Finite Group Databasebeta

← C11×#23099 #14600292

Subgroups — C11×#23099 #14600292

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C11×#2366C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic, complemented
4C11×#1972C212yesmaximal, complemented
5C11×#1957C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1770C211yesmaximal, characteristic, complemented
10C11×#1762C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117—21no—
18C11×#459C418yescomplemented
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#390—21no—
29C11×#390C2212yes—
30C11×#390C2212yes—
31C11×#388—22no—
32C11×#386—22no—
33C11×#384C2211yescharacteristic
34C11×#380—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C2×C11×D8—42no—
49C2×C11×D8—42no—
50C2×C11×D8C2×C418yescomplemented
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×#127—22no—
55C11×#127C2×C414yes—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11—42no—
59C4×D4×C11—44no—
60C4×D4×C11C2×C414yescomplemented
61C11×#117—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—22no—
77C2×C42×C11—21no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#106—42no—
81C11×C4⋊C8C2×C414yescomplemented
82C11×#102—24no—
83C11×#102—22no—
84C11×#102—22no—
85C11×#102—42no—
86C11×#102C2×C418yescomplemented
87C11×#97—42no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95D412yes—
92#23099C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C24×C11—22no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—21no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—81no—
110C2×D4×C11—81no—
111C2×D4×C11C22×C414yes—
112C2×D4×C11C22×C412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—82no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C11×D8—48no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11C22×C414yes—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—81no—
148C11×C4⋊C4C22×C412yes—
149C11×C4⋊C4#4112yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—82no—
155C11×C22⋊C4—82no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—44no—
159C42×C11—42no—
160C42×C11C22×C412yes—
161C42×C11#4112yes—
162C2×#459C2×C1111yescharacteristic
163#2366C2×C1111yescharacteristic, complemented
164#2354C2×C1111yescharacteristic, complemented
165#1972C2×C1112yescomplemented
166#1957C2×C1111yescharacteristic, complemented
167#1948C2×C1111yescharacteristic, complemented
168#1926C2×C1112yescomplemented
169#1879C2×C1112yescomplemented
170#1770C2×C1111yescharacteristic, complemented
171#1762C2×C1112yescomplemented
172C4×#102C2×C1111yescharacteristic, complemented
173C23×C11—22no—
174C23×C11—24no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11C22×D411yescharacteristic
188D4×C11—22no—
189D4×C11—24no—
190D4×C11—22no—
191D4×C11—24no—
192D4×C11—41no—
193D4×C11—42no—
194D4×C11—41no—
195D4×C11—42no—
196D4×C11—48no—
197D4×C11—84no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—48no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—88no—
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C8×C11—24no—
231C8×C11—22no—
232C8×C11—41no—
233C22×D8C22×C1112yes—
234C2×#127C22×C1111yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4C22×C1112yes—
237C2×C4×D4C22×C1111yescharacteristic
238C2×#117—21no—
239#459C4×C1118yescomplemented
240C2×#106C22×C1112yes—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×#102C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×#102C22×C1111yescharacteristic
245C2×#102C22×C1112yes—
246C2×#102C22×C1112yes—
247C2×#97C22×C1112yes—
248C2×C4×C8C22×C1111yescharacteristic
249#390—21no—
250#390C22×C1112yes—
251#390C22×C1112yes—
252#388—22no—
253#386—22no—
254#384C22×C1111yescharacteristic
255#380—21no—
256C4×C4⋊C4C22×C1112yes—
257C4×C4⋊C4C22×C1111yescharacteristic
258C4×C4⋊C4C22×C1111yescharacteristic
259#340C22×C1112yes—
260#340C22×C1111yescharacteristic
261#340C22×C1111yescharacteristic
262#336C22×C1112yes—
263C22×C11—42no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—82no—
270C22×C11—81no—
271C22×C11—82no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—81no—
277C22×C11C2×C4×D411yescharacteristic
278C22×C11#54611yescharacteristic
279C22×C11#55011yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C11#57611yescharacteristic
283C22×C11#57711yescharacteristic
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—81no—
290C4×C11—82no—
291C4×C11#44214yes—
292C4×C11C4×#4111yescharacteristic
293C4×C11#51811yescharacteristic
294C4×C11#55311yescharacteristic
295C4×C11#55511yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C23×C1112yes—
299C22×D4C23×C1111yescharacteristic
300C23×C4—21no—
301C23×C4—22no—
302C2×D8—42no—
303C2×D8—42no—
304C2×D8C2×C4×C1118yescomplemented
305C22×C8C23×C1111yescharacteristic
306C22×C8C23×C1112yes—
307C22×C8C23×C1111yescharacteristic
308#127—22no—
309#127C2×C4×C1114yes—
310C4×D4—24no—
311C4×D4—22no—
312C4×D4—42no—
313C4×D4—44no—
314C4×D4C2×C4×C1114yescomplemented
315#117—44no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4D4×C1111yescharacteristic
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C42—22no—
331C2×C42—21no—
332C2×C42C23×C1112yes—
333C2×C42C23×C1111yescharacteristic
334#106—42no—
335C4⋊C8C2×C4×C1114yescomplemented
336#102—24no—
337#102—22no—
338#102—22no—
339#102—42no—
340#102C2×C4×C1118yescomplemented
341#97—42no—
342C4×C8—22no—
343#95—22no—
344#95—21no—
345#95D4×C1112yes—
346C2×C11—82no—
347C2×C11—84no—
348C2×C11#236311yescharacteristic
349C2×C11C2×#44211yescharacteristic
350C2×C11#294611yescharacteristic
351C2×C11#332511yescharacteristic
352C2×C11#333211yescharacteristic
353C2×C11#339711yescharacteristic
354C2×C11#339911yescharacteristic
355C24—21no—
356C24—22no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—81no—
372C2×D4—81no—
373C2×D4C22×C4×C1114yes—
374C2×D4C22×C4×C1112yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C24×C1111yescharacteristic
390D8—48no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C22×C4×C1114yes—
399C2×C8C11×#4112yes—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4C22×C4×C1112yes—
411C4⋊C4C11×#4112yes—
412C22⋊C4—24no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—82no—
417C22⋊C4—82no—
418C42—22no—
419C42—22no—
420C42—44no—
421C42—42no—
422C42C22×C4×C1112yes—
423C42C11×#4112yes—
424C11#2309911yescharacteristic, direct product factor, Sylow
425C23—22no—
426C23—24no—
427C23—42no—
428C23—41no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—41no—
434C23—42no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23C22×D4×C1111yescharacteristic
440D4—22no—
441D4—24no—
442D4—22no—
443D4—24no—
444D4—41no—
445D4—42no—
446D4—41no—
447D4—42no—
448D4—48no—
449D4—84no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—48no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—88no—
472C2×C4C4×D4×C1112yes—
473C2×C4C4×D4×C1112yes—
474C2×C4C11×AGL(1,ℤ/8)12yes—
475C2×C4C11×AGL(1,ℤ/8)12yes—
476C2×C4C23×C4×C1111yescharacteristic
477C2×C4C2×C11×#4111yescharacteristic
478C2×C4C2×C11×#4111yescharacteristic
479C2×C4C2×C11×#4111yescharacteristic
480C2×C4C11×H(5,𝔽2)11yescharacteristic
481C2×C4C11×H(5,𝔽2)11yescharacteristic
482C8—24no—
483C8—22no—
484C8—41no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22—44no—
491C22—82no—
492C22—81no—
493C22—82no—
494C22—81no—
495C22—82no—
496C22—81no—
497C22—81no—
498C22—82no—
499C22C2×C4×D4×C1111yescharacteristic
500C22C11×#54611yescharacteristic
501C22C11×#55011yescharacteristic
502C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
503C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
504C22C11×#57611yescharacteristic
505C22C11×#57711yescharacteristic
506C4—22no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—81no—
512C4—82no—
513C4C11×#44214yes—
514C4C4×C11×#4111yescharacteristic
515C4C11×#51811yescharacteristic
516C4C11×#55311yescharacteristic
517C4C11×#55511yescharacteristic
518C2—82no—
519C2—84no—
520C2C11×#236311yescharacteristic
521C2C2×C11×#44211yescharacteristic
522C2C11×#294611yescharacteristic
523C2C11×#332511yescharacteristic
524C2C11×#333211yescharacteristic
525C2C11×#339711yescharacteristic
526C2C11×#339911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2366C2semidirect
3. C11×#2354C2semidirect
4. C11×#1972C2semidirect
5. C11×#1957C2semidirect
6. C11×#1948C2semidirect
7. C11×#1926C2semidirect
8. C11×#1879C2semidirect
9. C11×#1770C2semidirect
10. C11×#1762C2semidirect
11. C4×C11×#102C2semidirect
18. C11×#459C4semidirect
50. C2×C11×D8C2×C4semidirect
60. C4×D4×C11C2×C4semidirect
81. C11×C4⋊C8C2×C4semidirect
86. C11×#102C2×C4semidirect
92. #23099C11direct (N × H)
163. #2366C2×C11semidirect
164. #2354C2×C11semidirect
165. #1972C2×C11semidirect
166. #1957C2×C11semidirect
167. #1948C2×C11semidirect
168. #1926C2×C11semidirect
169. #1879C2×C11semidirect
170. #1770C2×C11semidirect
171. #1762C2×C11semidirect
172. C4×#102C2×C11semidirect
239. #459C4×C11semidirect
304. C2×D8C2×C4×C11semidirect
314. C4×D4C2×C4×C11semidirect
335. C4⋊C8C2×C4×C11semidirect
340. #102C2×C4×C11semidirect
424. C11#23099direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C11×#23662
C11×#23542
C11×#19722
C11×#19572
C11×#19482
C11×#19262
C11×#18792
C11×#17702
C11×#17622
C4×C11×#1022
#2309911