Finite Group Databasebeta

← C2×C11×#1890 #14598151

Subgroups — C2×C11×#1890 #14598151

Order 2816.

2102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C2×C11×#518C211yesmaximal, characteristic
3C22×C11×#99C211yesmaximal, characteristic
4C2×C11×#381C212yesmaximal, complemented
5C11×#1890C218yesmaximal, direct product factor
6C2×C11×#342C212yesmaximal, complemented
7C23×D4×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C2×C11×#123—24no—
10C2×C11×#123—22no—
11C2×C11×#123C418yescomplemented
12C2×C11×#123C2214yes—
13C11×#518—22no—
14C11×#518—24no—
15C11×#518C2214yes—
16C2×C4×D4×C11—24no—
17C2×C11×#117—21no—
18C22×C11×C4⋊C4—21no—
19C22×C11×C22⋊C4—21no—
20C22×C11×C22⋊C4—21no—
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C2×C11×#99—24no—
25C2×C11×#99C2214yes—
26C11×#381—24no—
27C11×#381C2218yescomplemented
28C2×C11×#95—24no—
29C11×#342C2218yescomplemented
30C25×C11D411yescharacteristic
31C25×C11C2311yescharacteristic
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—24no—
35C22×D4×C11C2×C414yes—
36C22×D4×C11D414yes—
37C22×D4×C11D412yes—
38C22×D4×C11C2312yes—
39C23×C4×C11—21no—
40C23×C4×C11—21no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—21no—
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C414yescomplemented
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D414yes—
51C23×C4×C11C2312yes—
52C11×#123—216no—
53C11×#123—28no—
54C11×#123C2×C4116yescomplemented
55C4×D4×C11—216no—
56C4×D4×C11—216no—
57C11×#117—24no—
58C11×#117—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—28no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4C2×C414yescomplemented
77C2×C11×C22⋊C4D414yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2312yes—
81C2×C42×C11—22no—
82C11×#99—28no—
83C11×#95—216no—
84C2×#1890C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—22no—
88C24×C11—44no—
89C24×C11—44no—
90C24×C11C22⋊C414yes—
91C24×C11C22×C412yes—
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D412yes—
94C24×C11C2×D412yes—
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D412yes—
97C24×C11C2×D412yes—
98C24×C11#4114yes—
99C24×C11C2411yescharacteristic
100C2×D4×C11—28no—
101C2×D4×C11—28no—
102C2×D4×C11—24no—
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—24no—
108C2×D4×C11C22⋊C418yes—
109C2×D4×C11C22×C414yes—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—28no—
118C22×C4×C11—28no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—28no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—44no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11—41no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—48no—
137C22×C4×C11—48no—
138C22×C4×C11—44no—
139C22×C4×C11—84no—
140C22×C4×C11C22⋊C414yes—
141C22×C4×C11C22×C414yescomplemented
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D418yes—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—216no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—216no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4C22×C414yescomplemented
158C42×C11—28no—
159C22×#123C2×C1111yescharacteristic
160C2×#518C2×C1111yescharacteristic
161C22×#99C2×C1111yescharacteristic
162C2×#381C2×C1112yescomplemented
163#1890C2×C1118yesdirect product factor
164C2×#342C2×C1112yescomplemented
165C23×C11—28no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—44no—
172C23×C11—44no—
173C23×C11—44no—
174C23×C11—42no—
175C23×C11—48no—
176C23×C11—42no—
177C23×C11—48no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—84no—
181C23×C11—82no—
182C23×C11C2×C22⋊C412yes—
183C23×C11C2×C22⋊C414yes—
184C23×C11C2×C22⋊C412yes—
185C23×C11C4×D414yes—
186C23×C11C4×D414yes—
187C23×C11#12011yescharacteristic
188C23×C11#12012yes—
189C23×C11#12011yescharacteristic
190C23×C11#12114yes—
191C23×C11#12114yes—
192C23×C11#12312yes—
193C23×C11#12312yes—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×D412yes—
197C23×C11C22×D411yescharacteristic
198C23×C11C2×#4112yes—
199D4×C11—28no—
200D4×C11—28no—
201D4×C11—216no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—28no—
209C2×C4×C11—28no—
210C2×C4×C11—48no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—48no—
217C2×C4×C11—44no—
218C2×C4×C11—48no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11—44no—
222C2×C4×C11—84no—
223C2×C4×C11—88no—
224C2×C4×C11—88no—
225C2×C4×C11C2×C22⋊C414yes—
226C23×D4C22×C1111yescharacteristic
227C24×C4C22×C1111yescharacteristic
228C2×#123—24no—
229C2×#123—22no—
230C2×#123C4×C1118yescomplemented
231C2×#123C22×C1114yes—
232#518—22no—
233#518—24no—
234#518C22×C1114yes—
235C2×C4×D4—24no—
236C2×#117—21no—
237C22×C4⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4C22×C1112yes—
241C22×C22⋊C4C22×C1112yes—
242C22×C22⋊C4C22×C1111yescharacteristic
243C2×#99—24no—
244C2×#99C22×C1114yes—
245#381—24no—
246#381C22×C1118yescomplemented
247C2×#95—24no—
248#342C22×C1118yescomplemented
249C22×C11—24no—
250C22×C11—28no—
251C22×C11—24no—
252C22×C11—28no—
253C22×C11—24no—
254C22×C11—22no—
255C22×C11—24no—
256C22×C11—22no—
257C22×C11—24no—
258C22×C11—42no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—42no—
265C22×C11—44no—
266C22×C11—48no—
267C22×C11—44no—
268C22×C11—82no—
269C22×C11—84no—
270C22×C11#38612yes—
271C22×C11#38614yes—
272C22×C11#38612yes—
273C22×C11#45814yes—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C2×C4×D412yes—
276C22×C11C2×#12011yescharacteristic
277C22×C11C2×#12112yes—
278C22×C11C2×#12311yescharacteristic
279C4×C11—24no—
280C4×C11—44no—
281C4×C11—48no—
282C4×C11—44no—
283C4×C11—84no—
284C25D4×C1111yescharacteristic
285C25C23×C1111yescharacteristic
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—24no—
289C22×D4C2×C4×C1114yes—
290C22×D4D4×C1114yes—
291C22×D4D4×C1112yes—
292C22×D4C23×C1112yes—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—24no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4C2×C4×C1114yescomplemented
303C23×C4D4×C1111yescharacteristic
304C23×C4D4×C1114yes—
305C23×C4C23×C1112yes—
306#123—216no—
307#123—28no—
308#123C2×C4×C11116yescomplemented
309C4×D4—216no—
310C4×D4—216no—
311#117—24no—
312#117—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4C2×C4×C1114yescomplemented
331C2×C22⋊C4D4×C1114yes—
332C2×C22⋊C4C23×C1114yes—
333C2×C22⋊C4C23×C1114yes—
334C2×C22⋊C4C23×C1112yes—
335C2×C42—22no—
336#99—28no—
337#95—216no—
338C2×C11—21no—
339C2×C11—22no—
340C2×C11—21no—
341C2×C11—22no—
342C2×C11—22no—
343C2×C11—24no—
344C2×C11—44no—
345C2×C11#189014yesdirect product factor
346C2×C11C2×#38611yescharacteristic
347C2×C11C2×#45812yes—
348C24—21no—
349C24—21no—
350C24—22no—
351C24—44no—
352C24—44no—
353C24C11×C22⋊C414yes—
354C24C22×C4×C1112yes—
355C24C2×D4×C1111yescharacteristic
356C24C2×D4×C1112yes—
357C24C2×D4×C1112yes—
358C24C2×D4×C1111yescharacteristic
359C24C2×D4×C1112yes—
360C24C2×D4×C1112yes—
361C24C11×#4114yes—
362C24C24×C1111yescharacteristic
363C2×D4—28no—
364C2×D4—28no—
365C2×D4—24no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—24no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4C11×C22⋊C418yes—
372C2×D4C22×C4×C1114yes—
373C2×D4C2×D4×C1114yes—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—28no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—44no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—48no—
400C22×C4—48no—
401C22×C4—44no—
402C22×C4—84no—
403C22×C4C11×C22⋊C414yes—
404C22×C4C22×C4×C1114yescomplemented
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1118yes—
407C4⋊C4—28no—
408C4⋊C4—216no—
409C22⋊C4—28no—
410C22⋊C4—216no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—44no—
420C22⋊C4C22×C4×C1114yescomplemented
421C42—28no—
422C11C2×#189011yescharacteristic, direct product factor, Sylow
423C23—28no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—24no—
428C23—22no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—42no—
433C23—48no—
434C23—42no—
435C23—48no—
436C23—44no—
437C23—44no—
438C23—84no—
439C23—82no—
440C23C2×C11×C22⋊C412yes—
441C23C2×C11×C22⋊C414yes—
442C23C2×C11×C22⋊C412yes—
443C23C4×D4×C1114yes—
444C23C4×D4×C1114yes—
445C23C11×#12011yescharacteristic
446C23C11×#12012yes—
447C23C11×#12011yescharacteristic
448C23C11×#12114yes—
449C23C11×#12114yes—
450C23C11×#12312yes—
451C23C11×#12312yes—
452C23C23×C4×C1111yescharacteristic
453C23C22×D4×C1111yescharacteristic
454C23C22×D4×C1112yes—
455C23C22×D4×C1111yescharacteristic
456C23C2×C11×#4112yes—
457D4—28no—
458D4—28no—
459D4—216no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—28no—
467C2×C4—28no—
468C2×C4—48no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—48no—
477C2×C4—48no—
478C2×C4—48no—
479C2×C4—44no—
480C2×C4—84no—
481C2×C4—88no—
482C2×C4—88no—
483C2×C4C2×C11×C22⋊C414yes—
484C22—24no—
485C22—28no—
486C22—24no—
487C22—28no—
488C22—24no—
489C22—22no—
490C22—24no—
491C22—22no—
492C22—24no—
493C22—42no—
494C22—44no—
495C22—44no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—42no—
500C22—44no—
501C22—48no—
502C22—44no—
503C22—84no—
504C22—82no—
505C22C11×#38612yes—
506C22C11×#38614yes—
507C22C11×#38612yes—
508C22C11×#45814yes—
509C22C22×C11×C22⋊C411yescharacteristic
510C22C2×C4×D4×C1112yes—
511C22C2×C11×#12011yescharacteristic
512C22C2×C11×#12112yes—
513C22C2×C11×#12311yescharacteristic
514C4—24no—
515C4—44no—
516C4—48no—
517C4—44no—
518C4—84no—
519C2—21no—
520C2—22no—
521C2—22no—
522C2—21no—
523C2—22no—
524C2—24no—
525C2—44no—
526C2C11×#189014yesdirect product factor
527C2C2×C11×#38611yescharacteristic
528C2C2×C11×#45812yes—
subgroupG/H
center, socleC23×C11#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#381C2semidirect
5. C11×#1890C2direct (N × H)
6. C2×C11×#342C2semidirect
11. C2×C11×#123C4semidirect
27. C11×#381C22semidirect
29. C11×#342C22semidirect
48. C23×C4×C11C2×C4semidirect
54. C11×#123C2×C4semidirect
76. C2×C11×C22⋊C4C2×C4semidirect
84. C2×#1890C11direct (N × H)
141. C22×C4×C11C22×C4semidirect
157. C11×C22⋊C4C22×C4semidirect
162. C2×#381C2×C11semidirect
163. #1890C2×C11direct (N × H)
164. C2×#342C2×C11semidirect
230. C2×#123C4×C11semidirect
246. #381C22×C11semidirect
248. #342C22×C11semidirect
302. C23×C4C2×C4×C11semidirect
308. #123C2×C4×C11semidirect
330. C2×C22⋊C4C2×C4×C11semidirect
345. C2×C11#1890direct (N × H)
404. C22×C4C22×C4×C11semidirect
420. C22⋊C4C22×C4×C11semidirect
422. C11C2×#1890direct (N × H)
526. C2C11×#1890direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C2×C11×#5182
C22×C11×#992
C2×C11×#3812
C11×#18902
C2×C11×#3422
C2×#189011