Finite Group Databasebeta

← C11×#23914 #14601107

Subgroups — C11×#23914 #14601107

Order 2816.

1706 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
1C11×#3485C211yesmaximal, characteristic
2C2×C11×#536C211yesmaximal, characteristic, complemented
3C2×C11×#455C212yesmaximal, complemented
4C11×#3004C212yesmaximal, complemented
5C11×#2005C214yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1885C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic, complemented
12C2×C11×#137C2214yes—
13C11×#547—24no—
14C11×#546—24no—
15C11×#536—28no—
16C11×#536C2212yes—
17C11×#534—22no—
18C2×C11×C4⋊Q8C2212yescomplemented
19C2×C11×#124C2212yes—
20C11×#525C2212yes—
21C2×C11×#123—22no—
22C2×C11×#123—22no—
23C2×C11×C22⋊Q8—22no—
24C11×#518C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic, complemented
26C11×#455—28no—
27C11×#451—24no—
28C11×#448—24no—
29C2×C11×#104C2214yes—
30C11×#419C2214yescomplemented
31C2×C11×#101C2212yescomplemented
32C2×C11×#100C2212yes—
33C11×#407C2212yescomplemented
34C11×#339C2214yescomplemented
35C11×H(5,𝔽2)—24no—
36C11×H(5,𝔽2)—42no—
37C2×C11×#41—22no—
38C2×C11×#41—24no—
39C2×C11×#41—24no—
40C2×C11×#41—42no—
41C2×C11×#41C2312yes—
42C22×Q8×C11—24no—
43C22×Q8×C11—21no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11D412yes—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D412yes—
54C23×C4×C11C2311yescharacteristic
55C11×#137—28no—
56C11×#137—44no—
57C2×C11×Q16—24no—
58C2×C11×SD16—24no—
59C2×C11×M16C2314yes—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—24no—
63C11×#124—24no—
64C11×#124—22no—
65C11×#124D418yescomplemented
66C11×#123—216no—
67C11×#123—28no—
68C11×#123—24no—
69C11×#123—22no—
70C11×#123—24no—
71C11×C22⋊Q8—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8D414yes—
74C11×#121—28no—
75C11×#121D414yes—
76C11×#120—24no—
77C11×#120—22no—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C11×#117—24no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11C2312yes—
90C11×#104—28no—
91C11×#103—28no—
92C11×#101—42no—
93C11×#100—24no—
94C11×C22⋊C8—24no—
95#23914C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—22no—
97C24×C11C2×D412yes—
98C24×C11C2×D411yescharacteristic
99C11×#41—24no—
100C11×#41—24no—
101C11×#41—416no—
102C11×#41—48no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—416no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11C2×D414yes—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—48no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11C2×D412yes—
127C2×D4×C11C2×D414yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2411yescharacteristic
145C11×Q16—48no—
146C11×SD16—48no—
147C11×M16—24no—
148C11×M16—24no—
149C2×C8×C11—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—216no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—216no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—24no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D414yes—
165#3485C2×C1111yescharacteristic
166C2×#536C2×C1111yescharacteristic, complemented
167C2×#455C2×C1112yescomplemented
168#3004C2×C1112yescomplemented
169#2005C2×C1114yescomplemented
170#1897C2×C1112yescomplemented
171#1885C2×C1112yescomplemented
172#1785C2×C1111yescharacteristic, complemented
173C23×C11—21no—
174C23×C11—22no—
175C23×C11—21no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—42no—
179C23×C11—44no—
180C23×C11—44no—
181C23×C11—84no—
182C23×C11#12012yes—
183C23×C11#12014yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—28no—
186Q8×C11—24no—
187Q8×C11—48no—
188Q8×C11—44no—
189Q8×C11—44no—
190D4×C11—28no—
191D4×C11—24no—
192D4×C11—48no—
193D4×C11—48no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—84no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—28no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—48no—
208C2×C4×C11—44no—
209C2×C4×C11—48no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—84no—
215C2×C4×C11#12012yes—
216C2×C4×C11C22×D412yes—
217C2×C4×C11C22×D412yes—
218C2×C4×C11H(5,𝔽2)12yes—
219C8×C11—44no—
220C2×H(5,𝔽2)C22×C1111yescharacteristic
221C22×#41C22×C1111yescharacteristic
222C23×Q8C22×C1111yescharacteristic, complemented
223C2×#137C22×C1114yes—
224#547—24no—
225#546—24no—
226#536—28no—
227#536C22×C1112yes—
228#534—22no—
229C2×C4⋊Q8C22×C1112yescomplemented
230C2×#124C22×C1112yes—
231#525C22×C1112yes—
232C2×#123—22no—
233C2×#123—22no—
234C2×C22⋊Q8—22no—
235#518C22×C1111yescharacteristic
236C2×#117C22×C1111yescharacteristic, complemented
237#455—28no—
238#451—24no—
239#448—24no—
240C2×#104C22×C1114yes—
241#419C22×C1114yescomplemented
242C2×#101C22×C1112yescomplemented
243C2×#100C22×C1112yes—
244#407C22×C1112yescomplemented
245#339C22×C1114yescomplemented
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—44no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—44no—
254C22×C11—42no—
255C22×C11—44no—
256C22×C11—82no—
257C22×C11—164no—
258C22×C11C2×#12011yescharacteristic
259C22×C11C2×#12011yescharacteristic
260C22×C11#53411yescharacteristic
261C4×C11—22no—
262C4×C11—44no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—44no—
266C4×C11—44no—
267C4×C11D4214yes—
268H(5,𝔽2)—24no—
269H(5,𝔽2)—42no—
270C2×#41—22no—
271C2×#41—24no—
272C2×#41—24no—
273C2×#41—42no—
274C2×#41C23×C1112yes—
275C22×Q8—24no—
276C22×Q8—21no—
277C22×Q8—24no—
278C22×Q8—42no—
279C22×Q8C23×C1112yes—
280C22×Q8C23×C1111yescharacteristic
281C22×D4—22no—
282C22×D4—22no—
283C22×D4D4×C1112yes—
284C22×D4C23×C1111yescharacteristic
285C23×C4—21no—
286C23×C4D4×C1112yes—
287C23×C4C23×C1111yescharacteristic
288#137—28no—
289#137—44no—
290C2×Q16—24no—
291C2×SD16—24no—
292C2×M16C23×C1114yes—
293C4⋊Q8—24no—
294C4⋊Q8—22no—
295C4⋊Q8—24no—
296#124—24no—
297#124—22no—
298#124D4×C1118yescomplemented
299#123—216no—
300#123—28no—
301#123—24no—
302#123—22no—
303#123—24no—
304C22⋊Q8—216no—
305C22⋊Q8—24no—
306C22⋊Q8D4×C1114yes—
307#121—28no—
308#121D4×C1114yes—
309#120—24no—
310#120—22no—
311C4×D4—24no—
312C4×D4—24no—
313#117—24no—
314#117C23×C1112yes—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C42C23×C1112yes—
323#104—28no—
324#103—28no—
325#101—42no—
326#100—24no—
327C22⋊C8—24no—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11—42no—
331C2×C11—44no—
332C2×C11—82no—
333C2×C11#240311yescharacteristic
334C2×C11#302212yes—
335C24—22no—
336C24C2×D4×C1112yes—
337C24C2×D4×C1111yescharacteristic
338#41—24no—
339#41—24no—
340#41—416no—
341#41—48no—
342C2×Q8—24no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—24no—
348C2×Q8—24no—
349C2×Q8—416no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8C2×D4×C1112yes—
353C2×Q8C2×D4×C1114yes—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—42no—
362C2×D4—48no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4C2×D4×C1112yes—
366C2×D4C2×D4×C1114yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4C2×D4×C1112yes—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1114yes—
383C22×C4C24×C1111yescharacteristic
384Q16—48no—
385SD16—48no—
386M16—24no—
387M16—24no—
388C2×C8—24no—
389C4⋊C4—24no—
390C4⋊C4—28no—
391C4⋊C4—216no—
392C4⋊C4—24no—
393C4⋊C4C2×D4×C1114yes—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—28no—
397C22⋊C4—216no—
398C22⋊C4—24no—
399C22⋊C4—22no—
400C22⋊C4—24no—
401C42—22no—
402C42—22no—
403C42C2×D4×C1114yes—
404C11#2391411yescharacteristic, direct product factor, Sylow
405C23—21no—
406C23—22no—
407C23—21no—
408C23—22no—
409C23—22no—
410C23—42no—
411C23—44no—
412C23—44no—
413C23—84no—
414C23C11×#12012yes—
415C23C11×#12014yes—
416C23C22×D4×C1111yescharacteristic
417Q8—28no—
418Q8—24no—
419Q8—48no—
420Q8—44no—
421Q8—44no—
422D4—28no—
423D4—24no—
424D4—48no—
425D4—48no—
426D4—42no—
427D4—42no—
428D4—84no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—48no—
440C2×C4—44no—
441C2×C4—48no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—84no—
447C2×C4C11×#12012yes—
448C2×C4C22×D4×C1112yes—
449C2×C4C22×D4×C1112yes—
450C2×C4C11×H(5,𝔽2)12yes—
451C8—44no—
452C22—22no—
453C22—22no—
454C22—24no—
455C22—24no—
456C22—44no—
457C22—42no—
458C22—42no—
459C22—44no—
460C22—42no—
461C22—44no—
462C22—82no—
463C22—164no—
464C22C2×C11×#12011yescharacteristic
465C22C2×C11×#12011yescharacteristic
466C22C11×#53411yescharacteristic
467C4—22no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—44no—
472C4—44no—
473C4D42×C1114yes—
474C2—21no—
475C2—21no—
476C2—42no—
477C2—44no—
478C2—82no—
479C2C11×#240311yescharacteristic
480C2C11×#302212yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3485C2
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×#536C2semidirect
3. C2×C11×#455C2semidirect
4. C11×#3004C2semidirect
5. C11×#2005C2semidirect
6. C11×#1897C2semidirect
7. C11×#1885C2semidirect
8. C11×#1785C2semidirect
11. C23×Q8×C11C22semidirect
18. C2×C11×C4⋊Q8C22semidirect
25. C2×C11×#117C22semidirect
30. C11×#419C22semidirect
31. C2×C11×#101C22semidirect
33. C11×#407C22semidirect
34. C11×#339C22semidirect
65. C11×#124D4semidirect
95. #23914C11direct (N × H)
166. C2×#536C2×C11semidirect
167. C2×#455C2×C11semidirect
168. #3004C2×C11semidirect
169. #2005C2×C11semidirect
170. #1897C2×C11semidirect
171. #1885C2×C11semidirect
172. #1785C2×C11semidirect
222. C23×Q8C22×C11semidirect
229. C2×C4⋊Q8C22×C11semidirect
236. C2×#117C22×C11semidirect
241. #419C22×C11semidirect
242. C2×#101C22×C11semidirect
244. #407C22×C11semidirect
245. #339C22×C11semidirect
298. #124D4×C11semidirect
404. C11#23914direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C2×C11×#5362
C2×C11×#4552
C11×#30042
C11×#20052
C11×#18972
C11×#18852
C11×#17852
#2391411