Finite Group Databasebeta

← C11×#22226 #14599419

Subgroups — C11×#22226 #14599419

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#490C211yesmaximal, characteristic
2C4×C11×#127C211yesmaximal, characteristic
3C4×C11×#125C211yesmaximal, characteristic, complemented
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C11×#1926C212yesmaximal, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1864C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1847C211yesmaximal, characteristic, complemented
11C11×#1745C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2212yes—
17C11×#490C418yescomplemented
18C2×C11×#107C2212yes—
19C2×C11×#106C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C11×#390—21no—
27C11×#390—21no—
28C11×#390C2212yes—
29C11×#389C2211yescharacteristic
30C11×#389C2211yescharacteristic
31C11×#387—21no—
32C11×#387—21no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C43×C11C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C11×#127—22no—
51C11×#127C2×C414yes—
52C11×#125—22no—
53C11×#125C2×C414yescomplemented
54C4×D4×C11—42no—
55C4×D4×C11—42no—
56C4×D4×C11—44no—
57C4×D4×C11—44no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C11×#107—42no—
82C11×#106—42no—
83C11×#102—42no—
84C11×#102—42no—
85C11×#102C2×C418yescomplemented
86C11×#102C2×C418yescomplemented
87C11×#97—22no—
88C11×#97C2×C414yescomplemented
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95#22226C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—22no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11C22×C414yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C22×C414yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4C22×C412yes—
143C11×C4⋊C4C22×C412yes—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—44no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—41no—
152C42×C11—41no—
153C42×C11—42no—
154C42×C11—42no—
155C42×C11C22×C412yes—
156C42×C11#4112yes—
157C2×#490C2×C1111yescharacteristic
158C4×#127C2×C1111yescharacteristic
159C4×#125C2×C1111yescharacteristic, complemented
160#1992C2×C1111yescharacteristic, complemented
161#1961C2×C1111yescharacteristic
162#1926C2×C1112yescomplemented
163#1925C2×C1112yescomplemented
164#1864C2×C1112yescomplemented
165#1862C2×C1112yescomplemented
166#1847C2×C1111yescharacteristic, complemented
167#1745C2×C1111yescharacteristic, complemented
168C23×C11—24no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11C22×D411yescharacteristic
176D4×C11—24no—
177D4×C11—24no—
178D4×C11—48no—
179D4×C11—48no—
180D4×C11—42no—
181D4×C11—42no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—88no—
212C2×C4×C11C4×D412yes—
213C2×C4×C11C4×D412yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)12yes—
219C2×C4×C112−1+412yes—
220C8×C11—24no—
221C8×C11—42no—
222C2×#127C22×C1111yescharacteristic
223C2×#125C22×C1111yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C22×C1112yes—
227#490C4×C1118yescomplemented
228C2×#107C22×C1112yes—
229C2×#106C22×C1112yes—
230C2×#102C22×C1112yes—
231C2×#102C22×C1112yes—
232C2×#102C22×C1112yes—
233C2×#102C22×C1112yes—
234C2×#97C22×C1111yescharacteristic
235C2×#97C22×C1111yescharacteristic
236#390—21no—
237#390—21no—
238#390C22×C1112yes—
239#389C22×C1111yescharacteristic
240#389C22×C1111yescharacteristic
241#387—21no—
242#387—21no—
243#384C22×C1111yescharacteristic
244#382C22×C1111yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C4⋊C4C22×C1111yescharacteristic
249C43C22×C1111yescharacteristic
250#340C22×C1112yes—
251#340C22×C1112yes—
252#336C22×C1112yes—
253#336C22×C1112yes—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11C2×C4×D411yescharacteristic
262C22×C11#53511yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11#57511yescharacteristic
267C22×C11#57511yescharacteristic
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—81no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11#52012yes—
280C4×C11#54212yes—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C23×C1112yes—
284C23×C4—22no—
285C22×C8C23×C1112yes—
286C22×C8C23×C1112yes—
287#127—22no—
288#127C2×C4×C1114yes—
289#125—22no—
290#125C2×C4×C1114yescomplemented
291C4×D4—42no—
292C4×D4—42no—
293C4×D4—44no—
294C4×D4—44no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1111yescharacteristic
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42D4×C1111yescharacteristic
312C2×C42D4×C1111yescharacteristic
313C2×C42D4×C1111yescharacteristic
314C2×C42D4×C1111yescharacteristic
315C2×C42C23×C1111yescharacteristic
316C2×C42C23×C1111yescharacteristic
317C2×C42C23×C1111yescharacteristic
318#107—42no—
319#106—42no—
320#102—42no—
321#102—42no—
322#102C2×C4×C1118yescomplemented
323#102C2×C4×C1118yescomplemented
324#97—22no—
325#97C2×C4×C1114yescomplemented
326#95—21no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332C2×C11—84no—
333C2×C11#232611yescharacteristic
334C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
336C2×C11#321711yescharacteristic
337C2×C11#321911yescharacteristic
338C2×C11#323411yescharacteristic
339C2×C11#323511yescharacteristic
340C24—22no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—42no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4C22×C4×C1114yes—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C24×C1111yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8C22×C4×C1114yes—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4C22×C4×C1112yes—
387C4⋊C4C22×C4×C1112yes—
388C22⋊C4—44no—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C42—22no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—41no—
396C42—41no—
397C42—42no—
398C42—42no—
399C42C22×C4×C1112yes—
400C42C11×#4112yes—
401C11#2222611yescharacteristic, direct product factor, Sylow
402C23—24no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23C22×D4×C1111yescharacteristic
410D4—24no—
411D4—24no—
412D4—48no—
413D4—48no—
414D4—42no—
415D4—42no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—88no—
446C2×C4C4×D4×C1112yes—
447C2×C4C4×D4×C1112yes—
448C2×C4C11×AGL(1,ℤ/8)12yes—
449C2×C4C11×AGL(1,ℤ/8)12yes—
450C2×C4C23×C4×C1111yescharacteristic
451C2×C4C2×C11×#4111yescharacteristic
452C2×C4C11×H(5,𝔽2)12yes—
453C2×C4C11×2−1+412yes—
454C8—24no—
455C8—42no—
456C22—44no—
457C22—44no—
458C22—44no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22C2×C4×D4×C1111yescharacteristic
464C22C11×#53511yescharacteristic
465C22C11×#53611yescharacteristic
466C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
467C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
468C22C11×#57511yescharacteristic
469C22C11×#57511yescharacteristic
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—42no—
475C4—42no—
476C4—41no—
477C4—41no—
478C4—82no—
479C4—81no—
480C4—81no—
481C4C11×#52012yes—
482C4C11×#54212yes—
483C2—84no—
484C2C11×#232611yescharacteristic
485C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
486C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
487C2C11×#321711yescharacteristic
488C2C11×#321911yescharacteristic
489C2C11×#323411yescharacteristic
490C2C11×#323511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C11×#125C2semidirect
4. C11×#1992C2semidirect
6. C11×#1926C2semidirect
7. C11×#1925C2semidirect
8. C11×#1864C2semidirect
9. C11×#1862C2semidirect
10. C11×#1847C2semidirect
11. C11×#1745C2semidirect
17. C11×#490C4semidirect
53. C11×#125C2×C4semidirect
85. C11×#102C2×C4semidirect
86. C11×#102C2×C4semidirect
88. C11×#97C2×C4semidirect
95. #22226C11direct (N × H)
159. C4×#125C2×C11semidirect
160. #1992C2×C11semidirect
162. #1926C2×C11semidirect
163. #1925C2×C11semidirect
164. #1864C2×C11semidirect
165. #1862C2×C11semidirect
166. #1847C2×C11semidirect
167. #1745C2×C11semidirect
227. #490C4×C11semidirect
290. #125C2×C4×C11semidirect
322. #102C2×C4×C11semidirect
323. #102C2×C4×C11semidirect
325. #97C2×C4×C11semidirect
401. C11#22226direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4902
C4×C11×#1272
C4×C11×#1252
C11×#19922
C11×#19612
C11×#19262
C11×#19252
C11×#18642
C11×#18622
C11×#18472
C11×#17452
#2222611