Finite Group Databasebeta

← C11×#23949 #14601142

Subgroups — C11×#23949 #14601142

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic
2C11×#3004C212yesmaximal, complemented
3C2×C11×#391C211yesmaximal, characteristic, complemented
4C11×#2028C212yesmaximal, complemented
5C11×#2007C212yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1882C214yesmaximal, complemented
8C11×#1821C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C2×C11×#137C2214yes—
11C11×#554—22no—
12C11×#553—22no—
13C11×#552—22no—
14C11×#547—22no—
15C11×#544C2211yescharacteristic
16C11×#539—22no—
17C11×#537C2211yescharacteristic
18C11×#525—22no—
19C11×#525C2212yes—
20C11×#520C2212yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#451—22no—
24C11×#451—22no—
25C11×#448—22no—
26C11×#448—22no—
27C2×C11×#104C2214yes—
28C11×#419C2214yes—
29C11×#407C2212yes—
30C11×#391—22no—
31C11×#391C2212yes—
32C11×#391C2212yes—
33C2×C11×#95—22no—
34C11×#343C2212yes—
35C11×#343C2212yes—
36C11×#339C2214yes—
37C2×C11×#41—22no—
38C2×C11×#41C2312yes—
39C22×Q8×C11—24no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—42no—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C11×#137—28no—
50C11×#137—44no—
51C2×C11×Q16—24no—
52C2×C11×SD16—24no—
53C2×C11×M16C2314yes—
54C11×C4⋊Q8—22no—
55C11×#126—24no—
56C11×#125—24no—
57C11×#125—22no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D412yes—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121D412yes—
71C11×#121D412yes—
72C11×#120—22no—
73C4×Q8×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11—24no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11—42no—
90C2×C42×C11C2312yes—
91C11×#104—44no—
92C11×#103—24no—
93C11×#103—24no—
94C11×C22⋊C8—22no—
95C11×C22⋊C8—22no—
96C11×#95—24no—
97C11×#95—24no—
98#23949C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D411yescharacteristic
100C11×#41—24no—
101C11×#41—24no—
102C11×#41—84no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—48no—
109C2×Q8×C11—48no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4114yescomplemented
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—44no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C11×Q16—48no—
142C11×SD16—48no—
143C11×M16—24no—
144C11×M16—24no—
145C2×C8×C11—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—24no—
165C42×C11—22no—
166C42×C11—24no—
167C42×C11—42no—
168#3492C2×C1111yescharacteristic
169#3004C2×C1112yescomplemented
170C2×#391C2×C1111yescharacteristic, complemented
171#2028C2×C1112yescomplemented
172#2007C2×C1112yescomplemented
173#1896C2×C1112yescomplemented
174#1882C2×C1114yescomplemented
175#1821C2×C1111yescharacteristic, complemented
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11#12011yescharacteristic
182C23×C11#12011yescharacteristic
183C23×C11C22×D411yescharacteristic
184Q8×C11—28no—
185Q8×C11—24no—
186Q8×C11—48no—
187Q8×C11—44no—
188Q8×C11—82no—
189D4×C11—24no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—44no—
193D4×C11—44no—
194D4×C11—82no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—84no—
219C2×C4×C11#12012yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C2×#4112yes—
222C2×C4×C11H(5,𝔽2)12yes—
223C8×C11—44no—
224C23×Q8C22×C1111yescharacteristic
225C2×#137C22×C1114yes—
226#554—22no—
227#553—22no—
228#552—22no—
229#547—22no—
230#544C22×C1111yescharacteristic
231#539—22no—
232#537C22×C1111yescharacteristic
233#525—22no—
234#525C22×C1112yes—
235#520C22×C1112yes—
236C22×C4⋊C4C22×C1111yescharacteristic
237C22×C42C22×C1111yescharacteristic
238#451—22no—
239#451—22no—
240#448—22no—
241#448—22no—
242C2×#104C22×C1114yes—
243#419C22×C1114yes—
244#407C22×C1112yes—
245#391—22no—
246#391C22×C1112yes—
247#391C22×C1112yes—
248C2×#95—22no—
249#343C22×C1112yes—
250#343C22×C1112yes—
251#339C22×C1114yes—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11#45512yes—
264C22×C11#45612yes—
265C22×C11C2×#12011yescharacteristic
266C22×C11#52511yescharacteristic
267C22×C11#53511yescharacteristic
268C4×C11—22no—
269C4×C11—44no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11#54614yes—
277C2×#41—22no—
278C2×#41C23×C1112yes—
279C22×Q8—24no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—42no—
284C22×Q8C23×C1112yes—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4D4×C1112yes—
288C23×C4C23×C1111yescharacteristic
289#137—28no—
290#137—44no—
291C2×Q16—24no—
292C2×SD16—24no—
293C2×M16C23×C1114yes—
294C4⋊Q8—22no—
295#126—24no—
296#125—24no—
297#125—22no—
298#123—24no—
299#123—24no—
300#123—22no—
301C22⋊Q8—22no—
302C22⋊Q8—24no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8D4×C1112yes—
306C22⋊Q8D4×C1112yes—
307#121—22no—
308#121—22no—
309#121—22no—
310#121D4×C1112yes—
311#121D4×C1112yes—
312#120—22no—
313C4×Q8—22no—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—22no—
318C4×D4—22no—
319#117—22no—
320#117—22no—
321#117C23×C1112yes—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4D4×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C42—21no—
329C2×C42—42no—
330C2×C42C23×C1112yes—
331#104—44no—
332#103—24no—
333#103—24no—
334C22⋊C8—22no—
335C22⋊C8—22no—
336#95—24no—
337#95—24no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—22no—
341C2×C11—22no—
342C2×C11—82no—
343C2×C11#240411yescharacteristic
344C2×C11C2×#45511yescharacteristic
345C2×C11C2×#45611yescharacteristic
346C24C2×D4×C1111yescharacteristic
347#41—24no—
348#41—24no—
349#41—84no—
350C2×Q8—24no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—24no—
354C2×Q8—24no—
355C2×Q8—48no—
356C2×Q8—48no—
357C2×Q8—42no—
358C2×Q8—42no—
359C2×Q8C2×D4×C1112yes—
360C2×Q8C11×#4114yescomplemented
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4C2×D4×C1112yes—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—44no—
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1112yes—
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1112yes—
387C22×C4C24×C1111yescharacteristic
388Q16—48no—
389SD16—48no—
390M16—24no—
391M16—24no—
392C2×C8—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4C2×D4×C1112yes—
403C4⋊C4C2×D4×C1112yes—
404C22⋊C4—24no—
405C22⋊C4—24no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C42—24no—
412C42—22no—
413C42—24no—
414C42—42no—
415C11#2394911yescharacteristic, direct product factor, Sylow
416C23—21no—
417C23—21no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23C11×#12011yescharacteristic
422C23C11×#12011yescharacteristic
423C23C22×D4×C1111yescharacteristic
424Q8—28no—
425Q8—24no—
426Q8—48no—
427Q8—44no—
428Q8—82no—
429D4—24no—
430D4—42no—
431D4—42no—
432D4—44no—
433D4—44no—
434D4—82no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—48no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—82no—
458C2×C4—84no—
459C2×C4C11×#12012yes—
460C2×C4C22×D4×C1112yes—
461C2×C4C2×C11×#4112yes—
462C2×C4C11×H(5,𝔽2)12yes—
463C8—44no—
464C22—24no—
465C22—24no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22C11×#45512yes—
476C22C11×#45612yes—
477C22C2×C11×#12011yescharacteristic
478C22C11×#52511yescharacteristic
479C22C11×#53511yescharacteristic
480C4—22no—
481C4—44no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4C11×#54614yes—
489C2—21no—
490C2—21no—
491C2—22no—
492C2—22no—
493C2—82no—
494C2C11×#240411yescharacteristic
495C2C2×C11×#45511yescharacteristic
496C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3004C2semidirect
3. C2×C11×#391C2semidirect
4. C11×#2028C2semidirect
5. C11×#2007C2semidirect
6. C11×#1896C2semidirect
7. C11×#1882C2semidirect
8. C11×#1821C2semidirect
98. #23949C11direct (N × H)
113. C2×Q8×C11#41semidirect
169. #3004C2×C11semidirect
170. C2×#391C2×C11semidirect
171. #2028C2×C11semidirect
172. #2007C2×C11semidirect
173. #1896C2×C11semidirect
174. #1882C2×C11semidirect
175. #1821C2×C11semidirect
360. C2×Q8C11×#41semidirect
415. C11#23949direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30042
C2×C11×#3912
C11×#20282
C11×#20072
C11×#18962
C11×#18822
C11×#18212
#2394911