Finite Group Databasebeta

← C2×C11×#2063 #14600792

Subgroups — C2×C11×#2063 #14600792

Order 2816.

1134 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
1C22×C11×#108C211yesmaximal, characteristic, complemented
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C2×C11×#424C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic
5C22×C11×#102C211yesmaximal, characteristic
6C22×C11×#100C211yesmaximal, characteristic
7C11×#2063C218yesmaximal, direct product factor
8C2×C11×#343C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×C11×#108—24no—
17C2×C11×#108C2214yescomplemented
18C11×#428—22no—
19C11×#428C2214yescomplemented
20C2×C11×#107—21no—
21C2×C11×#106—21no—
22C11×#424—22no—
23C11×#424C2214yescomplemented
24C2×C11×C4⋊C8—22no—
25C11×#418—22no—
26C11×#418C2214yes—
27C2×C11×#102—22no—
28C2×C11×#102—22no—
29C2×C11×#102—21no—
30C2×C11×#102—21no—
31C2×C11×#102C2214yes—
32C2×C11×#100—24no—
33C2×C11×#100C2214yes—
34C11×#343C2214yescomplemented
35C25×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11Q814yes—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—22no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16D414yes—
57C2×C11×M16C2312yes—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C22×C8×C11—21no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11D412yes—
66C22×C8×C11D412yes—
67C22×C8×C11C2312yes—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117D412yes—
71C11×#117C2312yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C11×#108—28no—
83C11×#107—24no—
84C11×#106—24no—
85C11×C4⋊C8—28no—
86C11×#102—28no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#100—28no—
90C2×#2063C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—24no—
92C24×C11—22no—
93C24×C11—41no—
94C24×C11—41no—
95C24×C11—42no—
96C24×C11—82no—
97C24×C11—82no—
98C24×C11#4111yescharacteristic
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—42no—
116C2×D4×C11C2×Q814yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—82no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×Q812yes—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C11×M16—24no—
134C11×M16—22no—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—42no—
140C11×M16—42no—
141C11×M16C2×D414yes—
142C2×C8×C11—24no—
143C2×C8×C11—24no—
144C2×C8×C11—24no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—42no—
151C2×C8×C11—42no—
152C2×C8×C11C2×D414yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C42×C11—22no—
164C42×C11—22no—
165C22×#108C2×C1111yescharacteristic, complemented
166C2×#428C2×C1111yescharacteristic, complemented
167C2×#424C2×C1111yescharacteristic, complemented
168C2×#418C2×C1111yescharacteristic
169C22×#102C2×C1111yescharacteristic
170C22×#100C2×C1111yescharacteristic
171#2063C2×C1118yesdirect product factor
172C2×#343C2×C1111yescharacteristic, complemented
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—88no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11—88no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11#12111yescharacteristic
189C23×C11#12111yescharacteristic
190C23×C11C22⋊Q812yes—
191C23×C11#12612yes—
192C23×C11C2×#4111yescharacteristic
193D4×C11—24no—
194D4×C11—24no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—44no—
198D4×C11—44no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—82no—
205C2×C4×C11—82no—
206C2×C4×C11—82no—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22⋊Q812yes—
214C2×C4×C11C22⋊Q812yes—
215C2×C4×C11C22⋊Q812yes—
216C2×C4×C11C22⋊Q812yes—
217C2×C4×C11C22⋊Q812yes—
218C2×C4×C11#12612yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×Q811yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C8×C11—24no—
226C8×C11—24no—
227C8×C11—42no—
228C8×C11—42no—
229C23×D4C22×C1111yescharacteristic
230C22×M16C22×C1111yescharacteristic
231C22×M16C22×C1111yescharacteristic
232C22×M16C22×C1111yescharacteristic
233C23×C8C22×C1111yescharacteristic
234C2×#117C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1111yescharacteristic
236C2×#108—24no—
237C2×#108C22×C1114yescomplemented
238#428—22no—
239#428C22×C1114yescomplemented
240C2×#107—21no—
241C2×#106—21no—
242#424—22no—
243#424C22×C1114yescomplemented
244C2×C4⋊C8—22no—
245#418—22no—
246#418C22×C1114yes—
247C2×#102—22no—
248C2×#102—22no—
249C2×#102—21no—
250C2×#102—21no—
251C2×#102C22×C1114yes—
252C2×#100—24no—
253C2×#100C22×C1114yes—
254#343C22×C1114yescomplemented
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—44no—
262C22×C11—84no—
263C22×C11—84no—
264C22×C11—88no—
265C22×C11—88no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11#39612yes—
269C22×C11#39612yes—
270C22×C11#47112yes—
271C22×C11#47212yes—
272C22×C11C2×#12111yescharacteristic
273C22×C11C2×C22⋊Q811yescharacteristic
274C22×C11C2×#12611yescharacteristic
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11#39612yes—
279C4×C11#39612yes—
280C4×C11C2×#12111yescharacteristic
281C4×C11C2×#12111yescharacteristic
282C4×C11C2×C22⋊Q811yescharacteristic
283C4×C11C2×C22⋊Q811yescharacteristic
284C25—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4Q8×C1114yes—
294C22×D4C23×C1112yes—
295C23×C4—21no—
296C23×C4C23×C1111yescharacteristic
297C2×M16—21no—
298C2×M16—22no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16D4×C1114yes—
306C2×M16C23×C1112yes—
307C2×M16C23×C1112yes—
308C2×M16C23×C1112yes—
309C22×C8—22no—
310C22×C8—21no—
311C22×C8—22no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8D4×C1112yes—
315C22×C8D4×C1112yes—
316C22×C8C23×C1112yes—
317#117—21no—
318#117—21no—
319#117D4×C1112yes—
320#117C23×C1112yes—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C1111yescharacteristic
327C2×C4⋊C4D4×C1111yescharacteristic
328C2×C4⋊C4C23×C1112yes—
329C2×C22⋊C4—21no—
330C2×C42—21no—
331#108—28no—
332#107—24no—
333#106—24no—
334C4⋊C8—28no—
335#102—28no—
336#102—24no—
337#102—24no—
338#100—28no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—22no—
342C2×C11—84no—
343C2×C11#206314yesdirect product factor
344C2×C11C2×#39611yescharacteristic
345C2×C11C2×#47111yescharacteristic
346C2×C11C2×#47211yescharacteristic
347C24—24no—
348C24—22no—
349C24—41no—
350C24—41no—
351C24—42no—
352C24—82no—
353C24—82no—
354C24C11×#4111yescharacteristic
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4C2×Q8×C1114yes—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—82no—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×Q8×C1112yes—
385C22×C4C11×#4111yescharacteristic
386C22×C4C11×#4112yes—
387C22×C4C11×#4112yes—
388C22×C4C24×C1111yescharacteristic
389M16—24no—
390M16—22no—
391M16—22no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16—42no—
396M16—42no—
397M16C2×D4×C1114yes—
398C2×C8—24no—
399C2×C8—24no—
400C2×C8—24no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8C2×D4×C1114yes—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C42—22no—
420C42—22no—
421C11C2×#206311yescharacteristic, direct product factor, Sylow
422C23—22no—
423C23—22no—
424C23—24no—
425C23—42no—
426C23—42no—
427C23—44no—
428C23—44no—
429C23—82no—
430C23—82no—
431C23—88no—
432C23—82no—
433C23—82no—
434C23—88no—
435C23—82no—
436C23—82no—
437C23C11×#12111yescharacteristic
438C23C11×#12111yescharacteristic
439C23C11×C22⋊Q812yes—
440C23C11×#12612yes—
441C23C2×C11×#4111yescharacteristic
442D4—24no—
443D4—24no—
444D4—42no—
445D4—42no—
446D4—44no—
447D4—44no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4C11×#12112yes—
457C2×C4C11×#12112yes—
458C2×C4C11×#12112yes—
459C2×C4C11×#12112yes—
460C2×C4C11×#12111yescharacteristic
461C2×C4C11×#12111yescharacteristic
462C2×C4C11×C22⋊Q812yes—
463C2×C4C11×C22⋊Q812yes—
464C2×C4C11×C22⋊Q812yes—
465C2×C4C11×C22⋊Q812yes—
466C2×C4C11×C22⋊Q812yes—
467C2×C4C11×#12612yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C22×Q8×C1111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C8—24no—
475C8—24no—
476C8—42no—
477C8—42no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—24no—
483C22—24no—
484C22—44no—
485C22—84no—
486C22—84no—
487C22—88no—
488C22—82no—
489C22—82no—
490C22—88no—
491C22C11×#39612yes—
492C22C11×#39612yes—
493C22C11×#47112yes—
494C22C11×#47212yes—
495C22C2×C11×#12111yescharacteristic
496C22C2×C11×C22⋊Q811yescharacteristic
497C22C2×C11×#12611yescharacteristic
498C4—42no—
499C4—42no—
500C4—82no—
501C4C11×#39612yes—
502C4C11×#39612yes—
503C4C2×C11×#12111yescharacteristic
504C4C2×C11×#12111yescharacteristic
505C4C2×C11×C22⋊Q811yescharacteristic
506C4C2×C11×C22⋊Q811yescharacteristic
507C2—21no—
508C2—21no—
509C2—22no—
510C2—84no—
511C2C11×#206314yesdirect product factor
512C2C2×C11×#39611yescharacteristic
513C2C2×C11×#47111yescharacteristic
514C2C2×C11×#47211yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#108C2semidirect
2. C2×C11×#428C2semidirect
3. C2×C11×#424C2semidirect
7. C11×#2063C2direct (N × H)
8. C2×C11×#343C2semidirect
17. C2×C11×#108C22semidirect
19. C11×#428C22semidirect
23. C11×#424C22semidirect
34. C11×#343C22semidirect
90. C2×#2063C11direct (N × H)
165. C22×#108C2×C11semidirect
166. C2×#428C2×C11semidirect
167. C2×#424C2×C11semidirect
171. #2063C2×C11direct (N × H)
172. C2×#343C2×C11semidirect
237. C2×#108C22×C11semidirect
239. #428C22×C11semidirect
243. #424C22×C11semidirect
254. #343C22×C11semidirect
343. C2×C11#2063direct (N × H)
421. C11C2×#2063direct (N × H)
511. C2C11×#2063direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1082
C2×C11×#4282
C2×C11×#4242
C2×C11×#4182
C22×C11×#1022
C22×C11×#1002
C11×#20632
C2×C11×#3432
C2×#206311