Finite Group Databasebeta

← C11×#24298 #14601491

Subgroups — C11×#24298 #14601491

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#474C212yesmaximal, complemented
3C4×C11×#121C211yesmaximal, characteristic
4C11×#2057C212yesmaximal, complemented
5C11×#2023C212yesmaximal, complemented
6C11×#1988C212yesmaximal, complemented
7C11×#1874C212yesmaximal
8C11×#1852C212yesmaximal, complemented
9C11×#1797C211yesmaximal, characteristic, complemented
10C23×Q8×C11—21no—
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2212yes—
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C22×C11×C4⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C11×#474—28no—
23C2×C11×#107C2214yes—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#102C2214yes—
26C2×C11×C22⋊C8C2212yes—
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#388—21no—
30C11×#386—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C11×#340C2214yes—
35C11×#340C2214yes—
36C11×#336C2212yes—
37C22×Q8×C11—28no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—44no—
41C22×Q8×C11—44no—
42C22×D4×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11C2314yes—
50C11×C4⋊Q8—28no—
51C11×C4⋊Q8—28no—
52C11×C4⋊Q8—28no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8D418yescomplemented
55C11×#121—22no—
56C11×#121Q814yescomplemented
57C4×D4×C11—24no—
58C4×D4×C11—44no—
59C2×C11×C4⋊C4—28no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—28no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—24no—
75C2×C42×C11—21no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107—28no—
81C11×C4⋊C8—24no—
82C11×#102—28no—
83C11×C22⋊C8—24no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—21no—
87#24298C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—21no—
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—28no—
91C2×Q8×C11—28no—
92C2×Q8×C11—44no—
93C2×Q8×C11—432no—
94C2×Q8×C11—44no—
95C2×Q8×C11—44no—
96C2×Q8×C11—44no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11C2×Q812yescomplemented
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—28no—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11D814yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×Q812yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C8×C11—24no—
131C2×C8×C11—24no—
132C2×C8×C11—24no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4C2×D418yes—
142C11×C4⋊C4C2×Q812yescomplemented
143C11×C22⋊C4—24no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—42no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—42no—
152C42×C11C2×D414yes—
153C22×C4⋊Q8C2×C1111yescharacteristic, complemented
154C2×#474C2×C1112yescomplemented
155C4×#121C2×C1111yescharacteristic
156#2057C2×C1112yescomplemented
157#2023C2×C1112yescomplemented
158#1988C2×C1112yescomplemented
159#1874C2×C1112yes—
160#1852C2×C1112yescomplemented
161#1797C2×C1111yescharacteristic, complemented
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11C22⋊Q812yes—
174C23×C11C2×D812yes—
175C23×C11#13712yes—
176C23×C11C22×D411yescharacteristic
177Q8×C11—416no—
178Q8×C11—416no—
179D4×C11—24no—
180D4×C11—48no—
181D4×C11—42no—
182C2×C4×C11—28no—
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—21no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—28no—
194C2×C4×C11—28no—
195C2×C4×C11—22no—
196C2×C4×C11—416no—
197C2×C4×C11—41no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—84no—
208C2×C4×C11#12012yes—
209C2×C4×C11#12012yes—
210C2×C4×C11C22⋊Q812yes—
211C2×C4×C11C2×D812yes—
212C2×C4×C11C2×D812yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×Q811yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C112−1+412yes—
219C8×C11—44no—
220C23×Q8—21no—
221C2×C4⋊Q8—28no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C22×C1112yes—
225C2×C4⋊Q8C22×C1112yes—
226C2×#121C22×C1111yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C22×C1111yescharacteristic
229C22×C4⋊C4—21no—
230C22×C4⋊C4C22×C1112yes—
231C22×C42C22×C1111yescharacteristic
232#474—28no—
233C2×#107C22×C1114yes—
234C2×C4⋊C8C22×C1112yes—
235C2×#102C22×C1114yes—
236C2×C22⋊C8C22×C1112yes—
237#390C22×C1111yescharacteristic
238#389C22×C1111yescharacteristic
239#388—21no—
240#386—21no—
241#380C22×C1111yescharacteristic
242C4×C4⋊C4C22×C1111yescharacteristic
243C4×C22⋊C4—21no—
244#340C22×C1114yes—
245#340C22×C1114yes—
246#336C22×C1112yes—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11#47414yescomplemented
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×C22⋊Q811yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11C22×D811yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—48no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#44714yes—
277C4×C11#54812yes—
278C4×C11D4×Q812yes—
279C22×Q8—28no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—44no—
283C22×Q8—44no—
284C22×D4—21no—
285C22×D4C23×C1111yescharacteristic
286C23×C4—22no—
287C23×C4—21no—
288C23×C4D4×C1111yescharacteristic
289C23×C4D4×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C22×C8C23×C1114yes—
292C4⋊Q8—28no—
293C4⋊Q8—28no—
294C4⋊Q8—28no—
295C4⋊Q8—24no—
296C4⋊Q8D4×C1118yescomplemented
297#121—22no—
298#121Q8×C1114yescomplemented
299C4×D4—24no—
300C4×D4—44no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C23×C1111yescharacteristic
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C4⋊C4C23×C1114yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C42—24no—
317C2×C42—21no—
318C2×C42D4×C1111yescharacteristic
319C2×C42D4×C1111yescharacteristic
320C2×C42C23×C1111yescharacteristic
321C2×C42C23×C1111yescharacteristic
322#107—28no—
323C4⋊C8—24no—
324#102—28no—
325C22⋊C8—24no—
326#95—21no—
327#95—21no—
328#95—21no—
329C2×C11—24no—
330C2×C11—82no—
331C2×C11#240911yescharacteristic
332C2×C11C2×#44711yescharacteristic
333C2×C11#300411yescharacteristic
334C2×C11C2×#47411yescharacteristic
335C2×C11#307911yescharacteristic
336C2×C11#322611yescharacteristic
337C2×C11#323911yescharacteristic
338C24—21no—
339C24C2×D4×C1111yescharacteristic
340C2×Q8—28no—
341C2×Q8—28no—
342C2×Q8—44no—
343C2×Q8—432no—
344C2×Q8—44no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4C2×Q8×C1112yescomplemented
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—28no—
362C22×C4—21no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4C11×D814yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×Q8×C1112yes—
378C22×C4C11×#4112yes—
379C22×C4C24×C1111yescharacteristic
380C2×C8—24no—
381C2×C8—24no—
382C2×C8—24no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—28no—
386C4⋊C4—24no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—42no—
391C4⋊C4C2×D4×C1118yes—
392C4⋊C4C2×Q8×C1112yescomplemented
393C22⋊C4—24no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C42—22no—
399C42—22no—
400C42—22no—
401C42—42no—
402C42C2×D4×C1114yes—
403C11#2429811yescharacteristic, direct product factor, Sylow
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—22no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23C11×C22⋊Q812yes—
416C23C2×C11×D812yes—
417C23C11×#13712yes—
418C23C22×D4×C1111yescharacteristic
419Q8—416no—
420Q8—416no—
421D4—24no—
422D4—48no—
423D4—42no—
424C2×C4—28no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—22no—
438C2×C4—416no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4C11×#12012yes—
451C2×C4C11×#12012yes—
452C2×C4C11×C22⋊Q812yes—
453C2×C4C2×C11×D812yes—
454C2×C4C2×C11×D812yes—
455C2×C4C11×AGL(1,ℤ/8)12yes—
456C2×C4C11×#13712yes—
457C2×C4C22×D4×C1112yes—
458C2×C4C22×Q8×C1111yescharacteristic
459C2×C4C2×C11×#4111yescharacteristic
460C2×C4C11×2−1+412yes—
461C8—44no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22C11×#47414yescomplemented
476C22C2×C11×#12011yescharacteristic
477C22C2×C11×C22⋊Q811yescharacteristic
478C22C11×#53611yescharacteristic
479C22C22×C11×D811yescharacteristic
480C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
481C22C2×C11×#13711yescharacteristic
482C22C2×C11×#13711yescharacteristic
483C4—22no—
484C4—22no—
485C4—22no—
486C4—22no—
487C4—48no—
488C4—42no—
489C4—81no—
490C4—81no—
491C4C11×#44714yes—
492C4C11×#54812yes—
493C4D4×Q8×C1112yes—
494C2—24no—
495C2—82no—
496C2C11×#240911yescharacteristic
497C2C2×C11×#44711yescharacteristic
498C2C11×#300411yescharacteristic
499C2C2×C11×#47411yescharacteristic
500C2C11×#307911yescharacteristic
501C2C11×#322611yescharacteristic
502C2C11×#323911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#2057C2semidirect
5. C11×#2023C2semidirect
6. C11×#1988C2semidirect
8. C11×#1852C2semidirect
9. C11×#1797C2semidirect
54. C11×C4⋊Q8D4semidirect
56. C11×#121Q8semidirect
87. #24298C11direct (N × H)
103. C2×D4×C11C2×Q8semidirect
142. C11×C4⋊C4C2×Q8semidirect
153. C22×C4⋊Q8C2×C11semidirect
154. C2×#474C2×C11semidirect
156. #2057C2×C11semidirect
157. #2023C2×C11semidirect
158. #1988C2×C11semidirect
160. #1852C2×C11semidirect
161. #1797C2×C11semidirect
260. C22×C11#474semidirect
296. C4⋊Q8D4×C11semidirect
298. #121Q8×C11semidirect
353. C2×D4C2×Q8×C11semidirect
392. C4⋊C4C2×Q8×C11semidirect
403. C11#24298direct (N × H)
475. C22C11×#474semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4742
C4×C11×#1212
C11×#20572
C11×#20232
C11×#19882
C11×#18742
C11×#18522
C11×#17972
#2429811