21no—
251#532C22×C1111yescharacteristic
252#458—24no—
253#458C22×C1118yes—
254#456—21no—
255#455C22×C1112yes—
256#454—21no—
257#453C22×C1112yes—
258C2×#104—21no—
259#413C22×C1111yescharacteristic
260#410—22no—
261#410C22×C1112yes—
262#354C22×C1112yescomplemented
263#353C22×C1112yescomplemented
264#352C22×C1118yescomplemented
265C22×C11—22no—
266C22×C11—21no—
267C22×C11—41no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—41no—
272C22×C11—84no—
273C22×C11—161no—
274C22×C11C2×#12011yescharacteristic
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11—41no—
282C4×C11—44no—
283C4×C11—84no—
284C4×C11B(4,𝔽2)11yescharacteristic
285C4×C11B(4,𝔽2)11yescharacteristic
2862−1+4—21no—
2872−1+4—41no—
288H(5,𝔽2)—22no—
289H(5,𝔽2)—41no—
290H(5,𝔽2)C23×C1112yes—
291C2×#41—22no—
292C2×#41—21no—
293C2×#41—42no—
294C2×#41D4×C1111yescharacteristic
295C2×#41C23×C1111yescharacteristic
296C22×Q8—21no—
297C22×Q8D4×C1112yes—
298#137—22no—
299#137—41no—
300AGL(1,ℤ/8)—22no—
301AGL(1,ℤ/8)—41no—
302#135—42no—
303C2×M16—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—42no—
310C4⋊Q8D4×C1111yescharacteristic
311#127C23×C1111yescharacteristic
312#126—24no—
313#126—24no—
314#125—22no—
315#124—22no—
316#124—22no—
317#124—24no—
318#124—42no—
319#124D4×C1111yescharacteristic
320#124C23×C1111yescharacteristic
321#123—22no—
322#123—22no—
323#123—28no—
324#123D4×C1114yes—
325#123C23×C1114yes—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—44no—
333#121—22no—
334C4×Q8—22no—
335C4×Q8—24no—
336C4×Q8—22no—
337C4×D4—22no—
338C4×D4—24no—
339#117—22no—
340#117—21no—
341#117—22no—
342#117D4×C1112yes—
343C2×C42D4×C1111yescharacteristic
344#104—22no—
345#104—22no—
346#101—21no—
347#100C23×C1112yes—
348#99—22no—
349#99—28no—
350#99C23×C1114yes—
351C2×C11—21no—
352C2×C11—42no—
353C2×C11—41no—
354C2×C11—81no—
355C2×C11—82no—
356C2×C11C2×B(4,𝔽2)11yescharacteristic
357#41—22no—
358#41—22no—
359#41—41no—
360#41—41no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—41no—
365#41—44no—
366#41—41no—
367#41—41no—
368#41—42no—
369#41—41no—
370#41—42no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—81no—
381C2×Q8—81no—
382C2×Q8C2×D4×C1111yescharacteristic
383C2×Q8C2×D4×C1111yescharacteristic
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—42no—
390C2×D4—44no—
391C2×D4—41no—
392C2×D4C2×D4×C1112yes—
393C2×D4C2×D4×C1111yescharacteristic
394C2×D4C24×C1111yescharacteristic
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4C2×D4×C1112yes—
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1114yes—
403Q16—42no—
404SD16—42no—
405SD16—42no—
406D8—42no—
407M16—22no—
408M16—41no—
409C2×C8—41no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—42no—
420C4⋊C4—48no—
421C22⋊C4—22no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4—24no—
428C22⋊C4—48no—
429C22⋊C4C2×D4×C1114yes—
430C42—24no—
431C42—22no—
432C42—21no—
433C42—22no—
434C42—42no—
435C42C2×D4×C1111yescharacteristic
436C42C2×D4×C1111yescharacteristic
437C11#3356111yescharacteristic, direct product factor, Sylow
438C23—24no—
439C23—21no—
440C23—41no—
441C23C11×#12011yescharacteristic
442C23C22×D4×C1112yes—
443Q8—22no—
444Q8—41no—
445Q8—41no—
446Q8—44no—
447Q8—42no—
448Q8—41no—
449Q8—42no—
450Q8—42no—
451Q8—82no—
452Q8—82no—
453D4—22no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4—44no—
458D4—42no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—81no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—82no—
484C2×C4C11×#12012yes—
485C2×C4C11×#12011yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C8—42no—
488C22—22no—
489C22—21no—
490C22—41no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—41no—
495C22—84no—
496C22—161no—
497C22C2×C11×#12011yescharacteristic
498C4—22no—
499C4—21no—
500C4—22no—
501C4—41no—
502C4—44no—
503C4—42no—
504C4—41no—
505C4—44no—
506C4—84no—
507C4C11×B(4,𝔽2)11yescharacteristic
508C4C11×B(4,𝔽2)11yescharacteristic
509C2—21no—
510C2—42no—
511C2—41no—
512C2—81no—
513C2—82no—
514C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C11C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C11
prime radicalC11×#3018C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3550C2semidirect
2. C11×#3028C2semidirect
4. C11×#2201C2semidirect
5. C11×#2198C2semidirect
6. C11×#2126C2semidirect
7. C11×#2123C2semidirect
11. C11×#563C22semidirect
12. C11×#559C22semidirect
32. C11×#354C22semidirect
33. C11×#353C22semidirect
34. C11×#352C22semidirect
100. #33561C11direct (N × H)
181. #3550C2×C11semidirect
182. #3028C2×C11semidirect
184. #2201C2×C11semidirect
185. #2198C2×C11semidirect
186. #2126C2×C11semidirect
187. #2123C2×C11semidirect
241. #563C22×C11semidirect
242. #559C22×C11semidirect
262. #354C22×C11semidirect
263. #353C22×C11semidirect
264. #352C22×C11semidirect
437. C11#33561direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#30282
C11×#30182
C11×#22012
C11×#21982
C11×#21262
C11×#21232
#3356111