Finite Group Databasebeta

← C11×#24646 #14601839

Subgroups — C11×#24646 #14601839

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic
5C11×#2055C212yesmaximal
6C11×#2013C212yesmaximal
7C11×#1981C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1928C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#461—24no—
19C11×#440—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#398—21no—
31C11×#398—21no—
32C11×#391C2212yes—
33C11×#390C2212yes—
34C11×#389—22no—
35C11×#388—22no—
36C11×#382C2211yescharacteristic
37C11×#381—21no—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—24no—
50C2×C11×SD16—22no—
51C2×C11×SD16—42no—
52C2×C11×SD16—42no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—42no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#107—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—42no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#103—42no—
87C11×#103—42no—
88C11×#102—22no—
89C11×#97—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24646C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11#4112yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—82no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C11×SD16—28no—
130C11×SD16—48no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11#4112yes—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—82no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—42no—
158C42×C11—82no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161C2×#461C2×C1111yescharacteristic
162C2×#440C2×C1111yescharacteristic
163#2546C2×C1111yescharacteristic, complemented
164#2357C2×C1111yescharacteristic
165#2055C2×C1112yes—
166#2013C2×C1112yes—
167#1981C2×C1112yescomplemented
168#1960C2×C1111yescharacteristic, complemented
169#1940C2×C1111yescharacteristic, complemented
170#1928C2×C1112yescomplemented
171#1805C2×C1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11C22×D411yescharacteristic
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—41no—
181Q8×C11—41no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—42no—
185Q8×C11—42no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—41no—
189D4×C11—41no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—84no—
211C2×C4×C11#12112yes—
212C2×C4×C11#12112yes—
213C2×C4×C11#13714yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C8×C11—22no—
221C8×C11—41no—
222C8×C11—42no—
223C22×SD16C22×C1111yescharacteristic
224C22×SD16C22×C1112yes—
225C2×C4⋊Q8C22×C1111yescharacteristic
226C2×C4⋊Q8C22×C1112yes—
227C2×C4×Q8C22×C1111yescharacteristic
228C2×C4×D4C22×C1111yescharacteristic
229#461—24no—
230#440—24no—
231C2×#107C22×C1111yescharacteristic
232C2×C4⋊C8C22×C1111yescharacteristic
233C2×C4⋊C8C22×C1112yes—
234C2×#103C22×C1111yescharacteristic
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×#103C22×C1112yes—
238C2×#103C22×C1112yes—
239C2×#102C22×C1111yescharacteristic
240C2×#97C22×C1111yescharacteristic
241#398—21no—
242#398—21no—
243#391C22×C1112yes—
244#390C22×C1112yes—
245#389—22no—
246#388—22no—
247#382C22×C1111yescharacteristic
248#381—21no—
249C4×C4⋊C4C22×C1112yes—
250C4×C4⋊C4C22×C1111yescharacteristic
251C4×C22⋊C4—21no—
252#340C22×C1112yes—
253#336C22×C1112yes—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11C2×#12111yescharacteristic
260C22×C11#54611yescharacteristic
261C22×C11#55011yescharacteristic
262C22×C11C2×#13712yes—
263C22×C11#57712yes—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—24no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11—82no—
272C4×C11—81no—
273C4×C11#52511yescharacteristic
274C4×C11#53511yescharacteristic
275C4×C11#55311yescharacteristic
276C4×C11#55511yescharacteristic
277C22×Q8C23×C1112yes—
278C22×Q8C23×C1111yescharacteristic
279C22×D4C23×C1111yescharacteristic
280C23×C4—21no—
281C2×SD16—22no—
282C2×SD16—22no—
283C2×SD16—24no—
284C2×SD16—22no—
285C2×SD16—42no—
286C2×SD16—42no—
287C22×C8C23×C1112yes—
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1111yescharacteristic
290C4⋊Q8—24no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4⋊Q8—42no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×D4—22no—
297C4×D4D4×C1114yes—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C1112yes—
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C4⋊C4C23×C1112yes—
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C42—21no—
311C2×C42—22no—
312C2×C42C23×C1112yes—
313C2×C42C23×C1111yescharacteristic
314#107—22no—
315C4⋊C8—22no—
316C4⋊C8—42no—
317#103—24no—
318#103—22no—
319#103—24no—
320#103—42no—
321#103—42no—
322#102—22no—
323#97—22no—
324#95—21no—
325#95—22no—
326#95—21no—
327#95—22no—
328#95—22no—
329#95D4×C1111yescharacteristic
330#95D4×C1111yescharacteristic
331C2×C11—82no—
332C2×C11#241411yescharacteristic
333C2×C11#303911yescharacteristic
334C2×C11#304211yescharacteristic
335C2×C11#332012yes—
336C2×C11#340012yes—
337C24—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8C11×#4112yes—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4C2×D4×C1112yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—82no—
363C22×C4C2×D4×C1112yes—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1112yes—
367C22×C4C24×C1111yescharacteristic
368SD16—28no—
369SD16—48no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—22no—
378C2×C8C11×#4112yes—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—44no—
386C4⋊C4—44no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4C2×D4×C1112yes—
391C22⋊C4—24no—
392C22⋊C4—44no—
393C22⋊C4—82no—
394C42—22no—
395C42—22no—
396C42—42no—
397C42—82no—
398C42C2×D4×C1112yes—
399C42C11×#4112yes—
400C11#2464611yescharacteristic, direct product factor, Sylow
401C23—22no—
402C23—41no—
403C23—41no—
404C23—42no—
405C23—42no—
406C23C22×D4×C1111yescharacteristic
407Q8—22no—
408Q8—22no—
409Q8—41no—
410Q8—41no—
411Q8—42no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415D4—22no—
416D4—22no—
417D4—41no—
418D4—41no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—84no—
440C2×C4C11×#12112yes—
441C2×C4C11×#12112yes—
442C2×C4C11×#13714yes—
443C2×C4C22×D4×C1111yescharacteristic
444C2×C4C2×C11×#4111yescharacteristic
445C2×C4C2×C11×#4111yescharacteristic
446C2×C4C2×C11×#4111yescharacteristic
447C2×C4C11×H(5,𝔽2)11yescharacteristic
448C2×C4C11×H(5,𝔽2)11yescharacteristic
449C8—22no—
450C8—42no—
451C8—41no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—82no—
456C22—82no—
457C22C2×C11×#12111yescharacteristic
458C22C11×#54611yescharacteristic
459C22C11×#55011yescharacteristic
460C22C2×C11×#13712yes—
461C22C11×#57712yes—
462C4—22no—
463C4—22no—
464C4—24no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—82no—
469C4—81no—
470C4—82no—
471C4C11×#52511yescharacteristic
472C4C11×#53511yescharacteristic
473C4C11×#55311yescharacteristic
474C4C11×#55511yescharacteristic
475C2—82no—
476C2C11×#241411yescharacteristic
477C2C11×#303911yescharacteristic
478C2C11×#304211yescharacteristic
479C2C11×#332012yes—
480C2C11×#340012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×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
3. C11×#2546C2semidirect
7. C11×#1981C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
10. C11×#1928C2semidirect
11. C11×#1805C2semidirect
97. #24646C11direct (N × H)
163. #2546C2×C11semidirect
167. #1981C2×C11semidirect
168. #1960C2×C11semidirect
169. #1940C2×C11semidirect
170. #1928C2×C11semidirect
171. #1805C2×C11semidirect
400. C11#24646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C11×#4402
C11×#25462
C11×#23572
C11×#20552
C11×#20132
C11×#19812
C11×#19602
C11×#19402
C11×#19282
C11×#18052
#2464611