Finite Group Databasebeta

← C2×C11×#2664 #14611784

Subgroups — C2×C11×#2664 #14611784

Order 2816.

2354 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
1C22×C11×#126C211yesmaximal, characteristic
2C22×C11×#125C211yesmaximal, characteristic, complemented
3C11×#2664C2116yesmaximal, direct product factor
4C2×C11×#400C211yesmaximal, characteristic, complemented
5C2×C11×#399C211yesmaximal, characteristic
6C2×C11×#398C212yesmaximal, complemented
7C2×C11×#398C211yesmaximal, characteristic, complemented
8C2×C11×#397C211yesmaximal, characteristic
9C2×C11×#396C212yesmaximal
10C2×C11×#389C212yesmaximal, complemented
11C2×C11×#388C212yesmaximal
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C2×C11×#126—28no—
14C2×C11×#126C2218yes—
15C2×C11×#125—28no—
16C2×C11×#125C2218yescomplemented
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2212yes—
32C22×C42×C11C2212yes—
33C22×C42×C11C2211yescharacteristic
34C11×#400C2218yescomplemented
35C11×#399C2218yes—
36C11×#398C2218yescomplemented
37C11×#398C22116yescomplemented
38C11×#397C2218yes—
39C11×#396C22116yes—
40C11×#389C22116yescomplemented
41C11×#388C22116yes—
42C4×C11×C4⋊C4C2218yescomplemented
43C2×C11×#95C2212yes—
44C2×C11×#95C2212yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2212yes—
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2212yes—
49C25×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C11×#126—232no—
61C11×#125—232no—
62C2×C11×C4⋊C4—28no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—28no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4—44no—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C4⋊C4C2318yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2318yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—44no—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2318yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C42×C11—44no—
93C2×C42×C11D418yes—
94C2×C42×C11C2318yes—
95C2×C42×C11C2314yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11×#95C2318yes—
99C11×#95C2318yes—
100C11×#95C2318yes—
101C11×#95C2318yes—
102C2×#2664C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—24no—
107C24×C11—22no—
108C24×C11C2412yes—
109C24×C11C2411yescharacteristic
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11#4118yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2414yes—
146C11×C4⋊C4—216no—
147C11×C4⋊C4—216no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—216no—
154C11×C4⋊C4—216no—
155C11×C4⋊C4—48no—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—216no—
160C11×C22⋊C4—48no—
161C42×C11—48no—
162C42×C11C2×D4116yes—
163C22×#126C2×C1111yescharacteristic
164C22×#125C2×C1111yescharacteristic, complemented
165#2664C2×C11116yesdirect product factor
166C2×#400C2×C1111yescharacteristic, complemented
167C2×#399C2×C1111yescharacteristic
168C2×#398C2×C1112yescomplemented
169C2×#398C2×C1111yescharacteristic, complemented
170C2×#397C2×C1111yescharacteristic
171C2×#396C2×C1112yes—
172C2×#389C2×C1112yescomplemented
173C2×#388C2×C1112yes—
174C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—22no—
180C23×C11—44no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11C22×D412yes—
186C23×C11C2×#4114yes—
187C23×C11H(5,𝔽2)12yes—
188C23×C112−1+414yes—
189C23×C112−1+412yes—
190C23×C11C2511yescharacteristic
191C2×C4×C11—28no—
192C2×C4×C11—28no—
193C2×C4×C11—28no—
194C2×C4×C11—216no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
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—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—44no—
218C2×C4×C11—48no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11—48no—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C2×#4118yes—
227C2×#126—28no—
228C2×#126C22×C1118yes—
229C2×#125—28no—
230C2×#125C22×C1118yescomplemented
231C22×C4⋊C4C22×C1112yes—
232C22×C4⋊C4C22×C1112yes—
233C22×C4⋊C4C22×C1111yescharacteristic
234C22×C4⋊C4C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1112yes—
236C22×C4⋊C4C22×C1111yescharacteristic
237C22×C4⋊C4C22×C1111yescharacteristic
238C22×C4⋊C4C22×C1112yes—
239C22×C4⋊C4C22×C1111yescharacteristic
240C22×C4⋊C4C22×C1112yes—
241C22×C22⋊C4C22×C1111yescharacteristic
242C22×C22⋊C4C22×C1112yes—
243C22×C22⋊C4C22×C1111yescharacteristic
244C22×C22⋊C4C22×C1111yescharacteristic
245C22×C22⋊C4C22×C1112yes—
246C22×C42C22×C1112yes—
247C22×C42C22×C1111yescharacteristic
248#400C22×C1118yescomplemented
249#399C22×C1118yes—
250#398C22×C1118yescomplemented
251#398C22×C11116yescomplemented
252#397C22×C1118yes—
253#396C22×C11116yes—
254#389C22×C11116yescomplemented
255#388C22×C11116yes—
256C4×C4⋊C4C22×C1118yescomplemented
257C2×#95C22×C1112yes—
258C2×#95C22×C1112yes—
259C2×#95C22×C1111yescharacteristic
260C2×#95C22×C1112yes—
261C2×#95C22×C1111yescharacteristic
262C2×#95C22×C1112yes—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—88no—
269C22×C11#53214yes—
270C22×C11#53614yes—
271C22×C11#53714yes—
272C22×C11#53918yes—
273C22×C11#54118yes—
274C22×C11C23×D411yescharacteristic
275C22×C11C22×#4112yes—
276C22×C11C2×H(5,𝔽2)11yescharacteristic
277C22×C11C2×2−1+412yes—
278C22×C11C2×2−1+411yescharacteristic
279C4×C11—24no—
280C4×C11—24no—
281C4×C11—24no—
282C4×C11—28no—
283C4×C11—42no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—44no—
288C4×C11—44no—
289C25C23×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1111yescharacteristic
292C23×C4C23×C1112yes—
293C23×C4C23×C1112yes—
294C23×C4C23×C1111yescharacteristic
295C23×C4C23×C1112yes—
296C23×C4C23×C1111yescharacteristic
297C23×C4C23×C1111yescharacteristic
298C23×C4C23×C1111yescharacteristic
299C23×C4C23×C1112yes—
300#126—232no—
301#125—232no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4C23×C1118yes—
313C2×C4⋊C4C23×C1118yes—
314C2×C4⋊C4C23×C1114yes—
315C2×C4⋊C4C23×C1114yes—
316C2×C4⋊C4C23×C1114yes—
317C2×C4⋊C4C23×C1114yes—
318C2×C4⋊C4C23×C1114yes—
319C2×C4⋊C4C23×C1118yes—
320C2×C4⋊C4C23×C1118yes—
321C2×C4⋊C4C23×C1118yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4C23×C1114yes—
328C2×C22⋊C4C23×C1114yes—
329C2×C22⋊C4C23×C1114yes—
330C2×C22⋊C4C23×C1118yes—
331C2×C22⋊C4C23×C1118yes—
332C2×C42—44no—
333C2×C42D4×C1118yes—
334C2×C42C23×C1118yes—
335C2×C42C23×C1114yes—
336#95C23×C1114yes—
337#95C23×C1114yes—
338#95C23×C1118yes—
339#95C23×C1118yes—
340#95C23×C1118yes—
341#95C23×C1118yes—
342C2×C11—82no—
343C2×C11#266418yesdirect product factor
344C2×C11C2×#53211yescharacteristic
345C2×C11C2×#53611yescharacteristic
346C2×C11C2×#53711yescharacteristic
347C2×C11C2×#53912yes—
348C2×C11C2×#54112yes—
349C24—22no—
350C24—24no—
351C24—22no—
352C24—24no—
353C24—22no—
354C24C24×C1112yes—
355C24C24×C1111yescharacteristic
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4C2×D4×C1114yes—
379C22×C4C2×D4×C1114yes—
380C22×C4C2×D4×C1114yes—
381C22×C4C11×#4118yes—
382C22×C4C24×C1114yes—
383C22×C4C24×C1112yes—
384C22×C4C24×C1112yes—
385C22×C4C24×C1112yes—
386C22×C4C24×C1114yes—
387C22×C4C24×C1114yes—
388C22×C4C24×C1112yes—
389C22×C4C24×C1112yes—
390C22×C4C24×C1112yes—
391C22×C4C24×C1114yes—
392C4⋊C4—216no—
393C4⋊C4—216no—
394C4⋊C4—28no—
395C4⋊C4—28no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—216no—
400C4⋊C4—216no—
401C4⋊C4—48no—
402C22⋊C4—28no—
403C22⋊C4—28no—
404C22⋊C4—28no—
405C22⋊C4—216no—
406C22⋊C4—48no—
407C42—48no—
408C42C2×D4×C11116yes—
409C11C2×#266411yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—24no—
412C23—22no—
413C23—24no—
414C23—22no—
415C23—44no—
416C23—44no—
417C23—44no—
418C23—48no—
419C23—48no—
420C23C22×D4×C1112yes—
421C23C2×C11×#4114yes—
422C23C11×H(5,𝔽2)12yes—
423C23C11×2−1+414yes—
424C23C11×2−1+412yes—
425C23C25×C1111yescharacteristic
426C2×C4—28no—
427C2×C4—28no—
428C2×C4—28no—
429C2×C4—216no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—44no—
453C2×C4—48no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—48no—
457C2×C4—48no—
458C2×C4C22×D4×C1114yes—
459C2×C4C22×D4×C1114yes—
460C2×C4C22×D4×C1114yes—
461C2×C4C2×C11×#4118yes—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—44no—
466C22—44no—
467C22—88no—
468C22C11×#53214yes—
469C22C11×#53614yes—
470C22C11×#53714yes—
471C22C11×#53918yes—
472C22C11×#54118yes—
473C22C23×D4×C1111yescharacteristic
474C22C22×C11×#4112yes—
475C22C2×C11×H(5,𝔽2)11yescharacteristic
476C22C2×C11×2−1+412yes—
477C22C2×C11×2−1+411yescharacteristic
478C4—24no—
479C4—24no—
480C4—24no—
481C4—28no—
482C4—42no—
483C4—44no—
484C4—42no—
485C4—42no—
486C4—44no—
487C4—44no—
488C2—82no—
489C2C11×#266418yesdirect product factor
490C2C2×C11×#53211yescharacteristic
491C2C2×C11×#53611yescharacteristic
492C2C2×C11×#53711yescharacteristic
493C2C2×C11×#53912yes—
494C2C2×C11×#54112yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#125C2semidirect
3. C11×#2664C2direct (N × H)
4. C2×C11×#400C2semidirect
6. C2×C11×#398C2semidirect
7. C2×C11×#398C2semidirect
10. C2×C11×#389C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
16. C2×C11×#125C22semidirect
34. C11×#400C22semidirect
36. C11×#398C22semidirect
37. C11×#398C22semidirect
40. C11×#389C22semidirect
42. C4×C11×C4⋊C4C22semidirect
102. C2×#2664C11direct (N × H)
164. C22×#125C2×C11semidirect
165. #2664C2×C11direct (N × H)
166. C2×#400C2×C11semidirect
168. C2×#398C2×C11semidirect
169. C2×#398C2×C11semidirect
172. C2×#389C2×C11semidirect
174. C2×C4×C4⋊C4C2×C11semidirect
230. C2×#125C22×C11semidirect
248. #400C22×C11semidirect
250. #398C22×C11semidirect
251. #398C22×C11semidirect
254. #389C22×C11semidirect
256. C4×C4⋊C4C22×C11semidirect
343. C2×C11#2664direct (N × H)
409. C11C2×#2664direct (N × H)
489. C2C11×#2664direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C22×C11×#1252
C11×#26642
C2×C11×#4002
C2×C11×#3992
C2×C11×#3982
C2×C11×#3972
C2×C11×#3962
C2×C11×#3892
C2×C11×#3882
C2×C4×C11×C4⋊C42
C2×#266411