Finite Group Databasebeta

← C11×#24969 #14602162

Subgroups — C11×#24969 #14602162

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2538C211yesmaximal, characteristic
2D4×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2077C212yesmaximal, complemented
4C11×#2035C212yesmaximal, complemented
5C11×#1954C211yesmaximal, characteristic
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1872C212yesmaximal, complemented
8C11×#1834C211yesmaximal, characteristic, complemented
9C11×#1823C212yesmaximal, complemented
10C11×#1803C211yesmaximal, characteristic, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#396—22no—
26C11×#390—21no—
27C11×#389—21no—
28C11×#389—21no—
29C11×#385—22no—
30C11×#384C2211yescharacteristic
31C11×#384C2211yescharacteristic
32C11×#380C2212yes—
33C11×#380C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C22×Q8×C11C2311yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11C2312yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—42no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—44no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C11×#106—42no—
78C11×C4⋊C8—22no—
79C11×#103—22no—
80C11×#103—22no—
81C11×#103—42no—
82C11×C22⋊C8—42no—
83C11×C22⋊C8—42no—
84C4×C8×C11—22no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—22no—
88#24969C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11C2×D412yes—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11#4112yes—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11SD1614yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11—44no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4#4112yes—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—82no—
149C42×C11—42no—
150C42×C11—42no—
151C42×C11#4112yes—
152C42×C11#4112yes—
153#2538C2×C1111yescharacteristic
154D4×C4⋊C4C2×C1111yescharacteristic
155#2077C2×C1112yescomplemented
156#2035C2×C1112yescomplemented
157#1954C2×C1111yescharacteristic
158#1948C2×C1111yescharacteristic, complemented
159#1872C2×C1112yescomplemented
160#1834C2×C1111yescharacteristic, complemented
161#1823C2×C1112yescomplemented
162#1803C2×C1111yescharacteristic, complemented
163C4×#103C2×C1111yescharacteristic, complemented
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11C2×SD1614yes—
171C23×C11C22×D411yescharacteristic
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—41no—
175Q8×C11—41no—
176D4×C11—28no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—88no—
205C2×C4×C11#12312yes—
206C2×C4×C11#12312yes—
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C8×C11—42no—
216C8×C11—41no—
217C8×C11—41no—
218C2×C22⋊Q8C22×C1112yes—
219C2×C4×Q8C22×C1111yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C22×C1111yescharacteristic
222C22×C4⋊C4C22×C1112yes—
223C2×#106C22×C1112yes—
224C2×C4⋊C8C22×C1111yescharacteristic
225C2×#103C22×C1111yescharacteristic
226C2×#103C22×C1111yescharacteristic
227C2×#103C22×C1112yes—
228C2×C22⋊C8C22×C1112yes—
229C2×C22⋊C8C22×C1112yes—
230C2×C4×C8C22×C1111yescharacteristic
231#396—22no—
232#390—21no—
233#389—21no—
234#389—21no—
235#385—22no—
236#384C22×C1111yescharacteristic
237#384C22×C1111yescharacteristic
238#380C22×C1112yes—
239#380C22×C1112yes—
240C4×C4⋊C4C22×C1111yescharacteristic
241#340C22×C1112yes—
242#340C22×C1111yescharacteristic
243#340C22×C1112yes—
244#340C22×C1111yescharacteristic
245#340C22×C1112yes—
246#340C22×C1112yes—
247C22×C11—24no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11C2×#12311yescharacteristic
255C22×C11#54611yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11C22×SD1611yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C22×C11#57611yescharacteristic
260C22×C11#57811yescharacteristic
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#48314yes—
270C4×C11#52911yescharacteristic
271C4×C11#54011yescharacteristic
272C4×C11#55311yescharacteristic
273C4×C11#55511yescharacteristic
274C22×Q8C23×C1111yescharacteristic
275C22×D4D4×C1111yescharacteristic
276C23×C4—22no—
277C23×C4C23×C1112yes—
278C22×C8C23×C1111yescharacteristic
279C22×C8C23×C1111yescharacteristic
280C22×C8C23×C1112yes—
281C22⋊Q8—24no—
282C22⋊Q8—42no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—44no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4D4×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C4⋊C4C23×C1112yes—
301C2×C4⋊C4C23×C1111yescharacteristic
302C2×C4⋊C4C23×C1111yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4D4×C1112yes—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42C23×C1111yescharacteristic
310#106—42no—
311C4⋊C8—22no—
312#103—22no—
313#103—22no—
314#103—42no—
315C22⋊C8—42no—
316C22⋊C8—42no—
317C4×C8—22no—
318#95—21no—
319#95—22no—
320#95—22no—
321C2×C11—44no—
322C2×C11#242011yescharacteristic
323C2×C11C2×#48311yescharacteristic
324C2×C11#309811yescharacteristic
325C2×C11#329511yescharacteristic
326C2×C11#329811yescharacteristic
327C2×C11#332811yescharacteristic
328C2×C11#333311yescharacteristic
329C24C2×D4×C1112yes—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8C11×#4112yes—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4C11×SD1614yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4—82no—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C24×C1111yescharacteristic
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—81no—
383C4⋊C4—81no—
384C4⋊C4C11×#4112yes—
385C22⋊C4—24no—
386C22⋊C4—44no—
387C22⋊C4—44no—
388C22⋊C4—82no—
389C42—42no—
390C42—42no—
391C42C11×#4112yes—
392C42C11×#4112yes—
393C11#2496911yescharacteristic, direct product factor, Sylow
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23C2×C11×SD1614yes—
401C23C22×D4×C1111yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—41no—
405Q8—41no—
406D4—28no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—88no—
435C2×C4C11×#12312yes—
436C2×C4C11×#12312yes—
437C2×C4C2×C11×SD1612yes—
438C2×C4C11×#13712yes—
439C2×C4C2×C11×#4111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C2×C4C2×C11×#4111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C11×H(5,𝔽2)11yescharacteristic
444C2×C4C11×H(5,𝔽2)11yescharacteristic
445C8—42no—
446C8—41no—
447C8—41no—
448C22—24no—
449C22—24no—
450C22—24no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C2×C11×#12311yescharacteristic
456C22C11×#54611yescharacteristic
457C22C11×#54611yescharacteristic
458C22C22×C11×SD1611yescharacteristic
459C22C2×C11×#13711yescharacteristic
460C22C11×#57611yescharacteristic
461C22C11×#57811yescharacteristic
462C4—22no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4C11×#48314yes—
471C4C11×#52911yescharacteristic
472C4C11×#54011yescharacteristic
473C4C11×#55311yescharacteristic
474C4C11×#55511yescharacteristic
475C2—44no—
476C2C11×#242011yescharacteristic
477C2C2×C11×#48311yescharacteristic
478C2C11×#309811yescharacteristic
479C2C11×#329511yescharacteristic
480C2C11×#329811yescharacteristic
481C2C11×#332811yescharacteristic
482C2C11×#333311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×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
3. C11×#2077C2semidirect
4. C11×#2035C2semidirect
6. C11×#1948C2semidirect
7. C11×#1872C2semidirect
8. C11×#1834C2semidirect
9. C11×#1823C2semidirect
10. C11×#1803C2semidirect
11. C4×C11×#103C2semidirect
88. #24969C11direct (N × H)
155. #2077C2×C11semidirect
156. #2035C2×C11semidirect
158. #1948C2×C11semidirect
159. #1872C2×C11semidirect
160. #1834C2×C11semidirect
161. #1823C2×C11semidirect
162. #1803C2×C11semidirect
163. C4×#103C2×C11semidirect
393. C11#24969direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25382
D4×C11×C4⋊C42
C11×#20772
C11×#20352
C11×#19542
C11×#19482
C11×#18722
C11×#18342
C11×#18232
C11×#18032
C4×C11×#1032
#2496911