Finite Group Databasebeta

← C11×#24533 #14601726

Subgroups — C11×#24533 #14601726

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic, complemented
3C11×#2504C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2074C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic
8C11×#1880C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1805C212yesmaximal, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#448—24no—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×#103—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#397—22no—
29C11×#391—22no—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#386—21no—
33C11×#386—21no—
34C11×#382C2212yes—
35C11×#380—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—24no—
46C22×Q8×C11—42no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—24no—
58C2×C11×SD16—42no—
59C22×C8×C11—22no—
60C22×C8×C11—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×#121—22no—
65C11×#121—22no—
66C4×Q8×C11—24no—
67C4×Q8×C11—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—22no—
82C2×C42×C11C2312yes—
83C11×C4⋊C8—42no—
84C11×#103—24no—
85C11×#103—24no—
86C11×#103—22no—
87C11×#103—22no—
88C11×#102—42no—
89C11×C22⋊C8—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D412yes—
96#24533C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—24no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—28no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—44no—
107C2×Q8×C11—44no—
108C2×Q8×C11—48no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11C2×D412yes—
111C2×Q8×C11#4114yes—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C11×SD16—44no—
137C11×SD16—44no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—44no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—82no—
159C11×C22⋊C4—82no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—44no—
163C2×#448C2×C1111yescharacteristic
164C22×#103C2×C1111yescharacteristic, complemented
165#2504C2×C1111yescharacteristic
166Q8×C22⋊C4C2×C1111yescharacteristic, complemented
167#2074C2×C1112yescomplemented
168#2055C2×C1112yescomplemented
169#1893C2×C1111yescharacteristic
170#1880C2×C1112yescomplemented
171#1850C2×C1111yescharacteristic, complemented
172#1824C2×C1111yescharacteristic, complemented
173#1805C2×C1112yescomplemented
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11#12112yes—
182C23×C11#13512yes—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—22no—
186Q8×C11—24no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—48no—
190Q8×C11—42no—
191Q8×C11#12314yes—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—42no—
195D4×C11—84no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
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—22no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—84no—
221C2×C4×C11#12112yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4112yes—
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)12yes—
226C8×C11—41no—
227C8×C11—42no—
228C8×C11—41no—
229C23×Q8C22×C1111yescharacteristic
230C22×SD16C22×C1111yescharacteristic
231C22×SD16C22×C1111yescharacteristic
232C23×C8C22×C1111yescharacteristic
233C2×#121C22×C1111yescharacteristic
234C2×C4×Q8C22×C1112yes—
235C22×C4⋊C4C22×C1111yescharacteristic
236#448—24no—
237C2×C4⋊C8C22×C1112yes—
238C2×#103—24no—
239C2×#103C22×C1112yes—
240C2×#103C22×C1111yescharacteristic
241C2×#103C22×C1112yes—
242C2×#103C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×C22⋊C8C22×C1111yescharacteristic
245#397—22no—
246#391—22no—
247#391C22×C1112yes—
248#390C22×C1112yes—
249#386—21no—
250#386—21no—
251#382C22×C1112yes—
252#380—21no—
253#380C22×C1111yescharacteristic
254C4×C22⋊C4—21no—
255C4×C22⋊C4C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1112yes—
258#340C22×C1112yes—
259#336C22×C1112yes—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11#46414yes—
270C22×C11C2×#12111yescharacteristic
271C22×C11#54612yes—
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57712yes—
275C4×C11—22no—
276C4×C11—24no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11—82no—
283C4×C11C2×#12311yescharacteristic
284C4×C11#53411yescharacteristic
285C4×C11#55112yes—
286C22×Q8—21no—
287C22×Q8—22no—
288C22×Q8—24no—
289C22×Q8—42no—
290C22×Q8D4×C1114yes—
291C22×Q8C23×C1111yescharacteristic
292C22×Q8C23×C1111yescharacteristic
293C22×D4—21no—
294C22×D4C23×C1111yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4C23×C1111yescharacteristic
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—24no—
301C2×SD16—42no—
302C22×C8—22no—
303C22×C8—42no—
304C22×C8C23×C1112yes—
305C22×C8C23×C1111yescharacteristic
306C22×C8C23×C1111yescharacteristic
307#121—22no—
308#121—22no—
309C4×Q8—24no—
310C4×Q8—42no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4C23×C1112yes—
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4D4×C1111yescharacteristic
323C2×C22⋊C4D4×C1111yescharacteristic
324C2×C42—22no—
325C2×C42C23×C1112yes—
326C4⋊C8—42no—
327#103—24no—
328#103—24no—
329#103—22no—
330#103—22no—
331#102—42no—
332C22⋊C8—22no—
333#95—22no—
334#95—22no—
335#95—21no—
336#95—22no—
337#95—22no—
338#95D4×C1112yes—
339C2×C11—24no—
340C2×C11—161no—
341C2×C11#241211yescharacteristic
342C2×C11C2×#46411yescharacteristic
343C2×C11#304311yescharacteristic
344C2×C11#330112yes—
345C2×C11#332012yes—
346C24—21no—
347C24C2×D4×C1111yescharacteristic
348C2×Q8—24no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—28no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—44no—
356C2×Q8—44no—
357C2×Q8—48no—
358C2×Q8C2×D4×C1112yes—
359C2×Q8C2×D4×C1112yes—
360C2×Q8C11×#4114yes—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—44no—
377C22×C4—42no—
378C22×C4—82no—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1112yes—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1112yes—
383C22×C4C11×#4112yes—
384C22×C4C24×C1111yescharacteristic
385SD16—44no—
386SD16—44no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—44no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—44no—
402C4⋊C4—42no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—82no—
408C22⋊C4—82no—
409C42—22no—
410C42—22no—
411C42—44no—
412C11#2453311yescharacteristic, direct product factor, Sylow
413C23—22no—
414C23—22no—
415C23—41no—
416C23—42no—
417C23—41no—
418C23—41no—
419C23—42no—
420C23C11×#12112yes—
421C23C11×#13512yes—
422C23C11×#13712yes—
423C23C22×D4×C1111yescharacteristic
424Q8—22no—
425Q8—24no—
426Q8—22no—
427Q8—22no—
428Q8—48no—
429Q8—42no—
430Q8C11×#12314yes—
431D4—41no—
432D4—41no—
433D4—42no—
434D4—84no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—48no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—84no—
460C2×C4C11×#12112yes—
461C2×C4C22×D4×C1111yescharacteristic
462C2×C4C2×C11×#4112yes—
463C2×C4C2×C11×#4111yescharacteristic
464C2×C4C11×H(5,𝔽2)12yes—
465C8—41no—
466C8—42no—
467C8—41no—
468C22—22no—
469C22—22no—
470C22—24no—
471C22—24no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—82no—
476C22—82no—
477C22C11×#46414yes—
478C22C2×C11×#12111yescharacteristic
479C22C11×#54612yes—
480C22C2×C11×#13511yescharacteristic
481C22C2×C11×#13711yescharacteristic
482C22C11×#57712yes—
483C4—22no—
484C4—24no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—81no—
489C4—82no—
490C4—82no—
491C4C2×C11×#12311yescharacteristic
492C4C11×#53411yescharacteristic
493C4C11×#55112yes—
494C2—24no—
495C2—161no—
496C2C11×#241211yescharacteristic
497C2C2×C11×#46411yescharacteristic
498C2C11×#304311yescharacteristic
499C2C11×#330112yes—
500C2C11×#332012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#103C2semidirect
4. Q8×C11×C22⋊C4C2semidirect
5. C11×#2074C2semidirect
6. C11×#2055C2semidirect
8. C11×#1880C2semidirect
9. C11×#1850C2semidirect
10. C11×#1824C2semidirect
11. C11×#1805C2semidirect
96. #24533C11direct (N × H)
164. C22×#103C2×C11semidirect
166. Q8×C22⋊C4C2×C11semidirect
167. #2074C2×C11semidirect
168. #2055C2×C11semidirect
170. #1880C2×C11semidirect
171. #1850C2×C11semidirect
172. #1824C2×C11semidirect
173. #1805C2×C11semidirect
412. C11#24533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C22×C11×#1032
C11×#25042
Q8×C11×C22⋊C42
C11×#20742
C11×#20552
C11×#18932
C11×#18802
C11×#18502
C11×#18242
C11×#18052
#2453311