Finite Group Databasebeta

← C11×#24203 #14601396

Subgroups — C11×#24203 #14601396

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic
3C2×C11×#441C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic
5C11×#2043C212yesmaximal
6C11×#2016C212yesmaximal
7C11×#1985C211yesmaximal, characteristic
8C11×#1960C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1865C212yesmaximal
11C11×#1805C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C11×#557—24no—
15C11×#557—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—22no—
19C2×C11×#125—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#462—24no—
26C11×#441—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#97C2211yescharacteristic
36C11×#400—21no—
37C11×#395—21no—
38C11×#391C2212yes—
39C11×#389C2212yes—
40C11×#387—22no—
41C11×#382C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—24no—
52C2×C11×Q16—24no—
53C2×C11×Q16—22no—
54C2×C11×Q16—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yes—
62C11×#125—216no—
63C11×#125—28no—
64C4×Q8×C11—28no—
65C4×Q8×C11—24no—
66C4×Q8×C11—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11D414yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C42×C11—22no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2312yes—
90C2×C42×C11C2311yescharacteristic
91C11×#106—22no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#103—24no—
96C11×#103—22no—
97C11×#103—42no—
98C11×#103—42no—
99C11×#97—22no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#24203C1111yesmaximal, characteristic, direct product factor, Sylow
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11C2×D414yes—
124C2×Q8×C11C2×D412yes—
125C2×Q8×C11#4112yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2411yescharacteristic
137C11×Q16—28no—
138C11×Q16—48no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11#4112yes—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4C2×D412yes—
164C42×C11—28no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—42no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C2×#557C2×C1111yescharacteristic
172C2×#462C2×C1111yescharacteristic
173C2×#441C2×C1111yescharacteristic
174#2581C2×C1111yescharacteristic
175#2043C2×C1112yes—
176#2016C2×C1112yes—
177#1985C2×C1111yescharacteristic
178#1960C2×C1111yescharacteristic
179#1878C2×C1112yes—
180#1865C2×C1112yes—
181#1805C2×C1111yescharacteristic
182C23×C11C22×D411yescharacteristic
183Q8×C11—28no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—24no—
189Q8×C11—24no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—41no—
195Q8×C11—41no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11#12012yes—
219C2×C4×C11#12012yes—
220C2×C4×C11#13714yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C8×C11—22no—
228C8×C11—41no—
229C8×C11—42no—
230C22×Q16C22×C1111yescharacteristic
231C22×Q16C22×C1112yes—
232#557—24no—
233#557—24no—
234C2×C4⋊Q8C22×C1112yes—
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×#125—22no—
237C2×#125—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8C22×C1111yescharacteristic
240C2×C4×Q8C22×C1112yes—
241C2×C4×Q8C22×C1111yescharacteristic
242C2×C4×Q8C22×C1111yescharacteristic
243#462—24no—
244#441—24no—
245C2×#106C22×C1111yescharacteristic
246C2×C4⋊C8C22×C1111yescharacteristic
247C2×#103C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×#103C22×C1111yescharacteristic
250C2×#103C22×C1111yescharacteristic
251C2×#103C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×#97C22×C1111yescharacteristic
254#400—21no—
255#395—21no—
256#391C22×C1112yes—
257#389C22×C1112yes—
258#387—22no—
259#382C22×C1111yescharacteristic
260#340C22×C1112yes—
261#336C22×C1112yes—
262#336C22×C1112yes—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11#55011yescharacteristic
266C22×C11C2×#13712yes—
267C22×C11#57812yes—
268C4×C11—22no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—82no—
277C4×C11—81no—
278C4×C11#52511yescharacteristic
279C4×C11#53711yescharacteristic
280C4×C11#54611yescharacteristic
281C4×C11#54711yescharacteristic
282C22×Q8D4×C1111yescharacteristic
283C22×Q8C23×C1112yes—
284C22×Q8C23×C1111yescharacteristic
285C22×Q8C23×C1111yescharacteristic
286C2×Q16—22no—
287C2×Q16—22no—
288C2×Q16—24no—
289C2×Q16—24no—
290C2×Q16—22no—
291C2×Q16—42no—
292C22×C8C23×C1112yes—
293C22×C8C23×C1111yescharacteristic
294C22×C8C23×C1111yescharacteristic
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8D4×C1114yes—
299#125—216no—
300#125—28no—
301C4×Q8—28no—
302C4×Q8—24no—
303C4×Q8—24no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8D4×C1114yes—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4D4×C1112yes—
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C4⋊C4C23×C1112yes—
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C42—22no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42C23×C1112yes—
327C2×C42C23×C1111yescharacteristic
328#106—22no—
329C4⋊C8—22no—
330#103—22no—
331#103—24no—
332#103—24no—
333#103—22no—
334#103—42no—
335#103—42no—
336#97—22no—
337#95—21no—
338#95—21no—
339#95—22no—
340#95—22no—
341#95—22no—
342C2×C11#240711yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#301111yescharacteristic
345C2×C11#337412yes—
346C2×C11#339812yes—
347C2×Q8—22no—
348C2×Q8—24no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8C2×D4×C1114yes—
365C2×Q8C2×D4×C1112yes—
366C2×Q8C11×#4112yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1112yes—
377C22×C4C24×C1111yescharacteristic
378Q16—28no—
379Q16—48no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—21no—
388C2×C8C11×#4112yes—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—44no—
404C4⋊C4C2×D4×C1112yes—
405C42—28no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—42no—
410C42C2×D4×C1112yes—
411C42C2×D4×C1112yes—
412C11#2420311yescharacteristic, direct product factor, Sylow
413C23C22×D4×C1111yescharacteristic
414Q8—28no—
415Q8—22no—
416Q8—22no—
417Q8—22no—
418Q8—22no—
419Q8—24no—
420Q8—24no—
421Q8—42no—
422Q8—42no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4C11×#12012yes—
450C2×C4C11×#12012yes—
451C2×C4C11×#13714yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C2×C11×#4111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C11×H(5,𝔽2)11yescharacteristic
457C2×C4C11×2−1+411yescharacteristic
458C8—22no—
459C8—41no—
460C8—42no—
461C22C2×C11×#12011yescharacteristic
462C22C11×#54811yescharacteristic
463C22C11×#55011yescharacteristic
464C22C2×C11×#13712yes—
465C22C11×#57812yes—
466C4—22no—
467C4—24no—
468C4—22no—
469C4—42no—
470C4—44no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—81no—
475C4—82no—
476C4C11×#52511yescharacteristic
477C4C11×#53711yescharacteristic
478C4C11×#54611yescharacteristic
479C4C11×#54711yescharacteristic
480C2C11×#240711yescharacteristic
481C2C11×#300411yescharacteristic
482C2C11×#301111yescharacteristic
483C2C11×#337412yes—
484C2C11×#339812yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
105. #24203C11direct (N × H)
412. C11#24203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4622
C2×C11×#4412
C11×#25812
C11×#20432
C11×#20162
C11×#19852
C11×#19602
C11×#18782
C11×#18652
C11×#18052
#2420311