Finite Group Databasebeta

← C2×C11×#2620 #14611804

Subgroups — C2×C11×#2620 #14611804

Order 2816.

3566 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#124C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C11×#121C211yesmaximal, characteristic
4C22×C11×#117C211yesmaximal, characteristic, complemented
5C11×#2620C2116yesmaximal, direct product factor
6C2×C11×#396C214yesmaximal, complemented
7C2×C11×#394C214yesmaximal, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C2×C11×#384C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2211yescharacteristic
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2212yes—
14C24×C4×C11C2211yescharacteristic
15C2×C11×#124—28no—
16C2×C11×#124C2218yescomplemented
17C2×C11×C22⋊Q8—28no—
18C2×C11×C22⋊Q8C2218yescomplemented
19C2×C11×#121—28no—
20C2×C11×#121C2218yes—
21C2×C11×#117—28no—
22C2×C11×#117C2218yescomplemented
23C22×C11×C4⋊C4C2212yes—
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2214yes—
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2212yes—
30C22×C11×C22⋊C4C2214yes—
31C22×C11×C22⋊C4C2212yes—
32C22×C11×C22⋊C4C2214yes—
33C22×C42×C11C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#396C22132yescomplemented
36C11×#394C22132yescomplemented
37C11×#391C2218yescomplemented
38C11×#390C2218yescomplemented
39C11×#384C2218yescomplemented
40C2×C11×#95C2214yes—
41C25×C11C2312yes—
42C25×C11C2311yescharacteristic
43C22×Q8×C11—24no—
44C22×Q8×C11—24no—
45C22×Q8×C11—24no—
46C22×Q8×C11C2314yes—
47C22×D4×C11—28no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—48no—
52C22×D4×C11C2314yes—
53C22×D4×C11C2318yes—
54C23×C4×C11—24no—
55C23×C4×C11—24no—
56C23×C4×C11D418yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2314yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C11×#124—232no—
66C11×C22⋊Q8—232no—
67C11×#121—232no—
68C11×#117—232no—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4—48no—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C23116yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4—216no—
83C2×C11×C22⋊C4—48no—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C23116yes—
88C2×C11×C22⋊C4C23116yes—
89C2×C42×C11—24no—
90C2×C42×C11D418yescomplemented
91C2×C42×C11C2314yes—
92C2×C42×C11C2314yes—
93C11×#95C23116yes—
94C2×#2620C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—24no—
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—28no—
103C24×C11—28no—
104C24×C11C2×D414yes—
105C24×C11C2414yes—
106C24×C11C2412yes—
107C24×C11C2411yescharacteristic
108C2×Q8×C11—28no—
109C2×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—416no—
112C2×D4×C11—216no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—416no—
117C2×D4×C11—432no—
118C2×D4×C11—416no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—232no—
124C22×C4×C11—28no—
125C22×C4×C11—28no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—28no—
135C22×C4×C11—24no—
136C22×C4×C11C2×D418yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D4116yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C11×C4⋊C4—216no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—216no—
153C11×C4⋊C4—416no—
154C11×C22⋊C4—216no—
155C11×C22⋊C4—216no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—232no—
158C11×C22⋊C4—416no—
159C42×C11—28no—
160C42×C11C2×D4116yescomplemented
161C22×#124C2×C1111yescharacteristic, complemented
162C22×C22⋊Q8C2×C1111yescharacteristic, complemented
163C22×#121C2×C1111yescharacteristic
164C22×#117C2×C1111yescharacteristic, complemented
165#2620C2×C11116yesdirect product factor
166C2×#396C2×C1114yescomplemented
167C2×#394C2×C1114yescomplemented
168C2×#391C2×C1111yescharacteristic, complemented
169C2×#390C2×C1111yescharacteristic, complemented
170C2×#384C2×C1111yescharacteristic, complemented
171C23×C11—28no—
172C23×C11—28no—
173C23×C11—28no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11—48no—
187C23×C11—48no—
188C23×C11—416no—
189C23×C11—416no—
190C23×C11C22×D414yes—
191C23×C11C22×D412yes—
192C23×C11C22×D412yes—
193C23×C11C2×#4112yes—
194C23×C11H(5,𝔽2)14yes—
195C23×C112−1+414yes—
196C23×C11C2511yescharacteristic
197Q8×C11—416no—
198D4×C11—432no—
199D4×C11—416no—
200C2×C4×C11—28no—
201C2×C4×C11—216no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—232no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—24no—
217C2×C4×C11—48no—
218C2×C4×C11—48no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11#121116yes—
222C2×C4×C11C22×D418yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C2×#4114yes—
227C23×Q8C22×C1111yescharacteristic
228C23×D4C22×C1111yescharacteristic
229C23×D4C22×C1112yes—
230C24×C4C22×C1111yescharacteristic
231C2×#124—28no—
232C2×#124C22×C1118yescomplemented
233C2×C22⋊Q8—28no—
234C2×C22⋊Q8C22×C1118yescomplemented
235C2×#121—28no—
236C2×#121C22×C1118yes—
237C2×#117—28no—
238C2×#117C22×C1118yescomplemented
239C22×C4⋊C4C22×C1112yes—
240C22×C4⋊C4C22×C1112yes—
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1111yescharacteristic
243C22×C4⋊C4C22×C1114yes—
244C22×C22⋊C4C22×C1112yes—
245C22×C22⋊C4C22×C1112yes—
246C22×C22⋊C4C22×C1114yes—
247C22×C22⋊C4C22×C1112yes—
248C22×C22⋊C4C22×C1114yes—
249C22×C42C22×C1111yescharacteristic
250C22×C42C22×C1111yescharacteristic
251#396C22×C11132yescomplemented
252#394C22×C11132yescomplemented
253#391C22×C1118yescomplemented
254#390C22×C1118yescomplemented
255#384C22×C1118yescomplemented
256C2×#95C22×C1114yes—
257C22×C11—24no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—416no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—48no—
267C22×C11—48no—
268C22×C11—816no—
269C22×C11C2×#12114yes—
270C22×C11#53514yes—
271C22×C11#53614yes—
272C22×C11#53718yes—
273C22×C11#54218yes—
274C22×C11C23×D411yescharacteristic
275C22×C11C23×D411yescharacteristic
276C22×C11C22×#4111yescharacteristic
277C22×C11C2×H(5,𝔽2)12yes—
278C22×C11C2×2−1+412yes—
279C4×C11—24no—
280C4×C11—28no—
281C4×C11—44no—
282C4×C11—44no—
283C4×C11—44no—
284C4×C11—44no—
285C4×C11C2×#12118yes—
286C25C23×C1112yes—
287C25C23×C1111yescharacteristic
288C22×Q8—24no—
289C22×Q8—24no—
290C22×Q8—24no—
291C22×Q8C23×C1114yes—
292C22×D4—28no—
293C22×D4—24no—
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—48no—
297C22×D4C23×C1114yes—
298C22×D4C23×C1118yes—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4D4×C1118yes—
302C23×C4C23×C1112yes—
303C23×C4C23×C1112yes—
304C23×C4C23×C1112yes—
305C23×C4C23×C1112yes—
306C23×C4C23×C1112yes—
307C23×C4C23×C1111yescharacteristic
308C23×C4C23×C1114yes—
309C23×C4C23×C1111yescharacteristic
310#124—232no—
311C22⋊Q8—232no—
312#121—232no—
313#117—232no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—48no—
319C2×C4⋊C4C23×C1118yes—
320C2×C4⋊C4C23×C1114yes—
321C2×C4⋊C4C23×C1114yes—
322C2×C4⋊C4C23×C1118yes—
323C2×C4⋊C4C23×C11116yes—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—216no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4C23×C1118yes—
330C2×C22⋊C4C23×C1118yes—
331C2×C22⋊C4C23×C1118yes—
332C2×C22⋊C4C23×C11116yes—
333C2×C22⋊C4C23×C11116yes—
334C2×C42—24no—
335C2×C42D4×C1118yescomplemented
336C2×C42C23×C1114yes—
337C2×C42C23×C1114yes—
338#95C23×C11116yes—
339C2×C11—44no—
340C2×C11—84no—
341C2×C11#262018yesdirect product factor
342C2×C11C22×#12111yescharacteristic
343C2×C11C2×#53511yescharacteristic
344C2×C11C2×#53611yescharacteristic
345C2×C11C2×#53712yes—
346C2×C11C2×#54212yes—
347C24—22no—
348C24—22no—
349C24—24no—
350C24—24no—
351C24—24no—
352C24—24no—
353C24—24no—
354C24—28no—
355C24—28no—
356C24C2×D4×C1114yes—
357C24C24×C1114yes—
358C24C24×C1112yes—
359C24C24×C1111yescharacteristic
360C2×Q8—28no—
361C2×Q8—28no—
362C2×Q8—28no—
363C2×Q8—416no—
364C2×D4—216no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—416no—
369C2×D4—432no—
370C2×D4—416no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—232no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—24no—
388C22×C4C2×D4×C1118yes—
389C22×C4C2×D4×C1114yes—
390C22×C4C2×D4×C11116yes—
391C22×C4C2×D4×C1114yes—
392C22×C4C2×D4×C1114yes—
393C22×C4C11×#4114yes—
394C22×C4C24×C1114yes—
395C22×C4C24×C1114yes—
396C22×C4C24×C1114yes—
397C22×C4C24×C1114yes—
398C22×C4C24×C1114yes—
399C22×C4C24×C1112yes—
400C22×C4C24×C1112yes—
401C4⋊C4—216no—
402C4⋊C4—28no—
403C4⋊C4—28no—
404C4⋊C4—216no—
405C4⋊C4—416no—
406C22⋊C4—216no—
407C22⋊C4—216no—
408C22⋊C4—216no—
409C22⋊C4—232no—
410C22⋊C4—416no—
411C42—28no—
412C42C2×D4×C11116yescomplemented
413C11C2×#262011yescharacteristic, direct product factor, Sylow
414C23—28no—
415C23—28no—
416C23—28no—
417C23—22no—
418C23—22no—
419C23—24no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—28no—
425C23—28no—
426C23—48no—
427C23—48no—
428C23—48no—
429C23—48no—
430C23—48no—
431C23—416no—
432C23—416no—
433C23C22×D4×C1114yes—
434C23C22×D4×C1112yes—
435C23C22×D4×C1112yes—
436C23C2×C11×#4112yes—
437C23C11×H(5,𝔽2)14yes—
438C23C11×2−1+414yes—
439C23C25×C1111yescharacteristic
440Q8—416no—
441D4—432no—
442D4—416no—
443C2×C4—28no—
444C2×C4—216no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—232no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—28no—
458C2×C4—28no—
459C2×C4—24no—
460C2×C4—48no—
461C2×C4—48no—
462C2×C4—48no—
463C2×C4—48no—
464C2×C4C11×#121116yes—
465C2×C4C22×D4×C1118yes—
466C2×C4C22×D4×C1114yes—
467C2×C4C22×D4×C1114yes—
468C2×C4C22×D4×C1114yes—
469C2×C4C2×C11×#4114yes—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—44no—
474C22—44no—
475C22—416no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—48no—
480C22—48no—
481C22—816no—
482C22C2×C11×#12114yes—
483C22C11×#53514yes—
484C22C11×#53614yes—
485C22C11×#53718yes—
486C22C11×#54218yes—
487C22C23×D4×C1111yescharacteristic
488C22C23×D4×C1111yescharacteristic
489C22C22×C11×#4111yescharacteristic
490C22C2×C11×H(5,𝔽2)12yes—
491C22C2×C11×2−1+412yes—
492C4—24no—
493C4—28no—
494C4—44no—
495C4—44no—
496C4—44no—
497C4—44no—
498C4C2×C11×#12118yes—
499C2—44no—
500C2—84no—
501C2C11×#262018yesdirect product factor
502C2C22×C11×#12111yescharacteristic
503C2C2×C11×#53511yescharacteristic
504C2C2×C11×#53611yescharacteristic
505C2C2×C11×#53712yes—
506C2C2×C11×#54212yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC22×C11×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#124C2semidirect
2. C22×C11×C22⋊Q8C2semidirect
4. C22×C11×#117C2semidirect
5. C11×#2620C2direct (N × H)
6. C2×C11×#396C2semidirect
7. C2×C11×#394C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#390C2semidirect
10. C2×C11×#384C2semidirect
16. C2×C11×#124C22semidirect
18. C2×C11×C22⋊Q8C22semidirect
22. C2×C11×#117C22semidirect
35. C11×#396C22semidirect
36. C11×#394C22semidirect
37. C11×#391C22semidirect
38. C11×#390C22semidirect
39. C11×#384C22semidirect
90. C2×C42×C11D4semidirect
94. C2×#2620C11direct (N × H)
160. C42×C11C2×D4semidirect
161. C22×#124C2×C11semidirect
162. C22×C22⋊Q8C2×C11semidirect
164. C22×#117C2×C11semidirect
165. #2620C2×C11direct (N × H)
166. C2×#396C2×C11semidirect
167. C2×#394C2×C11semidirect
168. C2×#391C2×C11semidirect
169. C2×#390C2×C11semidirect
170. C2×#384C2×C11semidirect
232. C2×#124C22×C11semidirect
234. C2×C22⋊Q8C22×C11semidirect
238. C2×#117C22×C11semidirect
251. #396C22×C11semidirect
252. #394C22×C11semidirect
253. #391C22×C11semidirect
254. #390C22×C11semidirect
255. #384C22×C11semidirect
335. C2×C42D4×C11semidirect
341. C2×C11#2620direct (N × H)
412. C42C2×D4×C11semidirect
413. C11C2×#2620direct (N × H)
501. C2C11×#2620direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C11×C22⋊Q82
C22×C11×#1212
C22×C11×#1172
C11×#26202
C2×C11×#3962
C2×C11×#3942
C2×C11×#3912
C2×C11×#3902
C2×C11×#3842
C2×#262011