Finite Group Databasebeta

← C11×#23953 #14601146

Subgroups — C11×#23953 #14601146

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic
2C11×#3004C212yesmaximal, complemented
3C11×#2310C211yesmaximal, characteristic, complemented
4C11×#2028C212yesmaximal, complemented
5C11×#2007C212yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1882C214yesmaximal, complemented
8C11×#1822C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C2×C11×#137C2214yes—
11C11×#556—22no—
12C11×#555—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#544C2211yescharacteristic
16C11×#538—22no—
17C11×#537C2211yescharacteristic
18C11×#529—22no—
19C11×#525C2212yes—
20C11×#520C2212yes—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
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—
33C11×#381—22no—
34C11×#343C2212yes—
35C11×#343C2212yes—
36C11×#339C2214yes—
37C2×C11×#41C2312yes—
38C22×Q8×C11—24no—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—42no—
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C11×#137—28no—
47C11×#137—44no—
48C2×C11×Q16—24no—
49C2×C11×SD16—24no—
50C2×C11×M16C2314yes—
51C11×C4⋊Q8—22no—
52C11×#126—24no—
53C11×#126—24no—
54C11×#125—22no—
55C11×#125—22no—
56C11×#124—22no—
57C11×#124—24no—
58C11×#123—24no—
59C11×#123—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8D412yes—
63C11×C22⋊Q8D412yes—
64C11×#121—24no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121D412yes—
68C11×#121D412yes—
69C11×#120—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—24no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117—42no—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11D412yes—
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#23953C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D411yescharacteristic
100C11×#41—24no—
101C11×#41—24no—
102C2×Q8×C11—24no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—24no—
107C2×Q8×C11—48no—
108C2×Q8×C11—48no—
109C2×Q8×C11—42no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4114yes—
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—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2411yescharacteristic
134C11×Q16—48no—
135C11×SD16—48no—
136C11×M16—24no—
137C11×M16—24no—
138C2×C8×C11—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—42no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—24no—
164#3493C2×C1111yescharacteristic
165#3004C2×C1112yescomplemented
166#2310C2×C1111yescharacteristic, complemented
167#2028C2×C1112yescomplemented
168#2007C2×C1112yescomplemented
169#1897C2×C1112yescomplemented
170#1882C2×C1114yescomplemented
171#1822C2×C1111yescharacteristic, complemented
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11#12012yes—
178C23×C11C22×D411yescharacteristic
179Q8×C11—28no—
180Q8×C11—24no—
181Q8×C11—44no—
182Q8×C11—44no—
183Q8×C11—44no—
184Q8×C11—82no—
185D4×C11—24no—
186D4×C11—42no—
187D4×C11—42no—
188D4×C11—82no—
189D4×C11—82no—
190D4×C11—82no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
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#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11C22×D412yes—
214C2×C4×C11C2×#4112yes—
215C2×C4×C11H(5,𝔽2)12yes—
216C8×C11—44no—
217C23×Q8C22×C1111yescharacteristic
218C2×#137C22×C1114yes—
219#556—22no—
220#555—22no—
221#553—22no—
222#552—22no—
223#544C22×C1111yescharacteristic
224#538—22no—
225#537C22×C1111yescharacteristic
226#529—22no—
227#525C22×C1112yes—
228#520C22×C1112yes—
229C2×#117C22×C1111yescharacteristic
230C2×#117C22×C1111yescharacteristic
231#451—22no—
232#451—22no—
233#448—22no—
234#448—22no—
235C2×#104C22×C1114yes—
236#419C22×C1114yes—
237#407C22×C1112yes—
238#391—22no—
239#391C22×C1112yes—
240#391C22×C1112yes—
241#381—22no—
242#343C22×C1112yes—
243#343C22×C1112yes—
244#339C22×C1114yes—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11C2×#12011yescharacteristic
256C22×C11#52511yescharacteristic
257C22×C11#53511yescharacteristic
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—44no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—82no—
267C4×C11#54614yes—
268C2×#41C23×C1112yes—
269C22×Q8—24no—
270C22×Q8—21no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—42no—
274C22×Q8C23×C1112yes—
275C23×C4—21no—
276C23×C4C23×C1111yescharacteristic
277#137—28no—
278#137—44no—
279C2×Q16—24no—
280C2×SD16—24no—
281C2×M16C23×C1114yes—
282C4⋊Q8—22no—
283#126—24no—
284#126—24no—
285#125—22no—
286#125—22no—
287#124—22no—
288#124—24no—
289#123—24no—
290#123—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8D4×C1112yes—
294C22⋊Q8D4×C1112yes—
295#121—24no—
296#121—22no—
297#121—22no—
298#121D4×C1112yes—
299#121D4×C1112yes—
300#120—22no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—24no—
306C4×D4—22no—
307C4×D4—22no—
308#117—24no—
309#117—22no—
310#117—22no—
311#117—22no—
312#117—42no—
313#117C23×C1112yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4D4×C1112yes—
320C2×C42D4×C1112yes—
321C2×C42C23×C1112yes—
322#104—44no—
323#103—24no—
324#103—24no—
325C22⋊C8—22no—
326C22⋊C8—22no—
327#95—24no—
328#95—24no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—42no—
332C2×C11—82no—
333C2×C11#240411yescharacteristic
334C2×C11#302211yescharacteristic
335C2×C11#302211yescharacteristic
336C24C2×D4×C1111yescharacteristic
337#41—24no—
338#41—24no—
339C2×Q8—24no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—24no—
343C2×Q8—24no—
344C2×Q8—48no—
345C2×Q8—48no—
346C2×Q8—42no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8C2×D4×C1112yes—
350C2×Q8C11×#4114yes—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4C2×D4×C1112yes—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1112yes—
367C22×C4C2×D4×C1112yes—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1112yes—
370C22×C4C24×C1111yescharacteristic
371Q16—48no—
372SD16—48no—
373M16—24no—
374M16—24no—
375C2×C8—24no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4C2×D4×C1112yes—
386C4⋊C4C2×D4×C1112yes—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—42no—
396C42—24no—
397C42—22no—
398C42—22no—
399C42—22no—
400C42—24no—
401C11#2395311yescharacteristic, direct product factor, Sylow
402C23—21no—
403C23—21no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23C11×#12012yes—
408C23C22×D4×C1111yescharacteristic
409Q8—28no—
410Q8—24no—
411Q8—44no—
412Q8—44no—
413Q8—44no—
414Q8—82no—
415D4—24no—
416D4—42no—
417D4—42no—
418D4—82no—
419D4—82no—
420D4—82no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—48no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—84no—
441C2×C4C11×#12011yescharacteristic
442C2×C4C11×#12011yescharacteristic
443C2×C4C22×D4×C1112yes—
444C2×C4C2×C11×#4112yes—
445C2×C4C11×H(5,𝔽2)12yes—
446C8—44no—
447C22—21no—
448C22—21no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22C2×C11×#12011yescharacteristic
458C22C11×#52511yescharacteristic
459C22C11×#53511yescharacteristic
460C4—21no—
461C4—21no—
462C4—44no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—82no—
469C4C11×#54614yes—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—82no—
474C2C11×#240411yescharacteristic
475C2C11×#302211yescharacteristic
476C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3493C2
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. C11×#2310C2semidirect
4. C11×#2028C2semidirect
5. C11×#2007C2semidirect
6. C11×#1897C2semidirect
7. C11×#1882C2semidirect
8. C11×#1822C2semidirect
98. #23953C11direct (N × H)
165. #3004C2×C11semidirect
166. #2310C2×C11semidirect
167. #2028C2×C11semidirect
168. #2007C2×C11semidirect
169. #1897C2×C11semidirect
170. #1882C2×C11semidirect
171. #1822C2×C11semidirect
401. C11#23953direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#30042
C11×#23102
C11×#20282
C11×#20072
C11×#18972
C11×#18822
C11×#18222
#2395311