Finite Group Databasebeta

← C11×#23499 #14600692

Subgroups — C11×#23499 #14600692

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#421C212yesmaximal, complemented
3C11×#2896C212yesmaximal, complemented
4C11×#2317C211yesmaximal, characteristic, complemented
5C11×#2040C214yesmaximal, complemented
6C11×#2039C214yesmaximal, complemented
7C2×C11×#343C211yesmaximal, characteristic, complemented
8C22×C11×#41C2212yes—
9C22×C11×M16C2212yes—
10C11×#537—24no—
11C11×#537—22no—
12C11×#537C2214yes—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#121—22no—
15C2×C11×#121—22no—
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#421—28no—
20C2×C11×#104C2218yescomplemented
21C11×#419—22no—
22C11×#418—22no—
23C11×#417C2214yescomplemented
24C11×#417C2214yescomplemented
25C11×#416—24no—
26C11×#389—22no—
27C11×#385—22no—
28C11×#384C2212yescomplemented
29C11×#382C2212yescomplemented
30C11×#343C2214yescomplemented
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—24no—
37C2×C11×#41D414yes—
38C2×C11×#41C2314yes—
39C22×Q8×C11D412yes—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11D412yes—
43C23×C4×C11—22no—
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—22no—
47C2×C11×M16—24no—
48C2×C11×M16—24no—
49C2×C11×M16C2314yes—
50C22×C8×C11—22no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—28no—
53C11×#121—28no—
54C11×#121—28no—
55C11×#121—28no—
56C11×#121—28no—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117D414yescomplemented
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C11×#104—216no—
76C11×#103—24no—
77C11×#103—24no—
78C11×#102—24no—
79C11×#102—24no—
80C11×#95—24no—
81#23499C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—22no—
83C24×C11C2×D411yescharacteristic
84C11×#41—28no—
85C11×#41—28no—
86C11×#41—24no—
87C11×#41—24no—
88C11×#41—24no—
89C11×#41—24no—
90C11×#41—44no—
91C11×#41—44no—
92C11×#41—44no—
93C11×#41—44no—
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11C2×D414yes—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—28no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—84no—
107C2×D4×C11C2×D414yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—82no—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11#4114yes—
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C11×M16—24no—
128C11×M16—24no—
129C11×M16—44no—
130C2×C8×C11—24no—
131C2×C8×C11—44no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—84no—
139C11×C22⋊C4—216no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—22no—
144C42×C11—42no—
145C42×C11C2×D414yescomplemented
146C2×#537C2×C1111yescharacteristic
147C2×#421C2×C1112yescomplemented
148#2896C2×C1112yescomplemented
149#2317C2×C1111yescharacteristic, complemented
150#2040C2×C1114yescomplemented
151#2039C2×C1114yescomplemented
152C2×#343C2×C1111yescharacteristic, complemented
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—44no—
157C23×C11—44no—
158C23×C11—44no—
159C23×C11#12011yescharacteristic
160C23×C11#12011yescharacteristic
161C23×C11#12112yes—
162C23×C11#12412yes—
163C23×C11C22×D411yescharacteristic
164Q8×C11—24no—
165Q8×C11—24no—
166Q8×C11—44no—
167D4×C11—24no—
168D4×C11—24no—
169D4×C11—44no—
170D4×C11—44no—
171D4×C11—48no—
172D4×C11—44no—
173D4×C11—88no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—48no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—82no—
190C2×C4×C11#12012yes—
191C2×C4×C11#12114yes—
192C2×C4×C11#12114yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12314yes—
195C2×C4×C11#12314yes—
196C2×C4×C11#12412yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D412yes—
199C2×C4×C11C2×#4112yes—
200C2×C4×C11C2×#4111yescharacteristic
201C8×C11—44no—
202C22×#41C22×C1112yes—
203C22×M16C22×C1112yes—
204#537—24no—
205#537—22no—
206#537C22×C1114yes—
207C2×C22⋊Q8—22no—
208C2×#121—22no—
209C2×#121—22no—
210C2×#117C22×C1111yescharacteristic
211C2×#117C22×C1111yescharacteristic
212C22×C4⋊C4C22×C1111yescharacteristic
213#421—28no—
214C2×#104C22×C1118yescomplemented
215#419—22no—
216#418—22no—
217#417C22×C1114yescomplemented
218#417C22×C1114yescomplemented
219#416—24no—
220#389—22no—
221#385—22no—
222#384C22×C1112yescomplemented
223#382C22×C1112yescomplemented
224#343C22×C1114yescomplemented
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—88no—
237C22×C11#39412yes—
238C22×C11#39412yes—
239C22×C11C2×#12011yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11C2×#12411yescharacteristic
242C4×C11—44no—
243C4×C11—44no—
244C4×C11—44no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11#39414yes—
248C4×C11C2×#12112yes—
249C4×C11C2×#12312yes—
250C2×#41—22no—
251C2×#41—22no—
252C2×#41—24no—
253C2×#41—24no—
254C2×#41—24no—
255C2×#41—24no—
256C2×#41D4×C1114yes—
257C2×#41C23×C1114yes—
258C22×Q8D4×C1112yes—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4D4×C1112yes—
262C23×C4—22no—
263C23×C4D4×C1112yes—
264C23×C4C23×C1111yescharacteristic
265C2×M16—22no—
266C2×M16—24no—
267C2×M16—24no—
268C2×M16C23×C1114yes—
269C22×C8—22no—
270C22⋊Q8—28no—
271C22⋊Q8—28no—
272#121—28no—
273#121—28no—
274#121—28no—
275#121—28no—
276#117—22no—
277#117—22no—
278#117—22no—
279#117D4×C1114yescomplemented
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4D4×C1112yes—
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1112yes—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C42—21no—
293C2×C42C23×C1112yes—
294#104—216no—
295#103—24no—
296#103—24no—
297#102—24no—
298#102—24no—
299#95—24no—
300C2×C11—21no—
301C2×C11—22no—
302C2×C11—21no—
303C2×C11—22no—
304C2×C11—84no—
305C2×C11C2×#39411yescharacteristic
306C2×C11#301911yescharacteristic
307C2×C11#302011yescharacteristic
308C24—22no—
309C24C2×D4×C1111yescharacteristic
310#41—28no—
311#41—28no—
312#41—24no—
313#41—24no—
314#41—24no—
315#41—24no—
316#41—44no—
317#41—44no—
318#41—44no—
319#41—44no—
320C2×Q8—22no—
321C2×Q8—24no—
322C2×Q8—24no—
323C2×Q8C2×D4×C1114yes—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—28no—
327C2×D4—22no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—84no—
333C2×D4C2×D4×C1114yes—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—82no—
345C22×C4C2×D4×C1114yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1112yes—
350C22×C4C11×#4114yes—
351C22×C4C11×#4112yes—
352C22×C4C24×C1111yescharacteristic
353M16—24no—
354M16—24no—
355M16—44no—
356C2×C8—24no—
357C2×C8—44no—
358C4⋊C4—28no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—84no—
365C22⋊C4—216no—
366C22⋊C4—24no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42—22no—
370C42—42no—
371C42C2×D4×C1114yescomplemented
372C11#2349911yescharacteristic, direct product factor, Sylow
373C23—24no—
374C23—41no—
375C23—41no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23C11×#12011yescharacteristic
380C23C11×#12011yescharacteristic
381C23C11×#12112yes—
382C23C11×#12412yes—
383C23C22×D4×C1111yescharacteristic
384Q8—24no—
385Q8—24no—
386Q8—44no—
387D4—24no—
388D4—24no—
389D4—44no—
390D4—44no—
391D4—48no—
392D4—44no—
393D4—88no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—48no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4C11×#12012yes—
411C2×C4C11×#12114yes—
412C2×C4C11×#12114yes—
413C2×C4C11×#12112yes—
414C2×C4C11×#12314yes—
415C2×C4C11×#12314yes—
416C2×C4C11×#12412yes—
417C2×C4C22×D4×C1111yescharacteristic
418C2×C4C22×D4×C1112yes—
419C2×C4C2×C11×#4112yes—
420C2×C4C2×C11×#4111yescharacteristic
421C8—44no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—42no—
429C22—42no—
430C22—44no—
431C22—44no—
432C22—44no—
433C22—88no—
434C22C11×#39412yes—
435C22C11×#39412yes—
436C22C2×C11×#12011yescharacteristic
437C22C2×C11×#12111yescharacteristic
438C22C2×C11×#12411yescharacteristic
439C4—44no—
440C4—44no—
441C4—44no—
442C4—81no—
443C4—81no—
444C4C11×#39414yes—
445C4C2×C11×#12112yes—
446C4C2×C11×#12312yes—
447C2—21no—
448C2—22no—
449C2—21no—
450C2—22no—
451C2—84no—
452C2C2×C11×#39411yescharacteristic
453C2C11×#301911yescharacteristic
454C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
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. C2×C11×#421C2semidirect
3. C11×#2896C2semidirect
4. C11×#2317C2semidirect
5. C11×#2040C2semidirect
6. C11×#2039C2semidirect
7. C2×C11×#343C2semidirect
20. C2×C11×#104C22semidirect
23. C11×#417C22semidirect
24. C11×#417C22semidirect
28. C11×#384C22semidirect
29. C11×#382C22semidirect
30. C11×#343C22semidirect
60. C11×#117D4semidirect
81. #23499C11direct (N × H)
145. C42×C11C2×D4semidirect
147. C2×#421C2×C11semidirect
148. #2896C2×C11semidirect
149. #2317C2×C11semidirect
150. #2040C2×C11semidirect
151. #2039C2×C11semidirect
152. C2×#343C2×C11semidirect
214. C2×#104C22×C11semidirect
217. #417C22×C11semidirect
218. #417C22×C11semidirect
222. #384C22×C11semidirect
223. #382C22×C11semidirect
224. #343C22×C11semidirect
279. #117D4×C11semidirect
371. C42C2×D4×C11semidirect
372. C11#23499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4212
C11×#28962
C11×#23172
C11×#20402
C11×#20392
C2×C11×#3432
#2349911