Finite Group Databasebeta

← C2×C11×#2126 #14610547

Subgroups — C2×C11×#2126 #14610547

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal, complemented
3C11×#2126C218yesmaximal, direct product factor
4C2×C11×#354C212yesmaximal, complemented
5C2×C11×#353C212yesmaximal, complemented
6C22×C11×#41C411yescharacteristic, complemented
7C22×C11×#41C2211yescharacteristic
8C11×#532—24no—
9C11×#532C414yescomplemented
10C11×#532C2214yes—
11C2×C11×C4⋊Q8C411yescharacteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C411yescharacteristic, complemented
14C2×C11×#124C2211yescharacteristic
15C2×C11×#121—22no—
16C2×C4×D4×C11—22no—
17C2×C11×#117—22no—
18C22×C42×C11C411yescharacteristic, complemented
19C11×#410—24no—
20C11×#410C2218yescomplemented
21C2×C11×#99—22no—
22C2×C11×#99C2214yes—
23C11×#354C2218yescomplemented
24C11×#353C2218yescomplemented
25C2×C11×#41—22no—
26C2×C11×#41—41no—
27C2×C11×#41—42no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C2×C11×#41—41no—
31C2×C11×#41—41no—
32C2×C11×#41C2×C412yes—
33C2×C11×#41C2×C414yescomplemented
34C2×C11×#41D414yes—
35C2×C11×#41C2312yes—
36C22×Q8×C11C2×C411yescharacteristic
37C22×Q8×C11C2×C411yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11D412yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11D412yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2×C414yescomplemented
49C11×#127—22no—
50C11×#127C2×C412yes—
51C11×#127C2312yes—
52C11×#124—22no—
53C11×#124—22no—
54C11×#124C2×C412yes—
55C11×#124C2×C414yescomplemented
56C11×#124C2312yes—
57C11×#121—28no—
58C11×#121—28no—
59C4×D4×C11—28no—
60C4×D4×C11—28no—
61C11×#117—28no—
62C11×#117—44no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C42×C11—22no—
69C2×C42×C11—21no—
70C2×C42×C11—42no—
71C2×C42×C11C2×C411yescharacteristic
72C2×C42×C11C2×C411yescharacteristic
73C2×C42×C11C2×C414yescomplemented
74C11×#99—28no—
75C11×#99—24no—
76C11×#99C2318yes—
77C2×#2126C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11C22⋊C411yescharacteristic
80C24×C11C2×D412yes—
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—44no—
84C11×#41—44no—
85C11×#41—42no—
86C11×#41—42no—
87C11×#41—44no—
88C11×#41—44no—
89C11×#41—44no—
90C11×#41—44no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11C22⋊C412yes—
97C2×Q8×C11C22×C412yes—
98C2×Q8×C11C22×C412yes—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—48no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11C22⋊C414yes—
113C2×D4×C11C22×C412yes—
114C2×D4×C11C22×C411yescharacteristic
115C2×D4×C11C2×D414yes—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2411yescharacteristic
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—44no—
130C22×C4×C11—42no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—44no—
134C22×C4×C11C22⋊C412yes—
135C22×C4×C11C22⋊C412yes—
136C22×C4×C11C22⋊C414yes—
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D414yes—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—48no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—44no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—24no—
151C42×C11—48no—
152C42×C11C22×C412yes—
153C42×C11C22×C412yes—
154C2×#532C2×C1111yescharacteristic
155C2×#410C2×C1112yescomplemented
156#2126C2×C1118yesdirect product factor
157C2×#354C2×C1112yescomplemented
158C2×#353C2×C1112yescomplemented
159C23×C11—22no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—42no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C22⋊C412yes—
171C23×C11C2×C22⋊C412yes—
172C23×C11C22×D412yes—
173Q8×C11—42no—
174Q8×C11—42no—
175Q8×C11—42no—
176Q8×C11—42no—
177D4×C11—44no—
178D4×C11—41no—
179D4×C11—42no—
180D4×C11—44no—
181D4×C11—41no—
182D4×C11—42no—
183D4×C11—48no—
184D4×C11—48no—
185D4×C11—42no—
186D4×C11—48no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—48no—
210C2×C4×C11—88no—
211C2×C4×C11#9911yescharacteristic
212C2×C4×C11#9912yes—
213C2×C4×C11#9911yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C414yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C23×C411yescharacteristic
218C22×#41C4×C1111yescharacteristic, complemented
219C22×#41C22×C1111yescharacteristic
220#532—24no—
221#532C4×C1114yescomplemented
222#532C22×C1114yes—
223C2×C4⋊Q8C4×C1111yescharacteristic, complemented
224C2×#127C22×C1111yescharacteristic
225C2×#124C4×C1111yescharacteristic, complemented
226C2×#124C22×C1111yescharacteristic
227C2×#121—22no—
228C2×C4×D4—22no—
229C2×#117—22no—
230C22×C42C4×C1111yescharacteristic, complemented
231#410—24no—
232#410C22×C1118yescomplemented
233C2×#99—22no—
234C2×#99C22×C1114yes—
235#354C22×C1118yescomplemented
236#353C22×C1118yescomplemented
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×#9911yescharacteristic
253C22×C11C2×#9911yescharacteristic
254C22×C11C22×C22⋊C411yescharacteristic
255C4×C11—24no—
256C4×C11—21no—
257C4×C11—24no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—88no—
262C4×C11C2×#9912yes—
263C4×C11C2×#9912yes—
264C2×#41—22no—
265C2×#41—41no—
266C2×#41—41no—
267C2×#41—42no—
268C2×#41—42no—
269C2×#41—41no—
270C2×#41—41no—
271C2×#41C2×C4×C1112yes—
272C2×#41C2×C4×C1114yescomplemented
273C2×#41D4×C1114yes—
274C2×#41C23×C1112yes—
275C22×Q8C2×C4×C1111yescharacteristic
276C22×Q8C2×C4×C1111yescharacteristic
277C22×D4—21no—
278C22×D4—22no—
279C22×D4C2×C4×C1111yescharacteristic
280C22×D4D4×C1112yes—
281C22×D4C23×C1111yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C2×C4×C1111yescharacteristic
285C23×C4D4×C1112yes—
286C4⋊Q8—22no—
287C4⋊Q8C2×C4×C1114yescomplemented
288#127—22no—
289#127C2×C4×C1112yes—
290#127C23×C1112yes—
291#124—22no—
292#124—22no—
293#124C2×C4×C1112yes—
294#124C2×C4×C1114yescomplemented
295#124C23×C1112yes—
296#121—28no—
297#121—28no—
298C4×D4—28no—
299C4×D4—28no—
300#117—28no—
301#117—44no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—42no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C42—21no—
308C2×C42—22no—
309C2×C42—42no—
310C2×C42C2×C4×C1111yescharacteristic
311C2×C42C2×C4×C1111yescharacteristic
312C2×C42C2×C4×C1114yescomplemented
313#99—28no—
314#99—24no—
315#99C23×C1118yes—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—42no—
319C2×C11—42no—
320C2×C11—42no—
321C2×C11—82no—
322C2×C11#212612yesdirect product factor
323C2×C11C22×#9911yescharacteristic
324C24—21no—
325C24C11×C22⋊C411yescharacteristic
326C24C2×D4×C1112yes—
327#41—42no—
328#41—42no—
329#41—44no—
330#41—44no—
331#41—42no—
332#41—42no—
333#41—44no—
334#41—44no—
335#41—44no—
336#41—44no—
337C2×Q8—21no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8C11×C22⋊C412yes—
343C2×Q8C22×C4×C1112yes—
344C2×Q8C22×C4×C1112yes—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—21no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—48no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4C11×C22⋊C414yes—
359C2×D4C22×C4×C1112yes—
360C2×D4C22×C4×C1111yescharacteristic
361C2×D4C2×D4×C1114yes—
362C2×D4C2×D4×C1112yes—
363C2×D4C24×C1111yescharacteristic
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—24no—
373C22×C4—21no—
374C22×C4—24no—
375C22×C4—44no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—44no—
380C22×C4C11×C22⋊C412yes—
381C22×C4C11×C22⋊C412yes—
382C22×C4C11×C22⋊C414yes—
383C22×C4C11×C22⋊C411yescharacteristic
384C22×C4C22×C4×C1111yescharacteristic
385C22×C4C22×C4×C1112yes—
386C22×C4C2×D4×C1114yes—
387C4⋊C4—28no—
388C4⋊C4—48no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—44no—
394C42—21no—
395C42—21no—
396C42—24no—
397C42—48no—
398C42C22×C4×C1112yes—
399C42C22×C4×C1112yes—
400C11C2×#212611yescharacteristic, direct product factor, Sylow
401C23—22no—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—44no—
408C23—44no—
409C23—41no—
410C23—41no—
411C23C2×C11×C22⋊C411yescharacteristic
412C23C2×C11×C22⋊C412yes—
413C23C2×C11×C22⋊C412yes—
414C23C22×D4×C1112yes—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418Q8—42no—
419D4—44no—
420D4—41no—
421D4—42no—
422D4—44no—
423D4—41no—
424D4—42no—
425D4—48no—
426D4—48no—
427D4—42no—
428D4—48no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—48no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—48no—
452C2×C4—88no—
453C2×C4C11×#9912yes—
454C2×C4C11×#9911yescharacteristic
455C2×C4C11×#9911yescharacteristic
456C2×C4C2×C11×C22⋊C411yescharacteristic
457C2×C4C2×C11×C22⋊C414yes—
458C2×C4C2×C11×C22⋊C412yes—
459C2×C4C23×C4×C1111yescharacteristic
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—44no—
469C22—44no—
470C22—42no—
471C22—42no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22C2×C11×#9911yescharacteristic
476C22C2×C11×#9911yescharacteristic
477C22C22×C11×C22⋊C411yescharacteristic
478C4—24no—
479C4—21no—
480C4—24no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—88no—
485C4C2×C11×#9912yes—
486C4C2×C11×#9912yes—
487C2—21no—
488C2—21no—
489C2—42no—
490C2—42no—
491C2—42no—
492C2—82no—
493C2C11×#212612yesdirect product factor
494C2C22×C11×#9911yescharacteristic
subgroupG/H
centerC2×C4×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
socleC22×C11C2×#99
prime radicalC2×C11×#532C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C11×#2126C2direct (N × H)
4. C2×C11×#354C2semidirect
5. C2×C11×#353C2semidirect
6. C22×C11×#41C4semidirect
9. C11×#532C4semidirect
11. C2×C11×C4⋊Q8C4semidirect
13. C2×C11×#124C4semidirect
18. C22×C42×C11C4semidirect
20. C11×#410C22semidirect
23. C11×#354C22semidirect
24. C11×#353C22semidirect
33. C2×C11×#41C2×C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
55. C11×#124C2×C4semidirect
73. C2×C42×C11C2×C4semidirect
77. C2×#2126C11direct (N × H)
155. C2×#410C2×C11semidirect
156. #2126C2×C11direct (N × H)
157. C2×#354C2×C11semidirect
158. C2×#353C2×C11semidirect
218. C22×#41C4×C11semidirect
221. #532C4×C11semidirect
223. C2×C4⋊Q8C4×C11semidirect
225. C2×#124C4×C11semidirect
230. C22×C42C4×C11semidirect
232. #410C22×C11semidirect
235. #354C22×C11semidirect
236. #353C22×C11semidirect
272. C2×#41C2×C4×C11semidirect
287. C4⋊Q8C2×C4×C11semidirect
294. #124C2×C4×C11semidirect
312. C2×C42C2×C4×C11semidirect
322. C2×C11#2126direct (N × H)
400. C11C2×#2126direct (N × H)
493. C2C11×#2126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4102
C11×#21262
C2×C11×#3542
C2×C11×#3532
C2×#212611