Finite Group Databasebeta

← C11×#22654 #14599847

Subgroups — C11×#22654 #14599847

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C11C211yesmaximal, characteristic
2C2×C11×#427C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C11×#2352C212yesmaximal
5C11×#1949C212yesmaximal, complemented
6C11×#1854C212yesmaximal, complemented
7C11×#1852C212yesmaximal, complemented
8C11×#1846C211yesmaximal, characteristic, complemented
9C11×#1807C211yesmaximal, characteristic, complemented
10C11×#1807C211yesmaximal, characteristic, complemented
11C4×C11×#106C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C8×D4×C11C418yescomplemented
18C11×#427—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2212yes—
21C2×C11×#106—24no—
22C2×C11×#106C2212yes—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#388—22no—
32C11×#387—22no—
33C11×#386—22no—
34C11×#382C2212yes—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4—22no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2×C414yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11C2×C414yes—
57C4×D4×C11Q814yes—
58C11×#117—24no—
59C11×#117—42no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11C2311yescharacteristic
76C11×#107—24no—
77C11×#107—42no—
78C11×#106—22no—
79C11×#106—22no—
80C11×#106—22no—
81C11×#106—24no—
82C11×#106D414yescomplemented
83C11×C4⋊C8C2×C414yescomplemented
84C11×C22⋊C8C2×C414yes—
85C11×C22⋊C8C2×C414yescomplemented
86C4×C8×C11C2×C414yescomplemented
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92#22654C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—24no—
96C2×D4×C11C4⋊C414yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—82no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×Q812yes—
119C22×C4×C11C2×Q812yes—
120C22×C4×C11C2411yescharacteristic
121C2×C8×C11—28no—
122C2×C8×C11—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C2×D412yes—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4C4⋊C414yes—
144C11×C4⋊C4C2×D414yes—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—82no—
148C11×C22⋊C4C4⋊C414yes—
149C11×C22⋊C4C4⋊C414yes—
150C42×C11—44no—
151C42×C11—82no—
152C42×C11C22×C412yes—
153C42×C11C2×Q812yes—
154C2×C8×D4C2×C1111yescharacteristic
155C2×#427C2×C1111yescharacteristic, complemented
156C22×#106C2×C1111yescharacteristic, complemented
157#2352C2×C1112yes—
158#1949C2×C1112yescomplemented
159#1854C2×C1112yescomplemented
160#1852C2×C1112yescomplemented
161#1846C2×C1111yescharacteristic, complemented
162#1807C2×C1111yescharacteristic, complemented
163#1807C2×C1111yescharacteristic, complemented
164C4×#106C2×C1111yescharacteristic, complemented
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11C2×C4⋊C412yes—
173C23×C11C2×C4⋊C412yes—
174C23×C11#13514yes—
175C23×C11C22×D411yescharacteristic
176D4×C11—28no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—88no—
204C2×C4×C11C2×C4⋊C412yes—
205C2×C4×C11C2×C4⋊C412yes—
206C2×C4×C11C2×C4⋊C412yes—
207C2×C4×C11C2×C4⋊C412yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×Q811yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C8×C11—22no—
215C8×C11—22no—
216C8×C11—22no—
217C8×C11C4×D414yes—
218C23×C8C22×C1111yescharacteristic
219C23×C8C22×C1111yescharacteristic
220C2×C4×D4C22×C1111yescharacteristic
221C2×#117C22×C1112yes—
222C22×C4⋊C4C22×C1112yes—
223C8×D4C4×C1118yescomplemented
224#427—24no—
225C2×#107C22×C1112yes—
226C2×#107C22×C1112yes—
227C2×#106—24no—
228C2×#106C22×C1111yescharacteristic
229C2×#106C22×C1111yescharacteristic
230C2×#106C22×C1111yescharacteristic
231C2×#106C22×C1112yes—
232C2×#106C22×C1111yescharacteristic
233C2×C4⋊C8C22×C1111yescharacteristic
234C2×C22⋊C8C22×C1111yescharacteristic
235C2×C22⋊C8C22×C1111yescharacteristic
236C2×C4×C8C22×C1111yescharacteristic
237#388—22no—
238#387—22no—
239#386—22no—
240#382C22×C1112yes—
241#380C22×C1112yes—
242#380C22×C1112yes—
243C4×C4⋊C4C22×C1112yes—
244C4×C22⋊C4—22no—
245#340C22×C1112yes—
246#340C22×C1112yes—
247#340C22×C1112yes—
248C22×C11—24no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—24no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11#42714yescomplemented
258C22×C11C22×C4⋊C411yescharacteristic
259C22×C11D4211yescharacteristic
260C22×C11#54711yescharacteristic
261C22×C11C2×#13512yes—
262C22×C11#57712yes—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—44no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11—82no—
271C4×C11C2×C4×D411yescharacteristic
272C4×C11#52011yescharacteristic
273C4×C11D4×Q811yescharacteristic
274C4×C11#55411yescharacteristic
275C22×D4D4×C1111yescharacteristic
276C23×C4—22no—
277C23×C4C23×C1111yescharacteristic
278C23×C4C23×C1111yescharacteristic
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8C2×C4×C1114yes—
284C22×C8C2×C4×C1114yescomplemented
285C22×C8C23×C1111yescharacteristic
286C22×C8C23×C1111yescharacteristic
287C22×C8C23×C1111yescharacteristic
288C22×C8C23×C1111yescharacteristic
289C4×D4C2×C4×C1114yes—
290C4×D4Q8×C1114yes—
291#117—24no—
292#117—42no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4D4×C1111yescharacteristic
297C2×C4⋊C4C23×C1112yes—
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1112yes—
300C2×C4⋊C4C23×C1112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4D4×C1111yescharacteristic
305C2×C22⋊C4D4×C1111yescharacteristic
306C2×C42—22no—
307C2×C42—22no—
308C2×C42C23×C1111yescharacteristic
309#107—24no—
310#107—42no—
311#106—22no—
312#106—22no—
313#106—22no—
314#106—24no—
315#106D4×C1114yescomplemented
316C4⋊C8C2×C4×C1114yescomplemented
317C22⋊C8C2×C4×C1114yes—
318C22⋊C8C2×C4×C1114yescomplemented
319C4×C8C2×C4×C1114yescomplemented
320#95—22no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95—22no—
325C2×C11—24no—
326C2×C11—42no—
327C2×C11D4×C4⋊C411yescharacteristic
328C2×C11C2×#42711yescharacteristic
329C2×C11#291211yescharacteristic
330C2×C11#328212yes—
331C2×C11#333712yes—
332C24C2×D4×C1111yescharacteristic
333C24C2×D4×C1111yescharacteristic
334C2×D4—24no—
335C2×D4C11×C4⋊C414yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—82no—
351C22×C4C22×C4×C1112yes—
352C22×C4C22×C4×C1112yes—
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×Q8×C1112yes—
358C22×C4C2×Q8×C1112yes—
359C22×C4C24×C1111yescharacteristic
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—28no—
367C2×C8—28no—
368C2×C8C22×C4×C1112yes—
369C2×C8C22×C4×C1112yes—
370C2×C8C22×C4×C1112yes—
371C2×C8C22×C4×C1112yes—
372C2×C8C2×D4×C1112yes—
373C2×C8C11×#4112yes—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—44no—
382C4⋊C4C11×C4⋊C414yes—
383C4⋊C4C2×D4×C1114yes—
384C22⋊C4—44no—
385C22⋊C4—44no—
386C22⋊C4—82no—
387C22⋊C4C11×C4⋊C414yes—
388C22⋊C4C11×C4⋊C414yes—
389C42—44no—
390C42—82no—
391C42C22×C4×C1112yes—
392C42C2×Q8×C1112yes—
393C11#2265411yescharacteristic, direct product factor, Sylow
394C23—21no—
395C23—21no—
396C23—22no—
397C23—21no—
398C23—21no—
399C23—22no—
400C23—22no—
401C23C2×C11×C4⋊C412yes—
402C23C2×C11×C4⋊C412yes—
403C23C11×#13514yes—
404C23C22×D4×C1111yescharacteristic
405D4—28no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—88no—
433C2×C4C2×C11×C4⋊C412yes—
434C2×C4C2×C11×C4⋊C412yes—
435C2×C4C2×C11×C4⋊C412yes—
436C2×C4C2×C11×C4⋊C412yes—
437C2×C4C23×C4×C1111yescharacteristic
438C2×C4C22×D4×C1111yescharacteristic
439C2×C4C22×Q8×C1111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C2×C4C11×H(5,𝔽2)11yescharacteristic
442C2×C4C11×2−1+411yescharacteristic
443C8—22no—
444C8—22no—
445C8—22no—
446C8C4×D4×C1114yes—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22C11×#42714yescomplemented
457C22C22×C11×C4⋊C411yescharacteristic
458C22D42×C1111yescharacteristic
459C22C11×#54711yescharacteristic
460C22C2×C11×#13512yes—
461C22C11×#57712yes—
462C4—22no—
463C4—22no—
464C4—22no—
465C4—22no—
466C4—44no—
467C4—82no—
468C4—82no—
469C4—82no—
470C4C2×C4×D4×C1111yescharacteristic
471C4C11×#52011yescharacteristic
472C4D4×Q8×C1111yescharacteristic
473C4C11×#55411yescharacteristic
474C2—24no—
475C2—42no—
476C2D4×C11×C4⋊C411yescharacteristic
477C2C2×C11×#42711yescharacteristic
478C2C11×#291211yescharacteristic
479C2C11×#328212yes—
480C2C11×#333712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#427C2semidirect
3. C22×C11×#106C2semidirect
5. C11×#1949C2semidirect
6. C11×#1854C2semidirect
7. C11×#1852C2semidirect
8. C11×#1846C2semidirect
9. C11×#1807C2semidirect
10. C11×#1807C2semidirect
11. C4×C11×#106C2semidirect
17. C8×D4×C11C4semidirect
51. C22×C8×C11C2×C4semidirect
82. C11×#106D4semidirect
83. C11×C4⋊C8C2×C4semidirect
85. C11×C22⋊C8C2×C4semidirect
86. C4×C8×C11C2×C4semidirect
92. #22654C11direct (N × H)
155. C2×#427C2×C11semidirect
156. C22×#106C2×C11semidirect
158. #1949C2×C11semidirect
159. #1854C2×C11semidirect
160. #1852C2×C11semidirect
161. #1846C2×C11semidirect
162. #1807C2×C11semidirect
163. #1807C2×C11semidirect
164. C4×#106C2×C11semidirect
223. C8×D4C4×C11semidirect
257. C22×C11#427semidirect
284. C22×C8C2×C4×C11semidirect
315. #106D4×C11semidirect
316. C4⋊C8C2×C4×C11semidirect
318. C22⋊C8C2×C4×C11semidirect
319. C4×C8C2×C4×C11semidirect
393. C11#22654direct (N × H)
456. C22C11×#427semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C112
C2×C11×#4272
C22×C11×#1062
C11×#23522
C11×#19492
C11×#18542
C11×#18522
C11×#18462
C11×#18072
C4×C11×#1062
#2265411